UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A comparison of various ore reserve estimates at the Buckhorn Mine, Eureka County, Nevada Tilkov, Mit D. 1989

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
UBC_1989_A6_7 T54.pdf [ 20.57MB ]
Metadata
JSON: 1.0052363.json
JSON-LD: 1.0052363+ld.json
RDF/XML (Pretty): 1.0052363.xml
RDF/JSON: 1.0052363+rdf.json
Turtle: 1.0052363+rdf-turtle.txt
N-Triples: 1.0052363+rdf-ntriples.txt
Original Record: 1.0052363 +original-record.json
Full Text
1.0052363.txt
Citation
1.0052363.ris

Full Text

A COMPARISON  OF VARIOUS ORE RESERVE  AT THE BUCKHORN MINE,  ESTIMATES  EUREKA COUNTY,  NEVADA  By MIT D . TILKOV B.Sc,  The U n i v e r s i t y  A THESIS SUBMITTED  of Waterloo,  1975  IN PARTIAL FULFILLMENT OF  THE REQUIREMENTS  FOR THE DEGREE OF  MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF GEOLOGICAL  We a c c e p t t h i s to  the  thesis  required  THE UNIVERSITY  as  SCIENCES  conforming  standard  OF B R I T I S H COLUMBIA  March  1989  © M i t D. T i l k o v ,  1989  In  presenting this  degree at the  thesis  in  University of  partial  fulfilment  of  of  department  this or  thesis for by  his  or  scholarly purposes may be her  representatives.  permission.  of  Geological  Sciences  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  April  3, 1989  for  an advanced  Library shall make it  agree that permission for extensive  It  publication of this thesis for financial gain shall not  Department  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  is  granted  by the  understood  that  head of copying  my or  be allowed without my written  Abstract An  abundance  of  production blasthole i n Nevada  provides  computerized  data the  various  body i s  a bulk mineable, that  Forty  data,  blasthole  data.  over  drillhole and  The  to  known of  for  t h e methods  each  common  analysis  the  best  predictors  of  reflect  o v e r a l l t r u e grade  the  smaller mining  size  Some b l o c k  based,  models  and  model  distance  compared  During the  while  block  inverse  by  course  and  and  to  each  of  this  geostatistical  and i n some  cases,  questioned.  because the  grade  small,  grade  these block  actual  from  major  statistical  estimating  of  derived  i m p o s e d on them  four  calculated  gold-silver  m i g h t be d i c t a t e d  o f d a t a were e m p l o y e d  that  regardless of  that  production data.  the  showed  of  ore-  from e x p l o r a t i o n  i n some c a s e s .  polygonal  t h e m s e l v e s were  Results important  various  a  constraints  to.  system.  estimated  size  geological For  epithermal  springs  choosing  block  e s t i m a t e s were  many  techniques  of  study  The Buckhorn  w i t h 12 b l o c k m o d e l s  examined  not.  geostatistical  study,  larger  had  did  and  hosted,  models,  effect  s p a c i n g was  configurations  other  block  were compared  the  datasets  others  volcanic  and  B u c k h o r n Mine  a comprehensive  techniques.  formed i n a M i o c e n e h o t  drillhole  block  grade'estimation  separate  drillhole  Cominco R e s o u r c e s '  opportunity for  evaluate  deposit  from  exploration  any  size  interpolation  models, at  mining  blocks  method  although less given  distribution  location, of  the  is  used  accurate tended  ore  to  blocks  which  were  calculated block  eventually from n e a r e s t  size  correct  models  unknown s h a p e was  sulfide of  to  And  accurate,  that,  existence  estimates of the  proposed further  stable,  in  estimates  some o f  realization)  a d d i t i o n to the  the  are  small  geometrically of  the  separating  imposition of  zone o u t l i n e  o f which there of  true,  tonnage  and  G.F.  refined  from  a second  type  was  little  basis  reserves,  and  Mine.  iii  for  measurably  calculating  conditional  Raymond (Raymond 1 9 7 9 ,  here,  was  grade.  of  generally models  oxide  w i t h i n which ore  recoverable  method  by  and  generate block  Buckhorn  ore  orebody.  finally,  and as  all  f a i r l y accurate,  possible  b o u n d a r y , an o r e  the  probability  to  (one  o c c u r and o u t s i d e  improved the  used  be s e e n as  e x p l o r a t i o n composites,  predicting  1984),  the  found  geological  likely  the  of  Because  exploration composites,  can  approximations  It  mined.  was useful  found of  estimates  to  1982,  be  the  various  of  ore  the  and most  methods  reserves  at  T a b l e o f Contents  page Abstract Table of  ii Contents  List  of  Tables  List  of  Figures  iv vii viii  Acknowledgements  x  Chapter 1.  INTRODUCTION  1  2.  GEOLOGY OF THE BUCKHORN DEPOSIT  8  3.  A V A I L A B L E DATA AND BLOCK MODELS  13  3.1  EXPLORATION DATA  13  3.2  BLASTHOLE DATA  14  3.3  BLOCK MODELS  15  3.4  3.3.1  Introduction  >  3.3.2  Four Foot B l o c k Models  15  3.3.3  Twenty F o o t B l o c k M o d e l s  18  3.3.4  Sixty  19  Foot B l o c k Models  SUMMARY OF BLOCK MODELS AND DATASETS  15  19  4.  STATISTICS  21  5.  ORE RESERVE CALCULATIONS  31  5.1  INTRODUCTION  31  5.2  POLYGONAL ESTIMATES  32  5.3  INVERSE  32  DISTANCE iv  5.4  KRIGING 5.4.1  Variogram Analysis  5.4.2  Some O b s e r v a t i o n s  5.4.3 6.  35 35 on V a r i o g r a m  Modelling  38  Kriging  49  and Back A n a l y s i s  CONDITIONAL PROBABILITY  52  6.1  52  THEORY 6.1.1  Introduction  52  6.1.2  The C o n d i t i o n a l D i s t r i b u t i o n  52  6.1.3  Distribution of  Sample G r a d e s  and  Block Grades Kriging Variance  Constant  6.1.5  Combining 3-Parameter Lognormal Data with R e l a t i v e Variograms Determining the Constant R e l a t i v e  60  Blasthole  61  Kriging Variance  CALCULATION OF CONDITIONAL PROBABILITY 6.2.1  7.  8.  59  62  Example C a l c u l a t i o n Of C o n d i t i o n a l Probability  6.3  56  6.1.4  6.1.6  6.2  .  66  DISCUSSION  70  COMPARISON OF RESULTS  79  7.1  INTRODUCTION  79  7.2  METAL GRAPHS  79  7.3  ORE RESERVE CHARTS  88  7.4  SUMMARY CHART AND RANKING OF THE RESULTS  94  7.5  EXAMINATION OF SCATTERGRAMS AND BENCH PLANS  97  7.6  SIXTY FOOT V S . TWENTY FOOT ESTIMATES  101  7.7  CONSTRAINED V S . UNCONSTRAINED ESTIMATES  102  7.8 USING CONDITIONAL PROBABILITY ESTIMATES CONCLUSIONS  103 107  v  References  109  Appendix A -  B e n c h Maps o f  Raw D a t a and O u t l i n e s  110  Appendix B -  B e n c h Maps o f  Results  120  Appendix C -  Ore R e s e r v e R e p o r t s  Appendix D -  L i s t i n g of Values  Calculated  L i s t i n g of Difference  Variograms Generated Method  Appendix E Appendix F -  233 Variogram 254  Scattergrams  by Maximum 261 267  vi  List  of  Tables  page Table  I.  Table  II.  Table  Table  III.  IV.  Summary o f  b l o c k models  Simple s t a t i s t i c s of and b l a s t h o l e d a t a  and d a t a s e t s  the  exploration "  Parameters used to generate d i s t a n c e weighted estimates e x p l o r a t i o n composites  for kriging  Table  VI.  Parameters used probability  to  Table  Table  Table  IX.  X.  XI.  34  50  Parameters used  Table VIII.  inverse from  41  V.  VII.  27  O r e r e s e r v e s p r e d i c t e d by u s i n g t h e " r o t a t e d " v a r i o g r a m compared t o k r i g e d e x p l o r a t i o n e s t i m a t e and " a c t u a l " f o r t h e BUCKG m o d e l  Table  Table  20  calculate  conditional 65  Comparison o f b l a s t h o l e i n d i c a t e d reserves w i t h r e s e r v e s c a l c u l a t e d by e a c h e x p l o r a t i o n method f o r t h e BUCK b l o c k m o d e l  89  Comparison o f b l a s t h o l e i n d i c a t e d reserves w i t h r e s e r v e s c a l c u l a t e d by e a c h e x p l o r a t i o n method f o r t h e BUCKG b l o c k m o d e l  90  Comparison o f b l a s t h o l e i n d i c a t e d reserves w i t h r e s e r v e s c a l c u l a t e d by e a c h e x p l o r a t i o n method f o r t h e BUCK60 b l o c k m o d e l  91  Comparison of b l a s t h o l e i n d i c a t e d r e s e r v e s w i t h r e s e r v e s c a l c u l a t e d by e a c h e x p l o r a t i o n method f o r t h e BUCK60G b l o c k m o d e l  92  Summary c o m p a r i s o n o f  95  vii  ore  reserve  methods  . . . .  List  of  Figures  page Figure  l.  L o c a t i o n map  Figure  2.  Regional  2  g e o l o g y map  encompassing  the  of  an  area  B u c k h o r n mine  Figure  3.  G e o l o g i c a l map o f  Figure  4.  Figure  5.  Two methods o f a c c e p t i n g o r r e j e c t i n g b l o c k s w i t h i n an o u t l i n e Partitioned log probability plot of 20' e x p l o r a t i o n c o m p o s i t e s  23  Log p r o b a b i l i t y p l o t o f compared t o p a r t i t i o n e d  25  Figure Figure  Figure  Figure Figure Figure Figure  6. 7.  8.  9. 10. 11. 12.  the  9  B u c k h o r n mine  11  17  b l a s t h o l e data exploration data  Log p r o b a b i l i t y p l o t s showing t h e e f f e c t o f adding a c o n s t a n t o f 0.005 o p t . t o the o r i g i n a l data to c r e a t e a 3-parameter lognormal d i s t r i b u t i o n  28  G r a p h i c a l e x p l a n a t i o n o f the polygon w e i g h t e d method o f c a l c u l a t i n g b l o c k grades  33  Modelled r e l a t i v e BEX d a t a  variogram of  38  Modelled r e l a t i v e BEXG d a t a  variogram of  the the 39  Experimental r e l a t i v e BBH d a t a  v a r i o g r a m from  Experimental r e l a t i v e BBHG d a t a  v a r i o g r a m from  the 47 the  Figure  13.  The c o n d i t i o n a l  Figure  14.  E x p e c t a t i o n s o f o r e and w a s t e d e r i v e d from n o r m a l l y d i s t r i b u t e d b l o c k grades  55  Probability p l o t s o f p e r f e c t and imperfect lognormal d i s t r i b u t i o n s  57  Figure  15.  distribution  48  viii  54  Figure  Figure Figure  16.  17. 18.  The e f f e c t o f e s t i m a t i n g o r e and w a s t e p e r c e n t a g e s from i m p e r f e c t n o r m a l distributions Cumulative p r o b a b i l i t y of actual blocks given Computer p r i n t o u t actual  of  p l o t of the grades k r i g e d block grades  the  g r a d e s and k r i g e d  comparison  58 . . . .  74  between  estimates  76  Figure  19.  Metal graph f o r  the  BUCK b l o c k m o d e l  80  Figure  20.  Metal graph f o r  the  BUCKG b l o c k m o d e l  81  Figure  21.  Metal graph f o r  the  BUCK60  82  Figure  22.  Metal graph f o r  the  BUCK60G b l o c k m o d e l  ix  b l o c k model  83  Acknowledgements  The funding  and t h e  allowing during  author  time  without  opportunity off  work  support.  Russ's  and h i s  boss,  now  down t o  work  and  problems t h a t  Christopher,  has  (I  also  arise  And s p e c i a l  publish  attend  likes  sentient  predictors of Susan's  i n the  easily  have  employ.  retired,  thanks  e a r t h approach to simple  decided to  This  "go  it"  I n p a r t i c u l a r , Russ f o r encouragement ore  reserve  and  problems,  and u n d e r s t a n d a b l e  influenced  me  the  in  for  mineral industry  greatly  t o my w i f e ,  patience  with the  end.  and  c l a s s e s when n e c e s s a r y .  in its'  hope)  research  if  my a p p r o a c h t o  solution  of  day t o  day  i n my j o b .  thanks  whose  this  turmoil  as  guides  converse  times  Cominco L t d . f o r p r o v i d i n g the  philosophy of keeping things  a l l possible,  the  to  to  just  a part-time student my  to  to  company m i g h t  Sproule,  this  indebted  a p e r i o d o f unprecedented  when t h e  at  is  of  with  IBM,  reality,  is  late  VAX,  and my k i d s , nights  Calcomp,  although stretched  encouragement  I d i d n ' t want t o ,  Susan,  to  finish this  J a i m e and  and a b s e n c e s and  other  sub-  at  times,  held  thing,  now p a r t i c u l a r l y a p p r e c i a t e d .  x  to  when  at  1  1.  The deposit in  Buckhorn hosted  Eureka  Resources  and  1).  retains  extending  oxide  is  ore  et  are  oz/ton  al.,  1988) .  Although there  was  since  started  heap  the  at  been  early  by  an  outside  this  model.  using and  inverse  ordinary  inverse  I n 1985, distance  cubed the  Gold  0.04  cutoff  mining  and  was  pit  was  gold  (Munroe  on  the  operation  reserves  company u s i n g  interpolation,  minable  activity  ore  the  silver  oz./ton  c u r r e n t open p i t  Initially,  oxide  Only  grade  and  faults  surface  Published  and an open p i t  open  Gold  depth.  r e s e r v e s were r e c a l c u l a t e d  k r i g i n g and  distance  ore at  gold  consulting  model w i t h k r i g e d b l o c k grades  i n a near  the  (24%).  a l o n g NNW t r e n d i n g  oz./ton  1984.  located  o f Cominco  interest.  technology.  gold  southwest o f  operation.  the  is  venture  ore c o n t a i n i n g  1900's,  It  Equinox Resources  sporadic  up i n F e b r u a r y o f  calculated  and  sulfide  leach  a 0.02  has  joint  encountered  m i l l i o n tons of  silver  a  disseminated  open p i t  rocks.  60 m i l e s  proceeds  downward i n t o  using  3.1  0.6  property  is  mined i n the  extracted  is  net  w i t h ore grades  z o n e and  and  low g r a d e e p i t h e r m a l  volcanic  L t d . (76%)  a 20%  mineralization  reserves  small,  T h e mine  International  fractures  are  a  by a l t e r e d T e r t i a r y  (Fig.  Resources  silver  is  C o u n t y , Nevada a p p r o x i m a t e l y  town o f E l k o  Bar  Mine  INTRODUCTION  were  a 20'  block  designed  using  by C o m i n c o L t d .  lognormal k r i g i n g , redesigned  model because e s t i m a t e s u s i n g  this  using  method  the most  2  c l o s e l y resembled the  first  mined tonnage  year's  production.  a v a i l a b l e a f t e r the f i r s t made t o results. can be  figures available for  Although  The b l a s t h o l e r e p o r t e d from  into  is the  blasthole  data  few months o f o p e r a t i o n , no attempt  compare estimates from e x p l o r a t i o n  o f head grade material  and grade  d r i l l i n g to  was was  blasthole  data i s the o n l y data on which p r o d u c t i o n the mine because no other r e l i a b l e measure  available. crusher  Ore and  is  dumped  from  samples are taken  stockpiled  sporadically  3 every  2 or  3 hours  from the  d o c u m e n t i n g where in  some c a s e s ,  grade have  i n the main p i t  whether  stockpile,  the  current  questions, better  not  is  was  least  of  is  is  being  no  good way  sampled  from and,  coming from the main p i t , o r from o t h e r  of  small pits  a low which  property.  study  the  estimates  c u b e d method  ore  There  ore  an o r e s t o c k p i l e  b e e n m i n e d on t h e The  conveyors.  o f which  tonnage  t h a n by  designed  and  to  was why t h e r e  grade  kriging.  answer  by  the  Other t o p i c s  a  number o f  appeared to  inverse to  be  be  distance  investigated  include: 1) by  Effect  of  Estimation Block Size:  geostatisticians  kriging  will  average one  generate  and  that  is  close  that  the to  and f u r t h e r m o r e , estimate grades is  true  if  individual  average that If  reserve  that  for very  interested  block,  but  intuitively, and  the  in  (the  whole  s h o u l d g i v e an a v e r a g e of  all  of  the  result  correct  on  for estimation  purposes  is  deposit one b l o c k  mining c u t o f f ,  is  if  used  below  be s u r m i s e d of  to  global  calculate  9 equal  (i.e. size is  grade.  This an  that  for  reserves, if  only  the  blocks,  slightly this  a one  (including  equal to  0 tons  If  to  grade of  any e s t i m a t e  cutoff  cutoff  made.  F o r example,  i n t h e m i d d l e whose g r a d e at  is  p r e d i c t i n g the can  spacing,  any a t t e m p t  block grade which i s  d i v i d e d up i n t o  and 8  drillhole  ourselves  deposit),  samples  used,  are  estimation  g r a d e w i l l p r o b a b l y be below  the  it  accepted  block size  small s i z e mining blocks  is  estimated  commonly  which  original exploration  we a r e f o o l i n g  purposes  is the  figures  best block s i z e the  of  p h i l o s o p h y must be a d o p t e d .  b l o c k was kriging)  regardless  one  mine p l a n n i n g different  that  It  grade, of  the and  ore).  t h e r e may above analogy  the is  4 continued  down  estimate to  to  a  t h e mine d e s i g n  Buckhorn)  than  drillholes  are spaced  because i n  m i n i n g no  to  estimate unless chosen mining at  below  least  20  a  scale,  block  50'  x  it  size  50'  x  is (20'  20'  one  is  impressed  estimate  cutoff  grade.  there  is  is  correct  reasonable  to  above  of  s m a l l e r m i n i n g b l o c k s may n o t  each o f  the  predicted,  a better  the  block  grades  has  been  might be,  that the  what d i f f e r e n c e  2 b l o c k models  reserves block  2)  been  amply over  only exploration because i t  evidence samples.  average is  above  have  that  true  the  been  a  estimated  Although  expected  global  60'  on t h e  Ore  Zone  x  20'  60'  at  have grade  accurately  d i s t r i b u t i o n of  at  tonnage one w i t h  blocks.  the  mining  scale  and  grade  there  x 20'  x  20' It  was  b l o c k w o u l d be l o w e r  sulfide  Outlines:  interpolation demonstrated the  years  drillholes  was o b v i o u s  of  in  x  based  of  the  geostatistics  and t h a t  average"  20'  expected than  for  importance  of  size.  Effect  constraining has  grid),  l a r g e r b l o c k would  the  were g e n e r a t e d ,  and one w i t h 60'  ore 20'  reserves  (Buckhorn  obtained.  To s e e  blocks,  ore  20*  exploration  cutoff.  o v e r a l l picture of  and  x  probability  been e s t i m a t e d  a grade  at  20'  block that  w i t h i n the  have  x  on  block contained  1  to  by a " c o r r e c t on  F o r any 50'  some  more i m p o r t a n t  block size  on a f a i r l y r e g u l a r 50'  that  cutoff  one  mining  that  to  within geological  by  numerous  (e.g.  David,  within the  mineralization  belonging  to  the  sulfide was  a different  S i m i l a r l y , only oxide  The  zone  practitioners  1988). oxide  In t h i s zone  ore would not  more  boundaries  erratic  statistical blastholes  of  study,  were  used  be m i n e d , and  showed  population were  used  of for  5 comparison. geological datasets "ore".  H o w e v e r , as w i l l boundary  that It  the  is  by  areas,  author  this  "smoothing"  of  them.  b l o c k models  composites  within  account,  result  ore reserve estimates 3)  on t h e s e  figures.  "ore  These  Estimates: estimates  of  are  dangerous  were  and  that,  most  in  inverse  is  high  between  enough  distance  especially  the  and  and  inverse  anisotropies  if  anisotropies  resemble  in  the  d i s t a n c e methods  will  a variogram  an e s t i m a t e  w h i c h most distance  Somewhere  in  t h e r e may be a power o f the  kriged  variogram  are  a regular grid.  it  outline.  polygonal  i n t e r p o l a t i o n method so  same  cases,  distance  modelled),  generate  Distance  is  were  to  Inverse  sample s p a c i n g cubed  on  1  to production  H u i j b r e g t s , 1978).  t h a t would  20  exploration  when t h e power o f  (we d o n ' t know where b e f o r e h a n d ) ,  inverse  account  (Journel  geological  b o u n d a r y on  kriging with  through to  a polygonal estimate  encircles  original  only  compared  and  that  or  idea rigorously,  models,  Polygonal  effect,  resembles  this  information w i t h i n the  told  rocktype  intuitively  new g e o l o g i c a l  later  showing closely  the  which took the  which resembles  nugget  an  many o t h e r  an i m p o r t a n t  To t e s t  r a n g e f r o m an e s t i m a t e pure  if  is  of  unwarranted e x t r a p o l a t i o n  2 block  Various  We a r e o f t e n  This  in  zone" o u t l i n e were u s e d  b a s e d on b l a s t h o l e Accuracy  and  type  m i n i m i z e s numerous e r r o r s  in  ore grades.  this  data  is  and i m p o s e d t h i s  For estimates  a second  c a n be d e f i n e d w h i c h  2 f u r t h e r b l o c k m o d e l s were g e n e r a t e d and 60"  is  that  in itself  taken i n t o  p o p u l a t i o n mixing which  and/or  there  has e n c o u n t e r e d .  boundary  that  if  Buckhorn  the  derived  boundary w h i c h , of  the  author  felt  quantitatively mineralized  in  be s e e n ,  was d e c i d e d t o  estimate— taken  into  A t Buckhorn, was c h o s e n  (no  t r y polygonal  6 estimates  and  (straight  average)  other  v a r i o u s powers  estimates  of  the  In  cubed  on a l l kriged  Cominco  were of  accurate  various  prospects  for  block estimator  question reserve  they  a  without  the  at  20  see  if  3 block models,  these  distance  the  inverse  b l o c k model  1  it  w o u l d work  and t o  Probability  most  compare  Estimates:  geostatistical  Raymond. is  the  kriged  of  relative over  Early  the  attempts  estimates  as  an  Consequently,  Raymond's a p p r o a c h o f  at his  method  developed  1984).  using  to  using  w h i c h he h a s 1982,  studies  Pivotal  B u c k h o r n were g r i m .  attempt  With to  Blasthole be  p a r a l l e l block  of  model u s i n g  block estimates  b e n c h and w i t h i n t h e  was n o t  reserves  For each  p r e v i o u s l y mentioned  which contained  outlines.  The  it  "conditional  ore  each other,  but  o r 60'  blocks was  on b l a s t h o l e  Great care  from a c t u a l  4 exploration  zone o u t l i n e  based  and most the  calculated  the  20'  last  o n l y how w e l l  performed a g a i n s t  with the  data.  Data:  addressed  estimates  compared  production blasthole models,  for the  zero  .  Comparison  how w e l l  was u s e d  any o f  of  probabilities  that  ore  behaviour  geostatistics  ordinary kriging  to  than  the  G.F.  1979,  important  inverse  conditional  seemed r e a s o n a b l e  5)  by  (Raymond  1 1  the  1985,  years  probability  better  other  practical  of  v a r i o g r a m s and  indicated  if  Conditional  to  performed  calculation  12  of  p e r i o d 1979  philosophy  see  was m o n i t o r e d t o  the  f r o m power  estimates.  Effectiveness  During the  past  of  distance  i n order to  interpolator that  method t o 4)  inverse  particular,  o r i g i n a l mine d e s i g n  equally well this  power t e n  would p e r f o r m  cubed method. distance  to  of  was  block  w i t h and  constructed d a t a on  taken  to  each  ensure  7 that the  partial  block percentages  outlines,  and t h a t  reporting  tonnages  blasthole  estimates  either  set  of  completely  these  derived so  within  "block either  that  samples  were c a l c u l a t e d  the  the  various  partials"  were  from e x p l o r a t i o n  total  would be  on t h e  tonnages  exactly  the  outlines  edges used  when  drilling  estimated  same,  imposed  or  from  and would on  of  lie  the  block  parameters  were  models.  For  each  model,  simple  calculated,  distributions  histograms  and  calculated,  back e s t i m a t i o n  10  separate  available blasthole It  block  is  the is  an  problem o f blocks  estimates  calculation  best  possible  individual p r e d i c t i n g the  of  and  be  to  of  were  and e a c h  derived  ore  the  Buckhorn numbers  Mine,  is  the  this  — tons of  grade that  is  devoted  reserve  the  of  the  best  from  the  best  cutoffs.  goal  of  calculation ore,  used  grade o f  i n the  this  would ore,  mining  deposit  study.  prior  In the  result  in  tons of waste,  calculation.  all  possible  by t h e  the  the  separate  grade o f best  be u s e d of  but  to The  estimate of  The  potential  mainly  estimate.  related,  which w i l l  economic  the  ore  and  grade  reserves,  determine  t h i s work i s  d i s t r i b u t i o n and a v e r a g e  above  of  cutoff  compared  p r o v i d i n g the  block  a production decision,  the  were  by u s e  variograms  were e m p l o y e d ,  could  note that  to  crucial  that  made between  within  company t o  separate  techniques  calculations  important to  distinction of  graphs,  and e x a m i n e d  data.  determining  grade  were m o d e l l e d  probability  reserve  statistical  case four and  8  GEOLOGY OP THE BUCKHORN DEPOSIT  2.  The  gold  Tertiary angle  and  volcanic  normal  silver flows  fault  volcanic  formed  i n near surface  hosted  the  Regionally, unconformably which are the  the  western thrust  of  the  lower  assemblage fault  western  surface facies  Buckhorn mine Paleozoic  of  plate  (Fig.  and i s  w h i c h were d e r i v e d f r o m eastern  carbonate  and  the  to  is  east  suite,  represented  post-thrusting  and t h e w e s t e r n  to  the  Roberts  the  west  the  siliceous  of  assemblage  west whereas east  and west referred to  l o c a l l y by t h e  of coarse  as the  of  and v o l c a n i c u n i t s  north,  made up l a r g e l y  and  eastern  shows up t o  units  assemblage.  along  the  rocks  referred to  a few m i l e s  A third  been  B a s i n and  volcanic  volcanic  Generally,  2).  the  the  assemblage  and s i l i c e o u s to  high  t h e many  sedimentary  juxtaposed  the upper p l a t e trace  in  and  and  are exposed  along  States.  carbonate  areas.  altered  w h i c h have  by two a s s e m b l a g e s  are  o v e r l a p assemblage,  Canyon f o r m a t i o n  by  s i m i l a r to  sedimentary  which surfaces  outcrop  area  United  siliceous  fault,  is  volcanic  eastern  B u c k h o r n and C o r t e z  rocks  the  Tertiary  assemblages  Mountains t h r u s t  hosted  environments  southwestern  western two  is  metal deposits  spring  broadly represented  allochthonous  the  hot  Paleozoic  autochthonous  Locally,  The d e p o s i t  precious  the  overly  Buckhorn  with mineralization l o c a l i z e d  systems.  other  Range p r o v i n c e o f  at  clastic  erosion  of  rocks.  To t h e  the the of  of  the  as  the  Brock rocks  both  the  north  |Qa I 1 A L L U V I U M I Ti  j J r i | JURASSIC  INTRUSIVE  |TERTIARY  INTRUSIVE  1 P o 1 PALEOZOIC  OVERLAP  1 T v |TERTIARY  VOLCANICS  1 Ws | WESTERN  SILICEOUS  | T g |TERTIARY  GRAVELS  f E c " ] EASTERN  CARBONATE  Fig. 2. R e g i o n a l G e o l o g y Map o f an a r e a encompassing the Buckhorn mine (after Munroe, Godlewski, and P l a h u t a , 1988).  10 of  the  the  Buckhorn d e p o s i t ,  Paleozoic  rock types  fan  deposits,  include which  andesite that  In  basalts  include  relatively  Tertiary sinter  the  fan  On t h e  basaltic  Pit  andesite,  to  the  In  areas  about  fault  the  close  is  limits  a  of  3),  are a l s o  area of  the  350  basal  feet  of  Buckhorn m i n e r a l i z a t i o n . sediments  s i m i l a r to  the  and s i l i c e o u s  the  which  earlier  hot  spring  around the  dominant  some o f  the  open p i t ,  fault one  the  altered.  main  rocktype  younger  is  Miocene  and a b r e c c i a  feet  to  unit  gives clay  1,000  way to  o r e body on e i t h e r  feet  200  zone.  and  zone  i n width.  feet.  extends  other  side  of  the  angle  The  whereas the oxide  Laterally,  montmorillinite  the  been  clay  The u p p e r  Both the  silver. to  have  a major N10°W h i g h  been o x i d i z e d  sulfide gold  of  about  volume has  volcanics  The a l t e r a t i o n  strike  a depth of  reduced  from the  to  contain  the  transition  by u p t o  of  reeds.  (Fig.  along the  altered  zones to  area  f r o m 100  thirds  sulfide  pelites,  mineralization,  feet  extends  third  thickness  and more s p e c i f i c a l l y ,  argillically  alteration  one  the  material  fossil  but t h e r e i n the  ranges  of  some  study  of  3,000  and  intrude  northeast.  extensively for  hosts  clastic  mine p r o p e r t y ,  sediments exposed just  coarse  containing  North Buckhorn  foot  a r e o v e r l a i n by y o u n g e r  deposits,  deposits  a 750  are o v e r l a i n  Miocene b a s a l t i c places  stocks  units.  Tertiary alluvial  J u r a s s i c quartz monzonite  appears  to  structure  two  lower  and  the  kaolinite and define  the the  (Plahuta,  1986). As  evidenced  presence of  by  explosion  sinters, breccias  argillic i n the  alteration,  vicinity  of  and  the mine,  the the  •m400  Tbrl  Feet  BRECCIA  T_sJ M I O C E N E  SEDIMENTS  MIOCENE  1 7000  BASALTIC  ANDESITE  EARLY TERTIARY FANGLOMERATE STUDY PIT  AREA  OUTLINE  6000  LU  1 5000  Tb  Fig. 3. Munroe,  G e o l o g i c a l map of the Buckhorn Mine G o d l e w s k i and P l a h u t a , 1 9 8 8 ) .  O O O  (after  mineralization environment. provided  has  The h i g h  conduits  basaltic  The o c c u r r e n c e  hydraulic t u r n cause to  deposit  of  for  alteration  into  and s i l v e r the  porous,  to  indicates  pressure  from the  fractured host  area  that  sporadic initiated  w h i c h would  cooled  rocks.  the  mineralization.  buildup,  b o i l i n g horizons  deposit  spring  and p r e p a r e d  and s t o c k w o r k  system r e l i e v e d  hot  and f r a c t u r i n g i n t h e  breccias  f r a c t u r i n g and l o w e r e d gold  surface  hydrothermal f l u i d s  explosion  a sealed  i n a near  angle f a u l t s  f o r hot  andesite  breaching of  been d e p o s i t e d  fluids  in and  13  3.  3.1  A V A I L A B L E DATA AND BLOCK MODELS  EXPLORATION DATA  Exploration regular  50'  rotary  drill  x 50'  and f i r e  silver  grades  was  collar  The  a  few  the  other  horizontal drilling areas  of  the  indeed  the  labs.  are  10'  from  silver.  and t h e r e f o r e to  a  d a t a comes from  every  and  blasthole  geological  the  Although there  estimates  of  d a t a and were  information  available  boundary i n f e e t  lag  vertical,  that  spaced  from  the  of  There  property,  holes less  no a d e q u a t e  there  are  provided  t h a n 50'  were v a r i o u s  for  campaigns  of  which defined  drilled  in different  years  method o f  and t h e  constitute  series  of  different  supports.  the  reliability  rotary drillholes  of  various  different  the  series  rotary  by  the  different  only  assayed  comparing e i t h e r  and  diamond d r i l l h o l e a s s a y s a g a i n s t various  few  calculating  in clusters,  therefore  a  the  all  The i n c l i n e d h o l e s , might  but  were i n c l u d e d b e c a u s e t h e s e and  rotary  distances  open p i t ,  holes,  T h e r e was  gold  oxide/sulfide  drillholes  variograms.  i n the  the  from e x p l o r a t i o n d r i l l h o l e s ,  The o n l y the  close on  on  different rotary  of  of  on  hole.  diamond  information  both  approximately  sampled  be compared  rotary d r i l l h o l e s  inclined  were  from b l a s t h o l e s ,  study.  location of  for  could not  in this  drilled  The m a j o r i t y which  assayed  assays  grades  the  were  were a v a i l a b l e  a r e no s i l v e r  ignored  grid.  cuttings  collar  silver  drillholes  rotary d r i l l h o l e s ,  or  against  each o t h e r . oxide  All  zone  and f e l l  shown on F i g u r e Raw  10'  such that starting  samples  middle of  elevation  Bench p l a n s  of  if  the  they  were w i t h i n  rectangular  study  the area  3. drillhole  the  accepted  w i t h i n 100'  each weighted at  were  samples composite  6900'  bench.  were c o m p o s i t e d fell  with i t ' s  Composites  showing  the  within a  of  20'  center  less  to  20'  lengths  m i n i n g bench  vertically  t h a n 5'  in  the  were d i s c a r d e d .  e x p l o r a t i o n composites  c a n be f o u n d  in  Appendix A . Altogether generated,  of  there  3.2  spaced upper  from  w i t h i n the  the  main  composites  rectangular  North  study  Buckhorn  area  pit  was  i n A p p e n d i x A)  are  comparison.  blastholes  (shown  approximately 20'  Therefore values cutoffs  for gold  constant  silver  12 -  a r e sampled  assayed  fairly of  for  data  exploration  BLASTHOLE DATA  The  fire  3,670  which 2,432 f e l l  where p r o d u c t i o n available  were  any  are not used  apart.  only.  Although  to heap  gold  recovered  for  the  represent  a total  of  production data to  of  ratio  leaching is  open p i t  or d a i l y production ore  There are  Blasthole  ring  the  silver  14'  bench p l a n s  from t h e  silver  from  on t h e  cuttings there  at  the  15:1),  process  is  considered design,  for  the  collar  and  appears  (about  to  the low  a bonus  be a  recovery (<  and  40%). silver  or to  determine  mine  assays  available  that  limits.  8,752 b l a s t h o l e the  cuttings  end o f J u l y ,  1986.  The  outline  of  the  perimeter  the  mined out  All  blastholes  was n o t  3.3  of  the  i n d i v i d u a l b l a s t s was u s e d  area w i t h i n which ore are  i n the  encountered  until  oxide later  sulfide  calculated.  mineralization  1986,.  Introduction  To s a v e on c o m p u t e r t i m e 6840) were m o d e l l e d . both for  benches  within  mining a  material.  This  estimates  3.3.2  mined  above  outlines  represent  estimate of  and b l a s t h o l e  the  immediately  total  c o u l d be  area  the  on  6840  1.155  only  a well  i n that  (6860 and  sampled  there  T h e volume and  is  area  adequate  which  contained  6860 b e n c h e s , tons  sufficient  against  2 benches  b o t h b e n c h e s and on t h e  million  considered  production  data  and b e l o w .  on of  was  and c o s t s ,  The 2 benches r e p r e s e n t  exploration  sampling  to  of  ore  within  together and w a s t e  generate a  exploration  2  ore  reliable reserve  compared.  Four Foot B l o c k Models  One o f actual  the  aims  of  p r o d u c t i o n tons  estimates fixed  the  determine  BLOCK MODELS  3.3.1  the  r e s e r v e s w o u l d be  zone; in  to  generated  boundaries.  polygonal  estimates  and from  this  study  grade both  To do t h i s c o u l d be  in  is  with 20' a  to  compare e s t i m a t e s  exploration  and 60'  b l o c k models  consistent  compared t o  ore  manner  estimates  of  reserve within so  on b o t h  that 20'  and 6 0  block sizes  1  such that  same o v e r a l l t o n n a g e , on t h e  2 benches.  a 4'  This  all  x 4'  three  x  block  20'  calculations block  s i z e was  reported  m o d e l was  chosen  the  generated  f o r two  principal  reasons: 1) very  Representative  small  closely  there  the  are, 2)  block  the  60'  fit  block  at  20'  origins  of  4' into  blasthole  least  blocks the  blocks a 60'  polygonal  spacing  boundaries.  at  least  9 c l o s e s t neighbour  4'  blocks.  evenly  into  3 b l o c k models  block,  would  is  d i v i d e evenly  exactly  that  to  into  20'  the  e a c h 20'  blocks  and  60'  are exactly  represent  and 9 20'  the  12',  60'  blocks.  the  block,  same, 225  are contained  4'  in a  block. Because  boundaries) was  used  different  outlines  a r e i m p o s e d on t h e to  determine  blocks block  inside  the  which  percentages  In t h i s  way,  larger blocks  very  exactly  the  1/225  of  is  its  224/225 o f  the  N o r m a l methods a block  if  it's  later  block of  when is  accepting  center  is  zone  4'  model  the  were w i t h i n a  number o f calculate  represented  f o r example,  might  the  of  a large  be w e i g h t e d total  area to  or r e j e c t i n g  outside  to  was  calculating  outside  the  ore  valid  4'  fractional  within p a r t i c u l a r boundaries.  same t o n n a g e  estimated,  volume  small blocks  were u s e d  and,  limits,  block models,  Then,  (block p a r t i a l s )  l a r g e r b l o c k s i z e models  whose g r a d e  (mined  various  b o u n d a r y and w h i c h were o u t s i d e .  the  drawn  size divides  and t h e  25 o r i g i n a l  hand  sample  on a v e r a g e ,  sizes  blocks  traditional  average  The 4'  Because  c o u l d be c a l c u l a t e d  b l o c k s w h i c h c o u l d be r e c o m b i n e d i n g r o u p s  resemble  Because  polygonal estimates  be  by as  by e a c h 60'  block  little  reserves  of  as  because  estimated.  blocks  a boundary.  tend  to  throw  Figure  out  4 shows  r  METHOD 1  +  +  + 408 TONS  USUALLY, CENTRE  BOUNDARY.  1, ?|  +  IF A BLOCK'S  I S I N S I D E THE IT I S  ACCEPTED.  +  1)  RESULT'  THE 6 0 ' BLOCK I S  REJECTED 2)  ~7T  KEPT  -  3)  +  -  0 TONS.  2 2 0 ' BLOCKS ARE 816 TONS.  54 4 '  KEPT  -  BLOCKS ARE  881 TONS.  +  •  A ORE ZONE OUTLINE  6ir  METHOD 2 THE  METHOD  LARGER  WEIGHTED OF  4'  USED  BY THE NUMBER  BLOCKS  QUALIFIED. 1)  WEIGHTED 2)  +  +  +  408 TONS  RESULT«  TONNAGE I S  | :  A  +  +  + +  +  +  <  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  + +  54/225  881 T O N S . 3 2 0 ' BLOCKS ARE  RETAINED. 12/25. 17/25 3)  THAT  THE 6 0 ' BLOCK I S  RETAINED. -  HERE.  BLOCKS ARE  WEIGHTED  2 5 / 2 5 , AND -  ,i A  AS  881 TONS.  4  + > / + • +  881 TONS.  4 ' BLOCKS,  ABOVE,  +  i  ORE ZONE OUTLINE  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  /  Fig. 4. Two methods o f a c c e p t i n g o r w i t h i n an o u t l i n e . Method 2. i s u s e d  r e j e c t i n g blocks i n t h i s work.  18  the  difference  employed  3.3.3  in  for this  results  method  and  the  one  study.  Two 20'  b l o c k models  were g e n e r a t e d .  The  actual  block  and  i n i n i t i a l production  size  planning.  Each block  the  falls  block  mined l i m i t s contained  within  along  with  calculate  the  actual  blocks  conservative  ore  which g e n e r a l l y than  subset  blasthole composites  20' the data  later  to  of  files  (even i f study  on t h e  which  was  could  the  which  outside  (see  small  be u s e d this  the  to  model,  first.  model t o  that  estimate  second  completely  A  A p p e n d i x A)  calculated  the mined l i m i t s ) . and  were  generated  Chapter  which contained  were  statistics  of  composites  were  Simultaneously,  were c r e a t e d  these  the  a r e a maximum o f  on b e n c h p l a n s ,  4'  along  block.  digitized  from  100% o f  blocks  later For  a subset  partials  if  f r a c t i o n was  4% b e c a u s e t h e r e  (shown  4'  number o f  outline.  i n a 20'  represents  A l l blocks  selected  only exploration  block  boundary.  any  model i s  opt.  blocks  if  a percentage  zone o u t l i n e contained  limits.  w i t h i n the  block  used  first  tons of m a t e r i a l  based  contained  or blastholes  zone o u t l i n e  see  location  multiples  Again,  of  straddling  tonnage  0.01  rationale).  to  and,  block  20'  408  t h e mined  outline,  exactly  The s e c o n d  better  it,  the  p e r c e n t a g e s were 4'  inside  within  outline  represents  were c h e c k e d  blocks  used  this  Twenty F o o t B l o c k M o d e l s  the  25  between  graded 4.  for  for  this  tonnages  exploration only  drillhole  inside These  and  the  ore  files  are  generate variograms,  and  to  generate estimates  3.3.4  polygonal,  for this  block model.  the  60' 20'  w h i c h were 6840 and The  inverse  distance,  b l o c k models block  were g e n e r a t e d  models.  completely  second  contained  was  a  those  inside  The f i r s t  or  in exactly  60'  model  partly inside  subset large  the  Although the  the  the  same way  contained  mine  which blocks  selected  60'  contained  blocks  or  ore  partial  are  slightly  larger  it  approximates  the  drillholes  4'  and  20'  block models.  therefore  the  smaller  of  A l l t h r e e models blocks  the  stored. which  w h i c h were  zone b o u n d a r y .  b l o c k s i z e was  spacing  on  blocks  blocks  this  the  blocks  limits  60'  exploration d r i l l h o l e spacing,  3.4  kriged  6860 b e n c h e s and b l o c k p a r t i a l p e r c e n t a g e s were  represented  and  and  S i x t y Foot B l o c k Models  The as  various  fit  inside  the  chosen  and  share the  than  also the  60'  50'  because fits  the  same o r i g i n  blocks.  SUMMARY OF BLOCK MODELS AND DATASETS  The These various  net  are  result  is  summarized  datasets  w h i c h may be u s e d  6 block in  models  Table  and b l o c k m o d e l s , elsewhere i n the  I.  and  4 separate  In order to  s h o r t names text  and  have  figures.  datasets.  refer been  to  the  assigned  20  Table Summary  o f Block  I M o d e l s and  Datasets  Short Name  #Blocks or Composites  W i t h i n Mine W i t h i n Ore Limits ? Zone O u t l i n e ?  4 FOOT  70,775  yes  no  6840-6860  4FOOTG  46,331  yes  yes  6840-6860  BUCK  2,999  yes  no  6840-6860  BUCKG  2,089  yes  yes  6840-6860  BUCK60  386  yes  no  6840-6860  BUCK60G  305  yes  yes  6840-6860  Bench  Block Models 4x4  1  20x20  1  60x60•  Exploration Composites BEX  2,432  no  no  6600-6900  BEXG  1,036  no  yes  6780-6880  BBH  8,752  yes  no  6780-6880  BBHG  6,315  yes  yes  Blasthole Samples  6780-6880  21  4.  I n any data  is  that  ore  reserve  considered  can  be  obtained  their  results  probability  graph i s  is  used  out it.  the  "it's  is  One o f the  any  close  indicator  data  over  of  understand  the  the nature of  the  a  normal  a  g r a p h was the  histogram  chosen)  last  we  to  of  "sell" of  methods  hear  about  results  kriging  of  having  multigaussian,  their  complexity,  study w i l l  c a n be u s e d  determined  line point  t o management  this  or  to  effect  are  or  rigorously  curve or s t r a i g h t  Because  estimation if  fit  (examples  difficult  time)  the  few p e o p l e  deleterious  One f u r t h e r o b j e c t i v e  much s i m p l e r  of  the  results  and much more c o m p l e x  the  distributions  show t h a t  important  usually  that's  newer  offset  are often  company.  90%  of  and p r o b a b i l i t y k r i g i n g ) .  t h e s e methods mining  —  which type  enough" and  most  Very  d r a w n , and a b e s t  a r e employed t o  non-perfect  the  evaluation of  confirmation  way  A l t e r n a t i v e l y , various  methods  a statistical  sample d a t a .  in  ( d e p e n d i n g on  that  study,  important.  lognormal nature of test  STATISTICS  effort  from a c l a s s i c a l  is  in a be  to  (probably made  to  statistical  study. T h e a u t h o r has drillhole, and  has  and r e m o t e found,  from  parameters  separate  numerous  sensing  almost  appearing datasets data  studied  c a n be  datasets  without  over the  exception,  explained  populations.  geochemical,  by Where  past  geophysical, 5 or 6  years  that non-lognormal  inappropriate mixing of classical  statistical  s u c h as mean and v a r i a n c e a r e r e p o r t e d f o r t h e s e mixed  datasets, of  they  splitting  (David,  are nearly meaningless. up t h e s e  1988),  partitioned One  and  separate, a  way  What i s  (usually)  of  such  method  has  been  whether  in  1976),  and w i l l  study,  of  c o n d i t i o n a l p r o b a b i l i t y estimate  described the  later)  data i s The  indicate  points  first every  and t h a t  curve.  on  were u s e d t o  the  and t h e single  they  a best curve  of  last  the  to of  the  is,  20'  fit  exploration  modelled which  original  this  (which w i l l assumption  be  that  However,  the  2 or  not  if  placed  point,  it  c a n be  above t h e curving  below  define  straight line  shows t h a t a  "bell"  up t o  be  of the  shaped defined  create  one shown f o r a l l  a of  composites?  show t h a t  a r e added t o g e t h e r data points  is  gently  the  adequately  a ruler  more p o p u l a t i o n s  which resembles  the  c a n be drawn  seem t o  is  histogram  does  can  a  line  last  plot  from  a p r o b a b i l i t y graph  when added i n t h e p r o p e r p r o p o r t i o n s , add  5)  case of  composites  straight  o r second  the  U s i n g S i n c l a i r ' s method,  Fig.  on  construct  define  samples  The q u e s t i o n  20'  demonstrated  In the  which would  p o i n t on  seem  cumulative p r o b a b i l i t y the  dependent  exploration  glance,  Examination  distribution  which,  non-zero  At f i r s t  the  points.  here.  a lognormal d i s t r i b u t i o n .  seen t h a t  resulting  lognormally d i s t r i b u t e d .  through the  line,  critically  (BEX) d a t a s e t  5).  between  is  2,388  original (Fig.  the  the  and  (Sinclair, use  a way  fact.  documented  be u s e d  is  lognormal populations  testing  p o p u l a t i o n s h a v e any b a s i s  needed  if  two s t r a i g h t 2  line  populations  lognormal populations  (A and B ,  i n t h e p r o p o r t i o n A=60% and B=40%,  c a n be a p p r o x i m a t e d ( c h e c k p o i n t s ,  were  Fig.  the 5).  23  N= 2 3 8 8 -  PROBABILITY LOWER LIMIT 0.000 0.001 0 .001 0.002 0.003 0.004 0.005 0.008 0 .011 0.015 0.020 0.028 0.039 0 .054 0 .075 0.104 0.143 0.198  %  6 . 2 ****** 0.0 3 . 0 *** 4 . 5 ***** 3 . 7 **** 4 . 5 **** 9 . 0 ********* 8 . 3 ******** 7 . 5 ******* 8 . 9 ********* 1 0 . 7 *********** 1 0 . 5 ********** 8 . 1 ******** 6 . 0 ****** 4 . 3 **** 1.8 ** 1.4 * 0.8 * BEX DATA  ( CUM % ) LOWER LIMIT 0.000 0.001 0 .002 0 .003 0.004 0 .005 0.007 0 .010 0 .014 0.019 0.026 0.036 0.049 0.066 0 .091 0.124 0.169 0.230  %  0.0 2.9 3.1 2.6 2.4 3.8 6.4 8.4 9.5 12.1 12.4 10.7 8.1 5.4 3. 3 1.9 1.2 0.6  *** *** *** ** **** ****** ******** ********* ************ ************ *********** ******** ***** *** ** * * BBH DATA  F i g . 5. Partitioned log probability plot o f 20' exploration composites. The h i s t o g r a m b e l o w shows a large number o f low grade samples which cause the original curve to d e p a r t from a perfect lognormal distribution.  By lines  s t u d y i n g the  resulting  on a p r o b a b i l i t y g r a p h ,  from a p p r o x i m a t e l y  Also,  a  whereas o n l y  it  265)  was  to  selected  construct this  the  define  second  set  f o r which there  drawn f r o m  samples)  one  or  It  the of  was ore  this  the  90% o f  the  should  be above  0.01  outlines  3 "ore zone"  grades is  other  members  of  0.010  0.010  opt.  grade c u t o f f  that  that  were u s e d  to  examined  in  b l o c k models  study. A conservative  there  was  a  mining  boundary i s  b o u n d a r y was outline  considered  "greater  than  nearest  composite  essentially  0.01  opt.  outlined  Figure  5,  grades  zones which  then  it  should also  t h a n 0.01  separate  were  data  blasthole  graph  population below  0.01  "A". (8%  resulting (Fig.  ore  zone  closer  to  the  than  to  the  opt.  by 0 . 0 1  The opt.  line gold  p r o b a b i l i t y graph, population  a number o f  6)  one  if  "A" i n  values  which  (BEXG d a t a s e t ) ,  within  data  W i t h i n each o f f o r the  the  created,  represents  probability  to  include  outline  The  t h a n 0.01  which  (10%)  opt.  datasets  dataset).  lies  the modelled  e x p l o r a t i o n data w i t h i n the the  The  composites"  a r e bounded  According  bench f o r  data).  because i t  less  zone t r u l y r e p r e s e n t s  which are l e s s Two  (blasthole  exploration  which  encloses  drawn on e v e r y  conservative  exploration composites. the  0 . 0 35  opt.  of  p o p u l a t i o n B s h o u l d be above  samples.  straight  a range  seen t h a t  1,300  as  can d e f i n e  is  c a n be  28% o f  (approximately  to  sample  population A (approximately opt.,  one  0.005 o p t .  some p r o b a b i l i t y t h a t population.  lognormal populations,  were  along the  exploration  the then  with  represents  and one  same  zone  (BBHG  on  a log  plotted  the  new d a t a s e t s composites  higher there and  which  modelled are  values  9% f o r  the  25 1 .000 i  i  II  i  i  i  i  i  i  i  i  i  i  i  _  \  A  \  °  a  BEXG DATA (N = 1032) BBHG DATA (N = 6308)  _ D. 100 z o h—  —  — —  \  NJ o  * o^.  UJ Q  <  cr o Q O 0.010 O  — •\  —  * ^ \ A  c .001 0. i  i  i 2  II  i 10  i 30  i  i 50  PROBABILITY  LOWER LIMIT 0.003 0 .004 0 .005 0.007 0 .008 0.011 0 .014 0 .017 0 .022 0.028 0.035 0 .045 0 .056 0.071 0.090 0.113 0.143 0.180 0.228  %  i 70  i  T TMTT j j i n i j.  * ** * ***** ******* ******* *************  0.003 0.004 0.006 0.007 0.009 0.012 0.015 0.019  *********** ******** ****** ****** ** ** * * * BEXG DATA  o!o3o o!038 o!048 0*.061 0.077 0.097 0.122 0.154 0.195 0.245  ************ **********  i 90  i  1 98  I 99.9  ( C U M %)  LOWER  c .5 *  1 .4 1 .8 0.5 c. 3 7 .3 1 .2 12.5 11 .8 10 . 3 10.9 7 .9 6 .1 c .9 2 .4 1 .7 1 .5 0 .9 0 .5  i  "  o!o24  %  0.8 * 2.1 ** 1.1 * 3.0 *** 5 . 7 ****** 6 . 3 ****** 7.8 * * * * * * * * 10.2 * * * * * * * * * * 10 . 2 * * * * * * * * * * 11.2 * * * * * * * * * * * 11.0 * * * * * * * * * * * 9.0 * * * * * * * * * 6.0 * * * * * * 4.6 * * * * * 3.2 *** 2.1 ** 1.6 ** 0.9 * 0.6 * BBHG DATA  Fig. 6 Log probability plot of blasthole data compared t o p a r t i t i o n e d e x p l o r a t i o n d a t a . T h e s t r a i g h t l i n e i s t h e m o d e l l e d p o p u l a t i o n A f r o m F i g u r e 5. B o t h sets o f data r e p r e s e n t e d above a r e drawn from w i t h i n t h e o r e o u t l i n e i n t e r p r e t e d from t h e graph i n F i g . 5 •  blastholes)  w h i c h compare f a v o u r a b l y  w i t h the  t h e model p o p u l a t i o n " A " .  The b l a s t h o l e  is  by  accurately  represented  the  expected  10% from  d a t a w i t h 6,308  straight  line  samples  model.  The  e x p l o r a t i o n d a t a shows s m o o t h i n g t h a t was a p p a r e n t o n l y s u b t l y the  raw d a t a — n a m e l y a s l i g h t u n d e r e s t i m a t i o n o f t h e  of  composites  expected  at  higher  overestimation of the percentage This  is  weighted  consistent  with  averaging  process  composites, fewer  and  samples  i n the  Both the slight  tendency  indicates  that  f o r the  is  the  to  "rise"  i n the there  to  graph.  grid  on t h e  Generally predicted  the  exploration  t h e BEXG data  the  and BBHG  was s o  that  there  in  the are  composites).  between  the  this  show a 2nd and  probably  certainly  due  to  than  a  50  1  exclusively  This  gives  a slightly  the  high  grade  categories.  have  accurately  seems  zones o f  higher  grades.  or not,  the  grade d i s t r i b u t i o n s i n t h i s  outline  are  datasets  to  to  higher  be b e l i e v e d  o f samples.  the  1,032  blastholes  almost  modelling  which i n d i c a t e s  2 types  that  the  of unexpectedly high grades,  t h a t whether t h e model i s  identical  created  plotted points  grades  existence of these d i s c r e e t  and b l a s t h o l e  grades.  and w h i c h were a l m o s t  samples  the  lower  d r i l l h o l e s w h i c h were c l o s e r  pattern)  number o f  however,  also  between  is  slight  when u s i n g  fact  (only  For the  i n h i g h e r grade ore areas.  than expected  nearly  higher  exploration data i t  at  a  originally by t h e  percentage  and  result  blasthole  a r e a few a r e a s  apart  Notice  which  exploration dataset  irregular  collared  expected  accentuated  s m a l l e r number o f (not  o f composites  e x p l o r a t i o n and t h e  5th p e r c e n t i l e s  but  it  grades  in  that The  there  is  little  reason f o r  on b e n c h e s  e x i s t e n c e o f any  only  o r no  generating  where t h e r e was sampling  bias  bias  blasthole c o u l d be  27  Table Simple S t a t i s t i c s  Data  n  the  E x p l o r a t i o n and B l a s t h o l e  Arith. Mean  Arith. Variance  Relative Variance  Log Mean  Data  Log Variance  1 0  1 0  BEX  2432  0.031  0.00224  2.3  -1.82  0.311  BEXG  1036  0.043  0.00276  1.5  -1.55  0.162  BBH  8752  0.037  0.00310  2.2  -1.71  0.288  BBHG  6315  0.047  0.00380  1.7  -1.51  0.162  checked the  in this  way.  four datasets  because, method,  in  for  There i s (e.g.  be  actual  further  probability constant model.  another  value 2  of  which approach a  "non-ore  ore  is  the  simple  to  create  a constant of gold  to  compute  b l o c k models  sill  relative  value  should  statistics (Section  to  the  is,  0.005 o p t .  an  will  be  5.4.1).  to  add a  lognormal  added t o  produces  conditional  be  conditional  this  lognormal  in a  populations  a 3-parameter  grades line  calculated  lognormal  integral  of  probability  variance  reserve estimation;  straight  later  outline"  the  of modelling  which  were  The p o p u l a t i o n  choosing  These  statistics  conditional  s e c t i o n on v a r i o g r a p h y  arithmetic  be u s e d  in  simple  variances  used.  same way t h a t  i n d i v i d u a l grades  set  should  are  method  1982)  the  Raymond's  variograms.  approach to  to  Relative  guide  F i g u r e 7 shows t h a t  original points  a  i n the  Raymond,  summarizes  use  variogram i n the  indicator analyzed  to  variograms  should  relative  A chart  (Table I I ) .  order  relative  variance  the  of  II  the  a series  model. probability  (BUCK and BUCK60)  of  This for  because,  28  I.000.  F  r  i  i—r  i—i—i—i—r  zn  o  i— \  0.100  M  o  ID O O  O <  o  Q 0.010 _j o o  0.001 0. 1  j  10  i i_  30  50 i  PROBABILITY  i 70  i  j90  ( CUM %  i_  98  F i g . 7. L o g p r o b a b i l i t y p l o t shows t h e e f f e c t ing a constant of 0.005 o p t . t o the original c r e a t e a 3-parameter lognormal d i s t r i b u t i o n .  according that  to  kriging  Raymond variances  (1982, are  1984), related  it to  is  99.9  )  the  a log  of adddata to  o n l y way t o  ensure  transformed kriged  grade. However  it  should  amplified  on f u r t h e r  in  lognormal  concept  one  is  Conceptually,  a  frequency  every  of  to  what c o n s t a n t  be  mentioned  later  single  one adds  sections,  which the  distribution  can  value to  here, that  a u t h o r has be  modelled  i n that  each  and  dataset  discreet  it  the  will  3-parameter  difficulty by and,  value,  be  with.  assigning  a  regardless it  doesn't  change it  the  frequency  appears  to  with which t h a t  generate a s t r a i g h t e r  probability  graph  altered  d i s t r i b u t i o n of  the  Modelling positive that  doesn't  the  constant  the  change the  does have and  The l o g n o r m a l  steeper  this  p r o c e d u r e c r u d e l y models  line,  the  probability plot  The c l o s e r  the  chance  that  the  the  truth.  The attempt  however  m o d e l l i n g the  h i g h e r mean  grade p o r t i o n  of  grade  values  into  population  the  is  of  the  still  The e f f e c t  predicted  the  is  steep  line  the  on  the  high for  better  come c l o s e  the  succeed upper,  effect  to in  high  of  the  by b r i n g i n g  the  high grades),  calculation of  w i l l be t h a t  variance  the  totally  (mainly as  fit  Effectively,  lognormal,  although the  i n the  best  the upper p o p u l a t i o n .  variance of  minimized  represented  and t h e  are  this  lognormal  p r e d i c t e d mean  the upper  is  population  grades. The  partition  advantage the  are modelled the  is  up  never  same o r d e r o f m a g n i t u d e  mean and v a r i a n c e . low and  data because,  population the  and l o w e r  is  variances  approximation w i l l can  with a  What happens  portion of  to  log  hasn't  and becomes l e s s  which represents  3-parameter  really  variance).  linear  original distribution is  the  lower  the  a  data.  however.  out  that  on  distribution  shifted  greater the  one  population  distribution flattens  the  The f a c t  plotted  that  lognormal  mean i s  (the  when  fact  lognormal  through the  log  the  an e f f e c t  line  the  line  occurs.  raw a r i t h m e t i c  3-parameter  relative  decreased.  value  data  the  is  correctly,  partitioned  represent  of  log  using that  Sinclair's  method  to  b o t h t h e u p p e r and l o w e r  and more i m p o r t a n t l y , probability plot  a c t u a l numbers o f  samples  accurately populations  further studies  provide percentages which  can  be  of  which  expected  from  either  shown  modelled  earlier.  different discreet  However, use better  than  modelled later  These  populations z o n e s as  not  population  if  they of  values it  doing  be  used  Buckhorn  3-parameter anything  d i s t r i b u t i o n on k r i g i n g  chapters.  can  a grade  c a n be shown t h a t  are for the  the  within  at  to  they  variances  as  was  separate  the  are located  in  distribution  is  study.  lognormal all.  range,  The e f f e c t will  of  be d i s c u s s e d  this in  31  5.  5.1  ORE RESERVE CALCULATIONS  INTRODUCTION  For  each o f  the  20'  and 60'  block models,  calculated using  10 d i f f e r e n t methods  distance  calculations,  based  probability. reserve  This  calculations  blasthole  results  Undiluted 2 benches benches  tonnages. any  volume  and a t o t a l  methods 20',  of  or  60'  whether  shared  each  of the  calculations  yield  and  the  therefore  directly  w i t h each  estimates  blasthole  at  constraints,  that  the  identical  different other.  20'  block  was  used)  cutoff  any  4',  (regardless and w h i c h same  total  block  reserve  tonnages w i t h i n the  outline  size  models  60'  on  different  Also,  a l l produced the vs.  were total  a 0.0  were c a l c u l a t e d  block  total  and  comparison of  2  partial  calculations  tonnages  data  the  f o r the  block  reserve  the  model f o r which r e s e r v e s  T h i s meant  kriged  on e a c h o f  c a l c u l a t i o n w i t h i n each model.  same o u t l i n e  the  reserve  The  grade  facilitated  e x p l o r a t i o n or  the  tonnage.  greatly  reserve  e x p l o r a t i o n ore  f o r each b l o c k f o r e v e r y model  b l o c k model produced i d e n t i c a l t o t a l This  inverse  4 block models.  weighted  that  were  and c o n d i t i o n a l  separate  calculated.  stored  6  t h e n be compared t o  and 6860) also  T h i s meant  grade.  of  was  w h i c h were  kriging  were c a l c u l a t e d s e p a r a t e l y  (6840  produce  40  which could  reserves  combined  to  in  reserves  2 polygonal,  ordinary  f o r each o f the  studied  percentages used  resulted  —  gold  can  be compared  32  5.2  POLYGONAL ESTIMATES  In  place  of  traditional  computer generated assigned  to  blasthole  on t h e  block. (one  any  Four  the  blasthole  direct  reports  the  tonnage  employed.  grade to  the  one w h i c h  of  the  center  a  The grade composite of  the  for exploration represented  or  small data  a subset  and two c o m p a r a b l e e s t i m a t e s  generated  blasthole  to  weighted of  with other the  20'  produce grade  the  the  for  each  polygonal  and g r a d e t h a t  models,  volume weighted  using  the  of  estimates  would h a v e  been  Because  various  the  the  models  in  fact  reported  exploration  o t h e r methods  down  p o l y g o n a l e s t i m a t e was n o t u s e d methods. and 60' what  estimate  polygon weighted  Instead,  b l o c k models  will (see  be  the  Fig.  4'  8 for  to  to for  blocks  and g r a d e s  referred  at  as  were the  a graphical  method).  INVERSE DISTANCE  Six all  the  and  interpolated using  were r e c o m b i n e d i n t o  5.3  was  production s t a t i s t i c s .  comparisons  explanation  were  The  block  polygon  is  zone o u t l i n e ) ,  mine i n t h e i r  4'  block  same b e n c h n e a r e s t  C).  d a t a was n o t the  model  outlines,  data.  (Appendix  the  4'  mined l i m i t s  ore  Reserve  represent  block  1  s u c h e s t i m a t e s were made — two  w i t h i n the  inside  4  hand drawn p o l y g o n a l  20'  inverse and 60'  distance  reserve  block models.  e s t i m a t e s were  T h e s e were i n v e r s e  calculated distance  to  for the  33  i i •  i  i  i i  i i  •  •  •  F i g . 8. G r a p h i c a l e x p l a n a t i o n o f the polygon weighted method o f c a l c u l a t i n g block grades. The s m a l l s o l i d b o x e s show t h e l o c a t i o n o f d r i l l h o l e s , whereas shaded areas r e p r e s e n t the sub-volumes within a large block w h i c h w i l l assume t h e g r a d e o f t h e n e a r e s t d r i l l h o l e .  zero  (IDO),  (ID2), fifth All  inverse  inverse distance power  (ID5),  (ID3),  inverse distance inverse  distance  to  o f t h e s e e m p i r i c a l models have been used  distance  drillhole  the  composites  d i s t a n c e weighted  to  in a practical straight  whereas some p o w e r .  h i g h e n o u g h power t o difference  distance the  tenth  in practice  It  of  to  the  (ID10).  inverse  study.  average o f each  squared  and a r e  o f the u n c e r t a i n t y o f knowing which  approach to use  IDO r e p r e s e n t s  the  cubed  (ID1),  and i n v e r s e  i n c l u d e d here because  be a  distance  a l l of the  the  other estimates  was e x p e c t e d  be c o m p a r a b l e t o  b e i n g t h a t d r i l l h o l e s on t h e  qualifying  that  a polygonal  is  ID10 would estimate,  b e n c h a b o v e and below  34  Table  III  P a r a m e t e r s Used t o G e n e r a t e I n v e r s e D i s t a n c e Weighted B l o c k Model E s t i m a t e s from E x p l o r a t i o n C o m p o s i t e s .  Composite  length  20'  Anisotropy  none  Minimum number o f s a m p l e s  accepted  5  Maximum number o f  accepted  12  samples  Maximum s e a r c h r a d i u s Rectangular  150'  search radius  150'  Power o f d i s t a n c e  0,  w o u l d h a v e some s m a l l w e i g h t vertically center  above  would  and  probably  assigned  below be  to  the nearest ranked  second  x 150'  1,  2,  them  3,  x  5 & 10  (the  composite and  30'  composites  to  the  third  block  in  the  weighting). The  search  parameters  were c h o s e n b e c a u s e initially  used  to  they  Buckhorn.  f o r open  Therefore,  the  b l o c k model which wasn't (BUCK b l o c k  model),  is  a r e shown i n T a b l e  are exactly  generate  m o d e l t h a t was u s e d  used  the pit  20'  the  by  distance direction.  estimates  that  c a l c u l a t e d f o r the the  ore  zone  at  to  20'  outline  t h e mine and  a l l other estimates  relative  were  p l a n n i n g at  No a t t e m p t was made t o w e i g h t  differently  These  cubed b l o c k  mine  t h e one u s e d  c a n be s c r u t i n i z e d c a r e f u l l y r e l a t i v e t o c o u l d have been g e n e r a t e d .  and  ID3 e s t i m a t e  i d e n t i c a l to  values  inverse distance  design  constrained  same  III.  any  that  inverse  preferred  The thought  ID3 of  as  m i n e went this  estimate the  into  was  used  geologist's  "gut  feel"  production.  i n every  before  this  cutoff  s t u d y was  geologists  category. initiated  feelings  best estimate before  be s e e n ,  look  reasonable  used  to  attempting pointed  to  out  prediction easier fact,  to of  distance kriged  an  ore  analyze that  of  tonnage  get  a  the  inverse  to  the  tonnage  at  the  the  reserve  seemed t o  serves  —  at  this  each grade c u t o f f  us  that  point,  to  the  of  should  it  without  should  produce  the  grade estimate tonnage.  it  that  out  predicting  f o r the  the  be  best  estimate of turns  a  w h i c h may be  However,  doesn't  methods,  comes c l o s e r  apparent  remind  a d v a n c e d methods  than the  distance  block  any c a l c u l a t i o n  performance o f  for  to  be  the  because  accuracy or usefulness  estimate  — the  may be  estimating  estimate.  results  ID3  feeling  fifth  of  the  the  and i t  this  when  fact  be i g n o r e d  regardless  generate  This  about  grade estimate should not  5.4  As w i l l  f o r m i n e p l a n n i n g c a n be  p a r t i c u l a r c a l c u l a t i o n performed w e l l  grades  the  that  is In  inverse blasthole  BUCK b l o c k m o d e l .  KRIGING  5.4.1  Variogram A n a l y s i s  The a p p r o a c h data  as  was  to  if  it make  was  taken i n the  the  this  study  only data a v a i l a b l e best  reserve  to  and t h e n compare t h e  blasthole  Therefore,  study  because the  calculation  production started, results.  was  exploration general  possible  estimates with the  aim  before known  a l l v a r i o g r a m s were c a l c u l a t e d  and  modelled  from  were u s e d made t o  to  exploration krige  the  determine  a  composites  exploration  and t h e data  parameters  before  better variogram derived  derived  any a t t e m p t  from the  was  blasthole  data. Three basic the  two e x p l o r a t i o n  compass 45°.  directions  the  b e n c h above  vertical  Actual,  a  0°  lags  increments  in  weighted  distance  plotting  and m o d e l l i n g  All  greater  types  (Appendix D c o n t a i n s values),  on t h e  the  variograms  horizontal  the  20'  to  of  the the  composites  with a 5°  For  window  drillholes.  calculated  directions the  by  direction  calculation.  were  of  principal  incrementing  vertical  determine  each  which  with  included  average  lag  for  results.  of  variogram  a listing  relative  was  v a r i o g r a m on t h e  of  but because c o n d i t i o n a l  rely  i n the  for  four  than 20',  lag distance  calculations  three  and  each s i d e  and below were u s e d  down h o l e  i n the  (north)  3 0 ° on  l o g n o r m a l and r e l a t i v e  lag  later  at  variogram, the  essentially  40'  and f o r  calculated  (BEX and BEXG)  window was  calculated,  on t h e  datasets starting  The s e a r c h  being  --  t y p e s o f v a r i o g r a m were  all  show of  the  consistent calculated  p r o b a b i l i t y estimates  variogram, the  relative  results variogram  as  defined  v a r i o g r a m was  modelled. The similar  three  types of  anisotropy  variogram value y(r)  i n the  exception dataset), at  the  variogram for  patterns.  at  the  first  NW-SE d i r e c t i o n (the  The lag  is  lognormal  the  NW-SE d i r e c t i o n  first  significant  both datasets N-S  direction  t h a n does the  lower  than  variogram  on  showed t h e lag.  The  all has  a  BEX  With  and one  exploration  lowest variogram major  lower  E-W d i r e c t i o n  f o r NE-SW. the  indicated  structural  value trend  determined be N 1 0 ° W  from g e o l o g i c a l (Plahuta 1986);  m a p p i n g on t h e therefore  consistent with expectations. define the  the  nugget e f f e c t .  exploration datasets  that,  although  150',  all  constant  the  after  stationarity  1024  that  gamma v a l u e s  to  cut  (Figs.  11  confirmed It  and  should  the  lags  less  thought  to  sample  pairs  grade o f  lags  only the  the first  beyond t h i s  angled they than  50',  was at  relative  held  in  core  lag  distance  longer  lag  150'  because,  demonstrated were  variogram clouds arrays on  (38  lags X  C o m i n c o ' s IBM  distances need n o t  the  opt.  be  calculated.  spaced  samples retained  structure  variogram values average  greater  grade than the  As m i g h t  variograms c o n s i s t e n t l y than at  and more d a t a  i n showing  resulting  showed  the  to  variograms  i n i t i a l l y were  distances.  l a g w h i c h were l o w e r  Blasthole  although close  be u s e f u l  0.015  of  reached  variograms  as  large  computing.  In general  of  Notice  relative)  values  directions  that,  the  about  lag distances  only to  sill  diamond d r i l l h o l e s would  to  subsequent  smaller  a l s o be n o t e d  and 1 0 .  v a r i o g r a m s were o n l y c a l c u l a t e d  of  with  f o r each  to  directions.  in five,  A l l final  be u n r e l i a b l e .  pairs  in a l l  on c o s t s  hope t h a t of  all  resulted  12)  which included in  constant  to are  9  and  calculated  x 5 directions)  down  that  lognormal  1977),  This  mainframe computer. 150'  the  anisotropies  were u s e d  a r e shown i n F i g u r e s  calculated  lags.  that  in a l l horizontal  (David,  simultaneously w i t h 4'  The models  v a r i o g r a m s were  assuming  thought  The v e r t i c a l v a r i o g r a m was u s e d  (actual,  values  The f i n a l  the modelled  v a r i o g r a m s a r e shown o n l y  variograms sill  property is  be  of  were these  average expected,  gamma v a l u e s  second  lag.  at  at  These  38  RELATIVE  VARIANCE  = 2.329  _©  '  1  o  o  N S E W X X •e—w •  NW-SE  —i—  50 Fig.  values  were  variograms, considered  9.  LAG  (FEET)  Modelled r e l a t i v e t h e BEX d a t a .  i n i t i a l l y noted but  were  variogram of  and p l o t t e d  not  t o o u n r e l i a b l e and  used  on e a r l y  versions  i n m o d e l l i n g because  inconsistent  between  of  they  the  the were  various  types of variograms.  5.4.2  Some O b s e r v a t i o n s on V a r i o g r a m  Having defined this  study,  a slight  the variograms digression  Modelling  which w i l l  be u s e d  later  in  i n t o the nature of variograms  is  39  S 5 •  2.0-  a •J <« >  2  RELATIVE  VARIOGRA  i.s-  VARIANCE  '  = 1.497" „ _--  „ 'JT  - „  „i - " - " ^  - - •*  LEGEND  b  RELATIVE  0  0  VERTICAL  *  +  NS -  0N-E --SoW  0.5-  X  K  E-W O  D  NW-SE 0.0 -  1 IO  1 30  1 SO  1 70  LAG  Fig .  10.  undertaken. have  one  discussion, the  time  part  of  variogram  of  the  monitor, based  on  1 ISO  110  1 190  (FEET)  particular shortest  section  were  of the thesis  i t not f o r the  spent the  on t h e e n t i r e p r o j e c t because author  modelling  that  clouds  would  a)  kriged  were  and a t t e m p t s  repeated,  drawn were  median squared  provide  made  pair  better  estimates. on  a to  of the b e l i e f  sophisticated  high  differences  50% o f on t h e  attempts  at  variograms which  Complex  c o l o u r coded  resolution  develop  might  following  t h e s t u d y o f v a r i o g r a m s a c t u a l l y consumed o v e r  w o u l d b) p r o v i d e b e t t e r variogram  I  Modelled r e l a t i v e variogram of t h e BEXG d a t a .  Although t h i s  been  I 90  better  and o t h e r  graphics variograms  percentiles,  40 or a  "different"  half  the  relative  v a r i o g r a m w h i c h was  mean s q u a r e d p a i r  value,  etc.  useful  i n f o r m a t i o n t h a n was  lognormal  These  differences  and r e l a t i v e  modelling the to  krige  best  the  prerequisite conditional  data  final  relative  of  of  0.020  proceeding  fashion  (including  the  was  20'  and  on  results,  to in a  performed.  The  the major a x i s  b l o c k models  of  (BUCKG)  similar  identical  category. the  kriged estimates ore  reserve  The e x p e r i m e n t  variogram  misinterpreting  C  and  is a,  and k r i g i n g estimates  tends to  robust  and  are not  very  in  support  that  "the  important"  1977). there  are s l i g h t  variograms  variogram predict cutoff  variogram  at  a  less  estimate.  difference (arbitrarily  a  vs.  above  total  0.042  the  differences  (Table I V ) .  slightly  (0.041 o p t .  4,600 tons other  basics  and  such t h a t  the  actual,  two k r i g e d e s t i m a t e s were c o m p a r e d .  calculate  statement that  two d i f f e r e n t  rotated  rotated  the  continuing  experiment  and one o f  Then t h e  range  However, the  a simple  pair  o r more  returning to  then  one  new,  from  reasonable  and  and p r o d u c e n e a r l y  grade  (David,  analyses),  9 0 ° away,  Both models  effects  After  most  v a r i o g r a m was  re-kriged.  David's  apparent  variograms a v a i l a b l e ,  the  desperation  a n i s o t r o p y was  every  in  p r o v i d e any  p r o b a b i l i t y and f i n a l c o m p a r i s o n o f  act  variances  relative  back  final  was  variograms.  as  d i v i d e d by t h e i r mean  variograms d i d n ' t already  calculated  of  lower  between chosen  the to  2  6 , 5 0 0 more grade  0.050 c u t o f f  estimates  the  differentiate  from  at  t o n s above  than  and  was is  results  The e s t i m a t e s u s i n g  opt.),  E v e n more i n t e r e s t i n g  in  the the  the  it  about  same g r a d e as  greater  that  when  t h a n 0.010  between  the  original  predicts  fact  the  similar  the the opt. and  41  T a b l e IV Ore Reserves P r e d i c t e d by U s i n g t h e "Rotated" Variogram Compared t o K r i g e d E x p l o r a t i o n E s t i m a t e and " A c t u a l " f o r t h e BUCKG Model.  BLOCK MODEL:  BUCKG  20' BLOCKS - WITHIN ORE ZONE OUTLINE  METHOD:  BHKRIGE  BLASTHOLE KRIGED -  RESERVES BENCH CUTOFF  ABOVE CUTOFF GRADE TONS  GRADE  OUNCES  "ACTUAL n  INSIDE GRADE BOUNDARIES TONS  GRADE  OUNCES  TOTAL  0.000  756122.25  0.040 30336.14  28070.44  0.007  184.60  TOTAL  0.010  728051.81  0.041 30151.54  124929.62  0.016  2012.15  TOTAL  0.020  603122.19  0.047 28139.39  276722.06  0.027  7487.60  TOTAL  0.035  326400.12  0.063 20651.79  143338.62  0.042  5952.25  TOTAL  0.050  183061.50  0.080 14699.55  183061.50  0.080 14699.55  BLOCK MODEL:  BUCKG  20*  METHOE  "GOOD"  EXPLORATION  RESERVES BENCH CUTOFF  BLOCKS - WITHIN ORE ZONE OUTLINE  ABOVE CUTOFF GRADE TONS  GRADE  OUNCES  •GOOD" KRIGED ESTIMATE INSIDE GRADE BOUNDARIES TONS  GRADE  OUNCES  TOTAL  0.000  756122.25  0.039 29523.88  408.00  0.009  3.73  TOTAL  0.010  755714.25  0.039 29520.15  86186.00  0.017  1500.25  TOTAL  0.020  669528.25  0.042 28019.90  350814.87  0.028  9654.29  TOTAL  0.035  318713.37  0.058 18365.61  182996.25  0.041  7531.16  TOTAL  0.050  135717.12  0.080 10834.45  135717.12  0.080 10834.45  BLOCK MODEL:  BUCKG  METHOD:  "ROTATED •  RESERVES BENCH CUTOFF  20' BLOCKS - WITHIN ORE ZONE OUTLINE EXPLORATION "ROTATED" KRIGED ESTIMATE  ABOVE CUTOFF GRADE TONS  GRADE  OUNCES  INSIDE GRADE BOUNDARIES TONS  GRADE  OUNCES  TOTAL  0.000  756122.25  0.039 29212.79  0.00  0.000  0.00  TOTAL  0.010  756122.25  0.039 29212.79  80163.87  0.017  1390.62  TOTAL  0.020  675958.37  0.041 27822.17  358860.69  0.027  9746.67  TOTAL  0.035  317097.69  0.057 18075.50  185966.44  0.041  7628.64  TOTAL  0.050  131131.25  0.080 10446.85  131131.25  0.080 10446.85  dissimilar tends to  estimates),  be c l o s e r  blasthole 137), the  the  kriging  and t h e  the  rotated  is  originally  modelled  predicting  higher  highest But  total  anisotropy  i n any o t h e r  ranges  even  is  actually  up on t h e  variograms.  conclusion  to  structures  than  The  been  This  constant  differential rapidly  true  lower  as at  occur  a  the  the  course reached:  the of  that  that  above,  of  most the  geology. the 4 5 ° showed  many v a r i o g r a m s the  data  is  from a l l  results,  the  lognormally  sample  of  magnitude  the  job  and  by  to  almost  s h o u l d have  continuity the  by  slight,  studying  calculated of  is  when  close  t o model  indicated  anisotropy  was m e n t i o n e d  reason  for  grades  better  highest  was no good  anisotropy  be  remains  slightly  in  of  to  vs.  than  Block  0.050 o p t .  fact  As  measure  grades  pairs  is  between  and d i r e c t i o n  of  structures. used  which  calculated  fairly  a  the  did  the  was  within  differentials.  7%  from  estimates  study.  above  variogram  determined  (204  is  d i r e c t i o n than that  variogram  variograms  anisotropies  category  and t h e r e  be a measure  discontinuities  often  in this  reserves  the  and i n  more l i k e l y  rotated  grade  estimate  still,  though  direction  the  more  the  variogram  grade  distributed  block  a c t u a l l y used  profitable  following  of  from t h e  v a r i o g r a m a r e a l s o more l i k e l y  i n the  were e x a m i n e d ,  actual  error  one m a r g i n .  Perhaps,  estimate  significantly  that  t r u e grade  a two t o  the  average  variogram  using  to  the  here  relate  to  includes y{h)  /  Buckhorn. at  are  areas  the m(h)  2  values.  highest  1977)  areas  where  showing grade  variogram which  (David,  These  toward  of  relative  boundaries  f r o m low b a c k g r o u n d  biased  gold  Within  of  where m(h) highest  grades the  has is  grade  increase  smaller  high  grade s t r u c t u r e s ,  although there  h i g h grade  differences  distance,  there  directional  trends  where s a m p l e d numerous  amongst  are  some p o t e n t i a l  samples  fewer  are  which  pairs.  be  detecting  achieving  by  Therefore,  similar, will  are  for  separated  t h a t m i g h t show up w i t h i n t h e  values  pairs  is  a given  the  subtle  h i g h grade  "drowned o u t "  high  areas by  grade/low  the  grade  boundaries. In other  words, u s i n g  v a r i o g r a m does not evaluated grade,  in  that  shows i s  relative  a high the  that  low v a l u e s , to  error  135°  and  not  the  show  different by  and  is  the  samples  better and  to  only  To p r o p o s e  instead  to  same  assume  is  are s i m i l a r  in  what  the  h i g h grade kriging, of this  might best but  h a v i n g an separate  of  actual  of  very  kriging  are  edges  it  estimate  a high  assumptions  or the  variograms  a different  or 4 a c t u a l or r e l a t i v e  block  weight  v a r i a n c e amongst  account  of not  numerous  a  Instead  lower  of  take  different  creating  indicators  the  grade ranges  i n h e r e n t drawback  where  modelled  applied  c a l c u l a t i o n o f every k r i g e d grade  forms  kriging,  the  a t r a n s i t i o n from v e r y h i g h t o  anisotropy  the  complex  probability  modelled  it  low g r a d e a r e a s  More  that  to  that  T h e v a r i o g r a m t e n d s t o p i c k up t h e  does  either  is  Unfortunately,  indiscriminately  way  e s t i m a t e s h o u l d be l o w e r .  where t h e r e  a  i n any  an e x a m p l e ,  g r a d e a r e a where a l l  on a v e r a g e ,  variance.  deposit.  indicate  B u c k h o r n as  in  the  structures  samples  within  areas. like  indicator  observation be k e p t these  associated  estimates  for  by  and  assuming  separate  and be  methods  have  kriging  variance  a  block  the  using  grades.  solution  to  this  problem,  v a r i o g r a m s were m o d e l l e d ?  what  if  3  By e x a m i n i n g a  variogram between for  cloud,  samples  Thus  in  the  the the  the  lag  the  50th  or  advantage  4 of  to  of  to  the  This  same  values  result is  wrong,  may  there  represent  those  that  be  be t h e  way  variograms.  between  the  the some  but  When  any two o f  error  samples  either  estimate used  were  the  in  Also  that  as d i s c u s s e d  the  kriging  from  relating  separate of  the  generated  above and t h e  in  various  between  b e e n computed  variogram  occur  often  that  i n the  0°  from  the  at  Buckhorn  elsewhere,  and  both variograms are  idea that variograms,  lognormally to  the  data.  possibility merit  which  Appendix E  anisotropy vary  rotated not  were  of the  relatively  case at Buckhorn.  values  composited  derived  structures  squared  differences,  v a r i e d tremendously.  might  always  the  p a i r w o u l d be u s e d  highest  one v a r i o g r a m w h i c h has  i n the  if  100%.  T h i s method m i g h t h a v e  t h e major axes o f  for the  although there  especially  grade)  to  Although k r i g i n g using a  then that  that  of variogram  show t h a t  and 4 5 ° e x c e p t  showed  squared  three  range,  and f i n a l l y  m i g h t a c t u a l l y show u p f o r e a c h  seems  the  assumed  calculated,  use.  fact  (anisotropics)  the  t h e n 90%,  difference  or c o n v e r s e l y ,  approximately  the  differences  a b l o c k w o u l d d e t e r m i n e w h i c h one  their actual  a listing  variograms  estimate  account  variograms. contains  squared  threshold,  variograms  same g r a d e s , structures  represent  c a l c u l a t i n g an a c c u r a t e k r i g e d  into  (regardless  differences  percentile  maximum s q u a r e d  the  3  absolute  being  c a l c u l a t i o n o f each o f the  selected  of  of  exceeds the  samples  all  (say)  of  squared d i f f e r e n c e s ,  70th p e r c e n t i l e  kriging,  takes  3 intervals  a l l p a i r s i n l a g windows p a s t  regardless  difference not  t h a t would  a b o u t 50% o f  t h e n 70% o f  determine  distributed  a r e a s where t h e  data, highest  grade d i f f e r e n t i a l s  exist.  d a t a on t h e  grade ranges,  make t h e  sure  of  divisions  d a t a used values  basis  to  used  that  varied  over  actual  or  calculate  to  the  on t h e  Essentially,  basis  the  k r i g e the  the  of  a  wide  relative  range  estimate.  If  all  values.  variograms  are  above would  the  than i f  It  used  the  of  10 o r  the 12  s i m i l a r , one c a n be  be b e t t e r  of  grouping  v a r i a b i l i t y ranges  b l o c k g r a d e were  grade estimate w i l l  of  idea presented  the  kriged  instead  the  grades  s h o u l d n ' t matter to  represent  if  these  structures. In a d d i t i o n  to  those  p r o d u c e d some f u r t h e r  1) for  modelling,  of  at d i f f e r e n t  only  3  particular, 110'  i n the  the  30°  samples the  windows  the  clustering  every of  the  separated  be t o o  the  i n the  horizontal  density  final  at  this  i n one  lag of  selection  direction.  In  approximately  showed up n i c e l y .  p a i r s at  useful  i n determining the  numerous p a i r s  by 50'  to  showed  and r e s u l t e d  in  window,  were  variogram study  Because  distance  of  represented  d i r e c t i o n and  100'  in  other.  that  shown c l e a r l y on t h e  c o u l d be made by c h o o s i n g the  sake  some c a s e s , window, in  distances,  graphs  4 5 ° and 1 3 5 ° d i r e c t i o n s  that  Also  for  most u s e f u l  These  lag  search  the  although proving not  were  windows w h i c h were u s e d . pairs  above,  observations:  Variogram clouds,  actual  discussed  other  the  v a r i o g r a m c l o u d s were i n c o r r e c t or  o f c r e a t i n g more p o i n t s  because  there  were  fewer  v a r i o g r a m w o u l d become  cases,  where  a  significant  on t h e  mistakes  smaller lag  windows  variogram curve.  samples  almost  the  in  a  small  In lag  r h y t h m i c a l l y s p i k y and  distance  was  dissected  by  short  l a g windows,  an a p p a r e n t l y n e s t e d v a r i o g r a m s t r u c t u r e  might  show u p .  2)  The p r e m i s e  variance  (or  examined  (i.e.  (inside  the  population was  a  that  relative David,  mix  of  significantly  1988).  lower 9).  and r e l a t i v e  that  samples  though  pairs the  is  theoretical  as  if  expectation  Although  all  ground because they  these  and  ideas  the a  is  that  was  be  but g e n e r a l l y ) which  in  actual, sense  average  sample  set's  and  variance  population  and  the  by  the same  therefore,  increase amongst  overall  to  sample  from the  will  was  relative  may make  to  there  the  variogram s i l l  tend  the  sill  c a s e m i g h t be e x p l a i n e d  mixing the  by noted  it  and  Where the  was  assays  inappropriate mixing of  each other  the  10).  predicted  between t h e  single  the  sample  variance.  On  c a n be d e f i n e d ,  the  variogram s i l l  should equal  the  fulfilled.  of are  the  above  based  although there out  for  some  h i g h as  population variance  deposit,  is  (Fig.  the  data  variogram s i l l  In f a c t  always,  calculated,  hand,  be  latter  to  (not  there  not  other  a test  closest  variogram values  the  phenomenon  The d i s c r e p a n c y  population generally even  might  i n the  composited  original dataset,  variograms.  as  population variance fact  the  This  observation  should equal  where o n l y one p o p u l a t i o n o f  in  than  lognormal  populations.  the  was m o d e l l e d ,  samples  (Fig.  this  of  variance coincided  variance  use  variogram s i l l  variance)  ore outline) relative  the  exhaustively  is  observations  only not  i n the  on  the  may be on shaky results  enough t i m e present  to  study,  f r o m one  test the  all  of  results  47  RELATIVE  VARIANCE  =  2.2  u < > < K  * j "  0 O OS  >  "  <*//  LEGEND  4"  o  w os  © O N S -fW NW S-E •  -1—  —I—  1  10 30 Fig.  11.  seemed  to  it  felt  was It  and  variogram direction  i n the context  these points  also  worth  50'. that  T h e r e may could  at the  be n e s t e d  have been  that a very  with  longer lowest  of the  Q  from  Buckhorn s t u d y ,  and  s h o u l d be m e n t i o n e d .  noting  directions  values showed  130  (FEET)  Experimental r e l a t i v e variogram t h e BBH d a t a .  that  N-S  —I—  70 90 LAG  be c o n s i s t e n t  is  1  e v e n t u a l l y m o d e l l e d and showed 135°  o  VER C TIAL  >  blasthole  slight  data  anisotropy  values  distances, of  structures, from t h e  y ( h ) at but  not  while  the  distances at  any  was  in  the N-S d i r e c t i o n showing  lag  inferred  the  the  lower 135° up  to  distance  exploration variograms.  48  w  RELATIVE VARIANCE = 1.7  — a  — B  > S < K O O  5  © ? ' H  ^  >  0- -o VERTICAL  w >  s  td  o — -o  NE-SW  X X  Q  •  E-W NW—SE  70 90 Fig.  LAO  12.  Generally  however,  essentially  isotropic  Finally, effect should  of  the  before  the  leaving  3-parameter  which  conditional  would  the  grade  2  value  + constant) . by d i f f e r e n t  (Figs. the  11 and  subject  to  calculated  constants  of  variograms,  a  relative  the  that  is  calculated  the  kriging  calculation  k r i g e d grades  applied to  the  calculation  from a 3-parameter  each l a g  T o make s u r e  with  indicate  12).  distribution  create  consistent  at  calculations  lognormal  order  be  probabilities  distribution,  affected  In  v a r i o g r a m from  blasthole  variograms  be m e n t i o n e d .  variance  (FEET)  Experimental r e l a t i v e t h e BBHG d a t a .  as  lognormal y /  (mean  would n o t  relative  of  be  variogram  models,  four separate  using  the  three  with constants  kriged  BEX d a t a s e t  estimates  identical. all  kriged estimates were g e n e r a t e d ,  of  0.002,  were  is  order to  make t h e  recalculated constants.  for  The f a c t unexpected  relative BEX  data  the  result.  When a r i t h m e t i c  to  new mean  value,  original Only  the  mean and  the  the  relative  reflected  arithmetic  variance  in  the  kriging  kriging  with  a  relative  into  denominator.  the  5.4.3  Kriging  There krige  the  is  where grades  little  to  composites were  is  variances  which  variogram that  the  different  same was n o t or  from  a constant will  will this  be  the  the  added  equal  the  identical.  change  is  are c a l c u l a t e d has  an  relative  derived  constant  and  In  also  during  constant  added  and B a c k A n a l y s i s  data.  d a t a was u s e d  changes  each  and C were  0  actual  variance  is  identically.  d a t a has  minus t h e  that  variances.  w o u l d be t h e  value which  resulting  is  using  an  and  variograms  only C  were m o d e l l e d  raw a r i t h m e t i c d a t a . every  same,  either  an a v e r a g e d  model  were v i r t u a l l y  kriging  variogram  Kriging with  variogram produces  four  difference  the  k r i g e d grades  20'  The  different  relative  and a n i s o t r o p i c s  that  all  the  shapes  BUCK  and 0 . 0 5 0 .  only  different  the  Ranges  the  the  one w i t h no c o n s t a n t ,  and  shapes o f  important —  e s t i m a t e now p r o d u c e s  0.005  compared  The r e l a t i v e  that  for  to  say  Once t h e calculate were  compared  about  t h e method  parameters kriged  removed  were d e f i n e d point  and t h e  both i n grade  that  samples  was  used  (Table V ) ,  to the  at  locations  actual versus  predicted  ranges  and  across  various  50  Table V P a r a m e t e r s Used f o r K r i g i n g E x p l o r a t i o n D a t a  Composite  length  20 '  Minimum number o f  samples  accepted  5  Maximum number o f  samples  accepted  12  Maximum s e a r c h Rectangular Relative ( y /  radius  search  150 '  radius  v a r i o g r a m BEX ( m + 0.005  )  150'  C„,C  x 150' 0.26  v a r i o g r a m BEXG ( y /  m  a  (135°)  a  (vert)  1  C„,C  0.45  relative geometry  of  conditional to  be i n t h e  estimates kriging Also for  to  ranges.  kriging  in  the  a  (135°)  a  (vert)  120 ' 70 ' 70 '  n/a  samples  used  probability),  the  variances ensure  by u s i n g  Because  variances  middle  the  are  (discussed  the  various d i d not  were h i g h e r n e a r  the  later  variogram,  in  suffer  was  the  section  on  samples  tended  outlines,  kriged  significantly  edges  relative  produce  o n l y by  the  grade  imposed  proportional effect  relative  variograms  influenced  and b e c a u s e h i g h e r  of  the  relative  which  back a n a l y s i s  that  1.05  )  2  Maximum k r i g i n g v a r i a n c e  variance  1.15  120 ' 90' 72  a (45°)  kriging  30'  )  2  a (45°) Relative  x  of  when  the  outlines.  indeed  accounted  kriging  variances  were p l o t t e d kriging  against  kriged  variances across  The v a r i o g r a m m o d e l s composites  grades  a l l grade were  were t h e n u s e d t o  and showed c o m p a r a b l e r e l a t i v e ranges.  deemed  acceptable  calculate kriged  block  and  the  grades.  20'  52  6.  6.1  CONDITIONAL  THEORY  6.1.1  Introduction  The G.F.  following  Raymond  disagreement  description  (Raymond as  to  is  1979,  whether  other  of  literature continued the  by  conditional  6.1.2  Raymond  here  method  is  term  but  used  to  here.  to  by  Raymond  p r o b a b i l i t y are used  called  usage  That  is,  it  refers  and  in this  is by  all  the with  in  its  by  some  avoid c o n f l i c t  traditional  w i t h the understanding that  referred  There  s h o u l d be  changed  and u s e d  the  use  is  strictly  to  references  to  context.  The C o n d i t i o n a l D i s t r i b u t i o n  Kriged that  block  there  is  grades  Although  further theoretical  property  known  smooth t h e mine t o  as  an a d v a n t a g e  property of  exploration grades,  the  being  unbias),  established  predicted  If  other  measure  estimated  (David, 1977).  boundaries  over  calculated  grades  conditional  true picture  cutoff  have  a simultaneously  (kriging variance). the  the  1984).  t h e method  p r o b a b i l i t y or  meanings  t h e method p r o p o s e d  1982,  name c o n d i t i o n a l  in  PROBABILITY  of  the  on  average  estimates  an o p e r a t i o n  and  tonnage  (a  tend  to  were  to  from k r i g e d e s t i m a t e s  grade  error  by k r i g i n g have  correct the  estimates  from  should  be  recovered, available data,  but  (geological  etc.)  general,  in practice,  upon  this  is  information,  which  better  there  usually  visual  production  selectivity  can  better  information  estimates,  blasthole  decisions  c a n be made.  lead  mining  to  a  In  higher  grade o f  o r e t h a n p r e d i c t e d by o r d i n a r y k r i g i n g f r o m e x p l o r a t i o n  samples.  The  attempts to will  have  ore  blocks  method  of  p r e d i c t the  on t h e  final  within  calculating  effect  that  conditional  t h e more a b u n d a n t  grade e s t i m a t e ,  the  probabilities  orebody.  and on t h e The  information  distribution  method  depends  of  on an  assumption o f normal data d i s t r i b u t i o n . When  one  expected  talks  average  about  grade  kriged  (x)  Kriging variance  (o )  is  deviation  the  predicted  from  prediction of  the  words,  although  exactly  as  knowledge the  data  2  error it  is  the  and c a n be t h o u g h t  fact,  for  the  properties  of  the  of  the  be  ore  ore  13,  both a  fraction  knowledge  of  all  root  of  blocks  w i t h k r i g e d grades  13).  the  the  an for  If  the  kriged above blocks  properties  the  squared  In  (based  above  cutoff  below  d i s t r i b u t i o n of is  cutoff  and t h e  can of  be  on  the  that  if  will  be  normal  as  some  will,  actual  average  normal  that  cutoff  be c a l c u l a t e d , the  other  kriging variance  T h i s means  grade  (a  grade won't  t r u e grades the  to.  block  estimate). the  or  referred  expected  with p r e d i c t e d grades  tonnage of  being  normal d i s t r i b u t i o n )  67% o f  square  predicted,  expectation  a standard e r r o r ) .  (Fig.  is  grade  as  a p a r t i c u l a r expected  Figure the  an  of  the  certain that  is  the  of  with the  there  be w a s t e and o t h e r s  actually  mean  nearly  (where o i s  block  magnitude  normally d i s t r i b u t e d ,  between x ± o  percentage  a  associated  is  predicted, of  the  of  grade,  in  will  grades  shown  in  grade  of  based  on  curve.  This  54  Kriged Cutoff  Grade  Grade  i  i  i  x-2o  x-o  x  i  x+o  x+2o  Grade F i g . 13. The c o n d i t i o n a l distribution. Given a k r i g e d b l o c k g r a d e (x) and kriging variance (a ), the a c t u a l b l o c k g r a d e s w i l l be n o r m a l l y d i s t r i b u t e d a b o u t t h e mean. A c e r t a i n p e r c e n t a g e o f b l o c k s whose k r i g e d grade i s above c u t o f f w i l l e v e n t u a l l y t u r n o u t t o be waste (shaded a r e a under t h e c u r v e ) . 2  average  grade  will  t o n s h a v e now  been  possible waste,  to  it  predicted  predict  is  not  be h i g h e r  eliminated. how  of  block  grades,  is  value  of  distribution  the  conditional  measure  of  As an  called  to  the  sample  suppose t h e r e  are  although  are expected  or block grades  conditional (the  to  the use  3 stockpiles  of  the  of  the  given  grades  be o r e  or The  estimated T h e mean  variance  about  conditional  representing  is  kriged estimate)  conditional  actual  it  be o r e .  distribution.  exploration  and  expected d i s p e r s i o n of  that  because waste  p r e d i c t which ones w i l l  expectation,  example  k r i g e d grade  Notice  many b l o c k s  possible  distribution  the  than the  waste,  this  is  is  a  mean.  distribution, low g r a d e ,  and  55  Low G r a d e Stockpile 67%  T  0.015  0.020  0.025  0.030  0.035  Grade F i g . 14. Expectations o f o r e and w a s t e d e r i v e d from normally d i s t r i b u t e d block grades. I f the kriged b l o c k g r a d e i s 0 . 0 2 5 and k r i g i n g v a r i a n c e i s 0 . 0 0 0 0 2 5 , (o = 0 . 0 0 5 ) , 16.5% o f t h e true block g r a d e s w i l l be w a s t e and 16.5% w i l l a c t u a l l y be o r e g r a d e .  mill  grade,  blocks  with  with cutoffs  a t 0.020  normal d i s t r i b u t i o n ,  there  (o = 0 . 0 0 5 o p t . ) ,  2  is  and 16.5%  kriging  t h e n based  on t h e  an e x p e c t a t i o n  a l t h o u g h even w i t h  low g r a d e s t o c k p i l e Conditional estimates  based  which e v e n t u a l l y  s h o u l d go  If a l l  a constant  that  16.5% o f a l l  w i t h k r i g e d grade o f 0.025 o p t . s h o u l d a c t u a l l y  waste s t o c k p i l e 14),  opt. gold.  a k r i g e d grade o f 0.025 o p t . have  v a r i a n c e o f 0.000025 o z / t o n  blocks  and 0 . 0 3 0  go  to the ore s t o c k p i l e  these e r r o r s ,  the average  to the (Fig.  grade o f the  would remain 0.025 o p t .  probability on t h a t will  data be  uses to  mined.  exploration estimate  data  tonnages  The c a l c u l a t i o n  is  and b l o c k and g r a d e s r e f i n e d by  subtracting from  the  kriging  exploration  "smoothing  variance  block  which c a n ' t resulting probable  block  conditional  the  assumed  statistically  with  are  calculated  a  results grades  the  estimation  are is  mine.  there  were  are  rarely  plotted  —  of  error  mined).  The  to  predict  new  at  least  two  distribution  is  this  verified  c a n be  is  and b l a s t h o l e  kriging  variance  production data  known  that  kriged  could  be  available).  complex.  problems,  and,  for  the  sample  practical  lognormal d i s t r i b u t i o n (Journel  distribution,  lognormal d i s t r i b u t i o n  distribution  more  estimated grades  normal  distributions  the  the  Sample G r a d e s and B l o c k G r a d e s  i n a corresponding the  be u s e d  exploration  having the  distribution  about  (an amount  in  The s e c o n d a s s u m p t i o n  blasthole  of  data  conditional  the  problem i s  grade  lognormal  Like  both  Distribution of  I n many  for  data.  (i.e.  i n advance the  the  uncertainty  is  the  remaining  the  can  discussion  real of  known  In p r a c t i c e ,  figures  to  The  deposit  normally d i s t r i b u t e d  kriging variances  6.1.3  e v e n when t h e  First,  be  exploration  estimates  according  1977).  distribution  preceding  to  variances  approximate  estimates using  a s s u m p t i o n s made.  grades  will  be e l i m i n a t e d  of production block  (David,  t o n n a g e and g r a d e  In  and  kriging  relationship"  conditional kriged  variance  the  also well perfectly  on l o g  grades  purposes, of  this  actual  and H u i j b r e g t s ,  characteristics  known.  follow  block 1978).  of  Unfortunately  lognormal.  p r o b a b i l i t y paper,  If  the grade  a lognormal  a straight  line  57  A.  2%  B.  50%  98%  2%  50%  Probability  98%  Probability  F i g . 15. Probability plots of perfect (A) and imperfect lognormal distributions (B). The c u r v e d portion of c u r v e B i s due to a l a r g e r than expected number o f low g r a d e s a m p l e s .  can  be  expected  transformed straight material linear  as  For the  grades o f  line,  but  around the in Figure  the  composites which of  the  estimate the correct  15a).  real  However  exploration  due  in  orebody,  part the  in  data  to  reality, rarely  an a b u n d a n c e  plotted  the  plot of  as  low  distribution  log a  grade  is  non-  15b.  simplicity,  problem for  study  (Fig.  the  example  case of  a normal  h a v e numerous  histograms. blocks,  distribution  If  conditional of  shown  actual  i n F i g u r e 16  distribution  low g r a d e these  samples  grades.  mineralized  included  composites  probability will block  of  illustrates  are  not If  in used  predict  the  the to the  erroneous  58  Low G r a d e Stockpile  ? %  0.015  0.020  0.025  .  0.030  0.035  Grade F i g . 16. The e f f e c t o f e s t i m a t i n g o r e and w a s t e p e r centages from i m p e r f e c t normal distributions. The number of miscalculated blocks will no l o n g e r be predictable.  assumption normal,  is  made  that  there  will  be  percentage  of  material  the a  d i s t r i b u t i o n of  serious above  cutoff  determination of  average  grade  same f i g u r e s  in  previous  opt.  and o  2  as  of  16.5%  2  to  t h a n 0.02  opt.  be w a s t e when i n f a c t  The l o g  show a s i m i l a r  and s i m i l a r l y , l e s s transformed grades imperfect  pattern  this  in as  of  blocks  predicting well  material.  example,  = 0.000025 o z / t o n ) ,  predicted  grade.  the  error  actual  as  5).  the  B a s e d on  the  ( k r i g e d g r a d e = 0.025 the  blocks  t h a n 16.5% w i l l  (Fig.  the  in  are  maybe 20% o r more w i l l  i n the  is  really  BEX d a t a s e t  at  still  be be  less ore  Buckhorn  59 In order to be  found  to  calculate  work  with populations  predictable  attributes  present  problem  a  subset  of  the  (i.e.  with  probability  interpolated  from the  correct  Raymond made  nearly  data, for  their  lognormal  constant  to  original  distribution  However,  the  but  block  with  by  the of  in  order  log  of  neither  In(grade  an  to  can  be  experimentally  transforming.  normal nor  c a n be  used  The  lognormal.  approximates  + constant)  that  have  distributions  raw g r a d e s b e f o r e is  will  were  distribution.  of  samples  calculate  grades  something  many g r a d e  the  doesn't  a lognormal  to  whose  addition  distribution  This  for  an  modelling  reserves. As  discussed  straighten for  the  out  the  was  added t o  variance  data,  is  block one  known as  of  the  a function to  of the  be  the  a  constant  of  probability plots In c a l c u l a t i n g the  grades before  no c o n s t a n t was  Constant K r i g i n g  Because  the  log  dataset.  BEXG d a t a s e t ,  6.1.4  earlier,  BEX  0.005 o p t . the  a known d i s t r i b u t i o n  models  imperfect  acceptable lognormal d i s t r i b u t i o n ore  must  BEXG d a t a s e t w h i c h i s  shows t h a t  derived  of  a way  BEX o r BBH d a t a s e t s ,  for  (1982)  probabilities,  normal or l o g n o r m a l ) . the  complete  conditional  be done t o  conditional  of  0.005 gold  to  distributions  conditional log  appears  probability,  transforming.  For  necessary.  Variance  nature of  the  both the  estimated,  major problems  proportional  of  k r i g i n g equations,  geometry o f  and t h e i r t h a t has  effect  —  as  the  grades. to grade  be  kriging  samples With faced  around  lognormal is  increases,  what's kriging  60 variance attempt  (or the could  geometries be f o u n d changes  obtain  i n the  estimated. a  has  all  of  relative  was,  for  the  c a n be  samples  variogram  around  kriging  used  will  o n l y due block  a square  relative  k r i g i n g variances  will  spacing  of  around  samples  to  be  drilling could  be  k r i g i n g v a r i a n c e tends  to  the  variogram square the  of  the  value.  mean When  only  the  if  block  In  the  to  are  around  f a i r l y constant.  to  values  estimate blocks which  change  to  variograms.  calculate  be  sample  way c o u l d  on a s q u a r e o r r e c t a n g u l a r g r i d  variances  the  to  a  variance  relative  that  if  the  d i v i d e d by t h e  used  is  for various  instance,  of  A l t h o u g h an  changed  kriging  been o b s e r v e d  from d r i l l h o l e s  block,  that  samples  constant  lag distance  grade o f  kriged  increase  w o u l d be s i m p l e r  c a n be done by u s e  it  increases.  p r o p o r t i o n a l l y w i t h grade squared,  every  the  it  the  there  reasonably  Because increase  t o model t h i s  pattern of  This  estimate)  kriging variances  Thus i f  expected.  at  be made  the  and g r a d e r a n g e s , to  pattern,  error of  the  effect  geometry  or  be e s t i m a t e d  is  changed.  6.1.5  Combining 3-Parameter R e l a t i v e Variograms  If  the  grades  can  Lognormal D i s t r i b u t i o n s  be assumed  t h e n k r i g i n g v a r i a n c e w i l l have t o to  predict  the  variance  distribution.  To do  as  +  is  y{h)  /  (m(h)  added  to  distribution,  this,  whereas  3-parameter  be c a l c u l a t e d  of the  be  the  relative  2  to m is  produce the  the  average  lognormal,  i n s u c h a way  as  3-parameter  lognormal  variogram i s  calculated  The c o n s t a n t  constant) .  grades  to  with  is  the  same  3-parameter of  all  one  that  lognormal  samples  used  to  61 calculate  y(A>)  correspond to  at  the  same a l t e r e d  At Buckhorn,  it  kriging  variances  arranged  relative  variograms  can  l o g n o r m a l model o f  6.1.6  the  the  constant  samples,  spacing.  If  grades  kriged.  there  in  sample  be  to  variance  same and t h e used  the  Alternatively, benches  if  relative  (as  actual at  is  regularly  a  relative  3-parameter  regard to of  the  the  provide  grade o f  the  size  to  be  pattern  or  block  blasthole  data  at  Kriging  theoretically  and t h e  blasthole  available,  reasonable  anticipated  blasthole  theoretical  pattern could  be  k r i g i n g v a r i a n c e c o u l d be u s e d  in  calculation.  exploration  identical  relative  and t h e s e  combination  kriging,  same c o n s t a n t  t o model  drilling  will  without  and a s m a l l s u b s e t o f  the  grades.  constant  with  now  data.  substituted  be made t h a t  grid  conjunction  variogram  no  The r e s u l t i n g  assume  Constant R e l a t i v e B l a s t h o l e  o n l y on  is  the  being estimated,  conditional probability  have  the  used  blasthole  could  locations,  is  be  relative  dependent from  the  blocks  the  to  exploration  to  kriging variance w i l l  d i s t r i b u t i o n as  possible  where  kriging  estimated  the  is  Determining the Variance  Use o f  The r e l a t i v e  h.  The  and b l a s t h o l e  (and t h e r e f o r e  3-parameter  blasthole  Buckhorn),  assumption  data the  the  lognormal is  will  variograms  are  same v a r i o g r a m ) distributions.  available  real blasthole  for  a few  of  d a t a c a n be  kriged. Because results  all  only,  estimates kriged  in this  estimates  v a r i o g r a m s were c a l c u l a t e d  from  study  are based  from  the  the  available  on  exploration  exploration blasthole  derived data  at  Buckhorn.  These b l o c k  variances  were c o n t o u r e d .  sampled  areas,  variances,  only  necessary,  one  the  60'  with  and two  grades By  visual  comparisons constant  f o r each o f  block models. other  were p l o t t e d  These  parameters  examination  with  20'  kriging  b l o c k models  a r e shown used  later  in  of  histograms  relative  the  and r e l a t i v e  kriging the  of  kriging  variances  and t h e in  best  were  other  for  T a b l e VI a l o n g  calculating  conditional  probability. Once t h e exploration  constant block  maximum r e l a t i v e higher in  relative  subsequent  too  unnecessary  at  did  6.2  all  suffer  now  examined  is  calculated,  to  see  if  there  Usually  any  block  k r i g i n g v a r i a n c e t h a n t h e maximum w i l l because  unreliable. Buckhorn because and  the  kriged  parameter sample  back e s t i m a t i o n  significantly  each block  the  This  was  density  showed  that  ignored would  2)  The a s s o c i a t e d  3)  A maximum a l l o w a b l e  be  considered was  adequate  kriged  grades  range.  the  following  information  available:  The e x p l o r a t i o n k r i g e d  a  PROBABILITY  i n t h e mine m o d e l ,  1)  is  with a  be  grade  i n any k r i g i n g v a r i a n c e  CALCULATION OF CONDITIONAL  For is  are  kriging variance  kriging variance.  locations  not  models  calculations  considered  in  blasthole  estimate.  exploration kriging variance. exploration kriging variance.  4)  The c o n s t a n t  blastholes.  5)  the  for  A knowledge  the  Other include  to  of  and,  if  3-parameter  parameters the  (probabilities)  lognormal  that  for  ore  shape the  required  gravity  so  (to  and f i n a l l y  to  of  the  constant  for that  tonnage,  prevent the  from p r o -  error  required  distribution.  are  c a n be c o n v e r t e d  consider  variance  expected  necessary,  specific  areas of waste), be  kriging  duction k r i g i n g of  distribution  value  relative  the  calculation  ore  fractions  an a r b i t r a r y minimum  meaningless c a l c u l a t i o n s  significant  cutoff  grades  in  must  specified. Therefore,  contains  assuming  k r i g e d grade  following  a block  and  relative  input parameters  which w i l l  calculate  1)  Cutoff  2)  Constant to  normal  the  been p r e p a r e d  kriging  a r e needed  conditional  to  variance,  run the  add t o  grades  the  3-parameter  log-  distribution.  Minimum  exploration  the  calculation.  4)  Maximum a c c e p t a b l e  5)  Constant  relative  kriged  exploration kriging  estimates. Specific  Then f o r each  gravity  block:  of  value  ore.  for  inclusion  kriging  variance.  variance  the  computer program  probabilities:  for  which  only  grade.  3)  6)  m o d e l has  of  in  production  1)  Check  kriged  grade,  maximum either 2)  or  if  allowable  variance  ignore  the  Assume  conditional  is  variance  variance. to  2  Transform  that  is  and  then  above  the  calculation  k r i g e d grade  likely  the  5)  Transform the  value  f r a c t i o n of  if  plus  obtain  last  the the  ore  the  calculating step  obtain  is  to  final  summarized  in Table V I .  0 . 0 35 and 0 . 0 5  (kriged  percentage log  opt.  gold),  +  a  log-  material cutoff  grade  of  block. grade  back t o  for  the  the  an  arithmetic  b l o c k tonnage  up t h e  models  for  each  t o n n a g e s and d e t e r m i n e  estimates  at  a total  for  was  4 cutoff of  16  to  block.  probability  The c a l c u l a t i o n  block  of  transformed  Buckhorn c o n d i t i o n a l  60'  grade  expected l o g a r i t h m i c  cutoff  global  the  blasthole  constant.  tally  used  and  for  the  conditional  parameters  constant  d i s t r i b u t i o n to  f r a c t i o n times  t o n n a g e above  exploration  variance.  the  predicted  and s u b t r a c t  Multiply  After  be above  the  by  conditional  calculate  ore  the  arithmetic  and c a l c u l a t e to  is  Multiply  obtain  the  20'  block  expectation  kriging  to  is  true.  k r i g i n g v a r i a n c e minus  6)  minimum e x p l o r a t i o n  constant.  normal model  the  below  kriging  —  is  is  relative  4)  grade  block  condition  constant)  the  the  Assume c o n d i t i o n a l  the 3)  if  the  block, the  new  deposit.  The  p r o b a b i l i t y runs p e r f o r m e d on e a c h grades  runs.  (0.01,  are of  0.02,  Ore r e s e r v e s  to  65  Table VI P a r a m e t e r s Used t o C a l c u l a t e C o n d i t i o n a l P r o b a b i l i t y  Block  size  20' 60'  or  Blasthole Constant  kriging variance added t o  Blasthole Constant Cutoff  kriging variance added t o  Specific  that  total  total  above  reserve  was  0.080  0.040  n/a  n/a  ore  ounces  on  a b e n c h were t h e  For  each  were  of  the  cutoff  For  metal  a  grades. cutoff grades  tons  and  (ounces  of  grade  range,  is  within  — tons  calculated same as other ranges  by  total  reserve and  then  conditional probability,  grade  the  result  cutoff  above  gold).  total  above 0.035  This  i n the  0.0  ounces  of  ranges,  and g r a d e  grade  c a l c u l a t i o n of metal  For this  0.050  0 .005  within cutoff  from  u n t i l the  reached.  BUCK60G  were c a l c u l a t e d  above  subtracted  repeated  BUCKG  estimates  work b a c k w a r d s  to  0.005  of  necessary  converting  0.005  types  To c a l c u l a t e  were  0.040  1.634  calculation. to  for  by k r i g i n g .  reserves  cumulatively  consider  other  ounces p r e d i c t e d reports,  0.080  0.010 0 . 0 2 0 0 . 0 3 5 to  20' 20'  BUCK60  Gravity  compare w i t h t h e  x x  BUCK  grades  grades  Minimum v a l u e  assuming  grades  x 20' x 60'  the  it  0.05  was opt.  opt.  by  procedure  was  to  0.01  range  (and t o n s )  above  0.01 by  o p t . were s u b t r a c t e d the  corresponding  possible to  the  to generate other  from t o t a l  kriged  reserve  reports  ounces above  block  reports  model. that  0.0  In t h i s  predicted way i t was  were i d e n t i c a l  and w h i c h c o u l d t h e r e f o r e  i n form  be compared  with  them.  6.2.1  Example C a l c u l a t i o n o f C o n d i t i o n a l P r o b a b i l i t y  To i l l u s t r a t e the  following  0.030  opt.  Assume  example  with  the  calculated parameter  the  a  is  as 0 . 0 8 0 , lognormal  0.035 c u t o f f  conditional  using  block  kriging  o f 0.005  d i s t r i b u t i o n and  is  variance variance  added t o  specific  probability calculation  probability,  a k r i g e d block grade o f  kriging  blasthole  a constant  will  0.28.  has  been  create  gravity  be  of  is  a 3-  1.6 34.  calculated  for a  grade.  The c o n d i t i o n a l 0.005  expectation  constant.  distribution, grade  of  calculated  relative  constant  The c o n d i t i o n a l  the  calculation  (x)  Before  t h e 0.005 c o n s t a n t  will  working must  be t h e k r i g e d g r a d e + with  the  lognormal  a l s o be added t o t h e  cutoff  (x ): c  x = 0.030 + 0.005 = 0.035 x  c  = 0.035 + 0.005 = 0.040  The c o n d i t i o n a l block  kriging  variance  variance  (o )  minus  2  the  is  the  exploration  blasthole  constant  relative relative  67 block  kriging  variance.  kriging variance  a  is  calculated  = ( 0.28  2  Arithmetic  -  as  0.08  (as o p p o s e d  to  relative)  follows:  ) x ( 0.030  + 0.005  )  2  = 0.000245  T h e l o g a r i t h m i c mean c a n now be c a l c u l a t e d  (x  using  / n  )  and  standard  logarithmic  variance  equations:  [1]  In  0.000245 -  /n ( 1 +  ) (0.035)  =  In  (1.2)  = 0.18232  =  In  In  (x)  -  In  [2] 0.18232  =  In ( 0 . 0 3 5 )  = -3.44357  -  (oj ) n  68 Above a probability  given (T)  cutoff  grade  and t h e g r a d e  (x ),  the  c  above  cutoff  ore  fraction,  or  (G) a r e c a l c u l a t e d  as  follows:  x  T  = 1 - F  [  In  c  —  °ln  +  j  [3]  In  G = —  [ 1  F  T  where  F(z)  cumulative  can  formula. into  l  be  normal  program used  read  Using [3]  actual  values and [4]  In  (T)  equal  to  )  ]  [4]  2  standard (i.e.  calculated  tables  David,  showing  the  1977, page 9 ) .  The  uses  previously,  an a p p r o x i m a t i o n and  substituting  above:  0.040 • In  /0.18232  Interpolating  —  calculations  = 1 - F [  = 1 - F  -  x  1 T  —  n  from  distribution  f o r the  equations  [ — o  /0.18232 +  )  0.035  2  (0.526)  F(0.526)  from t h e  table,  gives  ore  fraction  0.299.  0.035 G =  1 [ 1 - F  0.299 = 0.1169  0.040  [  /0.18232  In  /0.18232 [ 1 - F (0.099)  ]  )]  0.035  2  69 Again using The r e s u l t i n g which  was  this  gravity  g r a d e above  originally  subtracted for  a standard  to  yield  example is  cutoff  added  to  a grade o f  is  20'  1.6 34,  x  the  F ( 0.099)  table  c a n be  (G)  is  the  kriged  0.0538.  0.049 o p t .  20'  x 20',  tonnage  of  interpolated. The  constant  g r a d e must now be Assuming block  and k n o w i n g t h a t the  whole  size  specific  block  can  be  calculated:  62.42796 Total  B l o c k T o n s = 20 x 20 x 20 x 1.634  x 2000  = 408.03 Tons  Ore Tons = T o t a l  B l o c k Tons x T  = 408.03 x  .299  = 122.16 Tons  Therefore, cutoff,  the  0.049 o p t .  20'  tallying  block w i l l  122  is  tons o f  ore,  the  with constant  be s a i d  approximately  that  grade of  0.035 c u t o f f opt.  gold.  reserves  contribute  u n l i k e l y that  are d e a l i n g  kriged  up  122  above  Tons  a 0 . 0 35  at  a  opt.  grade  of  gold.  Although i t exactly  when  0.030 o p t . ,  and t h e  this  result  can  relative 30% o f will  grade o f  all  specific  be r e - s t a t e d .  variances, blocks  in fact  block w i l l  yield  Since  i n general  it  we can  w h i c h had an i n i t i a l  be f o u n d t o  these ore blocks  will  be above average  the  0.049  70  6.3  DISCUSSION  I n Raymond's method o f he u s e s p o i n t exploration  kriging  grades  variances  of  will  affect  not  and t h e kriged  on  the  centers  any  assumption  He s a y s  that  is  that  point  criticism  estimates don't In the  mining  estimates  grades  from  represent  where  the  In  computed  to for  data,  60'. the  60'  calculated  for  theoretical  blasthole  d e c i d i n g which k r i g e d mean. methods  the  is  described  is  constant  1986).  theoretically  the  around This  is  but  it  years, that  need  same as  method relative  the  point  size  kriging  is  and  block from  are kriged  assumed  to  be  kriging variance  is  probability  using  to  apply the David,  kriged  blocks  a  alleviates  (i.e.  kriged,  estimated  conditional  This  to  are  blasthole  best block d i s p e r s i o n  The  grid  precision,  comm.).  the  when 60'  and  block  by some a u t h o r s  and S i n c l a i r ,  chosen  contours  grades  the  mining  blocks,  no  to  argue  to  words,  spacing.  the  There  block  exactly  large  the  kriging  grades.  is  The  of  over  would  made  the  be  tested  are  other  for kriging  relative  (Raymond, p e r s .  here,  block s i z e  exploration  selective  grid  improve l o c a l  will  who  block  comparisons  exploration data. from  those  approach used  furthermore,  a  size  estimate except to  a p r a c t i c a l a p p r o a c h w h i c h he has draws  of  and f o r d e t e r m i n i n g c o n s t a n t  blastholes.  blasthole  dealing with conditional p r o b a b i l i t y ,  12'  superimpose  1977,  r e q u i r e d d i s p e r s i o n minus t h e  14'  any p r o b l e m o f  affine  variance  to  is  of  correction  1988; the  on a  Giroux  block  is  k r i g i n g variance  of  a similar size  according to  the  Another  (pers.  assumed  to  neither  It  conditional  variance).  distribution  grade).  parameter  his  latter about  is  subselected  to  the  would  that  BEXG and BBHG  calculating The  kriged  the  to  kriged  variances  expected  range  (i.e.  is  that  that  at  case of  Buckhorn,  the  results  3-  out  by  the  BEXG d a t a s e t  theoretically,  which render  any  What a b o u t  assumption?  the  of  this  represent  a  laid  the  case  of  as  which used  datasets  block  lognormal regardless  and t h e r e f o r e ,  lead  of  grade  Raymond m a k e s ,  exactly  In the  only  distribution  distribution irrelevant.  in  assumption  exploration  BEX d a t a s e t  modelled  (BUCK and BUCK60) obvious  the  the  lognormal d i s t r i b u t i o n  grade  add a c o n s t a n t  3-parameter  that  3-parameter  papers.  calculation  two m o d e l s It  was  when  (i.e.  3-parameter  case of  various  was no n e e d  doubts the  In the  the  reflects  every is  distribution  Raymond i n there  in  this  the  is  conditional  exploration kriging  assumption  the  of  earlier.  that  unbiased  errors  weakest o f  method  lognormal, that  (conditional  s u p p o r t e d by of  the  i n any way  are  and t h a t  of  and  is  described  variances  replicated  this  used  kriging  conditional kriged  is  only questionable  be  it  this  data  1988).  conviction that  regard  expectation),  n o r m a l i z e d shape  will  the  grades  with  as  conditionally  minus b l a s t h o l e  the  nor i s  blasthole  distribution  that  author's  made i n t h i s  is  dispersion  the  (David,  Raymond,  the  and  probability  blasthole  The  is  by  that  lognormal,  necessary,  assumptions  estimate  stated  is  be k r i g e d u s i n g  relationship"  made when d e a l i n g  conditional  kriged  comm.)  be  probability. is  "smoothing  assumption  Sinclair  assumptions  block which w i l l  study,  the upper  the  portions  72 of  the  BEX and  perfect  lognormal  distribution all (>  BBH d a t a s e t s  of  distributions.  actual  4 block models, 0.020  the  opt.  predicted  like  the  is  grades  will  as  the  3-parameter  20'  given  that  could  lognormal.  raw  in reality,  exploration  the  problem i s  c o r r e s p o n d i n g k r i g e d block grades are both  actually  variances. the  By u s i n g  available  populations,  is  should  that  problem.  without  Since, lower  is  regard  to  BEX  were a b o u t  the  case of  the  interest  (0.02  h i g h grade areas, perfect,  v a r i a n c e than i f probability  conditional  distributions  than they  opt. the  is  a much  the  constant  is will  should be.  still  the  gold),  all  the  being are  ranges than areas  applied  calculated  lowest there  of  different  low g r a d e  3-parameter  better  nearly  grade is  no  of  real  approximation,  predictor of  relative  been u s e d .  B u t when  hadn't  modelled  from  Buckhorn d e p o s i t ,  below  they  w i l l be h i g h e r  areas  the  be k r i g i n g  of  is  was  or  areas  same and  model  these  grade p o p u l a t i o n i s  of  In the  i n the  in  look  models.  data,  grade  mixing  of  distribution  calculated  i n c o r r e c t variogram  conditional  precise)  the  problem w i l l  a variogram which i s  k r i g i n g variances  although never kriging  the  ore  (that  not  higher  in  be  w i l l not  4 block  The c o n d i t i o n a l d i s t r i b u t i o n o f  b u t an  incorrectly.  ore  in  instead  anisotropies  be.  and t h e r e f o r e  the  —  the  a histogram  the  the  but p r e d i c t e d k r i g i n g v a r i a n c e s  lognormal  100% o f  data  the  were s i m i l a r , they  lognormal,  of  composites  i n any o f  in  that  potentially  l o g n o r m a l and  composites  near  predicted grades,  BEX d a t a s e t  lognormal)  means  The s h a p e  a l s o be  the  They i n d i c a t e  This  grades  i n any a r e a  gold),  Therefore, of  block  histogram of  modelled  respectively.  from  be w i d e r  this  variogram,  (and t h e r e f o r e  When g r a d e e s t i m a t i o n  is  the less  performed  73 for  a  block  there's  where  going to  distribution A  k r i g i n g used  be t r o u b l e ,  greater  of  amount  interest  be shown i n t h e better  in  to  alternative" proportional variogram to  the  to  use  variogram should  constant  the  that  relative  will  be  methodology  conditional with  estimation  is  the  ...  is  page  and  recent  will  a  of  the  tool  the  on  conditional to  use  the  when  in  page  which page  "favoured with  is  the  best  127).  The  page  squared 99).  will The  is  47).  yield  relative  equal  to  the  The t h e o r e t i c a l  variogram  c a n be c h e c k e d  2  dealing  It (ibid.,  relative  as y(h)/m{h)  is  42).  value  kriging variances  text-book  still  grade  (ibid.,  or  112).  page  sill  the  quotes  the  variogram  (ibid.,  assumptions  1988):  variogram  kriged  variance  the use  As  repaid with a  to define  ordinary kriging  variance reach  a  obvious  probability,  (David,  used  relative  (ibid.,  times  the  corresponding  D a v i d ' s most  logarithmic  with  choosing  in  v a r i o g r a m c a n be c a l c u l a t e d The  relative  into  variance  effort  to  ( D a v i d , 1988,  effect  go  of higher grade o r e .  basic  offered  kriging  43).  arithmetic  expectation  the  "Ordinary k r i g i n g  variance  population  the  approach  The r e l a t i v e page  frequency  estimate.  reserve  circumstances"  relative  kriging  chapter  is  ore  distribution.  (ibid.,  populations,  of the modelled  should  i n areas  support  Ordinary  2)  effort  m a i n l y from M i c h e l  geostatistical  1)  i.e.  reserve  summary  references,  most  —  Raymond's  following  of  minimize  next  g l o b a l ore  In order used  regardless  from b o t h  or variogram used.  variogram which w i l l areas  samples  will  yield  experimentally  74  Ii i i i i i  1 .000  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  _  i  o o  < inI i i i i  )E ( O Z . / T O N ) a  i  <  -  N  o  Q O  0.010  o  0.001  0.1  i  i  2  I  I  i  10  i  30  i  i  50  PROBABILITY  i  i  70  i  90  I  I  i  i  98  99.9  ( CUM % )  Fig. 17. Cumulative p r o b a b i l i t y p l o t o f the grades of actual (blasthole kriged) blocks given exploration k r i g e d block grades w i t h i n 2 g r a d e r a n g e s where t h e r e were a s i g n i f i c a n t number o f b l o c k s . T h e p l o t shows that actual block grades are l o g n o r m a l l y distributed a b o u t t h e mean ( k r i g e d g r a d e ) .  using at  back e s t i m a t i o n  Buckhorn  exploration to  be  using  techniques. both  and b l a s t h o l e  back  This  expectation  estimation  relative  and  was  checked  c o n t o u r maps  kriging variances  and  of  proves  true.  3)  The l o g n o r m a l c a s e  (David,  1988,  page 1 2 3 ) .  blocks  will  follow  a  is  most  "On t h e lognormal  common i n m i n i n g  basis  of  applications  experience",  distribution  with  estimated a  smaller  variance grade  (ibid.,  ranges  0.035 o p t . kriged  page 7 4 ) .  where  and 0 . 0 3 5  blasthole  Buckhorn  (as  and p a g e  the  one  309).  estimate, 18  1)  (variable  2).  important grade estimated perfect  ore  a  is  greatest  this  assumption  5)  within  ranges  The r e s u l t s ranges  of  are  that  -  contained,  assumption  1977,  page  on t h e  conditional  ordinary kriged  the  block  where  and  within 90%  there  the  of is  actual  the  not  a  average  kriged  same one  grades  estimates  comparisons  the  unbiased.  kriged  but o v e r a l l ,  that  is  best  assumption,  the  opt.)  at  the  be c o n d i t i o n a l l y  expected  c o n d i t i o n a l l y unbiased  is  kriged blasthole  0.065  actual  weak  exploration  between  the  effect  show a c c e p t a b l e  (0.020  estimate  that  is  made  who work w i t h o r d i n a r y k r i g i n g and  variograms.  The l a s t  assumption  geostatisticians.  described  will  (0.020-  lognormal  (David, the  two  1978).  kriging  opinion,  the  many g e o s t a t i s t i c i a n s  relative  by D a v i d  relationship  has  is  That  (1988,  VAR(Z*) "This  author's  the  d i s t r i b u t i o n of  approximately  case,  comparison o f  blocks  the  expectation  logarithmic data,  However,  actually  by  is  correspondence  grades.  the  have  shows  (variable  also  conditional  estimate  using  is  non-normal  In the  w h i c h may  probability  by  the  opt.),  within  estimated  by J o u r n e l and H u i j b r e g t s ,  the  approximation to  shows t h a t  most s a m p l e s  0.050  block grades  In  255  are the  -  predicted  4)  Figure  there  F i g u r e 17  page  = VAR(Z) been  also t r a d i t i o n a l l y is  the  "smoothing  well  accepted  relationship"  74): -  checked  o£ experimentally  very  well".  7  COMPARE ACTUAL VS. EXPLORATION KRIGED BLOCK GRADES MIN. MAX.  NORTH EAST ELEV I REG. VARIANCE 0.0 0.0 0.0 I CONST 0.000 99999.0 99999.0 99999.0 I POWER 2.000  VARIABLE ELEMENT 1 DEPENDENT AU 2 INDEPENDENT AU LOCATION VAR 1 MIDPT 0.92 1.74 0.62 0 21 0 1.60 76 2.70 0 122 0 4.16 21 5.71 0 4 0 1 7.16 B.69 0 2 1 10.10 0 11.62 0 1 13.02 0 0 H.66 0 0 0 16.65 0 17.84 0 0 0 19.18 0 0.00 0 0 0 0.00 0 0 24.19 0 0.00 0 0 0 0.00 0 0 0 27.88 1 248 TOTAL VARIABLE 2 MEAN 0.92  I RANGES MIN. 1ST INC NO.INC1 2ND INC I VARIABLE 1 0.000 1.000 2 1.500 I VARIABLE 2 0.000 1.000 2 1.500  MULTIPLIER DESCRIPTOR 100.0000 BBHG KRIGED BLOCK GRACES - •ACTUAL" 100.0000 BEXG EXPLORATION KRIGED BLOCK GRADES 20' BLOCK MODEL WITIN OUTLINE  FILENAME FILETYPE ACTUAL2G KRIGE BEXGKRIG KRIGE BUCKG GRID  < < VAR 2 MIDPOINTS > > 2.75 4.11 5.59 7.06 8.71 10.34 11.61 13.27 14.83 16.47 17.81 18.92 0.00 16 60 3 0 1 0 2 1 0 0 0 0 0 4 217 60 11 3 3 2 0 3 1 0 0 0 409 148 14 32 12 7 6 0 3 1 0 0 0 174 129 28 12 12 2 0 0 0 0 0 0 0 5 68 81 35 6 0 1 0 0 0 0 0 0 25 34 16 12 8 0 1 1 0 0 0 0 0 7 6 18 11 3 6 2 2 0 0 0 1 0 1 11 12 18 2 5 1 1 0 1 1 0 0 1 3 8 4 2 1 1 4 0 1 0 2 2 1 1 3 3 0 0 0 0 0 2 1 1 0 2 2 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 989 500 164 58 50 16 17 26 6 5 4 0 3  1.74 |2.75 4.11 5.59  ROW TOTAL 104 380 754 378 200 98 58 54 30 13 7 4 3 4 0 0 1 0 0 1 2089  7.06 8.71 10.34 11.61 13.27 14.83 16.47 1 7.8118.92 18.92 0.00  3.826  VARIABLE 1 MEAN 10.06 2.41 13.12 4.32 5.84 5.66 5.37 7.30 4.50 7.53 9.01 12.32 0.00 SO. 0.00 1.36 1.89 2.64 3.51 3.12 2.99 5.58 3.55 5.31 5.51 2.60 3.51 0.59 0.00 VARIA 0.00 1.84 3.57 6.97 12.29 9.71 8.91 31.11 12.59 28.23 30.40 6.75 12.29 0.34 0.00 0.002 0.000  3.848 2.290 5.865 0.363  ABSOLUTE DIFFERENCE VARIABLES(1-2) MEAN 9.14 RT MS 9.14 MN SQ 83.63 REGMS99.891  0.99 1.29 1.90 1.52 1.B9 2.62 2.30 3.56 6.86 0.819 0.473 0.404  2.65 3.52 12.42 0.403  2.91 3.94 3.51 4.48 12.29 20.10 0.247 0.263  4.88 6.33 40.04 0.376  7.11 7.98 63.61 0.469  6.67 7.87 61.91 0.350  7.00 8.19 67.08 0.298  3.05 3.80 14.43 0.052  5.00 5.61 31.44 0.098  6.60 6.62 43.80 0.122  0.00 0.00 0.00 0.000  1.791 2.451 7.352 0.523  CUMULAT1VES ABOVE LOWER LIMIT VARIABLE 1 LOLIM 0.00 1.00 2.00 3.50 5.00 6.50 8.00 9.50 11.00 12.50 14.00 15.50 17.00 18.50 20.00 NO. 2089 1985 1605 851 473 273 1 75 117 63 33 20 13 9 6 2 MEAN 3.848 4.017 4.589 6.268 7.955 9.59910.96412.09113.79715.78017.57419.14620.25621.46326.033 VARIABLE 2 LOLIM 0.00 1.00 2.00 3.50 5.00 6.50 8.00 9.50 11.00 12.50 14.00 15.50 17.00 18.50 20.00 NO. 2089 2088 1840 851 351 187 129 79 53 37 20 14 9 5 2 MEAN 3.826 3.827 4.108 5.691 7.94810.01411.34213.00714.31315.48117.36218.44719.54620.93623.963 1GIV2 3.848 3.845 4.038 5.109 6.241 6.592 7.012 8.054 8.42110.11712.32013.73713.63013.77515.958 TOTAL VARIABLE 1 I MEAN TOTAL VARIABLE 2 I MEAN  3.848 I SD 3.826 t SO  2.810 I VAR IA 2.428 I VARIA  7.898 ! V/(M»C**P) 5.893 I V/(M*C**P)  0.533 0.403  F i g . 18. Computer p r i n t o u t o f t h e c o m p a r i s o n between a c t u a l g r a d e s ( v a r i a b l e 1) and k r i g e d e s t i m a t e s ( v a r i a b l e 2) w i t h i n e s t i m a t e d g r a d e r a n g e s . 90% o f a l l o r e g r a d e k r i g e d e s t i m a t e s f a l l i n c o l u m n s 3,4 and 5 . The c o m p a r i s o n shows t h a t k r i g e d estimates are conditiona l l y u n b i a s e d i n t h e s e 3 r a n g e s (maximum d i f f e r e n c e is a p p r o x i m a t e l y 0.004 o p t . ) . However, i n o t h e r columns, t h e c o r r e s p o n d e n c e i s n o t as g o o d . A l l d a t a has b e e n m u l t i p l i e d by 100. The same p r o g r a m was u s e d i n back estimation and t o a n a l y z e some of the other "actual vs. predicted" comparisons.  77 In a d d i t i o n the  to  assumption t h a t  c a n be u s e f u l that  samples  across  boundaries  earlier  in  continuity  defined  inside the  boundary  the  variogram of cut-off. compute  section  along  "....  Actually,  variogram of  change  most  probably affect  that  the  geometry  of  w i t h i n the  in  this  to  sill  uses  geostatisticians  computed  about  page  37).  the  of  derived units  points,  samples  we  above  from  the  above  the  can the  simply  cut-off.  structural characteristics  cut-off.  ranges,  of  anisotropy)  The main changes  will  the variogram".  anisotropies  thesis  that  might  a l s o change,  deposit,  and t h e  differs  from  this  depending  d i s t r i b u t i o n of  ore  orebody.  illustrate  study,  are  grade o f  in this  the  barren  discussed  (ibid.,  be  o f nugget e f f e c t ,  p o i n t made  The i t e m i z a t i o n mainly  the  zone"  in selection  units  d r a m a t i c a l l y with the  The o n l y  grades  (magnitude  (as  200),  " g i v e s no i n d i c a t i o n  should  samples  the  page  obviously  variations  grade  105):  expect that  will  the  of  1988,  for  computing a variogram w i t h i n a p r e -  variance  selection  variogram  on  grade  page  grade  we do n o t  is  of  (David,  variograms which are  mineralized  lines  the  analysis,  the  support  on a c u t o f f  include  on v a r i o g r a m s )  extension  When t h e  ore  not  and t h a t high  (ibid.,  the  the  should  with  also provides  contour based  potential  page 3 7 ) ,  the  David  a pre-defined  i n a dataset  (ibid.,  Finally,  above,  for defining  samples  the  the  of  all  that  of  points  has  been p e r f o r m e d  c o n d i t i o n a l p r o b a b i l i t y , as  assumptions  when  these  they  which  employ  a r e commonly a  relative  implemented made by most  variogram  and  78 ordinary k r i g i n g to by  Raymond  common, use  of  is  everyday point  acceptable  if  — there  assumptions.  the  is  The  method  developed  elegant d e r i v a t i o n of minable reserves  kriging  contoured point grid  an  estimate ore reserves.  from  assumption  Although not exploration is  estimates derived no c h a n g e  of  made  that  used  estimates mining  from b l a s t h o l e  support.  here,  using  even  the  should  be  will  d a t a on t h e  be  to  same  79  7.  7.1  COMPARISON OF CALCULATED ORE RESERVES  INTRODUCTION  V a r i o u s methods ore  reserves.  grades  were  (Appendix  C)  B)  bench  to  Scattergrams  of  produced were  tonnages w i t h i n and  were u s e d  (Appendix examined  ranges  maps o f  the  idea  o f what t h e  F). to  data  into  a smaller  compare tonnage  resulting  predicted  explain  the  actual  and g r a d e  block grades amount o f  b u t methods  s p a c e were  of  block  reports  grades  above  and  and  cutoffs, (Appendix  d a t a gave a  distilling  required in  order  the to  patterns.  T h e s e methods  and t h e  f r o m them a r e d e t a i l e d questions  models  predicted  The v a s t  were,  amount o f  block  Individual reserve  and t o t a l  results  the  predicted versus  were c o m p a r e d w i t h e a c h o t h e r .  good  7.2  compare  raised  broad c o n c l u s i o n s  below.  Later,  each  i n Chapter 1 are re-examined  that of  c a n be drawn  the  individual  separately.  METAL GRAPHS  Four graphs  were c o n s t r u c t e d  for  each block model,  of  gold),  significant  for  both  to  show t h e benches,  mine c u t o f f s .  (Figs. total that  The g r e a t e r  19,  20,  amount o f was  above  21 and 2 2 ) ,  one  metal  (ounces  each  of  than 0.050 o p t .  cutoff  the is  BUCK *oooo  Fig.  19.  Metal graph for  the  BUCK b l o c k  model.  BUCKG  3SOOO  Fig.  20.  Metal graph for  the  BUCKG b l o c k  model.  BUCK60 40O0O  35000  Fig.  21.  Metal graph for  the  BUCK60 b l o c k  model.  BUCK60G  LEGEND  TOTAL  >  CUTOFF  0.010  >  CUTOFF  0.020  o >  Q >  1 IDO  INTERPOLATION  Fig.  22.  Metal graph  for  METHOD  the  r  1 KRIGE  CPROB  USED  BUCK60G b l o c k  model.  OUNCES  © CUTOFF  0.03S  • CUTOFF  0.050  84 not  a c t u a l l y m o n i t o r e d a t t h e mine  significant. (0.010 t o  They  0.020 o p t . ) ,  (> 0 . 0 3 5 o p t .  estimates,  the  low g r a d e  (<  (0.020  exploration estimates  where BH4 i s  the  4'  the polygon weighted  on t h e m o d e l ' s are  waste  referred  block size, to  The  graphs  as  20'  "actual".  meanings  shows,  estimate  as  for  obviously  both  be  rest  models. to  also  is  also,  lowest  tends  to  that  be  lowest  On t h e  directly  both kriged  cannot  be  calculated  i n the  other hand,  from  kriging  from e x p l o r a t i o n  a b b r e v i a t i o n s on between the  20' 4'  the  and 60' polygonal  blasthole  to  the  data  is are  c h o s e n method  grade c u t o f f s ,  compared t o  models,  total  the  and 20'  less block  amount o f m e t a l  a l l a v e r a g i n g methods  and o r d i n a r y  (polygon  kriging).  kriging  accurate)  block models. uses  across  ordinary  (and l e a s t  depending  blasthole  that  above l o w e r  i n b o t h 60'  inverse distance  BH20 o r  EX4 and EX20 o r E X 6 0 ,  of the  are very s e n s i t i v e  similar  either  size.  F o r example,  the  and o r e  Straight polygonal estimates  block  ore reserves  above 0.050 o p t .  from  estimates  expected,  models.  of  ore  shown w i t h 3 b l a s t h o l e  Comparing  t o method a t h i g h e r c u t o f f s  Notice  are  lean  opt.)  block estimate  results  sensitive  weighted,  opt.),  0.035  the e x p l o r a t i o n or the  b l o c k models  predicting  is  Similarly,  the  would  insensitive  The 60' of  of  b a s e d on e i t h e r  identical  to  o r 60'  while  s h o u l d be s e l f - e v i d e n t .  models  0.010  polygonal estimate,  a r e t h e p o l y g o n a l and p o l y g o n w e i g h t e d data.  other categories  gold).  Each o f  BH60 i s  represent  but the  invariably  estimates  above 0.05  o v e r 0 . 0 35 o p t . conditional  produces opt.,  category  for  probability,  one and 20'  which  g r a d e and k r i g i n g v a r i a n c e , and w h i c h any  of  the  other  methods,  is  85 consistently  either  the  best  closest  approximations of  cutoffs  shown.  This  is  estimate  the  actual  especially  close to  More  v a r i e s w i t h the  the  BUCKG  excellent  are  above also  estimates  e v e n comes  cutoff,  while  these  f o r the  any  of  the  the  ore  zone  other estimates instance,  on  kriging,  is  referring  every  shows curve.  I D 0 , I D 1 , ID2 and  Above 0 . 0 3 5 ,  the  the  graphs,  correct  o t h e r two  the  followed  three  closest  by c o n d i t i o n a l  the  only estimate  any  estimate  that  ounces  come No  (Figs. ore  20  for  and 2 2 ) ,  reserves  from ore  above any c u t o f f reported areas  reserve  of  the has a  above a g i v e n  unconstrained models,  reserves  the e x t r a  models  no method  range.  This  from b l a s t h o l e s low  method,  results no  in  from  m a t t e r how  c a n p r e d i c t m e t a l where t h e r e was a b s o l u t e l y no i n d i c a t i o n  o r e from e x p l o r a t i o n d r i l l i n g .  "new" o r e t h a t was Conditional the  to  c o r r e c t ore  a l l of  2 or 3  ID10.  exploration d r i l l i n g .  of  and 0 . 0 2 ,  predicting  block  smart,  0.01  c o n s t r a i n e d b l o c k models  of  to  estimates  opt.,  is  the  conditional probability  and I D 1 , and o v e r 0 . 0 5  chance  because  For  (ID0),  geologically  is  20), actual  referring  the  cutoff.  estimators.  of  above  confined  with  straight  metal  average  close  Still  predicts  good  are the  probability  (Fig.  0.0,  one  whichever o f the  specified  graph  agreement  Generally ID3  important,  is  t r u e f o r t h e BUCKG and BUCK60G  b l o c k m o d e l s where i n t e r p o l a t i o n was outline.  or  best  estimate  f o u n d when t h e d e p o s i t probability  be t h e  comes  estimates  close  safest,  and  between  ounces  represent  was m i n e d . to  o f the grade d i s t r i b u t i o n o f  produces very s i m i l a r appears to  These e x t r a  p r o v i d i n g not the  ore,  it  only also  the d i f f e r e n t models.  most s t a b l e  all-round  estimate  It of  86 ore  reserves  model  it  similar  is  regardless calculated.  (or  correct)  Assuming t h a t from the  average"  estimate of show a  t h e most  unbiased  inverse  20'  IDO  the  trend of trend of  always  and u s u a l l y  manner.  The  BUCKG  ore  reserve  production  does  allow  be p r o v i d e d agreement data),  "a c o r r e c t  fairly  accurate  it  does  not  o u n c e s above  any  provide and  is  a  good,  good e s t i m a t e s  for excellent  is  is  examined,  line  tends to  the  results  60'  opt.  tenth  of  from  is  itself.  above  lines  some  and  ounces  for The  in  0.05  the  opt.,  in exactly become  of  the  flat  at  might  be  cutoffs. there  are  other  important observation  b l o c k model  trend  flatten,  behaves  the  the  there  total  ounces  (ID10)  models,  if  reverses  most  l o w e s t number o f  For the  one  four graphs,  curve then  predicts  the  although  the  the  the  to  0.035 o r 0.05  there  the  distance  Finally, found,  a  However,  grades  calculations  inverse  either  block  distance  which the  opposite  will  contained  it  i n each o f  calculation  while  models.  generate  provides  What  which i n t u r n  providing  kriged blasthole  deposit.  also that  models  deposit  the  estimate of  of  to  probability.  Notice  the  four block  k r i g i n g does  i n the  grade.  distribution  at  or f o r which block  ( w h i c h show e x c e l l e n t  Kriging  on a v e r a g e  variance,  used,  v a l i d comparisons  show t h a t  ounces  cutoff  conditional  grade  also  total  significant  the  all  p r o b a b i l i t y and  estimate.  correct  kriging  for  BUCKG and BUCK60G m o d e l s  t h e s e two m o d e l s  is  No o t h e r method comes c l o s e  answers  between c o n d i t i o n a l  on  o f what d a t a  is  picture  within  figures  (tons  patterns that  a p p a r e n t l y a good the and  imposed grade)  can  be made  here.  approximation of  outline. at  that  the  The a c t u a l  t h e mine a r e based  on  87 straight  polygonal estimates  data.  The  mine  reconciliation polygonal  the  of  the  an i n v e r s e  BUCKG m e t a l  polygonal similar,  graph  the  pit  Fig.  the  polygonal reserves data  not  This  every  grade  production blasthole  have  if  they  and  which should  at  the  had  grade  on  average,  BH60 on  accident,  combine the  raw  basis,  production in (subtracting  a l s o work.  Kriged  "best e s t i m a t e " ,  A l l indications  are that  recovered  if  done  to  or  straight  On a m o n t h l y  the mine.  if  ore  reconciliation  was  These  predicted  predicted  the  higher  reserves  using  t r i e d to  reflect  the  BH4 and  the  are  conditional  kriging).  mine  of the  estimates  by l u c k ,  to  drilling  An e x a m i n a t i o n  predicted  method w i l l  mining  20'  (compare  reflect  either  with o r i g i n a l  w i t h the  comparing.  for  the  (BH20)  either  grade of  that  the  reconcile  before  from r e s e r v e s )  at  been  as  comparison  exploration  well  to  blasthole  and m o n t h l y  blasthole  show t h a t  daily  method p r e d i c t s  blocks  adequately  range,  grades,  by  60'  will  blocks  method w i l l  agree  statistics  as w e l l  either  not used  using  seems t o  i n t o ' 20'  shows  weighted  shown  boundaries,  a  from t h e  h a v e been c l o s e  production  about  is  (no e x p l o r a t i o n  designed  22).  design,  polygon  low g r a d e t o n s  blocks  blastholes  20),  these estimates  estimate  was  from  the  cubed c a l c u l a t i o n ) .  (Fig.  and  e s t i m a t e s would  actual)  estimate  distance  and t h a t  amount o f  vs.  from  on 20'  grade p r e d i c t e d  (BH4)  probability  designed  (predicted  production  bench p l o t s (using  was  derived  more g o l d kriged  were would  blasthole  outlines. I n summary, t h e the  v a r i o u s methods  seems t o  be t h e  graphs quite  show t h e  well.  best estimator  strengths  Overall, regardless  and  weaknesses  of  conditional probability of  b l o c k model  or  what  88 raw  data  methods  was  used  shown.  at  on " m e t a l  recover  o p e r a t i o n can  the  CHARTS  Many o f  same  the  charts  all  Instead  of  however, grade,  a  rank  but  these  tables  from b e s t estimates side  whether  the  tonnage,  grade,  conditional  given  in  from  reports  actual  the  from  charts  above  a  kriging  p r o v i d e the  to  and  in  been order  reserve  case  best  based  however,  essentially four  pages.  grade  cutoff  ore  (tons,  actual),  assigned. of  figure  rank  be.  and b e c a u s e estimate  an  Because  error  blasthole of  The  d e p e n d i n g on  to p r e d i c t the on  and  assigned,  or overestimated  may  ore  In a d d i t i o n ,  (compared t o has  the  These,  grade ranges.  method a t t e m p t s  exploration kriging,  general should  The  underestimated as  have  to  the planned  t h e p r e d i c t e d amount o f  printed,  probability  drawn  and X ) .  reserves  are then  or ounces,  of  ( A p p e n d i x C) i n t o  w i t h i n the  method  sufficient  I f more t o n s  be  IX  estimate  from p r o d u c t i o n b l a s t h o l e derived  can  worst  the  other  A comparison o f tons  has b e e n c a l c u l a t e d  of  not  economics  addition.  show  of gold)  to  is  each o f the  necessary.  VIII,  cumulative  error  on e i t h e r  also  in  reserve  showing  and o u n c e s  various  is  (Tables V I I ,  o f the  a percentage  the  conclusions  show a number o f t h i n g s distill  it  be d r a s t i c a l l y a f f e c t e d .  ORE RESERVE  reserve  compared t o  above c u t o f f " . gold,  grade w i t h i n grade ranges  7.3  least  H o w e v e r , i n most c a s e s ,  make c o m p a r i s o n s be m i n e d t o  —  the the  reserves estimate kriging  mined t o n s  and  TABLE V I I COMPARISON OF BLASTHOLE INDICATED RESERVES WITHIN GRADE CATEGORIES VS. RESERVES CALCULATED BY EACH EXPLORATION METHOD FOR BUCK BLOCK MODEL (20 FOOT BLOCKS. NO ORE OUTLINE). CUT-OFF  0.000 T 0 N N A  G E  a oio 0.020 0.035 0.050 -  CUT-OFF  0.000 _  G R  A D E  a oio _ 0.020 0. 035 0.050 -  CUT-OFF  0.000 -  0 U N C  E S  IDO ID1 102 KRIGE 161.9 179.6 228.2 228.7 0.359 0.289 0.096 0.094 5 3 7 2 EX4 EX20 1010 21&6 23S 1 243.3 a 141 0.048 0.007 4 2 1 EX4 EX20 CPROB IDIO 105 232. i 254.4 267.8 270.6 302.5 0.278 0.209 0. 1670. 158a 059 8 6 2 10 5 EX4 EX20 CPROB 1010 IDS 103 KRIGE ID2 IDO 110.6 119.6 126.5 126.8 129.4 13Z4 13a 2 147.9 14a 4 0.264 a 203 a 158 0. 1560. 139a 119 tt 073 0.016 0.012 9 8 7 6 5 3 2 4 10 KRIBE IDO ID1 ID2 103 ID5 1010 EX20 EX4 CPROB 12a 7 122.7 124.2 124.4 130.3 131.5 133.2 134.5 146.5 148.0 0.329 a 317 0.309 0.308 0. 2750.268 0.259 0.252 0. 1850. 176 10 9 6 3 8 7 5 • 4 2 1  BHK ID3 105 CPROB IDIO EX20 EX4 25Z5 262.7 31&8 325.7 375. 3407.3 450.3 0.000 0.041 0.251 0. 290 0.487 0.613 0. 784 0 1 4 6 8 9 10 BHK 105 CPROB ID3 ID2 KRIGE ID1 IDO 251. 1 275.9 287.0 294.6 304.7 316 0 322. 9 326.9 0.000 0.099 0. 143 0. 173 0.214 0.258 0.286 0.302 5 6 9 0 3 7 8 10 BHK ID3 102 KRIGE ID1 IDO 321.5 33a 1 34a 8 350.5 376. 6 395. 2 0.000 0.042 0.088 0.090 0. 172 0.229 0 1 3 4 7 9 BHK 101 150.3 151.7 0.000 0.010 0 1 BHK  17a7 0.000 0  LMTEPrriMATFTL . .  o n  EX4  BHK  0.004 0.005 0.000 0.200 1 0 EX4 IDIO BHK 0.014 0.014 0.015 0.067 0.067 0.000 0 1 1 EX4 BHK 0.026 0.027 0.037 0.000 1 0 105 103 ID2 101 KRIGE BHK a 041 0.041 0.041 0.04) 0.041 0.042 0.024 0.024 0.024 0.024 0.024 0.000 1 1 1 1 1 0 BHK IDO 101 0.076 078 0.080 0.050 0.025 0.000 2 1 0 UNTFRFSTIMATFTL . .  IDO ID1 1066 1154 0. 1430.073 3 1 EX4 EX20 IDIO a oio 3088 3468 3583 0. 1930.094 0.062 7 3 2 EX4 EX20 CPROB IDIO ID5 a 020 E132 6785 7141 7193 8067 0.294 a 219 0. 1780. 172 0.071 5 9 7 6 2 0.035 _ EX4 EX20 CPROB 1010 ID5 ID3 KRIGE ID2 IDO ID1 4595 4997 5266 5284 5332 5 4 7 7 5704 6097 6165 6274 0.771 0.208 0. 165 0. 1620. 154 0. 132 0.096 0.033 0.0220.005 9 8 7 6 5 4 3 2 1 10 0. 050 _ IDO ID1 KRIGE ID2 ID3 IDS IDIO CPROB EX20 EX4 9334 3658 3830 10207 11004 11738 12710 12751 12886 14236 0.354 0.331 0. 316 0.293 0.238 0. 183 0. 120 0. 117 0. 108 0.015 3 to 9 8 7 6 5 4 2 1  METHOD TONS ( X 10001 — _ X ERROR _ RANK  Amiflt BHK  1245 0.000 0 BHK  3826 0.000 0 BHK  8685 0.000 0 BHK  . . . nvmSFSTlMATFIl  EX20 IDIO CPROB IDS 103 ID2 101 KRIGE IDO 0.005 0.005 0.005 0.006 0.006 0.006 0.006 0.006 0.007 0.000 0.000 0.000 0. 200 0. 200 0.200 0.200 0.200 0.400 0 2 0 0 1 1 1 1 1 EX20 105 103 ID2 101 IDO KRIGE CPROB 0.015 0.015 a 015 0.015 a 0 1 5 0.015 0.015 0.015 0.000 0.000 0.000 0.000 0.000 0.000 0. 0000.000 0 0 0 0 0 0 0 0 EX20 IDIO IDS 103 102 101 IDO KRIGE CPROB 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.000 0.000 0. 000 0.000 0.000 a ooo 0.000 0.000 0. OOO 0 0 0 0 0 0 0 0 0 EX4 EX20 IDIO 100 CPROB 0.042 0.042 0.042 0.042 0.042 0.000 0.000 0.000 0.000 0.000 0 0 0 0 0 102 KRIGE 103 CPROB IDS IDIO EX20 EX4 0.082 0.082 0.084 0.086 0.090 0. 0950.036 0.037 0.025 0.025 0. 050 0.075 0. 125 0. 188 0. 200 0.213 3 6 7 1 2 4 5 1  _ METHOD GRADE (OPT. ) _ % ERROR _ RANK  . . . rWFRFSTTMATFTl  KRIGE 102 103 CPROB 105 EX20 EX4 IDIO 1396 1445 1576 1654 1803 1934 2023 2032 0. 121 0. 161 0.266 0. 329 0. 4490.554 0.626 0.633 3 10 8 2 4 5 6 7 105 CPROB 103 ID2 KRIGE 101 100 4002 4234 4302 4494 4713 4757 4312 0.046 0. 107 0. 124 0. 175 0.232 0. 243 0. 284 1 4 5 6 8 9 10 103 102 KRIGE ID1 IDO 8973 9 3 5 3 9354 10046 10620 0. 033 0.077 0. 077 0. 157 0.223 3 3 1 4 8  _ METHOD OUNCES _ % ERROR _ RANK  6306 0.000 0 BHK  14446 0. ooo 0 CO  TABLE  VIII  COMPARISON OF BLASTHOLE INDICATED RESERVES WITHIN GRADE CATEGORIES VS. RESERVES CALCULATED BY EACH EXPLORATION METHOD FOR BUCKG BLOCK MODEL (20 FOOT BLOCKS. WITHIN ORE OUTLINE). CUT-OFF 100 KRIGE ID2 103 CPROB IDS ID1 BHK IDIO EX20 EX4 0.0 0.0 0.4 2.9 7.B 14.8 i a g 314 73.6 101.9 2a i 1.000 1.000 0.9B5 a 898 0.720 0.474 0.290 0.000 0.403 1.623 ^631 I 7 7 S 5 4 3 0 2 8 9 IDO ID1 KRIGE ID2 ID3 BHK ID5 CPROB IDIO EX4 EX20 0. 010 _ 60.4 692 86.2 95.9 118 7 124.9 150.4 152 8163.8 186.4 193. 1 0.516 0.446 0.310 0.233 0.050 0.000 0.204 0.223 0.359 0.492 0.546 9 7 5 4 1 0 2 3 6 8 10 EX4 EX20 BHK CPROB IDIO IDS 103 ID2 IDO 0.020 IDI KRIGE 221.8 243.9 276.7 279.2 280.6 301.7 324.7 32a 9 335.7 338. 2 35tt 8 0. 1990. 118 0.000 0.009 0.014 0.090 0. 1730. 1890.213 0.222 0.269 7 4 0 1 2 3 5 6 8 9 10 EX4 EX20 1010 BHK 105 CPROB ID3 KRIGE ID2 IDI IDO 0.035 _ 105.5 114. 1129 7 143.3 143.9 147.9 159 9 183.0 188. G210. 1224. 1 0.264 0.204 0.095 0.000 0.004 0.032 0. 1160. 2770.302 0.465 0.553 6 5 3 0 1 2 4 7 8 9 10 EX20 KRIGE IDO 1010 ID1 105 EX4 102 103 CPROB BHX a 050 _ 131.3 135.7 135.9 136.6 138.7 14a 2 140.5 141.9 145.0 161.5 183. 1 0.283 0.259 0.258 0.254 0.243 0.234 0.232 0.225 0. 2080. 118 0.000 9 8 7 6 5 4 3 2 1 0 10 IMmjFSTIMATFn. . . urrnin .. n w - M - M TMOTFn. CUT-OFF 0.000 _  T 0 N N A G E  0.000 _  G R A 0 E  a oio _ 0.020 0.035 _ 0.050 _  CUT-OFF 0.000 _  0 U  N C E S  BHK EX20 IDIO ID5 ID3 ID2 CPROB KRIGE 101 100 EX4 0.000 0.000 0. 006 0.007 0.007 0.007 0.007 0.007 0. 0080.008 0.009 1.000 1.000 0. 143 0.000 0.000 0. 0000.000 0.000 a 143 0. 1430.286 3 3 0 0 0 0 0 1 1 2 1 EX4 EX20 ID10 BHK ID5 103 CPROB 102 KRIGE 101 IDO 0.014 0.015 0.015 0.016 0.016 0.016 0.016 0.017 0.017 a 018 0.018 0. 1250.082 0.062 0.000 0.000 0.000 0.000 0.063 0.063 0. 1250. 125 2 1 1 0 0 0 0 1 1 2 2 EX4 BHK EX20 IDIO ID5 ID3 CPROB ID2 IDI IDO KRIGE 0.026 0.027 0.027 0.027 0.027 0.027 0.027 0.028 0.028 0.028 0. 028 0.037 0.000 0.000 0.000 0.000 0.000 0.000 0.037 0.037 0.037 0.037 1 0 0 0 0 0 0 1 1 1 1 ID5 ID3 ID2 IDI KRIGE BHK EX4 EX20 IDIO IDO CPROB 0.041 a 04i 0.041 a 041 0.041 0.042 0.042 0.042 a 042 0.042 0.042 0.024 0.024 0.024 0.024 0.024 0.000 0.000 0.000 0.000 0.000 0.000 1 1 1 1 1 0 0 0 0 0 0 IDO IDI BHX KRIGE ID2 CPROB ID3 105 EX20 IDIO EX4 0.077 0.078 0.080 0.080 0.081 0.082 0.083 0.089 0.096 a 096 0.098 0.037 0.025 0. 000 0.000 0.012 0.025 0.038 a 113 0.200 0. 2000.225 3 2 0 0 1 2 3 4 5 5 6 IMFRFCTIMATFn . .  ID1 IDO KRIGE ID2 ID3 CPROB ID5 0 4 23 59 125 146 0 1.000 1.000 0.980 0.875 0. 6820.323 0.207 7 7 6 5 4 2 1 IDI KRIGE 102 ID3 0. 010 _ 100 1072 1219 1500 1632 1949 0.467 0.394 0.254 a 189 0.032 10 8 5 3 1 EX4 EX20 ID10 0.020 5B48 6500 7472 0.219 0. 1320.002 7 4 1 0.035 _ EX4 EX20 ID10 105 4394 4771 5414 5931 0.262 0. 1980.090 0. 004 6 5 3 1 0.050 _ IDO KRIGE ID1 ID2 1D3 ID5 EX20 1D10 CPROB EX4 10486 10834 10853 11473 12069 12494 12615 13063 13312 13732 0.287 0. 2G30.282 0. 2190. 1790. 1500. 1420. Ill 0.094 0. 066 3 10 9 8 7 S 5 4 2 1  emn BHK IBS 0.000 0 BHX 2012 0.000 0 BHK 7488 0.000 0 BHX 5952 0.000 0 BHX 14700 0.000 0  METHOD TONS <X 1000) X ERROR RANK  METHOD GRADE (OPT. ) X ERROR RANK  ... rM-M-mIM0TFT1. IDIO EX20 EX4 262 480 561 0.420 1.602 2.041 3 8 9 105 CPROB 1010 EX4 EX20 2386 2406 2580 2672 2837 0. 1860. 1960.282 0.328 0. 410 2 4 6 7 9 CPROB ID5 103 102 IDO IDI KRIGE 7535 8174 8882 9050 9371 9386 9654 0.006 0.092 a 186 0.209 0.251 0.254 0.289 3 2 5 6 8 9 10 CPROB ID3 KRIGE ID2 IDI IDO 6146 6572 7531 7634 8630 9309 0. 0330. 1040. 2650.283 0.450 0.564 2 4 7 8 9 10  METHOD OUNCES X ERROR RANK  VD o  TABLE  IX  COMPARISON OF BLASTHOLE INDICATED RESERVES WITHIN GRADE CATEGORIES VS. RESERVES CALCULATED BY EACH EXPLORATION METHOD FOR BUCK60 BLOCK MODEL (GO FOOT BLOCKS. NO ORE OUTLINE). CUT-OFF  UNDERESTIMATED...  ACTUAL  ... OVERESTIMATED.  IDO IDI KRIGE BHX ID2 CPROB ID3 EXGO 105 IDIO EX4 156. 1169 7 202. 0 222. 7 243.3 275. 1294.5 309.5 343. 1395.8 450. 3 0.299 0.238 0.093 0.000 0.092 0.235 0.322 0.390 0.540 0.777 1.022 5 4 2 0 1 3 6 7 8 9 10 EX4 BHK IDIO 105 103 ID2 EXGO CPROB KRIGE IDO IDI a oio 215 6 232.5 234.3 245.7 272. 4294.4 302.3 307.2 321.5 332.2 338.6 a 072 0.000 0.008 0.057 0. 172 0.267 0. 3000.322 0.383 a 429 a 456 3 0 1 2 4 5 6 7 8 9 10 EX4 EXGO IDIO CPROB ID5 ID3 BHK KRIGE 102 IDI 100 0.020 232. 1285.2 292.6 295.8 315.7 345.9 355.4 357.5 368. 1372. 8399.3 0. 1770. 168a 112 0.027 0.000 0.006 0.036 0.049 0. 123 a 347 0. 198 9 8 7 5 2 0 1 3 4 6 10 EX4 102 ID3 IDIO EXGO CPROB 105 100 IDI KRIGE BHX a 035 - 110.6 114.9 136.0 138.6 140.9 142.9 151.8 173.8 178.9 113.5 122.7 a 357 a 314 0.240 0.225 0.212 0.201 0. 152a 028 0.000 a 382 a 365 9 8 7 6 5 4 3 2 1 0 10 a 050 _ KRIGE IDIO IDS EX60 IDI 100 ID3 ID2 CPROB EX4 BHK 100.3 109.7 109. 7122. 1122.2 124.6 127.4 135.7 138 3 146.5 165.6 0.384 0.337 0.337 0. 2630.262 0.248 0.231 0. 1810. 1650. 115 0.000 9 8 8 7 6 5 4 3 2 1 0 0.000 -  T 0 N N A G E  CUT-OFF  0.000 -  G R A D E  a oio 0.020 _ 0.035 -  0. 050 _ CUT-OFF 0. 000 _  0 U N C E S  ItOUFSTIMATFTL . .  EX4 0.004 0.200 1 EX4 105 ID3 102 IDI 0.014 a 014 a 014 0.014 0.014 0.067 0.067 0.067 0.067 0.067 1 1 1 1 1 EX4 IDIO 105 KRIGE a 026 0.026 0.026 0.026 0.037 0.037 0.037 0.037 1 1 1 1 IDS 102 0.041 0.041 0. 0240.024 1 1 ID2 0.076 0.013 1 IM5HESTIMATFJ1..  100 IDI 1066 1076 0.078 0.069 2 1 EX4 IDIO 105 a oio _ 3088 3403 3487 0. 1180. 0280.004 3 2 1 EX4 EX60 IDIO CPROB IDS 103 KRIGE 0.020 _ 6132 7642 7677 7883 8182 9169 9273 0.362 0.204 0.201 0. 1790.148 0.046 0.035 10 9 8 7 6 4 2 0.035 _ EX4 102 103 IDIO EX60 CPROB IDS IDO 101 KRIGE 4595 4626 4776 5172 5728 5768 5793 6053 6355 7286 0.388 0.384 0.364 0.312 0.238 0.232 0.229 0. 1940: 1540.030 10 9 8 7 6 5 4 3 2 1 0.050 KRIGE IDI IDO IDS IDIO 103 ID2 EX60 CPROB 8327 9372 9664 9680 10106 10243 10363 10717 11188 0. 343 0.261 0. 2380.237 0.203 0. 192 0. 183 0. 155 0. 118 5 10 9 8 7 6 4 3 1  flrnm BHK 0.005 0.000 0 BHK 0.015 0.000 0 BHK 0.027 0.000 0 BHX 0.042 0.000 0 BHK 0.077 0.000 0 ACTUAL  METHOD _ TONS (X 1000) X ERROR RANK  . . . (^RFCTIMATFTI.  EXGO IDIO IDS ID3 102 101 KRIGE CPROB IDO 0.005 0.005 0.006 0. 0060.006 0.006 0.006 0.006 a 007 0.000 0.000 0.200 0.200 0. 2000.200 0.200 0.200 o. 400 0 0 1 1 1 1 1 1 2 EX60 IDIO IDO KRIGE CPROB 0.015 0.015 a 015 a 015 0.015 0.000 0.000 0.000 0.000 0.000 0 0 0 0 0 EX60 ID3 102 101 100 CPROB 0.027 0.027 0.027 0.027 0.027 0.027 0.000 0.000 0.000 0.000 0.000 0.000 0 0 0 0 0 0 EX4 EX60 IDIO ID3 IDI IDO KRIGE CPROB 0.042 0.042 0.042 0.042 0.042 0.042 0.042 0.042 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0 0 0 0 0 0 0 0 IDI IDO 103 CPROB KRIGE EXGO IDS IDIO EX4 0.077 a 078 0.080 0.081 0.083 0.088 0.088 0.092 0.097 0.000 0.013 0.039 0.052 0.078 0. 1430. 1430. 1950. 260 0 1 2 3 4 5 5 6 7 ... nVFKESTIMATFTl  BHK KRIGE CPROB EX60 ID2 ID3 105 EX4 IDIO 1156 1269 1518 1545 1571 1795 1923 2023 2091 0.000 0.098 0. 3130.336 0. 3590.553 0.664 0.750 0.809 0 3 4 5 6 7 8 9 10 BH( ID3 ID2 EX60 CPROB KRIGE IDI IDO 3501 3937 4191 4442 4546 4749 4906 4944 0.000 0. 125 0. 1970.269 0. 2990.356 0.401 0.412 0 4 5 6 7 8 9 10 BHK ID2 IDI IDO 9607 9902 9973 10789 0.000 0.031 0. 0380. 123 3 0 1 BHK 7513  _  METHOD GRADE (OPT. ) X ERROR RANK  METHOD OUNCES X ERROR RANK  0.000 0  BHK EX4 12683 14236  0. ono 0. 122 0 2 VO  TABLE  X  COMPARISON OF BLASTHOLE INDICATED RESERVES WITHIN GRADE CATEGORIES VS. RESERVES CALCULATED BY EACH EXPLORATION METHOD FOR BUCKGOG BLOCK MODEL (60 FOOT BLOCKS. WITHIN ORE OUTLINE). CUT-OFF 0.000 T  0 N N A  G E  0.010 0.020 a 035 0.050 -  CUT-OFF 0.000 -  6 R  A D E  a oio -  a  020 -  0.035 a 050 -  CUT-OFF 0.000 -  0 U N C  E S  a oio 0.020 0.035 0.050 -  ACTUAL  UNDERESTIMATED...  ... OVERESTIMATED.  IDO KRIGE 102 CPROB BHK 103 EX60 IDS IDIO EX4 0.0 0.0 0.0 a s 10. 1 21.2 21.8 25.0 31.2 38.3 101.9 1. 000 1.000 1.000 0.601 0.522 0.000 0.028 0. 178 0.467 ft 8053.600 7 7 7 5 4 0 1 2 3 8 6 IDO IDI KRIGE BHK 102 103 IDS CPROB IDIO EX4 EXEO 54.9 58.5 87.2 sa 6 92 1 101.8 12a 9 145. 3 167.3 isa 4 191.4 0.381 0.340 0.016 0.000 0.040 0. 1490.466 0.640 0.889 1. 1041. 160 7 4 1 5 0 2 3 8 6 9 10 EX4 EXEO CPROB BHK 1010 ID5 IDO 102 KRIGE 103 IDI 221.8 276 5 293.6 soas 311.8 323.6 34a 2 350.0 357.0 357. 1 365. 1 0.282 0. 104 0.049 0.000 0.010 0.048 0. 121 0. 133 0. 156 0. 156 0. 182 7 6 10 4 1 3 0 2 5 8 9 EX4 ID2 CPROB BHK IDIO ID3 EXEO 105 101 KRIGE IDO 105.5 na9 138.9 142 4 150.2 15a 0 isa 8 162 2 192 5 193.0 2225 0.350 0.261 0. 143a 122 a 074 0.026 0.015 0.000 0. 187 0. 1890.372 1 7 4 0 9 8 5 3 2 6 10 IDIO KRIGE EXEC 105 IDO ID3 101 EX4 CPROB 102 BHK 119.0 120.7 121.3 132 5 136.4 140. 1 140.5 147.2 147.6 175.3 11&7 a 323 a 321 0.312 0.308 0.244 0.222 a 201 0. 1980. 160 a 158 0.000 7 1 4 0 10 6 5 3 2 9 8 101  i o n  1MTPFSTIMBTFI1 . .  METHOD TONS (X 10001 X ERROR RANK  . . . rrm!F<rriMOTFn  101 IDO KRIGE EX4 IDIO 0.000 0.000 0.000 0.006 0.006 1.000 1.000 1.000 0. 143 0. 143 1 3 3 3 1 EX4 EX60 a 014 0.015 0. 1250.062 1 2 EX4 IDIO ID5 0.026 0.026 0.026 0.037 a 037 0.037 1 1 1 102 ID5 103 ID1 KRIGE CPROB 0.040 a 041 a 041 0.041 0.041 0.041 0.048 0.024 0.024 0.024 0.024 0.024 2  1  1  1  1  ItmSFTTTMATFTL..  BHK ID5 EXEO ID3 ID2 CPROB ft 007 0.007 0.008 0.008 0.009 0. 009 0.000 0.000 0. 143 0. 143 0.286 0.286 1 1 0 0 2 2 BHK IDIO ID5 CPROB ID3 102 IDI IDO KRIGE 0.016 0.016 ft 0160.016 ft 017a 017 ft 0170 017 0 017 0.000 0.000 0.000 0.000 0.063 0.063 0.063 0.063 0.063 1 0 1 0 0 0 I 1 1 BHK EXEO 103 CPROB ID2 IDI IDO KRIGE 0.027 0.027 0.027 0.027 ft 0280. 0280.028 0.028 0.000 0.000 0.000 0.000 0.037 0.037 0.037 0.037 1 1 1 0 0 0 1 0 BHK EX4 EXEO IDIO IDO 0.042 0.042 0.042 0.042 0.042 0.000 0.000 0.000 0. 000 0.000 1 0 0 0 0 0 BHK 102 IDI IDO KRIGE 103 CPROB IDS EX60 IDIO EX4 ft 076 0.077 0.077 0.079 0.080 ft 0810.081 a 086 0.089 0. 090 0.09B 0.000 0.013 0.013 0. 039 0.053 0.066 0.066 0. 1320. 171 0. 184 0. 289 0 1 1 4 4 2 3 5 6 7 8 n r n m  METHOD GRADE (OPT. ) X ERROR RANK  . . . nvFRprriMOTFn  ID1 100 KRIGE 102 CPROB BHK ID3 EX60 IDS IDIO EX4 0 0 0 78 89 142 166 197 219 232 561 1.000 1.000 1.000 0.451 0.373 0.000 0. 175 0.389 0.547 0.642 2964 7 5 6 7 4 2 0 1 7 3 8 BHK IDO 101 KRIGE ID2 103 IDS CPROB 1010 EX4 EXEO 959 988 1434 1483 1532 1683 2124 2307 2601 2672 2918 0. 331 0.311 0.000 0.034 0.068 0. 174 0.481 0.609 0.814 0. 863 1.035 7 6 5 4 0 1 10 2 3 9 8 EX4 EX60 CPROB IDIO BHK 105 102 IDO ID3 KRIGE IDI 5848 7434 7959 8256 839G 8574 9680 9758 9772 9858 10190 0.304 0. 115 0.052 0.017 0.000 0.021 0. 1530. 162 0. 164 0. 174 0.214 7 9 1 2 5 10 4 0 E 3 8 EX4 IDIO ID3 EXEO IDS ID2 CPROB BHK IDI KRIGE IDO 4394 5028 5761 5955 6163 6354 6624 6859 7929 7955 9353 0.359 0.267 0. 160 0. 132 0. 101 0.074 0. 034 0.000 0. 156 0. 160 0. 364 7 5 6 4 I 0 9 3 2 10 8 KRIGE 105 IDO IDIO EX60 101 102 CPROB BHK EX4 103 9541 10434 10466 10636 10702 10752 11000 11375 11857 13352 13732 0.285 0.219 0.216 0. 203 0. 198 0. 195 0. 176 0. 148 0. 112 0.000 0.028 7 6 5 3 4 0 10 9 2 8 1  _  METHOD OUNCES X ERROR RANK  LO  to  grade,  blasthole  "actual"  i n the  kriged  one  that  evaluating  does  a good  grade  range,  and t h e n t o  other  grade  ranges.  ounces p o r t i o n o f  the  well  t h e method b e h a v e s  and  grade  portions  polygonal  Conditional  the  refer  of  (EX4)  is  probability  appeal  average  is  ounces the  other  is  as  to  start  w i t h the  t h e most  item  c h e c k i n g how  look to  if  the  total  important  after  ranges, see  through  the  answer  is  of  actual  tonnage  pattern  is  hand,  method  error  in  goes  obvious.  EX4 as 6th,  ounces  the  7th,  and i t  come o u t the  ranked second  choice. i n the  loses  and  9th, 32.8%  in predicting grades  worst  estimate  a bad of  reasonably 0.050 o p t .  and of  estimate  tonnage close  in  cutoff.  exploration polygonal estimate  of  Looking  21.9%,  to  a l s o makes  combination  ounces  estimate.  7th,  to  back  EX4 makes t h e  above  total  an e s t i m a t e  f r o m 26.2%,  Looking  this  exploration  w i t h a 9.4% e r r o r .  chart,  opt.?  by 22.5%  the  the  Why d o e s EX4 do so w e l l  g r a d e manage t o  suggests that the  error  0.05  a 6.6%  rank drops t o  204%.  over  the  where  best estimate of  second  Together,  overestimated  become  to  overestimating  prediction  Its  percent  finally  tonnage.  chart  one method  VIII  the  0.050 w i t h o n l y  abruptly.  on  to  Table  its  grade,  method works  and t h e n  grade  table  to  ounces p o r t i o n o f  tonnages,  a  best to  (since that's  b a c k up t h e  total  r e f e r r e d to  predicting in a particular that  is  i n other  of  estimate  cutoff  and t h e n  is  there.  As an e x a m p l e ,  and t h e  just  be p r e d i c t e d c o r r e c t l y ) ,  consistent  what  well  job of  follow  chart  should  a  how  Usually i t  that  over  are  charts.  The b e s t way o f select  estimates  and the The  should  not  C o n d i t i o n a l p r o b a b i l i t y on  the  i n i t i a l comparison,  then  2nd  in  most  other  then  32.3%  fact  ranges (the  that  predicting gives  a  with errors  h i g h e r r o r s i n the  there even  are  50 o u n c e s  27% e r r o r ) .  any  there any  of  is  the  Overall, reserves  7.4  i n the  19.6% and  a r e due t o  ounces  of  lowest  grade  the  the  gold  —  range  c h a r t shows  that  outperforms c o n d i t i o n a l p r o b a b i l i t y (tons,  grade,  or ounces), will  do  and" t h a t better  in  these  charts for this  detail  as  show  the  full  study  and  they  detail can  f u r t h e r comparisons  of  all  ore  be r e f e r r e d  to  a r e made.  SUMMARY CHART AND RANKING OF RESULTS  last  how  they  across  chart  ( T a b l e XI)  conclusions rank  models.  tabulations  for tons,  the  that  ranks  were  the  percentage  were due o n l y t o waste  average  category.  ranks.  average  and  and o u n c e s ,  assigned  from  used  for  e r r o r made  ore  because,  T h i s may n o t  score  in a l l  as  was  is  be a p e r f e c t  are  best  as  well  of  the  the  grade  average  charts. seen  of The  earlier,  t h e models  actually  such  model,  the  reserve  i n some o f  s m a l l amount o f m e t a l The f i n a l  every  and t h e n  the  e r r o r s occurred here the  information in  each other w i t h i n a model,  method,  grade  lowest grade range wasn't large  to  For each  contain  summarizes t h e  c a n be drawn a b o u t w h i c h methods  relative  categories  the  0.6%,  range.  for that  a way t h a t  as  few  examination of  comparisons  calculated  The  and  very  more o r l e s s  Careful  10.4%,  no way o f p r e d i c t i n g w h i c h m e t h o d ( s )  given grade  quickly  9.4%,  lowest category  actually  no o t h e r method c o n s i s t e n t l y in  of  which  contained  d e r i v e d by a d d i n g t h e way t o  rank the  in 3  methods  95 TABLE XI SUMMARY COMPARISON OF ORE RESERVE METHODS  BUCK BLOCK MODEL  AVERAGE % ERROR TONS GRADE OUNCES AVERAGE RANK  TONS GRADE OUNCES -  TOTAL RANK  EX4 21.7 7.9 19.3  EX20 17.8 5.0 15.7  IDIO 14.5 6.4 12.9  ID5 14.1 3.7 11.4  ID3 15.2 1.8 13.2  ID2 15.6 1.2 14.5  IDI 19.4 1.2 18.4  IDO 21.5 1.3 22.1  KRIG 18.8 1.2 18.0  CPROB 16.1 1.9 14.2  EX4 6.50 2.25 6.75  EX20 5.50 1.50 5.25  IDIO 4.25 1.50 4.50  ID5 4.00 1.25 3.50  ID3 4.50 0.75 4.25  ID2 5.00 0.50 4.75  IDI 6.25 0.50 5.75  IDO 7.50 0.50 7.50  KRIG 6.50 0.50 5.75  CPROB 5.00 0.75 5.25  8.75  9.50 10.25 12.50 15.50 12.75 11.00  15.50 12.25 10.25  FINAL RANK  9  6  3  BUCKG BLOCK MODEL AVERAGE % ERROR EX4 EX20 IDIO TONS - 29.7 28.8 18.1 GRADE 9.7 6.6 6.6 OUNCES - 21.9 22.1 12.2 AVERAGE RANK  TONS GRADE OUNCES -  TOTAL RANK FINAL RANK  AVERAGE % ERROR TONS GRADE OUNCES AVERAGE RANK  TONS GRADE OUNCES  TOTAL RANK FINAL RANK  AVERAGE % ERROR TONS GRADE OUNCES AVERAGE RANK  TONS GRADE OUNCES  TOTAL RANK FINAL RANK  EX4 6.25 2.25 5.25  1  2  3  7  9  8  5  ID5 13.3 3.4 10.8  ID3 13.7 1.5 12.5  ID2 23.7 3.4 22.5  IDI 34.4 5.3 34.0  IDO 38.8 5.0 39.2  KRIG 27.8 3.1 26.8  CPROB 9.5 0.6 8.2  ID2 5.25 1.00 6.00  IDI 7.75 1.50 8.50  IDO 8.75 1.50 9.50  KRIG 7.75 0.75 7.75  CPROB 1.75 0.50 2.50  EX20 7.25 1.50 5.50  IDIO 4.50 1.50 3.25  ID5 2.75 1.25 2.75  ID3 3.00 1.00 4.00  13.75 14.25  9.25  6.75  8.00 12.25 17.75 19.75 16.25  4  2  3  5  9  10  8  6  7  4.75 1  BUCK60 BLOCK MODEL EX4 22.9 9.1 24.8  EX60 25.0 3.6 21.6  IDIO 10.9 5.8 18.6  ID5 18.0 6.8 15.4  ID3 19.7 2.6 18.2  ID2 21.2 2.6 19.9  IDI 23.0 1.7 21.4  IDO 25.0 0.3 24.2  KRIG 20.3 2.9 19.1  CPROB 22.0 1.3 20.7  EX4 6.00 2.25 6.25  EX60 7.00 1.25 6.00  IDIO 6.00 1.75 5.75  ID5 4.75 2.00 4.50  ID3 4.50 0.75 5.25  ID2 5.00 0.75 4.75  IDI 5.50 0.25 5.75  IDO KRIG 5. 75 4.75 0.25 1.25 6.50 5.25  CPROB 5.25 0.75 5.00  14.50 14.25 13.50 11.25 10.50 10.50 11.50 12.50 11.25 11.00 10  9  8  4  1  1  6  7  4  3  BUCK60G BLOCK MODEL EX4 48.3 11.3 38.9  EX60 42.5 5.8 37.0  IDIO 37.0 5.5 32.5  ID5 22.4 4.8 20.6  ID3 16.8 3.8 16.8  ID2 8.9 4.0 11.1  IDI 22.7 3.4 21.9  IDO 28.0 3.5 26.8  KRIG 17.1 4.4 16.3  CPROB 21.6 2.2 20.2  EX4 7.75 2.75 7.25  EX60 6.50 1.75 6.00  IDIO 6.75 2.00 6.00  ID5 4.50 1.75 5.00  ID3 5.25 1.50 5.25  ID2 2.75 1.25 3.00  IDI 5.75 1.00 5.75  IDO 6.50 1.00 7.25  KRIG 6.00 1.50 6.25  CPROB 3.25 1.25 3.25  17.75 14.25 14.75 11.25 12.00 10  7  8  3  7.00 12.50 14.75 13.75 4  1  5  8  6  7.75 2  because  much  simplifies methods, and  of  the  and  metal  ore  is  or  shows t h a t using  similar  results  in  perform w e l l  i n the  are s i m i l a r  and l e s s  than 11.0.  tons,  grade  these case  that latter  model;  probability  ranks c o n s i s t e n t l y  block models,  methods  seems t o  perform well  Notice overall  —  also that  percent  ID3 on t h e  ID2  well  and  that  ID2  ranks  showing Closer  in a l l  final  0.6%, the  ranks  rank  is  (BUCKG),  and 8.2% 60'  on  model  four block models, there  be b e s t .  come c l o s e ,  for  the  at  or even t h a t  the seem  inverse  60" m o d e l s ,  and ID5  block models,  is  Looking  the  20'  grade estimate  and  c a n be no way  any o f  for the  This  total  Furthermore, conditional  models.  model.  of  calculating  model  for  20'  BUCK b l o c k  be  the  inside  model.  final  9.5%,  shows t h a t  does w e l l  in  for  are  calculation  f o r the  errors  fall  block  o u t p e r f o r m c o n d i t i o n a l p r o b a b i l i t y c a n be  distance  was  of  20.2%.  competitors  t h e methods  that  with only  20'  p r e d i c t i n g b e f o r e h a n d w h i c h one w i l l  four to  for nearest  can  to use  no o t h e r m e t h o d ' s  for the  and  r a n k i n g shown.  their  respectively,  2.2%,  the  BUCK60G  while  makes e r r o r s  ounces  i x  ID2 and c o n d i t i o n a l p r o b a b i l i t y  than 8.0,  probability  or 3  and 22)  This  the  2  21  b e s t method  models,  of  On a v e r a g e ,  and  the  adequately  best  b l o c k models  composites  both  21.69%,  of  20'  two  (BUCK60G),  a search  best  it  (Tables V I I , v i i i ,  20,  probability.  the  reveals  19,  but the  r e l i a b i l i t y of  and t h a t  in  examination  conditional  only  are  charts  (Figs.  the  conditional second  obliterated,  detail  graphs  zone o u t l i n e ,  reserves  less  full  t o when a s s e s s i n g t h e  BUCKG and BUCK60G,  first  is  o f d e c i d i n g which  then the  T a b l e XI  the  detail  process  X) and t h e  referred  the  one  attained the  of  the  lowest  by any method  original  inverse  distance used  at  cubed, the mine.  provided was  20'  the  Lastly, provided Kriging  feel"  strength) whose  is  by  itself,  in  that  another  performance  c a n n o t be e v a l u a t e d  method  nearly  ore reserve estimates  error  just  this  is  time.  worst  measure o f  that  ( g i v e n t h e BUCK b l o c k model)  again that k r i g i n g , the  that  without taking k r i g i n g variance into  ignoring that  technique  "gut  estimate  guess at the  of  alone,  original  reserve  notice  one  greatest  The  best  an e x c e l l e n t  b l o c k m o d e l w i t h no o r e z o n e o u t l i n e  is  distance  of  Buckhorn.  account  supposed t o  relative  advance  at  always  (i.e.  be k r i g i n g ' s  weighted  averaging  to  any  other  estimator  having  the  production data  available.  7.5  EXAMINATION OF SCATTERGRAMS AND BENCH PLANS  Although results  both  which u s e f u l  a  the  and  scattergrams  really  reserve  offer  c a n be d r a w n .  estimates,  When one  scatter  plots  they  false  which  shows  basis,  use  another.  the  this This  that  security. least  plot  Many p e o p l e p o i n t t o amount  to j u s t i f y  of  scatter  t h e i r choice  r e a s o n i n g however,  is  flawed  a r e v i s u a l l y d i s c e r n a b l e on  and F ,  is  interested  in particular,  often  the  i n f o r m a t i o n from  (actual vs.  c a n be c o m p l e t e l y d e c e i v i n g ,  sense o f  showing  (Appendix B  very l i t t l e  b e s t method o f c o m p a r i n g t h e d a t a  fact  things  they  conclusions  comparing ore  In  maps  have been d u t i f u l l y r e p r o d u c e d h e r e i n  respectively),  not  bench  one  in that  into  scattergram  and, s o l e l y o f one  are  predicted).  lulling the  in  on t h a t  method o v e r there  a scattergram  are  two  which are  98  independent o f each o t h e r .  One  crude v i s u a l  appraisal  errors associated  and t h e  is  other  evaluation of line  grade  least  to  scatter  graph.  each  (hard  the  (0,0)  are  to measure),  drawn f r o m t h e  c a n be compared t o  error  associated  with  of  be  constant)  one  the  taken to  since  would appear t o What  the  show z e r o  conditional  scatter  a c t u a l grades  of  indicates  that  blocks that point  on  percentage  the  scatter,  of blocks that  of  identical  graph that is  best,  shows  or  else  show i d e n t i c a l  estimation  block grades,  o f the  least  extreme,  of  scatter if  the  scatter, grade  actual  is  the  in  one  to  o n l y measurement the  was  versus  amount o f  best  estimate  constant predicted  (any grades  do  show  is  the  differences  at  that  in  around is  it  it.  waste,  representative  expected  grade,  If  F o r any g r a d e there  is  of  for  be p o s s i b l e  are underestimated at  estimate  the that is  every  of  individual  to determine that  a  that  some p e r c e n t a g e  one c o u l d s e e  would  the  Any h o r i z o n t a l l i n e  — f o r any g i v e n p r e d i c t e d g r a d e t h e r e  block  an  least  predicted  are a c t u a l l y ore. the  is  "scattering".  distribution estimator  show  45° slope  shown i n A p p e n d i x F i s  particular  which  c a n be compared  which  d i s t r i b u t i o n s f o r every method.  scattergrams  estimate),  which provides the  the  then a p l o t  scattergrams  conditional on t h e  where  that  same b l o c k m o d e l t h a t  see  (a  intersections  i n which case the  i m p o r t a n c e was t h e v i s u a l amount o f  would  fit"  through  those  w h i c h c a s e t h e method p r o v i d i n g t h e In f a c t ,  scattering  w i t h an  of  The o n l y p l o t s  other  slopes  amount o f  c a n be m o d e l l e d by t h e 4 5 °  amount o f d e v i a t i o n f r o m t h e  two s c a t t e r s  choose.  the  "goodness  from t h e o r i g i n  on t h e  meaningfully scattering  average  how c l o s e  which passes  equal  the  the  of  is  grade.  the Were  99 any o f do as  these d i s t r i b u t i o n s good  a j o b as  probabilities square any  at  drilling  way  of  presence of course,  Buckhorn. pattern.  vast  can  on an  irregular grid,  numerous  other  l i n e a r unbiased" The  than  smoothed 60'  blocks.  can't  more s c a t t e r tend  to  show  appears of  the  to  IDI  from the  use.  a  Appendix foot  blocks  1  methods  data.  when  is  a  provide the  Kriging,  of  expectations  drilling  is  are c l u s t e r e d ,  the  make i t  best  fit  crude v i s u a l  the  show  predicted  therefore  polygonal  either kriging  "the  lines  other  the  and  On t h e  best  kriged  higher  better,  estimates  at  hand,  to  20' show  Buckhorn  the  than  also  slopes  estimates k r i g e d and  IDI e s t i m a t e s  seriously  ranges.  but  grades  for  T h e IDO e s t i m a t e  e s t i m a t e o f w h i c h method highest  more  grades  and t h e r e f o r e  other  grade  are  IDIO e s t i m a t e s  scatter  and  show  scatter  grades  IDIO and p o l y g o n a l  show more  are a l i t t l e  A l l methods show t h e i r  less  estimated  methods.  vary.  i n the  don't  The k r i g e d e s t i m a t e s  scatter.  the  45° line  models  ID2 o r IDI e s t i m a t e s  4 5 ° s l o p e s but while  therefore  same e x t r e m e s as  than  least  F,  block  and  same r e a s o n ,  The b e n c h p l a n s only  other  do i n f a c t  because  reach the  show t h e  estimates,  depart  20  scattering  to  conditional  because there  conditional  especially  t h a n IDI and I D O .  various  come c l o s e r  in Sixty  be s i m i l a r t o  less  of  might  d i s t r i b u t i o n without  o r when d r i l l h o l e s  models  than for  For the  the  they  estimate.  block  blocks  only  production  advantages t h a t  surprising.  20'  of  estimate of  and,  scattergrams  anything  of  this  production starts  none  is  a conditional  amount  provide  calculation  But t h i s  Also,  calculating a  be n u m e r i c a l l y m o d e l l e d ,  k r i g i n g d i d i n the  before  has  to  again they is  the  i n the  provide  b e s t one  to  same p l a c e s  100 since  every  estimate  was  exploration composites. g r a d e and the  a l l methods  same r e a s o n s  highs  in  the  areas  g e n e r a l shape  a r e a s where b l a s t h o l e not to  visual  choice of alone. the  types  Figure  18  comparison t h a t evaluating reserve  the  6)  c a n be u s e d different  should  outcomes  for  ore  amount o f  be p r o d u c e d  justify scatter to  give  mind t h r o u g h o u t  and a s s e s s  the  results  for  overall distribution  provides  a  and  i n the  back  versus  (Tables V I I , of of  different perspective  c o m p a r i s o n a f f o r d e d by  a more c o m p r e h e n s i v e t y p e  either  estimates  show t h e  or over estimating  a lesser  keep i n  shows  comparison  visually,  of  he c a n  c h a r t s shown e a r l i e r  show  are  w h i c h a r e made  s h o u l d n o t be u s e d t o  plots  a  also  therefore  o f d e t a i l e d comparisons of  basis  provide  visual  and  useless,  error.  (chapter  better  precise  in particular,  p i c t u r e s which  of gross  scattergrams are  exploration d r i l l i n g  on t h e  imprecise  ore.  maps and  b a s e d on  spacing.  of  help v i s u a l i z e possible  indications  large d r i l l h o l e  or  data confirmed the presence  B o t h maps and s c a t t e r  study to  show lows  those  f o r making t h e  a method  analyst  f a i l e d to  for  of  not  Scattergrams,  higher  l e n g t h and o r i e n t a t i o n )  are  reserve estimates here.  of the  (width,  say t h a t  methods  inappropriate  of  o n l y t h i n g t h a t c a n be compared i n a v e r y  larger  but  composites  because  the  is  some a r e a s  nearest  f a i l e d t o p r e d i c t some l o w g r a d e a r e a s  way i s  This  same 10 o r 12  A l l methods m i s s e d  — the nearest  those  Therefore  d e r i v e d from t h e  the  analysis, "actual".  VIII,  IX  reserve estimates block  grades,  or  of for  The o r e  and X)  also  because  they  which  in  turn  than the  simple block-by-block  scatter  plots.  These c h a r t s  q u a n t i t a t i v e l y , w h i c h methods important ore grade ranges.  are under For global  ore  reserve  right the  estimates,  d i s t r i b u t i o n of designed  economic This  open  idea  pit.  is  large  which  waste  is  are  really  As  were l o w e r if  selectivity, individual  reserves  the  grade  evaluate  one  are  really  within of  deposit.  says:  ore  and  irrelevant  for q u a r t e r l y or  the  basis  the  ( 1 9 7 7 ) when he  percentages of  for  yearly  occurrence  can  20'  the  is  not  the  models.  only capable  case at  correct  for  and  to  of  a 60'  be  block  A l t h o u g h any correct,  method t h a t  results  block  would  be e x a c t l y  a mining this  60'  This  Buckhorn.  be e x p e c t e d  block grades  is  block  from the  in  has  higher  a  ore  predicted. is  blocks is  is  20'  tabulated  method was  block cannot  being  ESTIMATES  reserves  mining  but t h i s  Not o n l y  the  predict  provide the  totally  say  t h a n from t h e  selectivity  blocks  their  the  d i s t r i b u t i o n of  block  as  to  FOOT V S . TWENTY FOOT  suspected,  acceptable  of  long  less  to  predicted."  SIXTY  models  as  to  s u p p o r t e d by D a v i d  i n the  be  20'  used  is  any c u t o f f  numbers  "which s m a l l b l o c k s  planning  the  above  These  which are  monthly p l a n n i n g ,  7.6  important thing  block grades  calculations  general  t h e most  the  is  correct  calculated  is  on a v e r a g e .  as w a s t e ,  predicted  small block  grade d i s t r i b u t i o n c o r r e c t ,  as  ore,  actually  b u t one  In other of  generally, ore  may be  the the  but the words,  nine  if  location one  60'  contained  20'  exact p r e d i c t i o n  incorrect,  but  that  there  is  102 probably  a valid  predicted  to  expectation  realization of  orebody t h a t  will  the  ore blocks  ore  intercepts.  be  the  in generally This w i l l t h a n one  representative  of  the  An e x a m i n a t i o n a block  the  designed  the  b l o c k models  7.7  7.3,  it  s h o u l d be  comparisons  and  7.4  constrained  60'  around  of  the  having  exploration  design  that  is  b l o c k model which  is  (Appendix F)  e s t i m a t e s have  predicted grades,  d o e s show  less  but t h i s  be t a k e n t o mean t h a t  scatter also the  is 60'  used.  demonstrated  by t h e  reserves  and r a n k i n g  ore  than  did  ounces o f  above  gold  predict in  that  the  grade  ore  in sections  estimates  predicted  better  a  couple  in a l l  the  very  of  produced  every  method o f  ore  reserve  calculation  ounces o f  gold  than the  corresponding constrained  were  higher)  thousand  low 0 . 0 1  7.2,  A l t h o u g h the  cases they  categories,  that (and  two e s t i m a t e s .  predicted  a zero c u t o f f ,  higher  those  other  any more o u n c e s above  the  shown e a r l i e r  zone o u t l i n e  estimates  and  benefit  of  spacing.  plots  should not  unconstrained  to  a 60'  b l o c k model  geometry  open p i t  was  CONSTRAINED V S . UNCONSTRAINED ESTIMATES  The  ore  on  20'  actual  further  i n an  scatter  by b l o c k b a s i s ,  However,  the  the  right location  result  when c o m p a r i n g a c t u a l v e r s u s expected.  possible  exploration d r i l l  of  c l o s e by b l o c k t h a t  In e f f e c t ,  mined, with  more a c c u r a t e  on  another  be w a s t e may be o r e .  becomes one  that  that  more  were u n a b l e opt.  cutoff  unconstrained  significantly estimate.  less This  103 is  s i m p l y one m a n i f e s t a t i o n  noted  by a l m o s t There  ore  can  is  be  in  is  defined  range  they  assumptions the  and a l l  belong zero  to  to  ore  a of  gaussian  zone o u t l i n e  grades  but  w i t h i n the  a definite high,  but the  distribution d i s t r i b u t i o n of  provided a set  probability  estimate of  how t o  the  use  global  estimates that  rocks  in  that  is  defined  outline  a  of  grades  the  data,  of  are  occurs related  grades a  which single,  values  relies and  Not by an  ore  form  on  expected  t h e o r y w h i c h goes  USING CONDITIONAL PROBABILITY ESTIMATES  the  as  which  7.8  to  based  This  population of  A l l of  that  is  a l l potential  requirement.  come  it  host  ore  this  Having  contact  zone and w a s t e r o c k .  zone i s  grade,  very  conditional  ore  the  introduction,  volcanics.  between o r e  cutoff  constrain  i n the  the  been  alteration  t h a n n o r m a l l y w o u l d be  altered  the  in  geological  make-up o f  lognormal d i s t r i b u t i o n .  producing  of  outline  from near  viable  inside  change  stated  has  reserves.  b l o c k model t o  was  gold  that  ore  changes i n rock t y p e ,  the  contact  derived  or  and i d e n t i f i a b l e  of  grades  calculated  change  as  amount o f  the m a t e r i a l  that  but  chemical  composition  within this in  the  a greater  economically  type  As w i t h a l l  in  numerically of  estimate,  drawn.  the  all  rock  a measurable  differences there  no  ever  c o u l d be i m p o s e d on t h e  reserve  there  "smearing" o f  anyone who has  was  pattern that  of  into upon  imposition  which  fulfilled  conclusion  that  the  conditional  reserves  best,  the  question  is  are produced?  Of the  four  is  block  104 models, model  the  b e s t one  which  following perfect  was  at  Buckhorn  constrained  are the  steps that  hindsight,  reserves,  to use  and t h e n  by  the  is  the  the  ore  BUCKG 20'  zone  a u t h o r would use  to  redesign  the  open p i t ,  to  do d a i l y  and m o n t h l y  block  outline. now,  with  calculate  global  reconciliation  at  mine:  1)  Krige  the  exploration  s u b s e t BEXG d a t a idea  of  using  maximum p a i r 2) al 3)  and t h e  3  20'  composites  BUCKG b l o c k m o d e l  using  (try  the  out  or 4 variograms which r e f l e c t  the  various  differences).  Calculate global  geologic  reserves using  condition-  probability. Produce  increasing closest design  inverse powers  in  In t h i s  and  Both grade  the  0.020 o p t . ,  pit  design  valued  to  and  the  case,  it  0.035  one  metal  above  conditional  close  comes  the  mine  probability the  or  same  conditional  p r o b a b i l i t y at  both  0.035  cutoffs.  opt.  the  to  ID5  the  as  very  with  which  w o u l d be e i t h e r  predict as  the  estimates  mine d e s i g n  The open cutoff,  but  block  over  0.020  into  the  calculations  which  decide  whether  or not  a block  would  be m i n e d .  Just  simulation,  these  inverse one  any  choose  and t h e  used  weighted  tonnage  grades  ID3 e s t i m a t e . tonnage  and  grade,  cutoff  estimate.  distance  distance  possible  possible  like  conditional  b l o c k models  geometrically  shape  of  the  will  correct  orebody  come c l o s e  economic  to  realization  given  the  being of  the  exploration  The near ore the  data. that or  J o u r n e l and one  of  ID2)  the  will  "Depending spatial  Huijbregts  (1978)  support the  t r a d i t i o n a l estimators be  similar  on t h e  a  nugget e f f e c t  correlation),  standard  estimators  optimum,  but  one o r is  only  geostatistical  to  a  the  close  (polygonal,  "best"  estimate.  the  degree  other  of  the  enough  to  the  analysis,  can  IDI  (i.e.,  structural  approach,  idea  tell  of  three  kriging i.e.,  which  a  is  the  open  pit  (perhaps  the  closest". 4)  Assuming t h a t  using  both  the  this  ID5  is  true,  and ID3  design  b l o c k models  ID4 m o d e l s h o u l d a l s o be c a l c u l a t e d a p p r o p r i a t e economic mine o r e , 5)  cost  respective 6)  input data  t o mine w a s t e ,  Calculate reserves open p i t  Calculate  in this  (price  using  each  method  within  each  p r o b a b i l i t y block values  and  above  cutoff,  by  calculated  reserves  predicted  made,  all  discarded will  give  grades  at  adjust  for  the  and  inverse most  pit  of  reserves. the  choose  it  perfect any  After  is  matches  mining  this  to  the  using  the  dilution  in  pit  design  method  whose  the  Report  reserves these  models  u n l i k e l y that  location.  fractions  c o m p a r i s o n has  distance  predictions  exact  the  distance  closely  inverse  because  cost  within  for ore  by c o n d i t i o n a l p r o b a b i l i t y .  minable ore  gold,  with  outlines.  reserves  generated  of  case)  etc.).  conditional grade  the  of  been  should  be  any b l o c k m o d e l  individual There i s  the  as  block  no n e e d  reserve  to  estimate  because, not  be  there  any r e l i a b l e  and t h e to  although  true effect  "lower"  the  from the  leach  7)  a  On  will  measure  of  this  parameter  percentage  of  gold  recovery  basis,  reconcile total  individual  conditional  blocks) The  "new"  added t o  Any o r e  ore  and  reserves  to  Produce  (instead  reserves  monthly  1)  and  date  between p r e d i c t e d  excellent, feasibility  grade;  steps  for  the  tons  of  the  treated from  cumulatively  the mine,  instead  and  then  These would of  and g r a d e ;  error  and a c t u a l ) ;  just 2)  two.  actual  (the  difference  and 4)  new o r e ,  to not  drilling.  followed  believes  that  study  been  excellent  reserves).  cumulative  from e x p l o r a t i o n  author and  3)  s h o u l d be  headings  predicted  should  subtracted  production reports.  tons  the  it  This  s h o u l d be  be  (not  generally  found o u t s i d e  not  report remaining  They w o u l d b e :  Had t h e s e  is  daily  probability  provide  zone o u t l i n e  show f o u r m a j o r g r o u p s o f  predicted  reported  outline  Buckhorn  to  that  should  i n i t i a l ore  subtracted  blast  at  volumes  exploration ore  exploration  8)  the  outlines  enough  reconciliation.  as  later,  the  10-15,000 tons o f m a t e r i a l .  large  original  to  blast  about  provide  will  pads.  p r o d u c t i o n estimate w i t h i n the  contain  there  o f m i n i n g d i l u t i o n w i l l p r o b a b l y be  day-to-day  estimate.  1984,  be d i l u t i o n ,  that  economic  would a l s o have  before  the  production started  results  calculations been more  would  have  performed f o r  accurate.  in  been the  107  8.  All have  of  the  drill  relates  spacing.  imposed and  i n i t i a l questions  been a d e q u a t e l y  s i z e which  on  this  like  approximation  or  b e s t one true  the  kriging.  accurate  more  complex  Some o f  the  calculating  no way  of  nearest  to  knowing  beforehand  should  all  3-parameter  lognormal  polygonal  or  f a i r l y accurate  of  the  of  the  inverse the  unknown  orebody.  these  like  --  However,  probability estimate,  which  other  methods  of  be  possible,  modelling  estimation  be  started  exploration  here,  "realization"  distribution a conditional  to  at  for  various  will  a workable  grade  need  if  study  choose a block  and n o t  constructed  the  less  this  important to  b l o c k models  block calculations  s h a p e and  there  is  estimates w i l l  be  "actual".  inverse  distance  cubed model  than the  k r i g e d g r a d e e s t i m a t e when compared  definitely  better  what  actually  was  is  as  alleviate  using  without  distance  to  original  block  gave b e t t e r , was  and on t h e  may p r o v i d e  The  It  before  mining s e l e c t i v i t y  will  distributions  ore  to  data  alone  distance  answered.  asked  Ore zone o u t l i n e s ,  the  multigaussian  CONCLUSIONS  the  fifth model,  the  while  same s i z e  application  by G . F . Raymond and  but  power  o r much b e t t e r ,  applied to Careful  mined,  of  modified  (ID3)  other (ID5)  outperformed  estimates  t h e mine  ID3  ore  for  zone  to  inverse  p r o b a b i l i t y and ID5 when an  was  the both  outline  model.  conditional in  at  methods i n c l u d i n g  conditional  block  used  this  p r o b a b i l i t y as  practiced  study,  extremely  is  an  108 robust,  accurate,  indeed  these  calculating  calculations global  reporting daily applying  and u s e f u l  all  of  ore  the  And f i n a l l y ,  techniques, estimate with  the  reserves,  attained  be  used  in  mine  discussed,  ore at  reserves, all  design, at  provides  and an e q u a l l y estimate,  full  stages  of  and  for  probability.  power  of  the  provides  the  of  the  error  best combination  and t o n n a g e s ,  as w e l l  best  geostatistical  both a very necessary unbiased  i m p o r t a n t measure  By  agreement  a l t h o u g h k r i g e d b l o c k v a l u e s were n o t the  and  Buckhorn.  excellent  with conditional  application of  which  calculating  production figures  refinements  estimate mining block grades reserves.  should  and m o n t h l y  w i t h b l a s t h o l e s was  in themselves,  way o f  as  linear  associated of  tools  global  to ore  109  References  David, M. (1977): E l s e v i e r , 364 p .  Geostatistical  Ore  Reserve  David, M. (1988): Handbook o f A p p l i e d Advanced Ore R e s e r v e E s t i m a t i o n . E l s e v i e r , 216 p .  Estimation. Geostatistical  G i r o u x G . H . and S i n c l a i r , A . J . (1986): G e o s t a t i s t i c s at Equity S i l v e r Mines L t d . : G l o b a l Reserves o f the South T a i l Zone by Volume V a r i a n c e Relations. i n Ore Reserve E s t i m a t i o n , Methods, M o d e l s and R e a l i t y ; Symposium P r o c e e d i n g s . David et a l . , eds., C a n a d i a n I n s t i t u t e o f M i n i n g and M e t a l l u r g y , p p . 2 1 8 - 2 3 7 . Journel, A.G., and Huijbregts, Ch.J Geostatistics. A c a d e m i c P r e s s , 600 p .  (1978):  Mining  M u n r o e , S . C . , G o d l e w s k i , D . W . , and P l a h u t a , J . T . ( 1 9 8 8 ) : Geology and M i n e r a l i z a t i o n at the Buckhorn M i n e , Eureka County, Nevada, i n Bulk Minable Precious Metal Deposits of the Western United S t a t e s ; Symposium Proceedings. Schafer et a l . , e d s . , Geological S o c i e t y o f Nevada, p p . 273-291. P l a h u t a , J . T . (1986): Geology of the Buckhorn Mine, Eureka County, Nevada. in P r e c i o u s M e t a l M i n e r a l i z a t i o n i n Hot S p r i n g Systems, N e v a d a - C a l i f o r n i a . Tingley, J . V . , and Bonham, H . F . , e d s . , Nevada B u r e a u o f M i n e s and G e o l o g y R e p o r t 4 1 , p p . 1 0 3 - 1 0 7 . Raymond, G. (1979): M i n e r a l i z e d Orebody.  O r e R e s e r v e P r o b l e m s i n an E r r a t i c a l l y CIM B u l l e t i n , V o l . 7 2 , N o . 8 0 6 , p p . 9 0 - 9 8 .  Raymond, G . ( 1 9 8 2 ) : Geostatistical Production Using K r i g i n g i n Mount I s a ' s C o p p e r O r e b o d i e s . No. 28, p p . 1 7 - 3 9 .  Grade E s t i m a t i o n P r o c . A u s t . IMM,  Raymond, G . ( 1 9 8 4 ) : Geostatistical Application i n Tabular Style L e a d - Z i n c Ore at Pine P o i n t Canada, i n Geostatistics for Natural R e s o u r c e C h a r a c t e r i z a t i o n ; NATO A S I s e r i e s , P a r t I . G . , V e r l y et a l e d s . , D. R e i d e l P u b l i s h i n g C o . pp. 468-483. Sinclair, A . J . , (1976): A p p l i c a t i o n o f P r o b a b i l i t y Graphs i n Mineral Exploration. Association of E x p l o r a t i o n Geochemists, S p e c i a l Volume N o . 4 , 95 p .  APPENDIX A  BENCH MAPS OF RAW DATA AND OUTLINES  LEGEND:  Grade  (opt.)  +  0.000  -  0.010  •  0.010  -  0.020  EB  0.020  -  0.035  m  0.035  -  0.050  •  > 0,050  Outlines Mined  Limits  "Ore Zone" O u t l i n e ( d e r i v e d from s t a t i s t i c a l  study)  BENCH BEX 20'  6880 DATA  COMPOSITES  +  ———.  • •  ffl  •  + + + +  +  + /  • ^  +  •  ~  \  \  +  +  Q -  +  BENCH BBH  6880  DATA  BLASTHOLES  BLASTHOLES  118  120  APPENDIX B BENCH MAPS OF RESULTS (6840* and 6860' ) The f o l l o w i n g bench p l a n s a r e s o r t e d f i r s t by b l o c k m o d e l , t h e n by b e n c h and f i n a l l y by m e t h o d . F o r any b l o c k m o d e l , 2 . s e t s of 13 plates, starting with the blasthole polygon weighted e s t i m a t e and e n d i n g a t exploration conditional probability, all show results on the same b e n c h so t h a t t h e d i f f e r e n t methods e a s i l y be compared w i t h each other and to "actual" blasthole results. 4' p o l y g o n a l e s t i m a t e s a r e n o t shown. In the case o f the c o n d i t i o n a l p r o b a b i l i t y p l o t s , the c u t o f f g r a d e i s i n d i c a t e d and c o n t o u r s r e f e r to the p r o b a b i l i t y of ore b l o c k s above the c u t o f f w i t h i n the contour. C o n t o u r s a r e a t 40, 6 0 , and 80% p r o b a b i l i t i e s and are plotted on top of "actual" b l a s t h o l e k r i g e d r e s u l t s for a given block model.  LEGEND; Grade  (opt.)  +  0.000 -  0.010  •  0.010  -  0.020  E  0.020 -  0.035  0.035  0.050  Method  •  -  BHK  Blasthole  or  BH20 BH60  B l a s t h o l e Polygon W e i g h t e d (20' & 6 0 ' )  or  EX20 EX60  E x p l o r a t i o n Polygon W e i g h t e d (20' & 6 0 ' )  ID10 ID5 ID3 ID2 IDI IDO  Inverse Distance to t h e i n d i c a t e d power,  KRIG  Exploration Kriging.  CPROB  Conditional Probability.  > 0,050  Block  Models  BUCK  20' B l o c k s , outline.  no  BUCKG  20' B l o c k s , w i t h ' "ore zone" o u t l i n e .  BUCK60  60' B l o c k s , outline.  BUCK60G  60' B l o c k s , w i t h " o r e zone" o u t l i n e .  no  Kriging.  121  JEDDOE  IDEBEB^I ]DE + DEBBB^EBEB + nEB^ OEBEB^B^EBn + DEBEB^EBEBEBEB^^ JDDEBEBE ][X]ni]piiP3rororXicpi 11 iixirnrxiiriiTirTifTirnrnrn • ••EBEBEBEBE jtdtddjmtd II Immmmmmmmmm ^••••••ffln+ + JEBnnDEBEBEBEBEBDEBEBEfflEBEBEB^EBEB ]••••••+ + + IDnnnnESEBEBEHEHEBfflfflEBEBEBfflfflfflDD ]•••••+ + + innnnnnnnEBEBEHEEBEaEBEHnn + n n • E B E B E B D D a D n n n + + + +' ^•••••••••EBEBEBDnEBn + ++ + • •• • • • • • • + ++ ++++ + ^ • • • • • • • • E B n E B E B n n + + + + + ++ + • • • • • + + • • • • + + ^ • • • • • • • • E B E B E B n n + + + + + + ++ + +nnEBfflDDEBnEBnnp + ^ • • • • • • • E B E B L B E H E H D + + + + + ++ ++ ++ ++ + + + + ••EBEBEBEBEBEBDDE IDEBEBDD + + + + + + + + + + + + + +••EBEBEB EBEBB3DDE \+ + D D D n n ^ E B + + + + + + + + + + • • • •••EBEBEBEBEBEBQ + + + + + + + + + + + + + + + + + +DEBEB• • + • + •EBEBEBS3B+ + + + + + + + + + • + + + + + DEB ••••••EBEBE + + + + + + -1- + + + + + + D D E EBOnnEBEBEBE + + + + + + + + + + + + DEB EBB ••fflfflEBanf .+ + + + n n n r j E B^E ^ E S E B ^ B B B B B B B ^EBEBEBEBEBnC V + +•• EBDEB^^fflDE JDDDEB EBDDEBEBEBEBI ]••• • • • • E E ]••• • •fflEBEBEBS ^ • • • • E B E B E B EBEBEB ]DDfflfflfflE8DDDDfflnn + DfflE8Ea JDEBEBEBEBDnnEBEannnfflfflfflffl IB EB ES • • • EB EB EB EB EB EB EB EB EB EB EB EB ^••••EBEB^ + •••EBEBEB + ••EBEB^^ • + •EBEBH!Bi3 •pDEBEBBB^ iDEBEBEB^BBBB^EBDEfflEB BBBI! J  H  H  H  H  H  H  B  B  H  H  H  T+ •EBEBEB  iannfflEBEB  |  R  BBBBB1I IBBBB^fflEBEB  EBD+ + + • EBDD+ + + • •+ + + + + ,+ + + + + + + + +++ + + + + +\+ + + + + + +  HEBDEBEB  EBDEBDnffl fflnnnnnnEBDDfflEBEB + ++++++++++++++ +++++++ ++++++++++ ++++++++ ++++++++++  + + + + +/+ o _  + + + H: + + + - P\+ + ++ + + + + + + + + "+•] + + + ++ + + y "t + 1 + CD 00 CD  \  X CD LJJ  CD  o ID CD  \£ X CD 1 _l  < ZD 1— CD  <  12  mm^mi ranfflE + OB^I mo•••EHE ]DfflfflnfflfflfflDD + l SDfflS ••EBDE JEBDDDEBE maX + ••EBDDEBEB + + JDnnnfflDEEBEfflfflfflffl^ +• ++ •••+ + + ••••••••BBBBDBBBB ++ + ^ • • • • • • • • B B B n n B n n + + + + ••EBEBEBEBnnn + ^ • • • • • • • • • • • • B D + + +++++nnnnnEBD+ +++++ + ^ • • • • • • • B E B B B D [ : + + + + + + + + D + EBD + + +•••+ + + ^•••••BnnBBBffl+ + + + + + + + ++ + + ••EHEBnDEBDEHDDf • ••EBDDDEBEBDD++ + + + + + + ++++ + + + •BBBBBDDDr + D i I D D E B i D + + + + + + + + + + ++ + + • • B B B B B B + + LJ+ 1+ +nnnnn^+ + + + + '+ + + + + +nn + EBDnEBfflEBEBEH+ + ++++++++++ + + + + + + ••EBEB + + • + ••EBEB/TJ i i ++++++++++ + + + + + + B B B E + + ••EE ++++++++++ + + • • • ^ B B B B B D D n B D B E ++++•+++++ + +E5EBBBBHBBnnEEBfflDDi + + + +EBnnDEB^fflDffliiiiiii^DfflEESDD + ++DDB^^BBBBBBBBBBBBBDnB^^Dn ^•••EB^BBBBBBBBBBBBBBnnnn^Bn iDDEBil^iEBEQQ^IIIIIIII + + + + +• IDOnil^iEBfflEBEBIIiii^iiDnfflEOEB +nBEBBEBBB^BBBB^BB ]nDDBBDffl + EBBBD+ +DDB 3 D B B B D D + +••+ + D B ^ ^ B ^ ^ iPDBBnBBB^^BB^BBBEB^BB ••••EB^M^^EBEHDEBEBEBiill + DnDMD^iMiEBEBEBEa^iI + DDDiffl^iii^iifflEBE9EElEHil + + n^B^B^^ffl^EHEBEM^B +\+n^fflBBE^BBBffiDBBfflffl^BB DiEBEBIIIillEBDDDESEBilll 1+ + • • • E B B ^ B B B B ^ B B B B B B iD + D D E B E B H I I E B S Q E B i l i l l i l 3 ^ i i i i l ^ i i f f l E B f f l i i ^ + DD 3B^^^BB^^BBBDBBnnDB ^illlllESEBiEQSiii^lll IBBBBBB^DD^B^BBBBl IHBBBBffiDDffin + EH^BD + IBUBBBD + + BD + DEBD + + •+ + ;  ]•• + + + • • + + + + + + + + + + + + + + + + + + + +\+ +V BD + + + + + + + + + + + + + + + + + + + + + + + + +\+ + + + + + + + + + + + + ++++++++++ + • + + + + + + + + + ++ + + + + + + + + + + + + v  1  ++++++++++ +\+ + + + + + + + + + + ++++++ +  + + +  o CD  tT  CD CO CD  X O O  I I 1 1 1 1 CD  o  ID CD  O C\J JZ CD  123  ^BDDBB + + + + + + BBBDDBBBBBDLj;C]BBHB + + + + + +EBEBEBDDDEBDDEBEBDDDDfflDEBBBBBBBBBD+ + + + + + + BBBnnnBBDBBDnBEBBBB BBBBBC3IZlBn+ + ++ • BBDDD+ + + ++ ++ + + + + + + BBBn + nBBDBBnnnnnan + +•••••+ + + ++ ++ + + + + LZOEB + +•BBnDDDD + + ++ +•••••+ + + + + + ++ +++ + + + • • • • • • + + •fflEDDDDD + + + + + ++ +++ ••••••+ + + + ++ + + + ••••Bffl+ + •+••••+ + + ++++++ + ••••+ ++ + + ++ +++ • •••BBB + + +•••• +++++++++++++++++ ++++++ ++++++ • + + + B B + + + + ++++++++++++++++++ + + + + + + + B D + + + + +++++++++++++•++++ + + + + + • • • + + + + + + + + + + + + + + +•• + ••••••+ ++ + + + •+++++++++++++ + + + +•••••••••+ + +++ + + ++++++++++•+++ + + + +EHD+ + + + + EBD + + + + + + + + + • • • + + + + +•••••+ + + + +MBD +BBBBBD + +DEHDDI + + + + + + +DBZOD • •EEDD + ++++ ++ D S B M I I I H I I M I I I I + + IBD + ++++EEBBHHHHHHHHHHHHMD+  • ••B^B^HHBffl^H^HHHB^BB^^B+  • •BED + + HHHDCIEBBB + + (ZlBBfflBBEBHH + + + + + +HHHDDfflBffl+ + • B B B B E B B H + +++ + +HHHDnBBBBBBDnBBBBffln  + + + +••• + + Dfflffl§^fflnnDfflDDD +  + ++•••+ +E^^BBEnBBBBnn + + +++++ + + ^ H ^ B B ^ f f l B B B B D +++++++ mm ++ ++ ++ B •••EEBffii •••BBB^ + + +••Efflffl^  EnnnnnroBBBBBn ^••+ + + BDI + +DEEO + + +nnB|§^ ^••BBBBBBI ^+ +BBB^BDfZiCOD + + +DB ••+•^^••EDBEfflD +•  • • • • • • I I H E I I I I D D + + nni3Z]  •+DHBn+nnB«Bnn + + +BBBB+ + +++++•+++ + + + + + + + + + + + + + + + + ++++++++++++ + + + + + + + + + + + + + + + + ++++++++++++ + + + + + + + + + + + + + +• + + + + + + + rt^f + + + + + + ++ + + + + + + + + + o CO + + + + + + + + + + +_ co CO + + + + + + + + • • + + D D E 1+ + +! ++++++++++++••-  r  CO  X o O  UJ CD.  \^  CD ZD CD  O CM X LU  o ia i  + + +• •+++++ ••+ + + + + • •  4-4-44-4-4+ + + + + + + +4-4-4- + + +  • • + + + + + + + +DEB • + + + + + + + + + DEB EB+ + + + +•+  B3EBD+ + EBEEO +  + +  +•  44-4-4-  B E B D B B B n + ++ + + • • • SEBnnnEBEan+ + + + + B B E +  >iona  + + ++ + B E D + + t)9'89 ++ + + S E B E B n n n n a a + + • + + mmmuum + + B ++ ++ B3fflB3EBEBnnnn+ + +unummmuum • • • • • + +0ESDnnEBEBEEDD + + ^^EBEBEBEBnn + n + + + • • + + EBDEB^^ B B B D E B B ^ ^ B B B E n ++++ + + ^^^EBfflEBEBD + n n + + + • • + +EBDffl^^ B B B D B B B ^ B ^ B B B n Q 1 ++ + + + + ^ B B B B D + B + + + + + • • + + + DEES ^ ^ B B E f f l f f l B E B ^ B B B n +++ ++ B E E S E D ++•++++••+++++ ++ +++ + + aLX]++l + ++++++ • • • + + ++ + • • • • + + ++ E B Q + + + + + + + + + nwffl •••EBD ++ + + EBEBnnn^ EBEBEBDD E B B E D B B B B E D ++++++ +DD^ • •+ + + + + + + 0 9 + B ^ B B D + + + + + + +DDEBBB BBBDnfflfflEBEB B^+ 4-4-4- + + + + 4-4-4BBBnBD+ ++++++++ +•• + + m\ 4 - 4 - 4 - + + + + +~~ BBBDBLJ + +++++++ + • • • ++m • + + + ++ ++ EBDD+ + B B E • ••••••+ + + + + + + + +• fflnnnnn+ + •BDDD+ + + + + + • ••••••+ + + + + + + + + + B B B mma+++ + + + + + • • E B ^ E B D D + + + + + + + + + +" • + • + + + ++ + B3Esn^Esnnnnn + + + + + + + •••+ + + WMWffiMM mn+ + + + + 4- + EBfflEBnnnDnnn+ + + + + + + + mo+ + + + +4- 4fflfflfflnfflnfflfflDnn ++++ +•• • • • • • • • • • • E B E E B ^ w + + ++ + + 4- + B B B B B E B B [ Z O C ] + + ++ + • • • • • + C1BEBB B + + + + + + 4- + EBEBB3nnnnn+ + • • • + + + • • • • • • • B B E E B + + + + + + 4- + • • • • • + + + + + D B B + + + + EBEBEBEBEBn + + + • • • • • • • • • [ & ! E D + + + 4- + • • • • • • + + + + • + • + + + 4-DBBBBD + + + + • • • • • • • • • + + + 4++ B B B B B E D [ Z O [ Z O + + + + + + +DEBEB^EB + 4 - 4 - 4 - ++••••+ + 4 4+ ^^fflEBEBfflnnnffln ++ + + + + + + EE + + + + ^fflEEfflfflDnnnn + + + + + + + + + 4-4- +DnDfflEBEBEBIZI+ + + + +DIZOEEI+ + + + +•••• + + + +• • • • E B E H E B O + +  w + + + + + +nnnEBEBnn +  ESQ + + + + + n n m f f l ++++++++++ ++++++  +m  + + + + + + +  H0N39  0  CD m 01  ION  BU  u  o  0 7\ 00 CD  i  cr>  o +++  + + + + + +Q> + + + + + + + + + + +• + + + + +'+ + + + + + + + + + + + + + + ++++++++++++++++++++++ ++••••+++++++++++++ + + •EBEBEB + + +•••++ + + •••+ + + +DEBI + DEBEBEB + +fflEBDn+ +••• + •••+ +OI ••••^••+•1 + ^ • + •••831  • ^BnnnB^BBDBBBB^BS EBEBEBBEBEB^^fflfflD + D B B B B B B ^ ^ B ^ E B E B • BannEBDEB^^fflfflEBnn^BBBBBB^fflDDffl !EBEBEBEBEEBDn^BBBBEEB+ + +EB !•••+ +nfflffl^^^^EBDD+ + + + inffln + DDEB^^EBEBEBnn+ + + EB^^^fflEBEBEBEBnnnn^^^fflEfflnnn • liEaEBEOEBEEBfflnDEBEBiiEBffiEaDDD EB^^EHEBEBEBEBEBfflfflfflfflEfflEBDDDDDD iEBEaEBEBEBi^i^iI^EaDnDDDDD +  ^ B B B B B ^ B B ^ B B + +••••• + • B B B B E n n B B B B B D + +••••+ + + BDD+ + n n B ^ ^ B B D + n n n a B + + + EQESEBEBDDnnDEBE0fflEBEBnDlllD + + + + + B ^ B ^ B B B E B n + DBBBnBBBB+ + ++ + + • •iEBIfflESfflEBEB + DEBEBEBEBiiiiD + DESfflEBD •EB^^i^^^^MIIIIIHIIIiDEBQSDD  ^ +  ffl||j|3|aE^BBBB|lB^  CZl L_l EB EB EB EB EZ1 EH H HoSHHHHHHHHHHLxIfflfflLxl  ••^BBBS++™5BB"B555553EBB^ + +++ + • B ^ + + + + +^B^DD + + + + +•••+ + + + + + + + •  •EBEB  + +••••EBEBnn + + + + +++ +++ + + ++ + +  • • • + + + + • • • • • • + • • + + + + + + + + + + + + + + + + +• • • + + + + • • • • • • • + • + + + + +. + + + + + + + + + + + • • •  • • + ++++ • • + ++++++++++++++++ • • • + + D B B B • • + ++++ • • + +++++++++ +++++++DBD+ +DEBBBB • ++ • • • + + + • • + + + + + + + + + + + + + + • • • • • • • • • • • • •  + + + + +•••••• + ••+ + + + + + + + + + ••••+ + +DEBDEBnnn + + + + + •EBEHEBDD ++•••+ + + + + + + +••••+"+ +•••••••  + + + + + + D B B n n n a n n n + + + + + •••••EBEHD + +•••••• + • + + + + + + E B n n n n n n + + + + + + + •••••EHEan + + • • E a n n + + + + • + + + + ••••EBEBEB •••••••BBnnnnnnBBB +++++ + • • + + •EBnnEBBEBBB B B B B B Q D ^ ^ Q D B n n O B B B + ++ + + + • • B B B B B B B B B B B B a n n n B n n n n n D D B B B n + +++ + ma B^EBnnnnEBEBEgfflfflnnfflEBBn + n n a + SHEBDDnfflEafflE0EBDDE^fflii^E8D +  1+ + 1+ !+  S3T  • EBBB • • B B M B ^ E n B E B B B B D n a B B ^ B •••••BfflBBnnEEBEBnnnaEBffl +nDn+DBEEnnDnDBBBDnDBEB + +++ + • B B B E D B B D n B E D D D B B B B +• ++ +•EBBDDnnDDBBDDnDnnn • ++ DDEBffiffln + D E 8 E D D D D n + +  BBBBEBBBBDDn BEBBBBEDDDaDD B E E n n n D D + +++ +  • • • • • • • • • + • • • • • • • + + ++ • • •+ •• •• •• •• •••^• •0 ++ ++ ++ ++ ++ + •••••••+ +• + ••••+ + + ++ + • ••EDBD+ + +••••+ + + + ++++ D+ n+ D• •D •n n• n• n• B• D• D• +• ++ ++ ++ ++ •••••••••••••+ + + + + + + + + + + + + • • + + • • • • + + • BDBffln+ +DBD+ ++++++++ + + + + + + + • • + + + + + • • + ++ • BBD+ + •••+ + + + •••+++++++++++ + + ++ ++ ++++ ++ +• +• +• +++•••••++++++• •• •• •• ++++++++++++++ + + + + + • + • • • • • • • • + + • • • ++++++++++++++ + +DBEBnnnD+ +BBBD ++++++++•••+++ + • • • ^ • ^ 4 - + •+ + B^BD + + ++++ + n B B n E E n n n ^ » B H H ^ + n n n B B B D n ++++++ a E e E H I | | | | | | | | | | E B D D D D D Q D  + + +••EBBHHHHHHHHHHHHHEDBBBEBD + DDBBBBB •••BUBBB •BBBBBH ••BBBBB ^•EBEBfflD + DfflfflEBBffliEII •••••+ EBDDfflEBEBfflDnDDDfflfflii + ++ ++++DB BBDED +• B B B B E D D D + E B B D + +• • • • + + [  + • • • • • + •£38 + • • • • • • • 3 1  •••••EBBBBBBBBBEBBB&  •••BBB^^BBnEBBBBBBBi •••BBB^^BBnnnBBEBE  + + +DDEBfflEBiliEBEBnD + DEBEBi • + + + D B f f i i i i I E B E B D D + DEBDE • • + •31 • ••EflBfflfflBHiBIM BDBfflEBHraDfflDBB  EDDBEi EDI ^BBBBDnBDMB^D fflfflBBD + D D E i l ^ B B + • • E D + • • • + + • •EE ++BBEQD  i^^Bnnn+ +• • • + + + B B B B n n n + + + + + + + + ++ + +•+ + • • • • • + + ++ + +++++•• + + + + ++ + + + + + + + +  ++  CD 00 CD  o L±J  OD  o ID OD  Q i—i  12  •EB^HB^BBEBBEEB BEE • •BB^B^BDBEBBBBIZOnBBB^ B B B ^ B B •••EDBBBBBDnBEBEDnDDBBB BBB^BBBBB ••••••BBfflnnnnnnBDnnnBBB BBBBBBBBEnnn + + • + +nBEfflnnDDDnEfflnnnBBBB E E E E B E B B D C O C O • • + + + nfflEBESDDDDDDEBnnDDDnnD BEEnnDnn+ ++• + • + Dnnsfflffln + DEBnDDnnn + + • + • • • • • • • • • • • + +++ + • • • • • • • • • • • • • • • • • + ++++ • • • • • • • • • • • + ++++ + • • • • • • • + + • • • • • + +++++++• • • • • • • • • • • + +++ +  • • • B C O D + + +• • • • + + ++ ++ ++ + + •+ • • • • • • • • + ++ +  •••••••••••••+ ++ ++ + ++ ++ + + ++••••••••• + • • • B E n + D E B B + + ++++++++++++++ + • • + + • • • • • • B E D + + • • • + + + + ++ + + ++ ++ ++ + + • • • • + • • • • •  • ••+ + + + + + + + + + + + + + + + + +••••••••+ +••• • + +++++++++++ ++++++• +• • •+ • • • • + + • • • + + + + + + + + + + + + + + + + DDfflEEDDDD + nEBESDD + + + + + + + +•••+ + + + n E B B B B n + D + D B i O D + + + + + + + QEBfflfflEBEBDDEBIlllliTDDDDDfflDn ++++ +DDEeEE^Hilllll||||ESDDDDQDG + + +• •B E E • • • • • • • • • • • • • S I D E B E E• •  +DDBBBBB^HBHBHHHHHHHH^BBBB^HB • ••EBEEfflEBffliiii^liiiilii^i^i^^D •EBEEBHHHHH^HHBHHH^^^^^^^^^ ••••EBiiliiiEBEBESiiEBEBEBEBEBil^^ii ••••BBHHBBDEEBBDBBBBBB^^B + ++ + B ^ B B B ^ n D E E B B n n E B B B ^ ^ ^ + ++ ^ ^ D B D +•BBBBBDBDnBBBB + +DBDIZI+ + • B B B B B B B B B B B B E  +•••••+nn^BBBBBBBBBB^^ + DDDDDDnEBffifflEBffiffimffiEBEBfflIS • •••BBBBBBBBBBBBBBBHI1B • • • B B B B B B B B B B B B B B E ^ ^ B  •••BBB^^BBBDnBBBB^HBB^ •+DDDBB^^^BBEnnEBBi • ++ +BB^^^^^BBnnDBBBi • •••ffliilili^DDDEBfflEBEBEBiS "~ ^ • • • • S M D E B E B E S i E B D S  •ES^ifflDDEBEBil^EB BBBBBBDnB^H^fflB ^ B n D E E D + n n B + +BDBBEnBBEBDD fflfflDDD +•••+ + + + • +•••••EH EBDDD B B B B n n n + +++++++++ + + • + • • • • • • • + ••••+++++++++++++++++•++••+++++ ++++++++++++++++++++++++•+++++ + + + + + + + + + + + + + + + + + + + + + + £EKP + + + + + + ++++++++++++ Q CD + + + + + + + + + + +, CD 00 CD  x CD  o  1I 1 11 1 CD  O ZD  c\J Q  CD  1  —  1  128  • BBB^^BBBS ••BB^BBBBBEBBBBBBDnEBB^ •••BBBBEBBDnEBBBnanaBBB • •••••EBSEafflnnDDfflfflDDnnfflEBBB  B B B ^ B B BBBBEBEBB  B B E B B B B B D n n n  ••••••fflfflfflDDDDDDEfflnnnnnffln E B B B B B B E n n n n n  • • • + +DBBBDnnnnDnnnnnnnnn BBBDDBDnnnnnD •+nnnBBBnnnBDnnnDnnDD+•••••••••••+•••• • • • • • • • • • • • • • • • • + + ++ +• • • • • • • • • • • • • • • + + • • • • • • • + + • • • • • • + ++ + + + • • • • • • • • • • • • • • + + • • • • • • • + ++ • • • • + ++ + + ++ + ++ • + • • • • • • • • • + + • • • • • • • • • • • • • + + ++ ++ +++ + + ++ • • • • • • • • • • • • • • • • • • • • • • + + + ++ + + + + ++ ++ ++ • • • • + • • • • • • • • • • • • • • + +++++++++++++ + + • • • • • • • • • • • • • • + ++++++++++++++++ + • + • • • • • + + • • • • • + + + + + + + + + + + + + + + + • • +• • +• • • • • + + • • • + +++++++++++++++ E E B E B n n n + • • • • • + + + + + + + + • • • + + + + D E a i E B i f f l D D D + DEQE9DD  ++++++ +nBBBBBBBBBB«B«Hnnnnnnnna  + ++ +DnnEBEBii^^iliiiiiii^DDDDEESD + +DDDDEE^IIIIIIIIIIII^EEEEEED +D D D B B ^ ^ H H H H H H H H H H H i •  • • E O E E E E I I I I I I I I I I I I I E  • ••EBEEIIIIIE • •••fflllllllE  •••H^iiiilDEfflBfflfflDBEfflBE^E + +++ ilill^DDffiBEfflDDDBBEIii + ++ iKliDDnfflfflBBBDfflBDEB^ + +nBDn +EDBBE  +nnnDDDDnBBBBBBBBEBE +nnnnnnnBBBBBBBBBEBE  • • • • B B B B B B E B B B E B B B B B • • • E B B E E B B B B B B B B B B ^ • • • B B B B B B B B B D B B B B i  • •  •••BBE^^^^BBBDnBBBS •••BEiiMEIfflfflDDDfflBEBE • • B B ^ ^ S ^ D E J D B B B B S  lillKi^fflDfflEBBBfflBDE  ^ i M B B E B B D D E ifflBifflEBEBDDDDI • • • E B D D D D + + D D B B B B B B D D D • • • • • +• + + + + + + • • • • • • • • • • BBBBBODD ++++++++++ + • • • • • • • • • • • • • • + + + + + + + + + + + + + + + + +• • • • • • +• + + • •+ ++++++++++++++++++ • • • • • • • + + + + + + + + + + + + + + + + + + + + + +• • p a n n e : ++  + ++++++++++++ o + + + + + + + + + + +,  CD  CD  00 CD  X CD  o  LD  tn  \^  o ZD CD  • • • •  CO  o  BU  o o  o  7^  ION  m _L  cn 00 CO  CO.  '+ + + + + + + + + + +  o +++++++++++++  + +• • • £ © • • + + + ++++++++ ++++++++ + +• • • • • • • • +  +++++++++++++++++  +CJEE  +•••••••••++ + + + + + + + + + + + + + + + - EHEBEBEH • • • • • • • • • • + + + + + + + + + + ••••SESSEBEB • •••••EEBEBD+ + + + + + • + +nnnnfflEBEBEHEHEBEH • •••EBEBE8EBEBD + + + • • • B B B D B n B B S l ^ ^ B f f i IBB + +DDnnEBEBEfflE5E5^^^^^^ESffl  ^BBBBBLCILTJ^^^BBBBBB Si^EaEBEBDDfflEB^M^ifflEBfflEBfflEB a^BBBBBBBB^^^BBDfflE ]BBfflBnfflBBBBBBBfflBDn IBBBBBBBBBBBBBBBDn 3BB^BBBBBBBBfflBBBBfflnDD+ 3^B^BBBBBBBBfflnnnnnnna+ ]^BBBBBBBBBBDDDnnnDBD+ iESfflfflEBBfflBBBBBnnnnnn^n+ + ^^BBBBBBBBBBDnniHHl+ + + "IR~lFfrJRfrlFEI[71]EBFf~lFRFFIFF-II 1MIHHIMMlM^I II Ii I IfflfflDDDD iBBBnnnnn 3BBflflBflBBBBBB^^DDDC][Z] +  • • • •  63T  • B B D n D D ^ B B B B B B B B B ^ ^ ^ B B B n n n + ++ + • •••••••BBBBBBBBBB^^BBB+ ++ ++ + + + • • • • • +••BBBBB^D+ + + +DBB+ + + + + + + + • • • • • + •••••EHEan + + + + + +++ ++ ++ + + + + • • • • • • • • • • + • + + • • • ++++++++++++++ + • • + • • • • • • • + • + + +++++++++++++++++ •+ • • • • • • • • • • • • • + +++++++++++++ + • • • • • • • • • • • • • • • • • • • • + ++++++++++++• + • • • • • • • • • • • • • • • • • • • • • • +++++++++++++ • • • • • • • • • • • • • • • • • • • • • • • • + •+ ++++++++++ • • • • • • • • • • • • • • • • • • • • • • • • • • • • • + +++ + • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • + + ++ + • • • • • • • • • • • • • • • • ••••••••••••••••••••••••fflnnnnnfflfflfflnnnnn ••••••BBBBBBD •••••••••••••••BBBDnnDDB • ••••EBBBBBBBB • • • • • • • • • • • • • • B B B D n n D D D D • •••BBBBBEBBB fflBBDnDDBBBDnDBBBEDBDnDD • •BEBBBBBB EBffinnfflBfflfflfflnnnBfflBfflfflfflBDDn BBUBBBB BBBBBBBBBBBB^BBBBBBBBBD  130  • EBEBEB •BBBEBB •BBH^HBH  B^BB EBBB EBEB^BBE  +DBE^B^BBBBEBB^  + nEBEB^^^EBEnDEBfflEBEBEBfflnDfflEflEBffl  + nDEBEBEBfflffiEBnnnEBEBEBEBnnDDfflEBEB + + nnnnEBfflfflnnnDDDEBnnnnfflEBEB  BBBBBBBBLTJDDLTJ  + + + + +nEBfflEBnnnnnDEBEBnnnEBfflEBn EBEBEfflEBEBEsnnnnnn + + + + +DEBfflfflnnnnnnDEBnnnnnnn EBEBEBfflB3nnnn+ + + + •••••fflfflDnnnnnDnnn+ + + n n D D D s a n n n n n n + + + + + • • • • • • • • • + ••••••+ + + + + •••••••••••••+ + + + + •••••••++••••••+ + + + + +••••••••••••• + + + + • • • • • • • + + + • • • • • + + + + + + + + + • • • • • • • • • • + + +• • • • • • • • • + •••••+ + + + + + + + + + + + • • • • • • • • • • + • • •EG E B D + • • • • +  + +++ +++++++ ++++ • • • +  + • • • • •  •fflnn+ + • • • + + + + + + + + + + + + + + + + •••+ + + • • • • ••••+ + + + + + + + + + + + + + + + + + • • + •••+ + + • • •  • + +++++++++++ ++++ + • • + • • •+ • • • • + +• • • + +++++++++++ + • + • • • B E D D E D + D E E D +  + + + + + + + +••+ + + + + DBBi!il!EDDD + DBBBD + + + + +•••^^••••••••••••^••••EIDD + + + DDDBBHIBBBBBBBBBBBBilBBBBBBn + ++ ++ + +DDBBBBBBBBBBBBBnnDDDBBBD • • • B E E E B ^ B B B B B B B B B B B B ^ E B ^ ^ D •  •  • B B B B E B B B ^ B B B B B B B B ^ ^ ^ ^ B EBEBEBEBOEBBBB^I  • •••  + ^BBBBBBB£  • • • • + EBBBBBDEBEBEBDnnnnnEBEBEBi + + + + •BBBBDDBBBDDDDDDBB&  + + + +DBBD+DBBBBBDDDDBE + + • • + • + + DE + + D D D D + +DE + • • • • • • • • [  + • • • EB EB EB EB EB EB EB EB EB EB EB EB EB EB EB I  DDDBBBBBBBBBBBBBBB^ • •fflEB E B E B E B EBEBDLTJEBEB EES  + ++ nBE^^BBBDnBBEi  • + +nnffl^^^fflEnn[~!EBEBEB£ •••HEfli^lii^^DDDDEBEBfflEaii  EBBB^BBBBB^B  + DBBBBBES  IBBB^BnnfflBffiBB^B^D +  lii^ilIEBESEBiEaEBffiDEBiiffl + liEB^iiiiEBiiEBDn + EBiiDD SEBEBEBEB^^ESEBEBEBDDDDDiEBDEB + ••EBffiDDEEBEBDD E3fflE^ifflfflnDDDDDDD + +BBEDn +  BB^^^^BBDDBBBBBD+ + + +nnDD BEBBEBD+ + + + + + + + + + +••• + • • • • • • + ••••+++++++++++++++++++••••++++ ••++++++++++++++++++++++++++++ + + + + + + + + + + + + + + + + + + + + + + *-f + + + + + CD + ++ ++ ++ + + ++ + + Q CO + + + + + + + + + + +_, CD CD  [ O  IE CD 1 1 1 UJ CD  CD ZD CD  LxJ CD i—<  131  • •EHEB • •EBEBEBEB • ••EHB3E5EB • ••EBEHEHEHfflEB iDDfflfflffl®ffltJ + + • ••••(••EBCJ+ y • ••£]••£ V+ _••±f + EHEBDDDDDf  + + +  oZD co  o o o CO  oCC CL  o  CM  cn  + ++ +  + + + + + • + ++++ + • • • + +++++ • • • • + + + + ++ ++DEBDD+ + + + + +n + n n f f l n c o fflnn+ + D + DEBEB3EBEB fflLBBjnnn+ + nEBEBEBEEBEBn  LT3unnn+  +DLT3EBEBB  •^••••fflEBEBEB  •••••EBEB +  [ £ • • • • • • • • • 8 3 E5DD+ + • • + • • •  + • LBffiD+ + + +nnBffl • • • + + + +DEBffl • • • + + + + +DEB • • + + + + + DEB •+++++++• ++++++++  EBEHD+ + + + + + + + + mmn+++++++  EBEBB3ESEBDD+ + + + + + + EBEHDD + + + + + + B3DEHnn+ + + + + + EBEBDEBESEBD + + + • + EBEBEBEBfflDEBEBD+ + + + + EHEBEBEBEBEBEBB3D+ + + + + E3EEEBEBEBDDffli3HEB+ + +  '•••EBEaannfflBB^ + + +  ! • • • • • • • + ++ + • ] • • • • • • + ++ + • ]DnnEBEBD+ + + +  ^••••••«ffln+ + + + ^ • • • • • • • • • + + + + + + +• ^••••••Lzroa + + + + + + +•• amn + nEBEBnnn • + DLT3LT3D  >iona  133  • • • • tSEHU  •  mn  •  _  • •gEBBJ,  + +nEBmBWEBES + n f f l ^  i l l •QOEH • m[Xlro^•c•lX][X]pI]l •EBffliMlEBD +IIDicpcnnpcocnrn EBEB + •LSfflEBEBEHEHn + + + II 1 u_t UJ nj rn rtl rtl rn m rnffl^ ffl tntljfflcu EBEBEBD • • • • • • • E B O + + + + EH • •••EBfflEB EH EBDEB EH EBEBEB EBEBEB • • • • • • • + ++++ + • • • • • • • B 3 E B E B E B E B E E B EBEBEB EBEBEB• • • • • ••••••••EBEBEBEBEBEBEBEBDD + • • • • E B E B E H a n n n n + + + + + + + + •••EBEBEHnnnnnnn + + + + + • ••••••••••••••ESQ • •  + +++• • • • • • • + +++++++ + + +++++•••••++••••++ + + + + + + + +nnEBfflnnEBnfflnnn +  •••••••••EBDfflfflDn  •••••••••EBfflEBDD  • •••••••fflEBfflEBEBD + + •••EBEBnnnB^nnn+ +  • •EBEBDD^BB+ + + + + + + + • ••••!! EB + + + + + + +++++++++++++++ +++++++++++•+++ ++++++++++++++•  + + + + + + +••••••••••• + + + + + +nnHEBB3EBEBEBnnnn + + • • • • • • E B E B E B EBEB EBD+ +  +++++++++  + nEBB3B3n + n + nEBfflB3B3D + + • •••••EBEBEB • •••EBEB EBEB  • •••EBEB  EBEBEBB3B3DD  ••••••••  + +++ + • • • • + + + DDES • • • • a s  ••••  •  • ••••EB • ••EBEfl • ••EBEB • EBEBEB  • EJ3DEBI  • •••••••'  ] + + + + +++++++++++ • fflEBSEBOn+ + + + + + + + ++++++ + • • • + + + + + + + + + + + +++++++ +++++++ ++++++++ + + + + + ++ + + + +++++++ + + ++ + +++++++ + ++ + + + ++ + O + ++ + + + CD  + + + ++ + + ++ + + + + + ++ + + +  + + ++ + + + + + + + + ++ + + + + + + + +++ + + + + CD 00 CD ZC CD  ~ZL  O  LU CO  CD ID CD  LO ro  o o  °  CD CD  en  o  134  ffluuu EffiuuuEB®  DOESE • • E S S E + •••EHEBESEH • •BE^B^ED + DEB^BBBB^^BB •••EHEEEBEBEBEH BBBBBEBBBDCJEBBBBBBBBB^ + EJDBEBBBE + + BBDDDBBBfflBrjfflBBBBBB^BBBBn • • • • • • • B D + + • ••••••BBBBBBBBBBBBEBLllZiD •••••••+ + + + + BDEB^BBB  • • S E B ^ B B M L J +^ ^ E B BBBB ++[JBBB^BB E B ^ B B B B B B ^ B B  • • • • • • • • • B B B B B B E B D n +• • • • B B B E E D I Z O + ++++ + • • • • • • • • • • B B B D D B E + + ++E n n B B B n n n n n n n + +++ + • • • • • • • • D D ECJBBIZO + + ++++• • • • • • • + +++++++ + • • • • • • • • • • E B B D D + + + + + + + + + LJLJLJEBLJ + + • • • • + + + • • • • • • • • B B B B B D + + ++ + + + + + + + n n B B D D B D B n n n + • • • B B E n n B ^ n n n + + + ++ + + + + + + + E D E B B B B B n n n • • B B D [ J ^ B B + + + + + + ++ + + + + + + n n B B B B B B n n n n + + u n n n n ^ E e + + + + + + + + + +nnDDnnBEBfflBEfflL~j+ + + + + + + + + + + + + + + + + + + +nBEBD +E+n B B B a n + + + + + + + + + + + + + • + + + + + DEBiiEBDDDDDfflEBEB + + + + + + + + + + + + + + • • ++++++++++++++• + +++ + • • • • + ++ DUES • • • • B E • • • • E B ^ • • • • a • • • • • • B D L 7 J + DEE • • • B E • • • E B B • B B B D • • • • • B E + +DDDEBEBEB + + D D B B + +D E E + UUEBEB • • B E E • • + LZBEB B E D D D B B B  EDLJEBBBB EBOEBBDIZO BBBBBDE • B^EEZD ••BBBBD EBDDDDEBEB BEBBBE  BBfZODBBBBS  ffluEBuuEBJ fflUUUUUUffluuE 3BLTJ+ + + + + + + + + + + +4- +4• fflEBDEDD+ + + + + + + + + + + + 4- 4-4+ • • • + + + + + + + + + + + + + + 4- +4+ + + + + + + + + + + + + + + + + + +4+ + + + + + + + + + + + + + + + 4- +4+ 4- + + + + + + + + + + ++•++ 4- +4+ + + + + + + + + + + + 4++++++++++ CD  T  o  ++ ++ ++ 4-+ ++ ++  + 4-4+ + + + ++ + + + ++ + + + + ++ + +4-4-4+ ++ + + + + + + +CD+ H + + + + O LO CD O CO ° CD \£ o X ZD 00. CD 00. ~ZL cr UJ o_ m H  o  o  o  o  135  ~+ + + + + + + +[ - • • • • + ++++++++++' ODEB^^^^EBDn+ + + + + + BBBBBB^BL~]DDBE + + IBB^BBBE 3 D + D-  SEBBBi  ]fflEBEB^^EBfflEfiEBESDn+ + + K+ IBBB^BBBBBDnDDB + l slBBB B E BfflffifflB • • • • • • • [ ! 3fflnnEBnnnnEHEBEHnnnn+ + 3ffiEBEHfflEHaEHnnEBnnnnnn+ +/+ • •fflfflSEBEBEBEESDDffll 3 EH E B E B B L X J C O I _ I + + • • • • [ DDEHEHEBEHfflnnn+ + + EnnEBEBEEBfflnnnnnn + n n n n D [ iB3fflfflEBnnn+ + + + + + + + + nEBEHEHfflnnnnnnnnn+ + ]••+ + + + + + + + + + + BBiiEiBBBBBBD + + + + + E B B D + + + + + + + + + + • ••BB^^BBBBBBIZl + + + + +/+ • ••+ + + + + + + + + + • • • B B B B B B ^ i l B B B + + + + +  n n n o n + + + + + + + + + + n ^ ^ e 3 E H E n n n n n ^ ^ f f l E B E H n n + + +/  [•••••+ + + + + + + +DDffi^HH^^EBnn+ + •BBBBEBBBBE }••• + + + +•+ + BBBBB^BBBBBB^BBBDDDDBBEBEBLj: E +!•••• +••••fJJ^B^BBBBBBBBBfflnnnnnnnDEBfflEBEHE JDDDDBB^^lBfflBBBBBBBBBBBB^fflEBnnnDnEHffl^ ;JBBBBBB^^BBBBBBBBBBB^BBBDDDBBBBB& /  igBBBBBBBBBBBBBL]BBD + + • • • [ lEBBBB^BBB^BBBBB^BB+ ••••£ IB^B^B^B^BBB^^^EDDBO ]aB3fflEBEBEBEBDDfflfflfflEffl^ES^^^BB^^^EBEHnnni BfflEEEBHEBEBDGEBEBEBEBEiEiii^^iiiiKIEBffll HDDnDEBDfflEBfflHiiiii IBBBBBSBS B B B B B B B E  ••••••^•n+ BBBBBEBESnDD ESIID • BBBBBDDinB  B B B B B B B B B B L I B B B B B B B ^ B B  BBBBDD^BBBBBBB^BB EB B + + Dffl^EB^ifflEBEiEBn + +nnnnBBBnnnn+ + + + +•••••••• + +++++•+++++++ +++++++++++++ ++ T T  o  \^  X CD  00 CD X CD LJJ DD  1 CD X OD  1  <X 1— CD  <  136  + +\ + +++ I - r • • + + + • + + ++ + + + + fr + + + + + +  • •••I  BDB + B B D  + + + + + +\+ DDBB+ +  EBEM^ + + + +  N  ^•^BDEBBBDBBi •^•^•^•••BDBBBBC  • • • ^ B B S I ^ B B B B D E E + "  ^••^ffl +^ ^ B B D B B B + + + BBBDfflBBBB^ • • • ^ + ^Ei^BBBBBDDBDD + B B B B B B B B B B I • HHffil! + • B B B B B B D B B B D B + BDBBBBBDBBi • • B ^ +B D D B D B D B D D B 4 X ] + HDBBDDBBE B B B D D D D B D B B B D B D + D +  + ++' B B ^ B B ^ B B B B B D B B E D D + LJ: + +/+  • • D B B B B B D B D • • • B B B E B B B + ++ I P B B B E B D + + + ++  EHiiBBBBIlBDDDB + + + + • • • • +DDBBBBUBBBDBB+ + • • • • • + + + + • • B D D B • • • • • • • • + +1 5EHEBEB+ + + + + + + + +•+ +DB^HUDBBBBB + + + + + EEIBEB + + + + + + ++ + + + B + D D ^ B B B B B B B + + + + + +/ • • • + + + + + + + ++ + • • B B B B B B B H ^ B B B + + + + + _ n n n ¥ + + + + + + + + + + + B13DBDB + + + B ^ B B B B B + + + +/ ] • • + • • + + + + + + + + • • •• • • B E 0 1 D + • + + B B B B ^ B D B + • + ++++++ + D B E D D E ^ ! • + • • + • • +•B3E5^H^HH • • • ^ • • + + + + n n n B B B B B D i • • D D B ^ B B ^ B H B H H B• • • • • B B B B B D D D B B B B B B E • • • • M ^ B B B + DBBBBi llIili^fflEBEBDDDEEHEBi ••••BBB^BBBDBDDDBBi H B B B B B B B + ++++ + • • • H B B B D B B ^ + ++ + • + / 1DBBBI I B D B B D B B D B D B B D ••EBfflDEBEB^^iiEBDDDDf B ^ B D + B B B ^ + BB^H^HH^BBBDBD|  BB+BBBBBBB DEDDDnnDEBEaEBaillE UDEBillllEiiESEDDEIIIIIIliE l D E I I I I I E I H E i E i l l l l l E D +7 ••••ElilllEDIESSEillllllllia ++ EpfJDDDDiiiliEEMEilEiiliinfflDED PEBEaEMiiiHEfflfflBDEBIIlfflnB BDilBBHHHBBBBBBDD + EBD + DD^ • • • • • • ^ B + BBBDBBD^HHMDBB •BBBBB+BiiiiiKi^n+ [^•BD+ ! ! • • • • • • • • • + + D B D i E i l § f f l + + + + + D B B ^ i D D + D+ + + + BBB + BHB + + + + EBBBED13BDBBB + +++++++•++ + + + + + + + D B n n B B n n + B++D+++++ ++++++++B+++++++ +•+++++ +++++++++++++++ r r f T + ++++++ + + + + • + ++^=H—H H- +O +++++ ++++ o CD  co CD x  CD O  LU CQ  NC  o XCD  O DJ X OD  + + + ++ + ++++++++ + + + + + +•••+ + + + + + ++ + + +•••+ + + + + + ++ + + fflEBunufflnnnnuu + ++ +  i n §• | | | j ninQ^n  ••••EDDDD ••HBBEEED+ + • • B B B B B D l Z l B ^ iBEBBB ++++ • • B B B B B E I Z l B ^ ISBBEBSi •••••• •••+nDDBnEnn BBBB••••••+ • ••+ +•BBDEBB BEBDnnnDDD+ + • •••••BBEEBBB^ + + +•••+ + + •••BEnnnnnDDBBB +++++++++ • • B B B E E D + +EEEBB +++++++++ • ••BBBBD+ + + + BEE • • • B B B B E + + + + B B B E D B B B B B B B B•+++++••• • +ffluuuuu + +•••• + + +•••• + ••••••+ •••• +++ ++ ++ + +•••+ + + + ++•BBBBBBB + + + DBBBBEBE B+ + • • • + +++ + + ••••+ + + + + + + + + + + + nnnEDDDEB + + + + + + + + + + + + + + +BBD + DBD+ + + + + + + + + + + + + + + + + BBL7J + DBL~J+ + +DBB+ + + + + + + + +••+ + + + + + + EDEBB^^ + nHB+ +BBD+ + BEB+ + + + + + + + + + + + + + + + +EHJBHHHDE1HH11+ + ^ B + + +BBD+ + + m++++••••••••• + + + + + + EELJ + + + + DBBHHHH^gBB+ ffluuuuuuuuu^ffl +B^L~J+ + + • • • • • + ++ +rjBBBEBBBBHI ^ ^ ^ • + + + +^BB + + +BBBBBBBBB^W B B B E D + + + + + +£i •EBEEBEBEBEBEBEEBiffiEBiilliii^ •••EED+ + + + + + EBEflfflfflfflfflEBEBfflnDEBiiiiiii^ H i l £ l ] B B B + + + + + H^BBEi + + + + + + + +il|fflfflQDD+ + + + + H ^+^ 1 ^ B + +••  + +1+ + + B M E f f l U U U + + + + + • ++ ++^HBEEDnnnnnnnn  + +•••• +•BBDDBBBB + •••+ + +DOB^ + +++++++ D E E + + + + + + + + EBB  EfflBDDD I^DD  Illl^QDD  •••BfflfflDQ IBDED ++ • BBB + + +DBB + DDDEiDEfflfflDD^iEBB+ + + + +BI ++ +••••••++nnnfflfflDDD + DE^^En IIIIIH^ +•••••+3 •B +++•••• • ••E^BBBB^BD[JEEED+ + B + ++ ++ ++ •• •• •• • • • • • • • • B E E + +••+ + + + ! B ^ ^ + + • • • •••••••••++ + ++ + + + + + +• + + + + ffl^DDDEEB  FFLB  • •••••••+ + + + + + • •+ +••+ + + + + ++ + + ++ + + + + ++ + + + + ++ + + + ++ +++  + + + +  + + + +  +++ + +++ + ++ + ++ ++ + + + O CD  ++ +  + + +DBBDDED ++++ ++ + + + + +••••••+ +  I O  O oo  CD CD  UJ CO  o ZD m  o CM X UJ  CD  —*  o  BU  o  o  o.  m o X cn CO  CD.  o 4-4-4- + • • • • • +  o ++++++++++ ++++++++++++++++  + + + + + + + + + + + + + + + ++  + + + +nnnnfflEHD + + + + + + + + + + + + + + + + +  + + + + + + + + + + + + + DLBEB • • + +B«BEfflfflfflD+ + + + • + + + nnnnnfflnnffin • • • + + ^ • • E B H H ^ D D + + ^E+ +n^fflfflnnEHnnnn • • • + + + +LT3EBH + n n n a n n E ^ ^ ^ f f l f f l a f f l H B 3 n E B E B ••E8D + + + E f f l H + nnnfflan + ffl^^fflffl^HH«^EB 4-4-4- 4 - B D D B B B B 4 - 4-  • + + +BHHfflEBB3EBD+ + + + + + + + + + ••••EHEHffln  • • • E B +D D D H +nfflEBnn+ ++ ^ B B B B B B B ^ B • • • E B E a n n n + + + E B n n n D + + ^ B B B B H B B E I + EB  + nEBEBEB^EBn^fflEDEBDnann^liBBBBfflD+ + +  • +4 - ^ B ^ B B ^ B B B B E B B B B B B B B ^ B B [ H 4 - + + EB + + H ^ H HI H HI H ^ H EB EB EB &B EB H H Mllll^EBEBEB' ' B D n f f l B B B B B ^ E H B E B B B B B B B B ^ ^ E B • • B B B B B ^ ^ E H E B B B B B ^ B B ^ E I B C ] - -  • •fflfflEHBB^^^EBEl^^EHEBnS^EBnnnn ••ffl^BBB^^BB^fflffln + nnn + + + •  • •Ei^EiBBB^EiBBEiEIffln + [_l4- + + + + • • ••^SBBEifflfflfflffl^Ei^EBEB + + + • • • •  + • • B E B B B B E E B E B E B B B n +• • • • • + +  + nnnEBHfflBBB^fflafflfflLT3EBLT3B3fflnnBB^+ + + + +  ++  + +nnEHESEHBBB+ + + + + +EDEBfflEBili+ + +^EB  4-4-4lii^ffllfflDDa+ + + ++ + B B B ^ ^ ^ B E D D D +  • + + + + + +nnDBBBBBBBBBB^^fflEHEEBfflfflnn^^fflE  • + + + + n y yB BJ | ^  EB HI inl E_l O E_l C D  + n EBffl^  B H H B B B B E HI Hi H H H ^ HB! H HI E  ESDDfflnDDnn++D + ffliEiilllii^iiiiE0iiiD + + + +EBBED 4- 4- 4 - D ^ 4 - D D D D ^ B B B B B B B 4 - + + +D^ffl+ + + + + + _ I + D E E 4- + +D^^4- + DIHIIIIEBDD + 4 - 4 - 4 - 4 - D 4 - 4 - 4 - 4 - 4 - 4 - + • + + + EBEBE+ + D ^ ^ + + f f l B + 4-^^BDDDD 4- 4- + + + + • • • + + +  • + + + +EBB3EB+ 4- 4 - D B D 4 - D B B D 4 - D 4 - 4 - 4 - 4 - D 4 - 4 - 4 - 4 - 4 - 4 - 4 - B E D 4-4-4- 4-Dffl^ffl4- 4- 4-nEHD4-Dfflffl4- 4-D4-4-4- + 4-4- + 4-4-4-4-4-  -t-nnnn-f  4 - n n n n E B ^ ^ ^ f f l f f l n f f l f f l f f l f f l n 4 - 4-4-4-4-4-4-4-4-4-4D D D D D B ^ ^ E E B D B E B D 4 - 4- 4-4-4-4-4-4-4-4- 4- + • • • • + • •••-t- 4 - B ^ B B D D B B B B 4 4- 4- 4- 4- 4 - B f f l f f l B D D D O D D D 4 - 4- 4 - D B B B B B B B B E D B B B B 4 - 4- 4- 4 - D B B B B D D D • • • 4 - 4 - 4- 4- 4 - D B E B B B B B B B E B E B 4 - 4- 4- + • EH EH EH EB • " • • 4-4-4-4-4-4-4- 4- 4 - B B E B B B B E ^ B B B D D D D D D D B E B D O 4-4-4-4-4-4-4- 4- T - D B B B B B B B ^ B B B D O D D D D D B B B D D 4- 4- 4 - • • 4- 4- 4- 4 - D B B B ^ E ^ ^ ^ E B D D B B D D D D D B  4- 4-nnann4-nfflEHEH^^^^EBa^^^fflEBDnB3fflnn4-nEHffl  4- 4 - D D D D B B E B E E I ^ ^ B D D ^ E B D D B D D D D B B B  4- 4-aDDDBBBfflBB^EBBDBBE^DDDBBEBBBB • DDDBBBEBfflBBEEEBBB^BDDEBBBBDB • •EEBfflEBEBffliiiEBEBEi^SfflS^DEBEBEBfflliffiffi BDDDBBBBBBEBB^^BEBBBB^BB DDDBBBBB^+ 4+ilifflEBEBIEBEBMII Bfl 1 1 1 + + 4 + + + D + DfflfflODDDD |4-4-4-4-4-4-4-4-4-4-4-DDD4-4-  I++++++D+D++DD4++ EB4-4-4-4-4-4-4-4-4-4-4-44-4-4-44-4-44- 44- 44-4-4-  8ei  139  ++ + ++ + + ++ + + ++ +  ++++++++ + + + +1 + + + + + +••••+ ++ + + +1 ++••••••+•++ + + +DI  • • • • • E f i E f l E B n E B D n n + +DI  • • ^ E 8 E B ^ E M ^ E B + +•!3 B B B B H B L J B  B B ^ B B B ^ B ^ ^ B E B l B B ^ B B B B B E ^ ^ ^ B B B B B ^ B B B B B L J E BBBBBBBLjnB^BBBBB^BBBBBBBBIZlLJLJn BBBEBBE[JLJEE^BLJBBffl^BBEBBB(ZlLJLJ[Zi ++  EEHEnnnnfflDffiBEBEBfflnDEH^^^EBfflfflfflfflEBDnnn + + EEBfflnnnEfflnnEBEB^^^fflffl^^^fflEBfflfflnnnnDn+ + + B • • • •  EBLJLJLJBBnBEBB^BBBB^BEBBLJ ++ ++• • + + + •EBELJ[ZOLJ[JEnBBB^lilBBBBBBB[J + ++ + + ++ + +  ••BBBLJBnn[jnBBEBBBBBBBBBB+  + +++++++  • { J B B B i S B + + ••EBEHEESEBEBEBEBEBEBEBEBESD+ + + + + • • • • • B E B ^ B E B + + ++ B B B D D B B B B B B E B B E B n + ++ • • • •  • • • • E E B D + + + +•••+ +BBBBEnnE^^BD + n n n D +• • • • + + + + + + + + + + + + BBfflEBnBB^^Ennnnn +• • • • +  + + ++ ++ ++ + ++ D B E B B E D E ^ ^ ^ B n n n n  +  + + + + + + + + + + + + DD + EafflDDDfflEBD + +fflfflfflDD + DD • B D + + + + + ++ • + + + 4XOLJBBLJLJLJBLJLJ + + LJBBLJ + + • • + + +•••+ + + +DnnDQDEQEBii++iE + DfflfflE+ + BEEBD+ +• + + + + + +• • • +• + +LJLJffl^BBB^BBB + + + + +[ + ++++ + EDDDDfflB^iiiiiDfflDnnBfflD+ + +i + + +OB B B B B B B B ^ B D D + +•••BOBBBB ++ B B ^ BBDn+DDDBDiiffl • EBEi " B ^ B +++BBiiffi ^ + +• ^ E B D + +illiBBBBD + B D D i l i i i l i i + + + + + + •+ + +lilEflE0EBDfflO + D D D E 9 ^ I H H I + + + + + + + ++ +BBBD[JBfflBBBBBBB^BBB^BBLJLJLJ + + +EaBDDD + DBfflBBBffiBBBiiiEBEDDD • •••+ + + fflB^i^BBBffliiiE^^DDD H H B H H H B H H B f f l n n + + H H H H H H B H H H B D S + ++++  D  ••+nnnBDB^^^BB^^^BBB^BDD  ••••BMBEE^i^iiil^iiBBfflfflB •BBB^I^BBBBBBEiiiilBBEDn •B^iii^BBBBBBBiilllBBBDnffl  + B B B ^ B B ^ B B B B B ^ B B B B B ^ B + +•  + + + D D E ^ i i i ^ f f i f f l E E E B I S I I i i I ^ i f f i + +•  + + + B§liiiiIDDDDBfflBBBiDBifflBBffln BD^iiilliliDDDDDEED+DEDBBBDDE • + + LJBBBLJBBB^BLJBBEB B + DBiBDBBiiiE++ S E E D BBBB^EDB +B ^ L J + + • • • • •BDnSfflBEfflEDDDi^n+DDiiiBii^D+DDD • BDBBDDDnD + + + • • + + + D B B B B B B B + + • • •EEELJLJLJLJ • EBDD + + ++ + + + ++ + + ++ + + + +  + + ++ ++ + ++ +rjBBEBBBBn + nn + + + ++ + + + + + + L J B B L J B B B E + + + + + + ++ + + + + + + • • • • • • • + + + + + ++ + + + + + + + + + + • • • • • + + + + + ++ + + + + + + + + ++  ++  I  o  CD  o  00 CD X CD UJ OD  CD ZD  m  LO  Q  ++ ++ • ++ • ++++++++ + + DI + + + + + •••••+ + + +DI + +•••••• + •+ + + + • ! ESEBESnDEHEBEBEBEHESnn + + • • • • ^^•••BflBBBE EBBBBBBEBnffl^^BBBB^BBfflfflEBfflEBEBDDnn fflfflfflfflffiEBEennEflE^^EBnfflE^^^EEBEfiESfflEBnnnn+ + fflEBfflnnnEBfflaEBEfflfflEBEEBE^^^^EBfflffifflnnnnn+ + EfflfflDnEBEBEBfflEBEEBEEEBEBfflEBEBESfflfflEBfflnn+ + + + + + + + • •EEBffl • • • • • • DEE LB EBEB EH EBEBEBfflEBEBfflD + + + + + + + + + • ••EHEBH3EBEBnnnnfflEBEEBEBfflEBEBEBEHSfflEBn+ + + + + + + + • ••BBBE1B + • • • E B B B E B B B B B B B B D C + + + +••• • • • B B B E E + + ••EBEBEBDEBEBEEBEBEBEBEBEBESEBD + +•••• • •••EEBEBD+ + + n n n n + nfflfflEBEHEBnnEBEBEBEBDDnDnn + •••••+ + + + + + + + + + + fflfflfflEBfflnfflffl^^^Eannnnn • • • • + + + +.+ + + + + + + +nnHEHEQnnffl^^EBEBnnnnn • + + + + + + + + + + +nnnnHDnDEEBn + DfflaEBEBnnaD • EBD+ + + + + + + •+ + D + EnnEBfflnnnEEBD + + +•• + + +••••+ + DDDnDDEBEBEBilinDEBEBDDEBEBEBn + D E B D n + + • + + •+ + +•••••• + B D f f l ^ B B B ^ B B B + n E ^ n + + + EHBBBBB + + + + + n E ^ B B B D B E B B B B B ^ B B n n D B B D + + +ffl ++DDB^^BHHHHHHHHHHHB^^BDDDD+DaBB ++ Dffl^^BfflBBBBBBBBBBBBElEBEEinEBnnnnEBn • •BIl^iiBBBBliliBBBBBBBBBBBBBISlO ++ fflfflE§lilfflBffl§8E2EMElBBBBBB^BBBB^nn + + + + DE EBEBEBEBSIIHIEOEBfflHIIIIIIIIIIEBQDT ++•• BBnnEBBBBBBBBBDBBB^BBBBBB^D[ll+ ++ • • + + +HBH^EBBEBffla + n n D B + + + DBBBBBinBBBEBBfflBB i ^ E n n + + + B B D B n + DBBEBBBBBEB • • • • + +DEB EB • •••••••EE ^ B B ^ ^ C O • • + nnnEEOB •••EBBEEffl • BBS iBBBnn • B^H + L7JBBB^ i^EBnnn + + + D B B ^ B ^ iBBLDBB • + E3BI1BBBBB ^ • • • • E B E B 1EBEBEBEBD • fflffll •••BBEB+fflDBBBBBBB B+DBBBBBBBBB^DBBBB E D E E B i f f l f f l i i l i i f f l + DEBEDD fflfflE^EIllE+DEDDD BDDDBBB^^nnnnn BBBBI • B B E B f f l n n n n a n +n n n ++ +n B B B B B B ^ n + n n •fflEBEfflDDD+ + + + + + + ++ + • B B B B ^ B ^ i n n n n • • • • • + + + + + ++ + + ++ + + n B B n E B B n n + + • + + + + + + + ++ + + ++ + + + • • • • • • • + + + + + + + + + + + + + + ++ + + + + • • • • • • + + + ++ + + + + ++ + + ++ + + o ++ + + + ++ +  o  CD  O  00 CD JZ CD ZZL 11 1 1 11 DD  CD ID CD  ro Q  + + + 4- + 44  +••  4 4- + • + ++++++ ++++•£ + + + + • • • • • • + + + + + Ol • • • • • • • • + • + + • + +1 E E E f f l L J B B E B E B B n + LJBI ^ ^ ^ ^ 11II1E0E0E9E9 ^••EEBEBEBEBfflunuu ^fflB3DnDESEBnfflEBEHfflEBEBEBffl^^^^fflEBEflEBnnDDD+ + ^fflEBDDDEBEflnEB EBEBEB^ EH EBEBEfl^ 03 EBEBEBnDnnnnn+ + + EEBfflnDEHEBfflfflEEEBEBEflEBfflEHfflEBEBEHEBfflEHnnn+ +++++ + fflnfflfflfflDDEannnnEfflfflfflEBfflfflEBfflfflfflffln+ ++ ++ + ++ +  + + + + ++ +  • ••E8EH^EHEBnnnEBEBfflEBEBEHfflEHEafflfflfflfflDD+  • •••EB^H^EBnnDEBEBEHEHfflfflfflfflLHEBEBEBfflfflnn+ + + + • • • • ••EB EBB^fflDDDDfflfflffllJEBEBEe EBEBEB EH EBEBEBEBD + • • • • • • •••EBHEBEB+ + + • • • • +•EBEBEBEBEBDB3EBfflB3fflDnnnnn • • • • • • • + 4- 4- + 4- + 4- 4 + + B B B B B Z J B B ^ B B C J L J [ J [ Z O • • • • + + + 4 4 + + 4 + 4 + 4 •fflfflBBEB EBDDH3 EBEBEB E B D Q n n n • • 4 4 4 4 4 4 4 4 4 • • • • • EH • • EH EB S O + • EB EB EB EH • • • • • • • • 4 4 + + + + n + nnnEnnEBEBnnnEBEBEB + + • • • • • • • • + +•••••+ + nnnnnEBEBEBEB^EBnEBEBnnEBEBEBnnDEflnnnnn + + n n + D n n n n n n + B 3 n f f l ^ H ^ H ^ ^ ^ B 3 + n E B ^ n + + + •EBEBEBEBEB + ++++D B ^ f f l ^ B B E B B B B B ^ D B n n n f f i B [ Z l + + D E B B B B B 4 + • • EB^^ • • • • • • • • i i EBEBDQ • • • +DDES E + + • BffliSllBilBBBBBBBBBBBBilfflBEBnnnLJBBB • • B E ^ B B B B B ^ B ^ B B B B B B B B B B B B | ^ D + +1  i^H  j  |  ^ IBV IH IB^ \"\ \ |"j |~~| | | j j j j | !II1ISE9E0E9QE91E0ES^II1I111DL1 + + + •••••BBBBEfflBBBDEDEfflE 3UUU+ + + + 4B^BBBffl[JBBBBBBfflBffl£ l^EBfflD + 3IIIE + + ^ u E B L J + uEB EBEBEB EBEBEB EBJ 3EBUUU SESfflDD • • • • • +DEBEBi • •••••EBDEBi • •••••fflEEHE • •EBEHEBEBEBEBEB1 • BEBB^I • B^B^BI 3EBUUEB + LJBBB^^! 3EBUUU + ++ LJB^^B^BBLJLJfflB^^I 3EBEBEJ • ••E^BBBBB^DDDLJBfflEBE • B B B B B ^ B E L j a E B B B+ fflLJEBBBBBB BDBBBBBLJBBBB^BBBEB iSEBIIIIi^DDfflEBDD BEBLJBBBBBEBEJEBBEBLJLI BEDB^fflBfflBEEBEfflBDDBBBB^^fflfflnntZO EBfflfflfflEHfflnnnnn + n n n + + + D E B ^ f f l E B ^ B ^ n n n n • •E B•B•B•E •L •J L+J E + J + ++ ++ ++ ++ + ++ L •J E BE EB DB E^B^BBBELDJILZJI EE JJ + + ++ + • •+ + + + + + + + + 4 4 4 4 + + • • • • • • • • + + 4- + + + + + + + + + + + + ++ + + • • • • • • • + + 4- + + + + + + + + + 4 + + + O + 4 4 4 4 4 4 4 4 CO oo CD m  o  [  CD CD  CO  CD ZD CD  CM Q  + + + ++ ++ + •53  + + BB + +•• + •+ + + + BBB + + + + • • • • • • • +•••EM  • • • • • • • • + nnnnnnEBSH  BBEBDBBBBBBBLIDBB^BB •• ^••••BE ^^EB^BBB^^BEBDD ^^BBB^BB^^BBBBDEJn iEBBBB^^^EBBDnnnnnn ^ B E E E E B B E B E B E B E B E M M B E E D n n n n ^ B B D B D E B B B E B B B E B B B B B E B B n B n n L j :  +n n  ++ + • •  BBBBDBBBBBBBBBBBBBBBBBBnnnnD+ + + + + BnBBnBBBnBBBBBBBBBBBBBBnnnn[_l + + + + + • • ••B^^BnDBBEBBBBBBEBBBBBDBD+ + + + + • ••offl^^^fflEBnnfflfflfflfflfflEfflfflfflffifflfflEBEnnn+ ++ • • • • •••^^•••••BEnEBEBBBEBEBEnDDnDnQ • • • • B B B B +  + +nDnnDDfflfflfflfflESEBEBEBEBaEBnnnnnn  •••••EBCI+ + + + + + + + + nDEBfflEeEgnESEBEBfflEHfflnnnnn  • •••+ + + + + + + + + + + + BBBBBBEBBBBBBBB[_inn  • • • + + + + + + + +nnnnnnEBEffiEBEHEBDDE5EBEBfflEBnnn • • • • + D + +DDDDDDDEBET]nE9fflDnnfflEBE9DDnDDfflE8DnD + +•••••+ + •••••££) EH EB^^^ESEBEHfflD DEB EBEHnnnDDEBEBEBD + + • • • • • • E B f f l n n n E H f f l f f l B B ^ B ^ E B L H n n D B f f l D + + ••E5EHEBEBEB + + + D n n E B ^ ^ ^ ^ ^ E a f f l E B B B B B ^ E B f f l n n n n D n n + DEBEBEBEHEB + + D B B B B B B B B ^ B B B B B B B B B B B B B n B n + nnBBB^B  +DDEEBBBBBBBBBBBBBBBB^EEEEDnDDEEE^^  ••BBBBBBBB^BBBBBBBBBBBBBBBBDnDDBBBB i B E S E B I I I K i S i l l i l l l l l l l l l l E S E O D D D E E O E B  • E0DIIIIIIE9E3SiiE0liiIiilllllEiE0SD->- +• • • • ^ B B B B D B B B B B B B B B ^ B B B B B ^ B B L 7 ] ++ + ++^ B B B B D B B B B B B B B B ^ B B B ^ B B [ J +  + + iiEIDDQEBffifflE8E8fflEBEBiiliiiEBiEaD • EBDDDDDESEBi^ii^ll^ilKI^EgfflEaD • •••••fflffl^EMIEililliiiliiEafflEB • •  • • • • • B B ^ ^ ^ ^ ^ B ^ B B B B • B B B B B ^ £ 1 ^ ^ ^ ^ £ I ^ B B B B  • •BBB^BBBBEBB^^B^BBBBB • BBB^^BBBBBEB^EIBB^BBBBB •OEBfilliiifflEfflEEBfflEil  • ••BEBElEiiiEiBBnEfflEBil  • •BB^BBBB^DCOBBBBBi  BBBffliiiiiliBfflBDEEBfflBBBBBEBfflEBB  B B B B B B B B B ^ B B B B B B B D B B B B B B B B B B  ]EBEB^BBBBBBBBBBBDD  JBBBBB^BBBBBD IBB^^^^BBBBBBBBBBBBBB^^BBBBBB-  BBBBBBBBBBn+••••+•BB^BB^BBBDBB BBBBBDDnn+ + + + + + + +••BBBBB^BBBDD  ••••••+ + + + + + + + + + + + n B n n B B B B n n n • • + • • + + ++ + ++ +++ + + +DnDBBBDD + + + +++++++++++++++++ • • • • • • • + + + + + + + + + + + + + + + + + -1-  +++ + ++ ++ + +  o  ^  Q  ^|-  00 CD X O CD  ^  CD  CD X CD  — Q i—'  143  ++ + + + + + +  + + ••••••++!  + ++ + u n u n u u u u u u E E B E  EfflnnnnfflEBnnfflfflnnnffli EBBBLJBEBEBEBBLJBEi  ^ ^ B B L J L J L J D  mmnnaana+aa ]••••+++••  BBBBnBBEBBEBEBBBEBBBEBEDnnnrj + + +••  EfflfflnnfflB3fflnnEfflEBfflEfflfflfflfflffiEBfflfflnDnnnn+ ••offl^^EfflEnnffifflEBEfflfflfflfflfflEafflnnEBEafflEBDn  ++ +• + nnn  ••••^BEBBnnnnfflnnBEBBBBBBEEBfflnnnn+a • • • • B B E B + + + E L J + •••••BBBBBEBBnnnn + + • • • • • • B B + + + + • + + nnnnnBEBBBBBnBBBnnnn  • • • • + +++++ ++ + • • • • • • B B B B B B B B D E B D n n Q • • • + + + + + •+ + + B n D B B n B B B B B B B B B B B B B n B n • • • • • • + + DDnDDDEgE0EBDfflDDnDfflEBEBDDDDDfflffiDDD + + • • • • • • + DnnEBBBE^^^^BBnEBBBBEn++nBBBB  + + nnnBBnB^DDBBfflBHH^ffiBBnnnnnBnnnnDfflBBBB + + +DDDDililiEB^E8liIiiiEBfflDDnDDDDDDfflE8EBEaffl + D D S E B I I I I I I ^ I I I I I I I I I S E 8 D D D E S D + DDE  +DDEBHHHIHHHHHHHHHHHH^BEBBEDDDDEEEB ••EBBBHHH^HHHHHHHHHHHHHHHEDDDDEBB • •• •S•E•O• E E I I I I ^BE B B iEMEl iB^B^ lEl IBI iI I I I ^ ^ E S D D D E B E Q •+ D• +• H • •H••H•••H•••H•^^BB D BEB^ B^ B f^f l^BH B BH B« i H 1 B B B B + +•  ••BBBHHHHH^HHHHHHHHHHHMHHBBDDDDBBBB  ++ +  + +HHHHDDBBBE^BBBBi  BD + • • ED  • •••••EBEM^M^S • •EEEBBEBEfflB^^ •BBBBBBEBEBEBB^ • EBE9ii§ • • B B B ^ ^ BBDnBEEB^I • • ^ ^ ^ 1553 nri rn rn Dzi CD en m  fflBBBD m m m m  E  ^BBEBBBBLJHHHHHBBLJLJB • •••••^BBBLJB • ••••iiQE8EBDD EBBBBEBEBD[JHHH^BBBBB + + BfflBEBBBfflBnnnnnnnnBBBE^BBBBBBD BLlfflEBELJ[jn + + + + ++ + + L J L J B B E ^ B B E B B B n • • • • • • • + + + + + ++ + + + +LJfflELJBBEBfflBB • • + • • + + + + + + ++ + + + + + D D D B B f f l B E + + + + • + + + + + + + + + + + + + + +LJL1EBEBB+ + +++++++++++ + + + + + ++++++++++ 0  CO  00 CD  ZC CD O  LU CD  O ZD 00  O Q  144  + + EB + EB + EB + DEB + + DEB  + + + •+ + + + +  +m^i  + + + + + + • • • • + + + +D^|  + +nnnnnEBfflnn+ + + + r  _  B3EBDnnDEBEBEBfflEBnn+ +EBHHH B B SBEEDDBBBBBBBi ^^ElBDD^BBBBS IBBBElSEBSfflrTdDD IBB^EBEBEBEBE5DDD + B B B E E B E E n B E ^ B n n E ^ ^ E B E B B D D E D H - 4- + ^fflEBfflnnfflEBnnEBEBEBEBnnEBEB^^fflEBEfiEBDDnnn + + + ^EBfflnnnEBEBnfflEBfflEBfflEBEBEBfflEEBEBfflEBnnnnnn+ + + + EBEBfflDDDfflfflEBEBEBfflEB^B3EBEBfflEBEBEBEBEBDnn+ + + + + + + fflDLBEfifflnDEBEfflfflEBEBEBESffiEBEBEBEBEBEBEBEBDn + + + + + + + + • ••BB^BDnC]EEBEBBBBEBEBEDn + + ++ ++ + + • •'•ffl^BB^nnnEBEfflEEBfflfflfflEBBEBEBfflEBDDD+ + + • • • •••EBfiiBB^nnnDfflfflsnDfflEBfflfflEBnEBEBfflEBnnn + n n n • • • • E B ^ f f l + +DnDnnnDfflfflfflfflfflDEBEBEBfflfflnnnnnn • • • • • • • + +++++++ +DfflEfflfflfflnnffl^fflfflnnnnn • • • • + + + + + + + + • + + nnnfflfflEEBnnfflffl^ffl BDnnn + • • • + + + + + + + + nnnnnEDnfflEEBfflnnEBEBfflfflnnnn • • • • + + ++++ n n n D n E E B n n E n n n E f f l E a n n n f f l f f l n n D a n ••••••••••••••EfflfflEB^^fflnan + nfflEBEBnnnnnnnnn •E BHHHBBBBBBBB+ B nfflfflffin ^ E D 4 - L _+1 BDnfflfflfflfflffl EBEB + •+ nnnnnnEBDnnDfflfflEBfi^BB^fflEBn + + + + n n E S E ^ ^ ^ f f l f f l ^ ^m BBBB B B f f i E n n E f l f f l f f l n n + nfflfflfflfflffl im BV KH m j j | ^ ~ ^ j | ^ ~11~ "j p*~| + + D E S E B E e i l l l l i l i l l l l l l H i E B Q D D D D D + DE 4- D B B ^ ^ B B B B B B B B B B B B B B B ^ ^ i l B B D n 4- D E B S mn+ + • • • + EB ++ + • maa + lEBEBcnn + + nDfflEDDnfflffl L  •BBEBBEBEBB •BEBBBEBBB • • • • • + DEE •••••••ES ••••••EBB  ^EBfflD  ••BEBBBBB  •BEEEBiEiEMEa •fflfflEHIEMEIffl  JBEDBB JfflfflDDD  + DEE  + + DEaffiiElilEliffiEBDnnEBEBi • ••EBiiiiiiEHDDDDDEBfflEB IEBDD • + DSEBEHfflDEBfflDESEBfflfflEBEBO 3BBBBBBI B C B B B B B B B B B B B n B B B Q IfflDIiKIEBnnnEBDD EaEBDillEMEBDDnDn EBEBEHEBEBEBDDDDDDDEBEBD + nDEBEHEBIiMn+ +•  • ••EBDD+ ••••+ + + +++ + + ++ + + + + + + + nnnrjB^^DLl+ + + + + + + + + DnnnEBBn+ + + • •+ + + + + + + + +++++++++ +++++++++ 4- 4o + + + + + + + + 4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4o  + + + + + + + + + + ••BDD + + + + + + + -4- + + CD 4- 4-  [  oo  o  LD  CD X CD  m  ^1  CD X OD  LU CD —< OD  ffluufflut fflnn--  CPROB  •  EBuOOfr + + + • • • • + + • + • • H - + + 4- + y H + + 4-nn+\  4[  + +  +••••+ • •EB  EBD • •+ + • + +++ +  •••••+• •••••••• • •r_\fflEB £•••••+ + +  ••[•suSEBEsnnnn + ++ +  'EfflfflEEn3tennnann + + + fflfflfflfflDLTT ]•+ + + + • ••+ + + ++ • •••+ + ++ +++ +•••••++ • • • • + + +A+ + • • • •  • • • •  + , +•••••• •••••• "•• + + + ++++ +++++ +++ ++++ •••I •  + +••+ + + • + ++••+ +++ + +• • + + +••+ ++++ • • + + • + + • • • • + + + +DLJLJB + + • • • • • • • • + + + +LJLJEB + + • • • • • • • • + ++ ••BBj§fflnnn • • + •••••+ +DDD + ufflfflffllfflEBuuuu  E s n n n n n D n + DETjSnnEBEBEEBEESEBnnnna ^BBnnnBEnnnaeafflBEBBnBBnDnnnfflEB  3 E E E f f l B E B B n n n B B B B n n n n n n + DEDEHBB  3BBBBBBBnnnnnBB^^Bnnnnn+ + DBE 3EBEEBnnnnnnfflB^^Bnnnann  ]BBBnnBnDBBBBnnDnDDE 3BLJLJBBBB^S1BLJ + B a D B B B B ^ B D + LJLJB  iBBDBBBEBBBDnnn 3nnBBBBnnBBnnBB  3 BBDEBEBB+ + LJBEB 3 B B B B B B B D + + LJLJB •3LJ + + DLJE 1+ + + • |+ + + + + IBL7J+ + + + + IBBLJ + + + + + + +++ + ,  |+ + + + + • I+ +++ + I+ + ++ + !•+ + + + •  3LTJ+ + + + •  1 + ++ +  IEBBBBBBESBBBn+ + +  5BBBBBBDDBBBn+ + + ^BEflBfflEBnDEBBnn + + •  ••+ + • • +• • • • • • • B • • • • • +• +  IELJ + + + + + 3U+ + + + +  IBLJ + + + + + !•+ + + + 1DO++++  I +DBBE + 3D + D ^ ! l t l + 3LJ + B E B D  ]•••& 3C1ELJB  BBBBEBBBBB  + +••+ + + • + + +••+ + + + + + ••+ + +••+ + + + + • • + + • + + ••••+ + + + •••EH  ++ • • • • • • • • + ++  oso°o  +nnmmma  + + • • • • • • • • + + +BBBBHEEEE • • + •••••+ + • • • + •EHEBEB^EBEHnnnn • • • • • • • • + ••EBDDffl EES EBEEEE3 ! £ • • • • • ^BBEEBEBEEDDBBBBEBBBBEBnEBEBB B^BBEBBBBEEDDBEEE••••••+•••BEE!  +  ++++++++  + +EEEE+ + + + + + + + BE + EBBEE+ + + + + + + E B B B B B B B n n D E E B B ^ ^ B n n n n n + +DBBI • • • • • E E B E B E E D E + + + 01z89 • EBEBEBEBEBEBDDDDDDEBEBililEBaDDnDDt BDE§|!P§|BBE^] + + + BBBBBEEEnDBBBBBBBEBBBEB + ++ EBEBDDEBEBfflEBWEan + DDDEa + ++ EBDDEBEBEBEBMEaD + D D E a BE + + + BBEBBBBBBBBEEEB ++ EEBBBBEBEBBBBBB I f f ! EBE+ BDE+ + E B B D D B B B E + +DBBB __••+ + + • + +EDB BEBI mn++++ ffluul • + +UUEB BE+ BEEEEE E+ + ::io9i ++• BBBEBEBBEEEE+ + + + + + + • • • • • B B ++ +++ BBBBE+ + + + + + + B E + + + + +E BBBBB+ + + + + + + + BE + + + + + + BBBEBBBE+ + + + + + + • +++ •++++++ BBBBBBBEBLJ+ + + BE + + + + + .•+ + ++ •+++++ EBD+ + + + + • + •++++++ E+ • •+ + + + BE + + + + BEEEBB +EBBE+ BBBBBBBBBBBE+ + + BEEEED B E + E^i^[l + B E E B B B E + + +E BBEEEBEE BE+BBBE B E B E B B E • E B B E D + + EBB •EB • • • • 0 • •+ + E B B B ^ B B B E •BBBB •E+EEBBBBBED BBEBBBEBEn ••••EBBBBBEE BDEBBBQBB •••EEBBB •••••E +E+  aoddo  >jona H0N33  0  14  -o CD CO CD  zn CD  1I1 L_U CQ  ZC OD CD  ^  CD ZD CD  1  _l  < ZD 1— CD <  nwmmmwmm  •B^B^BBB+ + B B B B E B B L 7 J + E!] B B B B B E B D E ^ D  +mmmmmmaamm mwmamm •EB  + amm + DDEB  0  60  ••El^BBEBDB + + HBBBBBEE!] BBBBDB^I + DEBI + +H5  BENCH  686Q  BUCKG BH20  am •+ ••  + +BBBBD ++ + E B U U S U H ++ ++ + + +  • • • ^  •  • • • • • • + BED + E B E D  -+ + • • • • • • +•••••••• •••••••••fflffl  •EBDE  Bfflnnnnnnfflffl^^ • • • • • • • E B B B  • ++ • ++  •BL7JB^BBC] + + • ••EBEBEBEBEBBEB+ + + •EBEB+ + B B B B B ^ + + + B+DBEBBBB+ + ^^••fflEBEB^BBD + •E8^QffliiHIEB + H i + S I I I I I l i H B + D B B B B B B B D EBL7J + EB^EB + B B B B B B B ^ Q + IDffll • E l [ ! • • • • • BEBDn • B B B B B B B B B D + B B B B B B B B B D EBD + n n ^ B B E B E H n • • +• • • • 0 3 + + + + nfflEBnn+ + • EBnnfflEBfflDEBffl  aaaaama + amm  man  EBDnnnnfflD + n  •••EBEBD+ + • • B + ++ ••EBE8E8EBEBEBi EBEBDEBEfiEBHEBEOi EBEBnOEBEBSfflii EBDIIOBBI •BDBBEBB BEDBBBBB BEEEM •EBB  • ffl  • • •  B E E  + aamma + aaai  • + DE0EBEQDE3DDE BEDDB+DDBBf • • • • + EE + B E D + DE • +D+ DEE • • • B E E  •J  15  HBEBBBBB I BBEBBBEBBBBEEBHH + +BBBEEBBEBBEBDEBHB +EEBEEEBEEBBEEEEBE +BBBEEEBBEBBEEEBBBB BBBBBEEBEE +BBBE+EEBEEBEEEEBBB EBBEEE+ + + +••••• + + • • • E B B + DEBfflDDDDD + •fflffluuuuu + +•••••• + + • • • • • • +•••••• + n n n n B B + •+••••+ + •••••• • ••••• ••••BBB •• + • • •• BEBEBEB BBBEE+ + + + +• EE +• • • • • • • BB +E E E • • • • • • + • +B B E + + + + + B B B E • • +••••+ + E E• • •+ + + + + ^ B B ++ +BBBBBE + EEBDED + + + BEE • • + +nnBnn + + +EBBHHHHI + +QE0EBEBIIIIII1 •+BBBEE+ • ••EfliEBEBQIIIilll • ••Efl^iffliiliEBill + EEB^BEEHHHBBfl^ BE + +E B B + + •••••EQ + +E B B +•••EEB EE B B B B B E • ••••EB BEE E B E E E + E E E + +E EE B B a n n + E E + +E ++ +^ BBBBBE + +1 EBBBBBBBE + + +ffl^ • EHEHEBitlB E E E E E E E B B B B B O ••EBEHEBili ^ E E E + E E E B B ^ ^ ^ Q ••EBEBEflHi ^••+ + +BBBBBBBB + D D E a i i l i if l E + + + B B B i S B H B B B + + • B H H H H l i^••EBEEBEBEBESiBEBEBEB + + +B ^ H H H H H ^+ +E8EBEBIiEBDDDDD ••BEBBBE E+E + E ^^ ^ ^ • • • • • • IEE EE + + Bfl^E EE + + dfl^B + BHBB + EBBBfHEB +B B+ + E+ + O CD  O CD  00  CD X CD  o  CQ  CD \^ CD ZD CQ  O C\J X LU  • ••^BBBBBBBBEBBBB  BSBBBnDBBBBBEEBBBHB  EfflEEannnfflnnnEHnnnDESEB  •BEBEEEBBE^^EEBBBBE +EBBBEEEBBEBBEEEBBBB EEEEEEEEBBBEEEEEE •EEEEEEE BBBEEEEE • EEEEBBE EEEBBBB •••••• • •••  BEEEEEBE HIIBEEEBB ^EEEEEEE EEEEEEE  • ••••EB  • ••  • •••• ••••••••• BEEDDDBEEED EE •EllQD +D+ +^mD ffluuuuu ••••••+ + + + + t l ^ B E BEBEEE^HBB^EEHBfil + +EBB^tlBQ ^••••••••••••++•••••+ •+BBBED+ BEEB^BBB • ••EBSl^Eai l^flBBfl^^E + • EBBBBfl ++ B E B B B + +DEBSE3ffliEBEBii + EEBBB+ +nBEBBBBBH EEBBB^HBEn+ +BBBE • B B + + n B B ^ B B E + +EEE + • •+ + + B B B B B B E B B B B B + B+ EBB •  BBBBtBBBBBEi BBBBBS • ••BBfli  ID  •EEBEBBBBE ID • ••+ ID EE+ + +EE BE+ +EEE • •EBEBEB^EB^B E+EBB^^EEE B + O B B ^ B E f l• • • ^••••••+ +EB • • • !&••• + • IBEEE  O CD  [ O  ++ ++ + • ++ O CD 00 CD X O LU CQ  O  o  X CQ  BBB^EBEBDEBEHEBEBEB EBEB^EB BBBEB^EBDDEBEBfflfflEBniZOESEBBB E EBfflfflfflEBDDEBEBEBEBEBDnnEBEBflEB EHEBEBEBnnnnnnDEHDDDnEBEB •fflEHEHDnnEBnn^^DnEBfflfflfflEe + DEBEBEBEBnnnnnEeESDDEBEBEBfflEB EBEBEHDDEBfflffl •••EBDnnnESfflfflDnnnnn ^EHEBEBCDEHEB • EEEBEBUUUUU SfflUUUUEEEB • • • • • • • • • • • • • • • EBDDDDfflEB • ••EBDESEB •••••• EBDnDDEB ••••••• •••• • • • EBEBEBEBEHD  • ••••  • EBEB •  • • • • • • • • • EBnnnnnnnnDn • • ffl^nnDD + DEB^EBD fflffltJLJDEB E B D D B B B + + • + + fl^EBEJ E B E B f f l E B D E B B B ^ B ^ E S B B ^ + + DEBEBEB^EB[J EBEBEBEBEBBBBBBBBBBBBBBDnDnEBEJEO EESEaEBEBEBBBBBBBBBBBBBBnDEBEBtBEBDn EBESDESEBESESESBBBBBBBBBBBBBEBEBESEB^BB^ E3DLJEB^iEBE3llBBB^EBB^BBBB^EB^^EB + EBDEBEHEHflBBBB^ilBBBBBB^fl^fl^EBEJ • ^BBB^EBfflEBfflD + EBEBEBEBEBtlEB^BB • B B B f f l D f f l E f f l n + rjEBEBEBEBf^EB^B • ••••EBEafflEBEaDDnnnEBEBEBEB • • • • + D E B E ^ f l E S n n + + EJDEB + • • + + •EHEBEBEHEBnDEBEHfflEBEBD • + + EBBEH! ESEJEBEB^fll 3EBfflG[ZlEBEBEBEBESEBEBJl^n ••fflE33ffl^^^nnnnEE • • E B E B E B ^ ^ f f l n D + DEBLJl • ••EB^^EBEBLJ+ + • • • & ^BBBBfl^DDEBEBEBEHEBEBilBEBtEi^ IDDfflfflEBfl^EBDfflLJEJES I D + LJEHEB^EBEBBEBEBEB IfflDBBf^fflDLJEJEBfl^EJ I B B ^ B B ^ B B ^ B B E I L J E J E J + BEI^EJ I^^EBLJLJEB^BB^EB EHEBEHEBLZ! + EBEQBBB ESEBEBEJLJEJ EB^ • • •  I  O & —  ^  O CD 00 (D CD CO  CD \^  o ZD CD  154  ^•^B^BOBBBBBBDaBB^  B B E ^ E B  B E B B B D D E B B B B D D B B B B B E E D D D D D D B E D D B B B E B D D D B D D B B D D B  •BfflfflfflEBnnnnnfflEHnnffl  •••BBBnDDBEDDDDDD  • • • • • • • • • • • • • • • •  B B B D D D D D • • • • • • •  • •DEEDED DDDDDD BDDDDDD DDDD BBEBBD DBB D BBBDBE BDDBElEBi  BBBBDDBB BDDDBBB EDDDDB DDD • DDDD •••••••• DDDDDDDDD ^BDDDDDBBBB + D + Dfl^BD 3D IlD + DDEBBEBD IBDDDBEDD IBDEBBBDD  IBBBEEDEBEB^^HI  ^•••^•BEBD + DBEEBE^H • ••EBDDfflfflEaEBDDDDDEBfflii BDBD+DBBBBBDDD+BBBD DD+ + DBEBBBBBBBBBBB • ••B^B^BBMBBBBB^ EDDESI BBDBBBBBBBBi DBBBB1 BBDDDBBBB1 DDBBBi EBEBDD + D E B E H I i i l i l fflfflDD + D E B G i i l l i i ^•••EaEBEafflEBiiEBK  •  •••••••^BDBBBg • ••BEE ^•••EE ^••EDDBDI 111  • •••  • •  • • • EBDD  CD CD  o  CD CO CD DZ CD  CD  LD CD  CD  ^1  CD ZD CQ  ro CD 1—1  155  ^^B^BEBBBBBBBDBB^H BBB^BB BEBBBEnDBBEBBEBEB^B B B ^ B E E B E BBBBDnnnDDBBnBBBBB B B B B B B E B B B fflEBfflEBnnnnnDfflfflnnfflfflfflfflE B E B B B B B B E B B E B B B B B E  •fflfflfflEBsnnnnofflfflnnfflfflfflfflE  •••BBBEnEBEnnnnnD B B E B C O B • • • • • E C O •EBEBDDDDD B B B E E B E •••••••• ••••••• EBDDBEB •••BDBD •••••• EDDEEB ••••••• •••• ••• BBBBEE BBBB ••••• • B E ' BBBBnnnnn • •BDBDDDDEBB B B B B B D B ^  B B  • ^ ^ B B B D D B B B B B  ••BHB^nnn+nB^En  EBEE^HHHHHHHHHHHHHBDBDBE ]E0EBEBSIIIIIIIIIIIIIiDESE8E0E8E0EB ^ ^ • • • • • • • • • • • • • ^ B B E B B H B  EBEBDEBEE!EBmill[iilEilllllEi^m[i[l!iD (••••BEBEDnBEBEB^^B (••iDDEBEBEEBDnnnEBEBMi ^EBD+DBBBBBDnnDBBBB BB++DBBBBBBBBBBBBB • •••^BEBEBEBBBB^ • ••BEBBBB^EEBE^ BEEEE^BEnnDBBEBS • BBB^fl^BBBEBBBB^I 3BB^^^^^BBDDBBBE^I ^•••HBEBEEBiElfflii l^fflDfflfflEBWEBDElfflfflE ^•••••••^BDBBEEEE^H^^^ • ^B  BBBBEE EBBBDD BDE CD CD  O CD  00 CD  [  X O  O  LD OD  CD ^ O OD  C\J Q  15  Hfl^ilBBBfflBBBBBBBBBil^ BBBBBBLJBBBBBBBBBfflB fflfflEBEB EBDnDDEB B3 EBEBEB EBEBEB EBfflEBfflsnnannEBEBnB3  EBBBBBBBLJBBEBLJBEE •••fflfflfflfflnnnnffinDDDEB •••••BED • • • B B B L J B • • • • • • • • •••••fflUU • • • • • • • • • • • • • • • • • • • • • • • • ••BBBB • BED  • •• •  BBBBBE • BED EDDBB  •  E B B B B D B  BEBffiBLJfflBE ^BBBBBBBBBB flBBBBBBBBB •BBBBEBBBB •^•••BBBB Mf,  EBBS  • ••BBBBE ^••BBEBBBE B^BLJBBBBBBBBBBfflBi BBBBBBBBEBBBE ••••BEBBBBBEE ••EBBBBEBBBE 3BEBBB 3BBBDB  mmm  liEBDEBffl  BBBS1B  IfflfflDDD  r  NEBBED BBBBLJB EBB  o  o CO  00  CO  o LlJ CQ  o  ZD CQ  • ••••  • • • • • • • • •  • • • • • • • • a  mmi  EB^E  • ••••••EEEEEEI^ ••••••EEEBE^BI ••••EEHBBBEBI ••BBEEBBBEBE ••EBBBBE^ mm • • • • • B IE H B H H B I IE H E mm ••••••••EB •••••••••BE BEBEn^BBBBBBB^B^E 1 3 ••••••BEEBB ••BBBaDBBBB EBEBEBEBDnDDDI •BBBBnnEBB •••BDDBBB EBEBEBnnnnnffli ••••BBBB BBnBBBBBBnnBnB^BBBBBB ••BEEBB IBBBBBBB BEBBBBBBBBBBBBBnni  IBBBBBB!  60'  0  BENCH  6860  :UCKG IDO  iiEBEEBDnEGEanffl BBBBBElBBBBnnnnnDD IBBBnBBBBBB BEBBBBBBEB ItlBBBBnnBEB lEBEBEBEBnaffl ^BEBBD BEE  ••  •EEEBBBBBBBI EEEEEEEEEE^ B B B B B B E B B B  B B D E E • • B B B E E D D E E E E E E E D E  •BBBB I I  BEDDnnnBEBB^^El  •••••  BBBBBBB DEI  mmmmmmnum\ ^ ^ E E E B E E B E B B B E B B ^ ^ E I E E E E E B E B B E B B E E B B  60  BENCH  6860  BUCKG KRIGE  ^ E B E E E D B B E B E B B E E B B B B B B B B ^BBBBDnDBBBBBBEEDBBBBBBBB B B B B B B B B B B E B B B B D B ^ B B B B B B B IBED BElElBBBnn BBBBBBBEBBB^BBnEBtl ^BDBBEEEE BBBBBEBBBBB^BBDEBB 3BBBBBHOBB BBEBfflnnnnn E E B E E D E E wmmmmmi EBEBEBEBEBEBEBDD H ^ E E B B B B I I I B^BEQEBEIBEM ElBBBBBBnn  ED BED BEE • •  •••••EEBBBBBB ••••BEBBBBBB • ••BEBIZOB BDDEEBE •••BEnDDDBB ••BBDEDDBBE ••BnnnnnBBB • • • • • • B B B B • • • • B E E B B • • • • • • • E B • • • • • • E B • • • B B B H  ^••EiEHfflEBfflEBfflBannnnnfflffl  0  BEl^  mwnm BBBnEnnnEBB^^Ei^  BBQEBB • ••  • B B B B B B B • • B B E E B B  ••• •••• ••••+  •••rjp + +••••••• +••••••••  E+ +  ••••••BBBBBE • ••••EBEBEBOEBE • ••EBEBD+ +• ESEBnnnn + •BBBEEEBBil  3+ + 3+ 2D  BBDBBBBBtlElEl B B B D B B E S E B B BEBDBBBBEB BEBJZI EBEBEB EBEBEB  mmu + +  HEBD+ +  • ••EBEBEB • ••EBEBEB ••EBEBEB  mummm  0  • •BElBBBEnEti • •BEIBBEEDBE  60'  mmm  ummmmi  BENCH  6860  BUCKG CPROB  C 0 1 0  B+ + +  £••••••••• BDDMMBBBD ESQ + • • • • • • • E l BBEDBBBBBMBDD •••••••BDD ED  3BDDDDEBEDDDE IBBDDBEBDDD +D B IDE ^EIBDBEIBBDDDDB !BDI + E]BBBfflDBBBBBBBBB!: I ^ B D B E I B B D D + Effl 3HBBBBBEEDDBB + ++mmmmnmmmmmmmmm • E1BBDDDBBB + + DDDDBS1 ++ DEB  + +> + +  mmuu  •EBDnnnnnEBEB^^  EBEBUU  • DEB EBEBEB  son  DBBI  am  DBE DD  DDD • + • • • • DDDEEDDDDDEE DDDBBDDDDBEB ESDDDnOOEBEBEBEEl • • • • • • E B EBEBEB • • • • • • B E E • • • • • B B •••EBEBEB  • •  !••  •• •••  BUCKG CPROB  0=020  •••••  ++••••••• +••••••••  w&nu wmmmua  16  • • Q Dffl  • C_  • •• •[  IfflEB + DEB i H D + Dffl  3EHEBESDDEB  • OSfflEHEHEHEHn • • ••••••EBEEO • ••EEEBEBEBEBEBEH EBEHEBEHEHEHEBann • • • • • • • E E • ••••••EH fflEBBEonnno • • • • • • • • • • • • EBEHEBnnann • • • • • • • •EHEHEHO EBnnnnnn • • • • • • ••••• • • • • • • • •EH ••EHfflD EHfflfflfflEBDffl  • • • • •  • •!!•  ••EHfflnnnfflEH  • + QE  •••EBB  • •EH EB EH EH EBEHsnnn  • +  • ••• • ••• • •• •  EBfflEBnn • • ESErJfBffiSn  EBO, •EH  I  o CO  o CO CO  co DZ CO  o  LJJ  CQ  LO  o o ZD CQ  ro o  o CQ  o or CL_  CO  16  • •  • ••EB • EBI  ••fflffl ••BdmBaffl  IBB + DEB HI • • t l B L J + CJfflB ^BBBDLJfflfflBBB EBBBBDBBfflfflBBB  •••BBBB •••BBBBBffl  • ••  BBBBD • ••••••EBEBEHEBEHEBEBEBEBESmnna  • • • • • • • •  •••••••• ••••••• ••••••• • ••BBLJ  EBEBBannnnn  +  ++ ++++++ • +++ + EBDDD • •EBEH ••••BB • •••B •••a  •••••••fflfflD  • • • • • • • a a a a n n n n n  EOEBEBDDDDD auuuuuu ffluuuuu  BBLJBBBD • BBBBB  • •[!•  + nnfflEB3fflB3ffln  • • a  • • a a n n n a a ••fflfflan+D+na  • • • • • • B S  a n n n a a a a  EBDESEBEBDDD BfflaBBDD •afifiann • • a a a a n  • •••BEB  • BEB ++  [ CD  o  O  o  LO  CD  CO CD  CD  zc o  CD  LU  CO  o  -  ^1  o  ZD CQ  CQ CD  en  CC/ rP  o  •BDBBBuL EBDEBEBSfflES  • • •  BBBBaaBBBBBB •BBBnnBBBBBB^BB  • E ^ T O B D • + •BBBBi^BnnEHEET  • + +IHHI1DDEBEB +  +BBBBBBE1QESBDD + • fflEBDDEBEBBI BDEDDEIBBBBBBB EBDEQEQESBBBBBBBESD + BBBBBBBBBBB fflDfflfflfflUBBBBBBEBD BBBBnBBBElBElB EEDEBSEH El • • • • • • S-13]  •BBBEBBBBB  mmmmmmmmmmmm  fIIIII  •EBB  3BEBE1BI IBBBBBBBBB +nnnDBBBBBB OJ LD QJ vZ& QJ QJ 62J QJ • • • • • E B  + •83  +  BBBDEB^B^  BENCH UCKG  XAJ  + EBB ummm  XL  :!•••••••  +EBBBBBB +BBBBEEE BE •BBBBEEB BEHBEBBll BDBBB s¥l BBBBEEBE! ^^EBLIIEHEB + DLIB BBBEEEBB [IJIlllBBE • • + E E EBDDEBDDEBEa HE1BBE • • + DB ••••••EBB + + ••EBB mmmurm B E E E uumm •••••EBBffl + •••• • B B E E E + +•• • • E B B •••EBEBEHEBEB BJ1BBB n + nm BEB + 4- + + •EBEBEBEBEBEBEBEBEB• • • • B B B B B B B E E B BD , •EBES^EBESEBD + D B ^QnEB^EBEBEBn + •  ••^BBBEBBBtl • BEBBBBEBBBBllHll •••E^BBBEBBBBBBtl + + E B ^ B B B B E B B B B B BR B + + •EBEBBBBHE8BBBBBB + + • • B B B B B B B B B B B B + + EEE^B  3EE1BBBB  B O B B E D  + +  +  |+ + + + V t i d  ifflDDfflfflfflnnffli IB^BBBEBLTJEBEBEBE I^EBEB^EEHEBfflan !BB3EBEHEHEBEBEBEB& lEB + ^HMEBEBETJEBEB fHEBEBEJEBEBEBDEBE 1^ + M^EBEBEBEBED fBfflEBEHEBfflEBDEBffli ]H + DEBB3fflEBEBDnn EBDEDEBEBEBEJEBEBl i + fflnnnnnnE EBnEBEBnDB3EBEBEBEBEBfflEBfflffinnnDEBnnnffl • fflfflfflfflfflfflfflfflEBEfflffl^fflffl^fflfflnfflDDEB • [•••fflEBEBEBEBEBEHnnfflB^fflffifflEB^EBDnDEB • [••EHEHEHE33EBEB • + • ••EBEBEBSEBEBDDD [DfflfflEBEBOffl + + + + + n n E B n n n n n DDI IEBEBEBSD ++Dffl^B^n EBD + + • EBLTJEBBI EBD + + + + DEB • EB + mmmi • + +• EBDD • + +• • ••EBB EBD •EBE 3BBBBBBBE 5 EBE33I EBEBE EHDE B  B  -  -  H  H  B  i  B  H  j  B  |  B  E  •••••••  EB EH EH • EH EH E fflfflDEBEB^BBEBD  EBnffiEHDDDEnn mi • +l ]• + • • • • •••••• • •^••H^mHEHH^HBBHBBBB + BBB^B^EB^DEBEBSi^BBBBBB Snffl^BBBB^fflEBDDEBBBBBBBB^ffl 3DEHBBBBB^n^EB^EB^BBBBBEHD+ + ]DnEB^BBBEBDBEBE^BBBBBBB^n + + innnn^B^BfflEHH^E^B^BBB^nEBnEBn ]EBnDEB^HBBBEinEHEBEBnEBfflB^EBnE3 BEBDEBnn + n n n + n n ^ IBBBBBB^EB + nnnDEHEHD^BBBBnDEH 3BBBBB^DEBEBESEEEB + E B B B B B B B ^ D + ID^BBBB^DEBD + ^ B B B B B B B B D + 1  + DEBnBEBBB^EB+ + + + + • E B E B ^ D D + • + + •  • • • ^ • • • E B D  + DfflnnEBnnn + EBD + + + + +  +•  ++++++  o 00 CD X CD  OD  CD  CD X CQ  O CM X CQ  • ••• + I EBDDDEfiEB EBEBEB  ++ +  • •BBBBEDEJBM • •BBBBEnDBflflHBLJBBBfi • • •+  •fflnnnn BEBBBD+  DDDfflnnnn^EBEBDEBi  • ••+ +nEB3nnfflfflH^EBEM SflilBBBElEJ IfUBBBB + ••••••fflfflnnEBaffifitit^fii IBBBBBB •••EBEBnnnnannfflEBE • •BBBLJD[J+ +DDEBE • ••BBBBLJ + ++ + •••EBBBE + E D D B B +•••••• • + +UEB +••••+ + + D B B B B B B B  + •••• ++  •  • ••1 + UUEBI + ++ EJBBI  B  EEJEJBEJLJEJB + D B B + + + • E D D +• + + +  +•••••  iDEBffl  + +  •••••• • •fl^B  IBDDB  • +i  BBBBBBBBBBDBI BBBBD + BBBDEBI Egn+ + l i i E B E B D D D + + + + + •  + BBHBBEBEJLJ+ + + + + + [!••••••••••••• ••••+DBBnnBBBB • ••+ ++ DDB^ + + ++ + + DEB + + + + + DEBEB + + g3iDDDE0E9  + DBBI  + + + E U H H H H H E  +  BB + + ++ BBEJ +  BBEDDn  BELIED MEBDD BBBBB E1E1EBBB  I+ + + !+ + +  +nnnBf^nBEBnn^^BB+ +  + +nnnnBB + + nnnBBnnn  i+ +  • ++ •••• iB + n n n n n + B + + + +••• • ••BflBBBBS ^ • • • • • • + + ++ + + • • • • • • • • • • • B B B + +••+ +++i ^E!+ + • • •••••••••+ ++ ^•f^+ + + • • • • • • • • • + ••++•• ++ +++ + fflfflUUUU ++ BEDCOD  I  O CD  o  00 CD IE CD  O  LU m  o o  o C\J  m  LU  ID  X  •  ••••  • ••EBEBEBEBS fflffl^HEBEHESEHDHfl^ EBDEBEBEBEBEBnQEflEl^  3BHHHHEBDDD ^••••EBDDDEB EBDEBEBEBS  fflEBffinnnnfflDDEBffl f^DDEBdi EBEBD + DDEBEBDDEBEB EBDEBDDDEBEBDDfflEB^^ •  DEBEBEBDDDDDDDEBEBEB  DDBBB3EBDDDDDDDEBEBEB  • DDEBEBEBEBf^DEB • DDEB EBEBEB!^ • DDEBEBJ^ + • • • • • + • • • •  •  • •EB 18 • DEB DUf^EBfflEBI  EBEBEBDDEBEBEBEBEBEBEBEBS DDEBEBEBEBEBEBEBEBG  • EBEBDfflEfflfl^flEB EBEHLTJEH E B B B D D i •  •••HHHi  EBEHEHEBrj  DEIS  fli  •EB  ^EB  •  EHEBEHEHnn  DfM  ID  +  EBDB  • •• • ••  •DBDDB • •••EB • BtlElB • •  ID+ + • • • B B B D B + + D D D B +HHHBEBDD+ + + • • • • • • • • E B E B E B EBEBEB EBEBEB • ••EBEBEQDD • • • • + • B B B D D D • ••+ + + EEI^DDD ^EB+ + • + DBiUfUHH H^SIDD flBDD + DBBE^HB IEDD B B E D D B B E D D B B B D D B  DBBB^SII  Jj|BBBBB  DDDDDBDEBB^DBI^BBBDB + +DDDDEB + + + D D D B B D D D + + + ••EBEBD +• • • • + B D D B + D D B D D D + H B B + + + • • • • BBDBBBBBB^flBDDBDDD + + ••• + •  •  ••DfflBBBB^BDffl^PlilBDB  D E D D B D D D D B • B B B D D D D D B B B D D D B B D D  BBBBDfflFl BBDDDD  an  o  CD  + +•• + +•• ++ + •+  B B D D D D O  co  CD  CD  X CD  CD ZD CQ  LU CQ  O Q  •  ••••  IBOBBBBfi  •••••^BOB ^•••B^BnBE EBBfflEBBnDBIl^BHBBE^ EEBEBEBfflEBESnDfflEB^FEfflDEEBEa EEBSnnnnESDEHEBEHEHEHnnES^  fflEBfflnnnafflnfflfflffl ••fflfflEDDnnnnn ••BBBfflnfflnnnn • •BBBHEl^BBflfl •••BBdfflH •  •••BBHB + • • • • E B + • • • •  IBBQQBBBBBBBB • •BBBf^BI  • •  • EBB  • HB  • EBEBEB'fflEBEBH^ffl BBDB BBBBBO B BBBBBO  nfl^B  • BB M BflBD ^^Bfflna  BQBEBBB BOflHffl BO  • EBHHH • •••  EEBn + E S D M • EBD + • • • E B  ••••+nBBBBBBBBB  SDD+ + +B  ^B^BD EBfflEDDEE  BBn+Q+BB^^HM BBBEBnB^dHH^n^HHH^BDn IBBBBBBBflfl^HBBBBnn iEBBfflnDB 1+  EEaDDEBEBEBfflEBi • EBDfflfflDDDDEB •EfflfflfflDDDD  +•  • •••fflBBBB^DBI •••••fflEn+ODDfflBBDDffl • + + DBfflffiDBIiifflDfflBBE B+DB^ffiQEEii^D++BBBD B D B +• s u s n + +•••• BBflHHH^ElB^n + nn  ^BtlEBBBHBH+ + • • BBBBBBHBQ+n  BBBBnn BBBD  BfflfflBBiiBD E8EEDDD BEDDDD O  ^  00 CD  CD LO  O  o UJ  m  ZD CQ  Q  • •  ••ES  BilBBBBBBf^fl ••• •• BBEl^B^B^dtl^fl^BBBBBBE BBEBBBBBDB^El^BBEEE: EBBBBBBDDBE^BDBBFl^BBBBfflEB EBBDDDBBDBBBBBBEB^ilElBBBBB BBBDDDBBDBBBBJIBBBBEI^BBBBBB BBBDDBBBEBBBB^^EIBBBBBBBB BDBBBDDDDBDDBBf^ElBBfflBfflBfflB BDBBBBBEBBBBflfl^HllBffifflE • DEEBEBr" • •EES ESI DDDBBI  + ••••1  • •••• • •  5 B BBfflffl B B B B B D DBdtlflElBB fflffiiffl EBBE ^ B D f ^ B B B B ^ B B B BS1J1B BBE I^Bfl^BBBBBBDBB Bil BEBBBB S i i l H I I l l l l l l l l i l ^ G BEE it^BBEB f!Q[; I^UEB  BB  IBB^BEEtl^BBBBHBBBBBBBEE  IHBBBBBEBBBBEEB^BBBBBHHE fflBBBD + D D D B ^ B ^ B B B B  BDBD + DBBBBBBBBiUBBBBBffiDDB BDDD + D B B ^ f l ^ B B B ^ B B ^ I l f f l f f l f f l B BBDDDDB^dfl^fl^BB^^DD BBBBDB^El^BB^ElflBB^BEjn BBB^il^BBBBBDD IBBElBBBBBfl^BBBBBfl^BDDB SB^ElBDDfflB^tlBB^BB^BDDB IDDDDBBBB^flB^ElfflBBBB IfflDDDHEOffiffl + fflDfflEfflEBfflDffl 3B+DBffiBBDBBBB^DEBfflffl IBDBB^BBBBBBBB+DBBBffl siBEiiifflniBiiiffl+nfflDDn BBDB^BB^SlBB^^ffl^BBBB^flEl^DDDD BBBBBEDDBB ^BBBBBBB^D+DD BBBBSBDEB BflBBEBiliDDD EBBBBD BBBBfUiiflSBD BEBEBB BBBDDB BBBDDB  b  °  S X 0  O  z  ^ CD  o  ^  <^> ZD  CD  ro o  —•  mmmmjMmMmmm  muummm  \mmwsm  ••••••fflEBEl^fflEBEBI ••••••••EEHEBEBEB^I • ••EBEBESEEBEBEBEBEBiM • •fflffifflEBEHEBDnEBEBLB^^EBDn  fflEsni  [••^•fflDDEHEaEB^BEBES I^BEBDEBEEfflEBffl^EB  mmmmssa+ mmmmmmmmmmmmm^umammmi + LTJEHEHEBEBI  fflfflfflDnnnfflfflfflEafflfflfflfflLHLHEa  IELJEB IDS  mmmmanmmmmmmmmmmnm 0  60' IDEHI  BENCH  6840  BUCKG  I EBD  \^mmmmmuummmmmmmmmmm^M\ EBEBnEBfflEBfflEBEBnDEBEBEBDEBEBEBEBl EBnnnEBEBEfflEBnnEBEBfflfflfflEBEBEB ••••B3H3B3EBEBE0EB •••EB  fflffl^ffl^fflfflEBfflEBfflEEBEBEBEBffl  ID2  CM  •  •••••EBEBE1E1I  • ••••SfflEBaESEBEBEBUE  mmmmmmmsisiaaiiimmmmmm mmmuuummmmm l^fflffluuuuuEB I^EBfflfflDDEBEBffl m EB EB EB • EB EE EB EB El EB EB EB EB EB EB EB  ••••B3fflfflfflB3B3EBEBEM •••EBfflEBEBEBDEBEBEBEBE  \mnmmmzmmmmi 3EBL7JEBB3EBEBEBEBEBE1EB  3EBEBB3fflnDEBEBEBE  0  ••••••I  60' •EBffl! •I  I l l  BENCH  6840  l I l I I I I i E I l i l l l l l l l l l E  •  Ilff  B3EBEBEBEBHdEBEBB3EBEBEBEBEBE  BUCKG IDI  o  • BBBUBBB  ••••••••• ipiiifini  fflfflfflfflfflDDHfflEfil  0  ••••fflfflBaEBESESEB^^^^^ • •••EflSEBfflfflEBfflElEill^El^ •••^fflEDfflfflfflffl^  mmmmwmnummmmmwmmm  3BBBBBBE  ^ IEflfRE RE RE RE E ^ BB BB !BB BE BB BE E a VmB B E BE t/v^ k  60 •IIIII  • • •  3BBE  31IIHIIIE IE1BBBBBBEB SBBBBBBBES  ELBHESfflfflffiEBtlllElBBBB EBfflfflEBEBEH^Ell  R « 4 n fflfflfflfflfflfflfflfflfflfflfflffl^  LJ I— IN v/ i I  BUCKG IDO  •  mmmmuuummmmmmmmm wwmmmmmmuuuwmmmmwm  L?[a  R F M P U  uuuuuummmmwmmmmmm,  IBB  mmmmmmmmmmmmmmmmme^i^m 3EBEH  EBEHEHE9I  •EBEBEB  • EB B D E  IBBBBi  mmmuummmmw,  isifflEBnnDnfflfflffl^^HBi IBBBDnnBBBEIlBBBI IBBDBBBBBBil i^EBBBEBBEfl  60'  0  6840  BUCKG KRIGE  3BBBB 1BBBB BBBBBEI EBE2I UBI BBBBB  3BBBB8  EH EH  BENCH  • • • • • B B E B B B B E E • • • • • B B B B B B B B E •••BBBBBBBBBIlllilfflB •••BBBEBBBBBIlilBBDLJ ••E^iiEBDDDEBEBEEIifflEBO ^BBBHEDEJfflBBBUBBB \ BBBBBBBBEBBUBB IBB BUBEBEBBBE \m B BB B B B B B B B 8  f f l E  m mW E  B +  8  Wm  • • EH EB EB • EB B B B B B B B B B B B B B B BBDDDEBBBNLTJBBBB • • • B B B B B B B B  •  BBUBBBBUE BHUBBBBB  BBBE  ^mmmmmwwmm  B B B B B E B  173  •  + +• • • IBD + LJ + B B B D B f f l I^EIBDBBEM  El BEJlTJBB B B B B B E i^fflUUEuuuuEB iSEBEfflnnnnnnffl iflBBBBfflBBLJlJBn  •EHES EBEBfflEafflEBDDESElifflEBEBfflEBEBDDnnD • EBEB + DEDDEEBEB•••••  •  BE •  3D  • + •+ + + • B B E B D E J D I U E B ++DB EfflDDQ BBD+ + • BBBL7JD + • L7JB11BBBB • + + • •BBBBE  BBE1 + • • • BBEf] • • ]BBBBBBBBBBBBE|iB^^  • EBfflDB BBBEDDBEBBffli ^BEDDBBBB^i ]DDL7JBDEBBE: •  3BBBBE;  BBBBBBBB BBBBBE^BBLJ +  • ••B • •+ + fflUUUE • ••• • BBBEUBBEU • BEBB^El BED •BEE^BBBBBB^UEBunnnnuE • • • IBBBBDL7JDBB • + + IBBBBEZOE1BB + + EEOHEllllllllBQESQDill • • • E B B B B B B B E 1 B L 7 J + + DBE1B BBDnDBBLJflE! B D D B E E •••[_>*; +-+ BDB+++++B •BnnnnnDD+ + DBL7J++ ••+ + + + + + + ElfMBD •+ + + + + Bt^ +++++ + O o CO 00  <—  CD  JZ CD  -z.  O  LU CQ  O  -—  CD  CD  O ZD CD  CD CD  O  or Q_ CD  0  60  BENCH  6840  BUCKG CPROB  0.020  + + v  ESEBDEBEB + LJESD  +•  ma + n • ++ ++ + •  0  60  BENCH  6840  BUCKG CPROB  0=035  • l l l l i l  lllll 3EBDEB 3B3DDBBDDDDB3B3 3B3B3B3DDDDDDEB  IfflEBEBEBEBEBEBDDEBD IfflEBfflEBEBEBDDDDD •DEBDDB3B3EBEBEBDDDDDD  + • + + +DfflEEBEBnnnn ••EB  EBES EBEBD EBD  •••si • ++ • + • • • • •  • ••EBEB EBEBDDDHHD EBDD + + + + + + DBBD+ +  EBEBEJnn EBEBD + + DEBEBDDD • EBEB EBEBD  DDEBE DEBDDDt DD+ + + + + + + D+ + + + + + + ++ + +  00 CD  CD  X CD  CD X CQ  LU CQ  O LO O •  o CQ CD  en  o1  O  o  CP  O CD  0  BENCH  6860 +  BUCK60 ACTUAL  BHK  BENCH  6860 +  BUCK60 BH60  ffl EH EH EB  •  EB  •  E ffl •  BB EB  • • • ffl • • •  EB EB +  • + • • + ••+ + + •• • • • + + + ++ + • + + + + + • • •• + ffl • EB + • + + ^ • ffl ffl • + + ffl ^ ffl ffl • + • ffl ^ • • ffl • • • ffl • M • • • EB + • + + + +  +  + + + +  I  CD  O  + + + + + + +  •  • + +  , o CD+  co •  ^  +  CD  ° CD  X CD  ^ ^  LD  m  CD  180  + + •  EB •  EB LB  EB LB  •  •  • + + • • ffl • • + • • + + • + • LB + EB • • + + + + + + • + • + + + + + • • • • + + + • • • LB + + EB •  •  •  E  •  EB + M EB  + + •  + • +  + LB  + • ffl ^ • LB EB  EB  a • +• • + •  +  •  +  +  +  + + +  4-  +  + + + + + + o + CO  +  +CO  00 CO  CO  o  LU  m  +  + o CO  o  ZD CD  182  EE +  • • ffl • ffl EH  • ffl • • ffl • • • • +•• • + + • • • + + + + + + + •+ + + + • + • • • ffl  ^ ffl ffl • ffl • • + + • • • + + + • + • • • • + •  + + ffl • • + + + ffl ffl ^ m • ffl + + • + EH • EH + • • • EH EH EH + • ffl ^ • EH  •  ii  •  H  ^  ffl  m  + EH • +  •  • + -f+ + -t-  + +  ffl ffl  +  • + EB • + + + + + + + b + + +° + +  [ CD  O  'CD 00 ' CD  X UJ OD  _  ° CD  ^ CD  ro  183  E  •  • E B +  E  f  f l EBBBBBB  • • • + +  • + + + + + • B •  + •  B EE H • + + • + + • E E + E  EB • • • •  + •  •  ffl  •  +  +  E + E E B  E + E E B ^ M  M  ^ • E B E BB+ + + + +  B B  E  fl  E  E B E ffl + +  + + + +b+ CO  E E B E + + + + + + gE Si + CO  o  o  CO  X O  ^ <J  LU  m  m  CM Q  n  f  184  EB • • ffl ffl ffl ffl EB  •  fflfflffl• • +ffl• • • • • •ffl• • • • • • • + • • + + • • • • • • • • • • + + + + + • • • • •  + + + + +  + + • EB  • • • • + • • • • • +  + + ^ • ffl • • • + • ffl ffl ffl ffl • ffl [1 ^ • EB  1 j  • ffl •  [1 n • EB • +  • ffl • • + + + + + + • • + + + + + + b + + +SEB + CD  CO CD JZ  CD O  LU CQ  O CD ^  CD ZD  CQ  185  rn m rn rn m  m m m mc±jc±j  1^ 1^  •fflfflfflnfflfflfflfflfflfflnn • • ^ • • • • • • • E n n n • •••••• + + • • • • • • • • • • + + +.+ + • • • • •+++++•+•••• + + +  • • • E ffl  • • • • • • +  ffl ffl  •  +  • ffl • + • + + + + + • • • + + + + 0 + + +5  [ CD  O  00  CD  o  CD  CD LU  m•  CD  ZD CD  O Q  CD CD cz o  o  m z:  O.  o zc  CT> 00  cn + 0 +  +  +  + + • + + + + • EH • • ffl  • EH  +  + • • EH  ffl •  • • + fflfflffl•• • + • EH ffl • ffl  •  • •  • • + + + • + • + ••+ + + + + • • ••+ + + + +••• • + • • • • + + • • + • • +fflfflfflnnfflfflnn EH + • • fflffl^fflffl EH EH + ^ ffl • • • EH  381  BENCH  4- ( K + 6861^.^  BUCK60 CPROB  0=010  BENCH  + +  6860  + +  BUCK60 CPROB  0.020  00 03  • • •  +  0  +  +  +  +  +  +  +  +  +  +  60'  + + +  BENCH  + 46860  BUCK60 CPROB  +  + +  0=035  • • + + • • • ffl a • • • • + + ffl • ffl ^fil • + +ffl• ffl • + BB EB EB a'  + + •  • • • • • • ffl ffl • ffl • ffl w •  4-  +  m  4-  + ffl + + • + 4- 4+ 4-  • EH •  4-  0  60' 4-  4-  4-  + + • 4-  4-  4-  +  4-  4-  4-  4-  360 BUCK60 CPROB  0.050  O  0  BENCH  6840  BUCK60 ACTUAL  -  BENCH  6840  BUCK60 BH60  + +  + + + + +  • • • + ffl • + • ffl ffl • • • • • • ffl • + + + ' • ffl • + • ffl ffl ffl + + • • • + + + + • ffl ffl ffl • • + + + + + • • ffl • • + • + + • ffl + • • + + • • + ffl ffl + ffl ffl +  +  ffl  4-  ffl  4-  +  ffl  ffl  +  • • • • • + 4 4 + + +  •  • ffl ffl • • • + • 4-  ffl ffl  +• • + +  +  + b +  I  CO  o  03 CO  x  o  2^  O  •  LU CO  O CO  ^1 o X CO  o CO X LU  194  + + + •  4-  +  +  +  4 - 4 - 4 - 4 -  • • ffl • + '  EB •  EB •  ^  ffl-  ffl  +  ffl  +  4-  +  ffl  •  +  4-  ffl  +  4-  4-  EB • ffl ^  • •  4-  EB • + + •  4-  •  •  +  4-  •  ffl  + ffl EB ffl  4-  4-  •  +  • + • • ^  • ffl • • ffl + 53 ffl+ • • • • ++ 4-  4-  ffl ffl ffl + + •  + • + + + + • +  +  +  •  •  4-  4-  +  4-  4-  +  4-4-  +  4-o4CD  O ^tCO CD  X  o O  LD DD  O CD  ^: o X DD  O Q  + • + + + + + + •• • + •  ffl • ffl • +  ffl ffl ffl ffl • ffl • ffl ^ + + +  ffl+  ffl+  +  + + •  + +  +fflfflffl 1  •  fflfflffl^Bfflfflffl  +  + + ffl + • + •  ffl • +  • ffl •fflffl • ffl • • + + • + + + + + + + + + + +b + UT  1  /  I  CD  1  •'  + =R + +  + + +fflfflfflffl  +  + •+ +  o 00 CD X CD  O CD CD ZD  CD CQ  LO O  196  +  • •  4-  •  + 4-  4-  4-  • • •  H III  • ffl ffl ffl • + •fflffl ffl • + + + •ffl^ • ffl fflffl+ + • + ffl+ + + + f f l f f l • • • • + + + +fflffl•ffl+ + • + + fflfflfflBHfflfflffl + ffl + + • + EB • + • ffl  ffl • +  •fflnnn+nfflH+n • + + + + + + • • + + +  4-4  4-  4-o4CD  [ CD  o 00  CD X CD OD  CD CD CD X DD  ro  CD  197  + • + + + + • • • • • • ffl ^  ffl  ffl ffl  • • +  ffl • + + + + + • ffl ffl B3 ffl -- ffl • • • • • + +- + • • • + + • a3 ffl ffl + ffl • • ffl ffl ffl • • ffl + ffl +  • ffl ffl • ffl ^ •  B3  -  +  ffl • +  + + ffl + ffl  • • • ffl  • ffl  • ffl  • ffl •  ffl ffl • • • + • ffl • • • • • + + + + + • • • + + + + CO + b  [  O  +  o  00 CO ZZ CD LU  CO  o  CD \£ CD ZD CO  C\J  o  CO  o  m  CO  cz o  o zc  cn o  fe  cn 00 -r^ o  cn  + 0 +  • + • • ffl  4 - 4 - 4 - 4 -  • + + + + • • • ffl • • ffl  4-  ffl • • • •  •  •  •  ffl  4-  ffl  ffl ffl • ffl • ffl ffl + • •  • • • • ffl • ffl  ffl  •  • • ffl ffl ffl ffl + 4- 4ffl • • + • ffl ffl •  4~  ffl  ffl  ffl  ffl  •  4-  •  •  •  4  •  •  •  ffl  ffl  •  •  ffl ffl ffl ffl ffl  • • ffl ^ ffl  •  •  •  •  ffl  +  4-  +  4-  4-  861  + + + •  + ffl  EB •  • EB  •  EB  • •  EB ffl •  ffl.ffl  • •  •  •  •  ffl  ffl  ffl  ffl ffl EB  ffl  •  ffl  ffl ffl EB ffl  ffl  + + •  + •  •  •  ffl •  ffl  • •  + •  ffl  •  •  • •  •  •  • • • • ffl D ffl  + • •  ffl EB  • ffl • • • • ffl ffl ffl • • ffl +  + •  ffl  EB ffl EB  •  +  •  ^ • • ffl ffl  ffl ffl ^ ffl • • • ffl ffl ffl + + • • • + + + + • ffl o + + + + +0 + CD  00 CD  X CD O  LU CD  O CD CD ZD CD  CD Q  200  + + + +  • •  • • + ^  ffl ffl  ffl • + + + ffl ffl • + •  ffl ffl ffl  • ••EB  •  EB ffl  • • ffl • • • + • + • ffl ^  +  + +•  •  EB •  ffl • • •• • ffl  ffl • ffl ffl • +  •  ffl ffl • ffl ^ ^  ffl ffl • • • ffl • • • ffl • ffl • + • +  ffl ffl  • ffl ffl ffl +  ffl ffl • • • • + + + +  •  •  •  +  +  +  +  + b CD  [ L  - -0 1  +  + o 00 CD  O CO  X CD  o  LD OD  X on  LD CD OD  0.8  BENCH  6840  BUCK60 CPROB  0=010  •  ffl  D ' E  E  BENCH  6840  BUCK60 CPROB  0.020  o to  BENCH  6840  BUCK60 CPROB  +  +  •  +  +  +  ffl  •  0.035  to o  204  ffl  ffl  • ffl • +  i  • I • + • ffl • • • + + + + + • + + + • + + + +o + oo ffl  O  CD  CD  CD  O CD  ZZ CD  CD  ZD OD  OD  O LO CD O  CQ CD OD Q_ CD  0  • ffl +  60  ffl ffl ffl  • ffl • • • BENCH  686  BUCK60G ACTUAL  - H  +  • • •  •  HK  to o (SI  BENCH  6860  BUCK60G BH60  CO  m x  CO  o  m  CO CL"  o  2:  o zc  o CO  o o  fe  CO 00 CO  +  CO  o  o  • ffl ffl • ffl • ffl • • ^ ^ ffl • •  +  Hfflfflfflr^fflffl  •fflfflffl^ffl+ +ffl•fflffl• •  ffl  • ffl• • • • ffl • • • ffl ffl ffl • • • • • • ffl • • • + • ffl ffl • ffl •  ffl  ffl  • ffl • • • • • • + + • • • +  • • ffl ffl ffl ffl ffl  LOZ  ffl  ffl  ffl  ffl  r\Vja  sggB  208  • ffl EB • +  1  fflfflfflfflffl  • • • • • • • ffl • ffl ffl fflffl + fflffl • ffl ffl  • ffl •  ••••ffl + ffl ^ • ffl F  + • • ffl • • + ffl ffl + • • ffl  •  • ffl • ffl +  +  +  •  •  1 o  CO  o  o CO 00  CO ZZ  o CO  o o  CO  o ZD CO  o  B B • B • B  • B B • + B E • B • B B + • B  • •  • • • • B  •  B • +  •  B  E B B  B + •  • B • B B  • ^ •  r  o  CD  +  B  + • O CD 00 CD ZC O  LU CQ  CD O CO  CD ZD CQ  210  ^ P  • • ffl ffl • •• ffl ffl • • ffl ffl ffl ffl  ffl ffl • • •  ^ P  • • • •  ffl  ffl  ffl ffl ffl •  • • • ffl + ffl ffl • ffl ffl ^  • + ffl ffl • • ffl • • •  1  • ffl + ffl ffl  + i j  o  [ CD  O  p  O CD 00  CD JZ  CD  co  • • CD  o  CD  o ID CD  • ffl • • • • • ffl fflffl• m  • • o  60'  BENCH  6860  BUCK60G ID2  •  +  • •  m  • • ffl  EB • • • • • EB  • •  • EB +  W  EB •  • EB • • • EB ffl ffl  • • • • m  m  • • • ffl  m  • • ffl  ffl  {f  m  ffl • ffl fflffl• EH • EE  • • • • ffl LB • EH  60'  0  • BENCH  6860  BUCK60G IDI  EB  ffl •  •  •  ffl  a ffl • • ffl ffl ffl  m  • • • ES EB m • • • EB ffl m  • • ffl ffl w ffl • • • • EB • ffl • • ffl  60'  0  ffl ffl  • EB BENCH  6860  BUCK60G IDO  ffl ffl ffl  w m  • •  'A  0  1 6 0'  BENCH  6860  BUCK60G KRIGE  YZA  ffl • •  EH EH  H  LJJ  I 11 m L±j t t l  m  m  uj  H •  EB • ffl •  EH  • ffl• ffl •• • • ^ ffl • • •  • • • ffl •  • • ffl  E?3  ffl EB  w2  ffl  ffl • ffl EB  ffl • • ffl ffl ffl  • ffl  ffl  ffl/ffl + ffl • ffl • • • • ffl • ffl  ffl +  • ffl •  • ffl • + •  LrjO  • ffl 0  60'  BENCH  6860  BUCK60G CPROB  0.010  +  • ffl + • • ffl • • • • ffl ffl • •  • •  BUCK60G CPROB  0.020  V7A  0  60'  BENCH  6860  BUCK60G CPROB  0.035  V?.  ffl • + • • • • • • •ffl• ffl • •  A  \ZZA  EB EB 0-4  0  60'  • ffl +  ffl • + • • • m ••••fflfflffl^ + • • ffl • ffl a EB u r n  + • • •  BENCH  6860  BUCK60G CPROB  0=050  m m  -f  + +  • •,  • • a  • • ffl  BENCH  6840  BUCK60G ACTUAL  -  BHK  220  • •ffl•  nam  -m0  60'  + ffl  • EB +  • + • •ffl• + •fflfflw  • • ffl  + • • • • •ffl• ffl • • • • • ffl ffl' + • ffl +  • ffl BENCH  6840  BUCK60G EX60  + • • • • • + • + • • • • W •fflw ffl • +  ffl ffl ffl •ffl• +  • • ffl • ffl  ffl '  ffl  •• + - -  • ffl  •  .ffl  ffl ffl ffl  ffl ffl  • ffl ffl ffl • • • ffl • ffl ^ •  H  •  • +  •  • ffl  • •  • . • ffl • ffl • + ffl • ffl + ffl • • • • ffl • • ffl • • • ffl • o  [ CD  O  o  00  CD X CD LD DD  CD O CD \C CD X DD  • ffl  ffl ffl ffl  •  • • ffl •  m  m  •  +  • a •  • ffl + ffl  • + • 0  60' ffl ffl  BENCH  6840  BUCK60G ID5  fflfflm  •  • • • • +fflffl rj  rj  •  • • • ffl • ffl m  u  m  • ffl EB EB  •  ffl ffl ffl •  • 0  ffl •  •  60'  BENCH  6840  BUCK60G ID3  • + •fflffl • ffl • ffl •  • ffl ffl ffl ffl + ffl • ffl  • • ffl ffl ffl ffl •  ffl  m  A  ffl ffl  VZA  EB BE EE •  m  u  BE • +  -RO-  u  •  u  BE  •  BB • ffl o  60  BENCH  6840  BUCK60G ID2  • ffl  ffl • • ffl ffl • ffl EE ffl ffl BB ffl ffl  ro to  to to  IDO  • ffl ffl EH  • ffl • ffl w m •fflfflfflffl 0  60'  BENCH  6840  BUCK60G KRIGE  ffl •  EH  +  EB  •  EB  EB  •  •  ffl •ffl• ffl  •  •  A  \AAA  +  0  60'  BENCH  6840  CPROB  0.010  +  • + EB + • +  BUCK60G  EB  •  44-  EB  +  •  +  4-  •  ffl • ffl • • ffl ffl • • ffl • •  to to  to o  o  60'  BENCH  6840  BUCK60G CPROB  0.035  • ffl  6cr  0  BENCH  6840 +  BUCK60G CPROB  0.050  + +  •  ffl +  •  ffl ffl ffl • ffl ffl• ffl ffl ffl •ffl• ffl •  APPENDIX C  ORE RESERVE REPORTS  234 BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK BH4  2 0 ' BLOCKS - NO ORE OUTLINE BLASTHOLE POLYGONS  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 447315. 316069. 171588. 100759.  06 06 56 50 69  0.032 0.042 0.053 0.075 0.098  19300. 18612. 16677. 12829. 9877.  41 36 51 23 07  163657.00 131245.50 144481.06 70828.81 100759.69  0. 0. 0. 0. 0.  004 015 027 042 098  688 1934 3848 2952 9877  .05 .85 .28 . 16 .07  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 357065. 237374. 127867. 71024.  37 44 50 25 62  0.026 14184. 0.038 13504. 0.049 11715. 0.069 8809. 0.091 6457.  09 82 43 50 70  187010.94 119690.94 109507.25 56842.62 71024.62  0 . 004 0 . 015 0 . 027 0 . 041 0 . .091  679 1789 2905 2351 6457  .27 .39 .93 .80 .70  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048. 804380. 553444. 299455. 171784.  00 50 06 81 37  0.029 0.040 0.051 0.072 0.095  47 18 94 73 79  350667.50 250936.44 253988.25 127671.44 171784.37  0. 0. 0. 0. 0.  1367 3724 6754 5303 16334  .30 .24 .20 .95 .79  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK BH20  33484. 32117. 28392. 21638. 16334.  004 015 027 042 095  2 0 ' BLOCKS -• NO ORE OUTLINE BLASTHOLE POLYGON WEIGHTED  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 471044. 341039. 181396. 103811.  06 31 19 87 56  0.032 0.040 0.049 0.069 0.088  19297. 18626. 16692. 12461. 9170.  97 38 19 75 27  139927.75 130005.12 159642.31 77585.31 103811.56  0. 0. 0. 0. 0.  005 015 026 042 088  671 1934 4230 3291 9170  .59 . 19 .44 .48 .27  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 372993. 255228. 129629. 71318.  37 75 56 81 37  0.026 14182. 0.036 13468. 0.046 11676. 0.064 8304. 0.082 5879.  02 36 21 92 01  171082.62 117765.19 125598.75 58311.44 71318.37  0. 0. 0. 0. 0.  004 015 027 042 082  713 1792 3371 2425 5879  .67 . 14 .29 .91 .01  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048. 844038. 596267. 311026. 175129.  00 12 75 69 94  0.029 0.038 0.048 0.067 0.086  98 74 40 68 28  311009.87 247770.37 285241.06 135896.75 175129.94  0. 0. 0. 0. 0.  004 015 027 042 086  1385 3726 7601 5717 15049  .24 .34 .72 .40 .28  BLOCK MODEL: METHOE i : RESERVES  -  BENCH CUTOFF  BUCK BHKRIGE  33479. 32094. 28368. 20766. 15049.  2 0 ' BLOCKS - NO ORE OUTLINE BLASTHOLE K R I G I N G - " A C T U A L "  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 502982. 374054. 196574. 111465.  06 62 56 44 62  0.033 0.039 0.047 0.064 0.082  19939. 19365. 17419. 12654. 9101.  61 01 31 91 51  107989.44 128928.06 177480.12 85108.81 111465.62  0. 0. 0. 0. 0.  005 015 027 042 082  574 1945 4764 3553 9101  .60 .70 .41 .40 .51  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 399611. 277440. 133432. 68266.  37 69 06 37 56  0.027 14567. 0.035 13897. 0.043 12017. 8097. 0.061 0.078 5344.  63 69 64 21 31  144464.69 122171.62 144007.69 65165.81 68266.56  0. 0. 0. 0. 0.  005 015 027 042 078  669 1880 3920 2752 5344  .94 .05 .42 .90 .31  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048. 902594. 651494. 330006. 179732.  00 31 69 81 19  0.030 0.037 0.045 0.063 0.080  23 70 96 12 82  252453.69 251099.62 321487.87 150274.62 179732.19  0. 0. 0. 0. 0.  1244 005 015 3825 027 8684 042 6306 080 14445  .52 .75 .84 .29 .82  34507. 33262. 29436. 20752. 14445.  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK EX4  2 0 ' BLOCKS -• NO ORE OUTLINE EXPLORATION POLYGONS  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE:  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 397620. 278762. 142897. 78939.  06 62 00 94 87  0.027 16613. 0.039 15594. 0.050 13894. 0.072 10350. 0.097 7620.  69 17 85 73 71  213351.44 118858.62 135864.06 63958.06 78939.87  0. 0. 0. 0. 0.  005 014 026 043 097  1019. 1699. 3544. 2730. 7620.  52 32 12 02 71  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 307175. 210397. 114125. 67515.  37 12 50 75 81  0.025 13460. 0.041 12456. 0.053 11067. 0.074 8479. 0.098 6614.  14 24 75 98 96  236901.25 96777.62 96271.75 46609.94 67515.81  0. 0. 0. 0. 0.  004 014 027 040 098  1003. 1388. 2587. 1865. 6614.  89 49 77 02 96  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048. 704795. 489159. 257023. 146455.  00 81 56 75 69  0.026 0.040 0.051 0.073 0.097  80 41 60 71 67  450252.19 215636.25 232135.81 110568.06 146455.69  0. 0. 0. 0. 0.  004 014 026 042 097  2023. 3087. 6131. 4595. 14235.  39 81 89 04 67  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK EX20  30073. 28050. 24962. 18830. 14235.  2 0 ' BLOCKS -• NO ORE OUTLINE EXPLORATION POLYGON WEIGHTED  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 422900. 287738. 144676. 71612.  06 31 00 81 19  0.027 16611. 0.037 15669. 0.048 13712. 0.068 9893. 0.095 6821.  42 67 55 31 41  188071.75 135162.31 143061.19 73064.62 71612.19  0. 0. 0. 0. 0.  005 014 027 042 095  941. 1957. 3819. 3071. 6821.  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 324866. 220923. 109588. 62848.  37 06 94 81 35  0.025 13458. 0.038 12465. 0.050 10955. 0.073 7989. 0.096 6064.  30 87 18 58 67  219210.31 103942.12 111335.12 46740.46 62848.35  0. 0. 0. 0. 0.  005 015 027 041 096  9 9 2 . .43 1 5 1 0 . ,69 2 9 6 5 . 61 1 9 2 4 . 91 6 0 6 4 . 67  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048. 747766. 508661. 254265. 134460.  00 37 94 69 50  0.026 0.038 0.048 0.070 0.096  71 55 74 89 08  407281.62 239104.44 254396.25 119805.19 134460.50  0. 0. 0. 0. 0.  005 015 027 042 096  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK IDIO  30069. 28135. 24667. 17882. 12886.  1934. 3467. 6784. 4996. 12886.  75 12 24 90 41  16 81 85 81 08  2 0 ' BLOCKS -• NO ORE OUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  I N S I D E GRADE  GRADE  OUNCES 1 7 1 3 2 . 94 1 6 1 6 1 . 00 1 4 2 4 9 . 68 1 0 0 6 8 . 12 6 9 6 9 . 46  TONS  BOUNDARIES  GRADE  OUNCES  170119.75 131963.56 159626.00 74256.00 75006.75  0. 0. 0. 0. 0.  006 014 026 042 093  971. 1911. 4181. 3098. 6969.  94 33 55 67 46  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 440852. 308888. 149262. 75006.  06 31 75 75 75  0.028 0.037 0.046 0.067 0.093  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 338917. 221576. 110649. 58148.  37 56 69 62 18  0.025 13675. 0.037 12616. 0.049 10938. 0.072 7926. 0.099 5740.  96 04 24 38 73  205158.81 117340.87 110927.06 52501.44 58148.18  0. 0. 0. 0. 0.  005 014 027 042 099  1059. 1677. 3011. 2185. 5740.  93 80 86 65 73  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 1 1 5 5 0 4 8 . 010 779769. 020 530465. 035 259912. 050 133154.  00 94 50 37 94  0.027 0.037 0.047 0.069 0.095  89 05 91 50 19  375278.06 249304.44 270553.12 126757.44 133154.94  0. 0. 0. 0. 0.  005 014 027 042 095  2031. 3589. 7193. 5284. 12710.  85 13 42 30 19  30808. 28777. 25187. 17994. 12710.  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK ID5  2 0 ' BLOCKS -• NO ORE OUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 472088. 335637. 154583. 75822.  06 81 25 06 75  0.029 17503. 0.035 16679. 0.044 14683. 0.064 9919. 0.088 6666.  23 17 68 09 90  138883.25 136451.56 181054.19 78760.31 75822.75  0 .006 0 .015 0 .026 0 .041 0 .088  824 1995 4764 3252 6666  .06 .50 .59 .19 .90  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 367151. 227745. 106292. 55700.  37 19 69 19 18  0.025 13500. 0.034 12521. 0.046 10514. 0.068 7211. 0.092 5131.  41 04 20 31 45  176925.19 139405.50 121453.50 50592.00 55700.18  0 .006 0 .014 0 .027 0 .041 0 .092  979 2006 3302 2079 5131  .37 .84 .89 .86 .45  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048. 839240. 563382. 260875. 131522.  00 00 94 31 94  0.027 0.035 0.045 0.066 0.090  63 21 87 41 36  315808.00 275857.06 302507.62 129352.37 131522.94  0 .006 0 .015 0 .027 0 .041 0 .090  1803 4002 8067 5332 11798  .41 .34 .46 .05 .36  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK ID3  31003. 29200. 25197. 17130. 11798.  2 0 ' BLOCKS -• NO ORE OUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 500648. 358044. 158157. 77454.  06 81 62 19 75  0.029 17892. 0.034 17208. 0.042 15097. 0.062 9788. 0.083 6447.  36 15 90 36 84  110323.25 142604.19 199887.44 80702.44 77454.75  0 .006 0 .015 0 .027 0 .041 0 .083  684 2110 5309 3340 6447  .20 .25 .55 .52 .84  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 391663. 239675. 104497. 52844.  37 81 62 00 18  0.025 13439. 0.032 12547. 0.043 10356. 0.064 6692. 0.086 4556.  79 84 09 59 36  152412.56 151988.19 135178.62 51652.82 52844.18  0 .006 0 .014 0 .027 0 .041 0 .086  891 2191 3663 2136 4556  .95 .75 .50 .23 .36  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048. 892312. 597720. 262654. 130298.  00 69 25 19 94  0.027 0.033 0.043 0.063 0.084  14 00 99 95 20  262735.31 294592.44 335066.06 132355.25 130298.94  0 .006 0 .015 0 .027 0 .041 0 .084  1576 4302 8973 5476 11004  . 14 .01 .04 .75 .20  BLOCK MODEL: METHOE »: RESERVES  -  BENCH CUTOFF  BUCK ID2  31332. 29756. 25453. 16480. 11004.  2 0 ' BLOCKS -• NO ORE OUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 518339. 376861. 163901. 75806.  06 75 56 81 37  0.030 18178. 0.034 17566. 0.041 15439. 0.060 9786. 0.081 6156.  04 91 52 78 12  92632.31 141478.19 212959.75 88095.44 75806.37  0 .007 0 .015 0 .027 0 .041 0 .081  611 2127 5652 3630 6156  . 13 .39 .74 .66 .12  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 408473. 245224. 108430. 48617.  37 44 37 12 30  0.025 13418. 0.031 12585. 0.042 10217. 0.060 6517. 0.083 4051.  90 02 93 25 18  135602.94 163249.06 136794.25 59812.82 48617.30  0 .006 0 .014 0 .027 0 .041 0 .083  833 2367 3700 2466 4051  .87 .10 .68 .07 .18  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048. 926813. 622086. 272331. 124423.  00 19 00 94 69  0.027 0.033 0.041 0.060 0.082  93 94 45 04 30  228234.81 304727.19 349754.06 147908.25 124423.69  0 .006 0 .015 0 .027 0 .041 0 .082  31596. 30151. 25657. 16304. 10207.  1445 . 0 0 4 4 9 4 .49 9 3 5 3 , .41 6 0 9 6 , .73 10207, .30  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK IDI  2 0 ' BLOCKS - NO ORE OUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 542868. 402696. 166578. 78042.  06 69 12 31 25  0.030 18474. 0.033 18026. 0.039 15905. 0.058 9667. 0.077 6021.  07 80 61 50 80  68103.37 140172.56 236117.81 88536.06 78042.25  0. 0. 0. 0. 0.  007 015 026 041 077  447. 2121. 6238. 3645. 6021.  27 19 11 70 80  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 432561. 249875. 109344. 46136.  37 75 62 00 66  0 . 0 2 5 13414. 0.029 12707. 0.040 10071. 0.057 6264. 0.079 3635.  34 53 93 37 89  111514.62 182686.12 140531.62 63207.34 46136.66  0. 0. 0. 0. 0.  006 014 027 042 079  706. 2635. 3807. 2628. 3635.  81 60 56 49 89  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 1 1 5 5 0 4 8 . 010 975430. 020 652571. 035 275922. 050 124178.  00 50 81 31 87  0.028 0.032 0.040 0.058 0.078  40 33 55 87 69  179617.50 322858.69 376649.50 151743.44 124178.87  0. 0. 0. 0. 0.  006 015 027 041 078  1154. 4756. 10045. 6274. 9657.  07 78 68 18 69  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK IDO  31888. 30734. 25977. 15931. 9657.  2 0 ' BLOCKS - NO ORE OUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE1 BOUNDARIES  OUNCES  TONS  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 552024. 413173. 168128. 73994.  06 19 62 69 87  0.031 18658. 0.033 18266. 0.039 16104. 0.057 9595. 0.077 5670.  23 96 95 54 32  58947.87 138850.56 245044.94 94133.81 73994.87  0. 0. 0. 0. 0.  007 016 027 042 077  391. 2162. 6509. 3925. 5670.  27 00 42 21 32  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 441162. 253123. 102979. 48698.  37 44 31 19 90  0.025 13439. 0.029 12764. 0.040 10014. 0.057 5903. 0.075 3663.  38 64 76 73 70  102913.94 188039.12 150144.12 54280.29 48698.90  0. 0. 0. 0. 0.  007 015 027 041 075  674. 2749. 4111. 2240. 3663.  73 88 04 03 70  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048. 993186. 666296. 271107. 122693.  00 62 94 94 81  0.028 0.031 0.039 0.057 0.076  59 61 71 27 02  161861.37 326889.69 395189.00 148414.12 122693.81  0. 0. 0. 0. 0.  007 015 027 042 076  1065. 4911. 10620. 6165. 9334.  99 89 45 25 02  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK KRIGE  32097. 31031. 26119. 15499. 9334.  2 0 ' BLOCKS -• NO ORE OUTLINE EXPLORATION KRIGED :ESTIMATE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 520102. 370317. 160458. 73309.  06 31 25 25 44  0.030 18052. 0.034 17494. 0.041 15218. 0.060 9635. 0.083 6069.  25 66 14 23 66  90869.75 149785.06 209859.00 87148.81 73309.44  0. 0. 0. 0. 0.  006 015 027 041 083  557. 2276. 5582. 3565. 6069.  58 53 90 57 66  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 406286. 240067. 99437. 47344.  37 56 25 75 34  0.024 12994. 0.030 12155. 0.040 9719. 0.060 5948. 0.080 3810.  03 95 38 64 72  137789.81 166219.31 140629.50 52093.41 47344.34  0. 0. 0. 0. 0.  006 015 027 041 080  838. 2436. 3770. 2137. 3810.  07 57 74 92 72  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 1 1 5 5 0 4 8 . 010 926388. 020 610384. 035 259896. 050 120653.  00 87 56 06 81  0.027 0.032 0.041 0.060 0.082  27 62 52 88 37  228659.12 316004.31 350488.50 139242.25 120653.81  0. 0. 0. 0. 0.  006 015 027 041 082  1395. 4713. 9353. 5703. 9880.  65 09 64 50 37  31046. 29650. 24937. 15583. 9880.  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK CPROB  20» BLOCKS - NO ORE OUTLINE CONDITIONAL P R O B A B I L I T Y  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 469696. 321283. 166759. 90210.  06 62 75 50 75  0. 0. 0. 0. 0.  030 037 047 066 086  .25 . 10 .56 .57 .57  141275 148412 154524 76548 90210  .44 .87 .25 .75 .75  0 .005 0 .015 0 .027 0 .042 0 .086  7 3 4 . , 14 2 2 0 6 . ,54 4 1 3 1 . ,00 3 1 8 6 . ,00 7 7 9 4 . ,57  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 359678. 221051. 107729. 57801.  37 37 19 44 45  0. 0. 0. 0. 0.  024 12994 . 0 3 034 12074 . 5 6 045 10046 . 8 1 065 7037 . 2 5 086 4956 .84  184398 138627 113321 49927 57801  .00 .19 .75 .98 .45  0 .005 0 .015 0 .027 0 .042 0 .086  9 1 9 . .47 2 0 2 7 , .75 3009,.57 2 0 8 0 . .40 4 9 5 6 . .84  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 1 1 5 5 0 4 8 . 010 829375. 020 542335. 035 274489. 050 148012.  00 00 00 00 19  0. 0. 0. 0. 0.  027 035 046 066 086  325673 287040 267846 126476 148012  .00 .00 .00 .81 .19  0 .005 0 .015 0 .027 0 .042 0 .086  1 6 5 3 . ,60 4 2 3 4 . .29 7 1 4 0 . ,55 5 2 6 6 . ,41 1 2 7 5 1 . ,41  18052 17318 15111 10980 7794  31046 29392 25158 18017 12751  .27 .66 .38 .82 .41  BLOCK MODEL: METHOE>: RESERVES BENCH CUTOFF  BUCKG BH4  2 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE BLASTHOLE POLYGONS  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE BOUNDARIES  OUNCES  TONS  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 374397. 287999. 163934. 97691.  31 25 12 44 56  0.041 0.045 0.054 0.075 0.098  17212. 16965. 15665. 12337. 9568.  70 49 06 18 37  48503.06 86398.12 124064.69 66242.87 97691.56  0.005 0.015 0.027 0.042 0.098  247 1300 3327 2768 9568  .21 .43 .88 .82 .37  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 290479. 212845. 120768. 68886.  87 75 50 00 75  0.037 0.041 0.051 0.070 0.091  12279. 12054. 10886. 8414. 6263.  08 28 00 78 66  42742.12 77634.25 92077.50 51881.25 68886.75  0.005 0.015 0.027 0.041 0.091  224 1168 2471 2151 6263  .80 .28 .22 .11 .66  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 664877. 500844. 284702. 166578.  25 06 69 50 31  0.039 0.044 0.053 0.073 0.095  29491. 29019. 26551. 20751. 15832.  80 77 06 98 03  91245.19 164032.37 216142.19 118124.19 166578.31  0.005 472 0.015 2468 0.027 5799 0.042 4919 0 . 0 9 5 15832  .04 .70 .09 .95 .03  BLOCK MODEL: METHOD: RESERVES BENCH CUTOFF  BUCKG BH20  2 0 ' BLOCKS -• WITHIN ORE ZONE OUTLINE BLASTHOLE POLYGON WEIGHTED  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE BOUNDARIES  OUNCES  TONS  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 390619. 314666. 175766. 101575.  31 37 00 44 69  0.041 17210. 0.044 17014. 0.050 15854. 0.069 12140. 0.089 9000.  97 23 34 29 51  32280.94 75953.37 138899.56 74190.75 101575.69  0.006 0.015 0.027 0.042 0.089  196 1159 3714 3139 9000  .75 .88 .05 .78 .51  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 304759. 231042. 125060. 69784.  87 81 31 19 31  0.037 12277. 0.040 12099. 0.047 10949. 0.065 8084. 0.083 5768.  66 39 97 48 87  28462.06 73717.50 105982.12 55275.87 69784.31  0.006 0.016 0.027 0.042 0.083  178 1149 2865 2315 5768  .27 .42 .48 .61 .87  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 695379. 545708. 300826. 171360.  25 19 37 69 06  0.039 0.042 0.049 0.067 0.086  64 62 32 79 39  60743.06 149670.81 244881.69 129466.62 171360.06  0.006 0.015 0.027 0.042 0.086  375 2309 6579 5455 14769  .02 .30 .53 .40 .39  BLOCK MODEL: METHOD: RESERVES BENCH CUTOFF  BUCKG BHKRIGE  29488. 29113. 26804. 20224. 14769.  2 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE BLASTHOLE K R I G I N G - " A C T U A L "  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE BOUNDARIES  OUNCES  TONS  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 406417. 350488. 190797. 113048.  31 12 44 19 69  0.042 0.043 0.048 0.065 0.081  17737. 17623. 16723. 12421. 9211.  18 80 65 31 31  16483.19 55928.69 159691.25 77748.50 113048.69  0.007 0.016 0.027 0.041 0.081  113 900 4302 3210 9211  .38 . 15 .34 .00 .31  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 321634. 252633. 135602. 70012.  87 69 69 94 81  0.038 12598. 0.039 12527. 0.045 11415. 0.061 8230. 0.078 5488.  95 74 73 49 24  11587.19 69001.00 117030.75 65590.12 70012.81  0.006 0.016 0.027 0.042 0.078  71 1112 3185 2742 5488  .21 .00 .25 .25 .24  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 728051. 603122. 326400. 183061.  25 81 19 12 50  0.040 0.041 0.047 0.063 0.080  14 54 39 79 55  28070.44 124929.62 276722.06 143338.62 183061.50  0.007 0.016 0.027 0.042 0.080  184 2012 7487 5952 14699  .60 .15 .60 .25 .55  30336. 30151. 28139. 20651. 14699.  240 BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCKG EX4  2 0 ' BLOCKS -• WITHIN ORE ZONE EXPLORATION POLYGONS  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 366269. 267811. 138834. 77438.  31 87 31 25 37  0.036 0.040 0.050 0.072 0.096  15151. 14827. 13411. 10056. 7437.  52 16 53 34 31  56630.44 98458.56 128977.06 61395.87 77438.37  0.006 0.014 0.026 0.043 0.096  324. 1415. 3355. 2619. 7437.  36 63 19 04 31  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 287933. 200018. 107206. 63109.  87 87 00 12 46  0.036 12055. 0.041 11818. 0.053 10562. 0.075 8069. 0.100 6294.  03 11 17 48 95  45288.00 87915.87 92811.87 44096.66 63109.46  0.005 0.014 0.027 0.040 0.100  236. 1255. 2492. 1774. 6294.  92 94 69 54 95  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 654203. 467829. 246040. 140547.  25 81 31 37 87  0.036 0.041 0.051 0.074 0.098  55 28 71 83 26  101918.44 186374.50 221788.94 105492.50 140547.87  0.006 0.014 0.026 0.042 0.098  561. 2671. 5847. 4393. 13732.  28 57 88 57 26  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  27206. 26645. 23973. 18125. 13732.  2 0 ' BLOCKS -• WITHIN ORE ZONE lDUTLINE EXPLORATION POLYGON WEIGHTED  BUCKG EX20  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 380908. 278615. 142310. 70943.  31 94 12 44 06  0.036 15149. 0.039 14873. 0.048 13358. 0.068 9726. 0.095 6718.  92 54 27 30 87  41991.37 102293.81 136304.69 71367.37 70943.06  0.007 0.015 0.027 0.042 0.095  276. 1515. 3631. 3007. 6718.  38 27 97 43 87  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 301577. 210772. 103142. 60384.  87 37 87 44 02  0.036 12053. 0.039 11849. 0.050 10527. 0.074 7660. 0.098 5896.  87 98 96 25 37  31644.50 90804.50 107630.44 42758.41 60384.02  0.006 0.015 0.027 0.041 0.098  203. 1322. 2867. 1763. 5896.  90 01 71 88 37  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 682486. 489388. 245452. 131327.  25 37 00 87 06  0.036 0.039 0.049 0.071 0.096  80 52 23 56 24  73635.87 193098.37 243935.12 114125.81 131327.06  0.007 0.015 0.027 0.042 0.096  480. 2837. 6499. 4771. 12615.  28 28 67 32 24  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCKG IDIO  27203. 26723. 23886. 17386. 12615.  2 0 ' BLOCKS - WITHIN ORE ZONE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 403675. 320475. 154240. 77193.  31 37 94 37 62  0.038 0.040 0.046 0.067 0.093  16178. 16046. 14786. 10407. 7170.  18 45 32 25 52  19224.94 83199.44 166235.56 77046.75 77193.62  0.007 0.015 0.026 0.042 0.093  131. 1260. 4379. 3236. 7170.  73 13 07 73 52  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 313050. 226423. 112085. 59404.  87 37 75 75 82  0.038 12612. 0.040 12482. 0.049 11162. 0.072 8069. 0.099 5892.  59 22 05 55 71  20171.50 86626.62 114338.00 52680.93 59404.82  0.006 0.015 0.027 0.041 0.099  130. 1320. 3092. 2176. 5892.  37 17 50 84 71  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 716725. 546899. 266326. 136598.  25 75 75 19 44  0.038 0.040 0.047 0.069 0.096  77 67 37 80 22  39396.50 169826.00 280573.56 129727.75 136598.44  0.007 0.015 0.027 0.042 0.096  262. 2580. 7471. 5413. 13063.  10 30 57 58 22  28790. 28528. 25948. 18476. 13063.  BLOCK MODEL: METHOE 1: RESERVES BENCH CUTOFF  BUCKG ID5  2 0 ' BLOCKS - WITHIN ORE ZONE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  OUNCES  OUTLINE  I N S I D E GRADE TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  4 2 2 9 0 0 . 31 4 1 2 2 9 2 . 31 351353.44 1 7 2 0 2 9 . 19 8 1 1 5 9 . 37  0.039 0.040 0.044 0.063 0.087  16644.41 16562.41 15613.44 10807.02 7066.89  10608.00 60938.87 179324.25 90869.81 81159.37  0.008 0.016 0.027 0.041 0.087  82. 948. 4806. 3740. 7066.  00 97 42 13 89  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 323886. 234436. 112102. 59078.  87 81 87 12 43  0.037 12487.85 0.038 12423.37 0.047 10986.46 0.068 7618.41 0.092 5427.57  9335.06 89449.94 122334.75 53023.70 59078.43  0.007 0.016 0.028 0.041 0.092  64. 1436. 3368. 2190. 5427.  48 91 05 83 57  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 736179. 585790. 284131. 140237.  25 19 31 31 81  0.039 0.039 0.045 0.065 0.089  19943.06 150388.87 301659.00 143893.50 140237.81  0.007 0.016 0.027 0.041 0.089  146. 2385. 8174. 5930. 12494.  48 88 46 96 47  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  29132.26 28985.78 26599.90 18425.43 12494.47  2 0 ' BLOCKS - WITHIN ORE ZONE IOUTLINE INVERSE DISTANCE  BUCKG ID3  ABOVE CUTOFF GRADE TONS  GRADE  OUNCES  I N S I D E GRADE TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 419391. 374772. 187027. 85892.  31 50 62 25 19  0.040 17060.00 0.041 17034.17 0.044 16323.52 0.060 11178.21 0.082 7026.43  3508.81 44618.87 187745.37 101135.06 85892.19  0.007 0.016 0.027 0.041 0.082  25. 710. 5145. 4151. 7026.  83 65 30 78 43  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 328880. 254804. 117830. 59062.  87 75 25 44 11  0.037 12469.78 0.038 12436.99 0.044 11199.06 0.063 7462.46 0.085 5042.16  4341.12 74076.50 136973.81 58768.33 59062.11  0.008 0.017 0.027 0.041 0.085  32. 1237. 3736. 2420. 5042.  79 93 60 30 16  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 748272. 629576. 304857. 144954.  25 31 87 69 25  0.039 0.039 0.044 0.061 0.083  7849.94 118695.44 324719.19 159903.44 144954.25  0.007 58. 0.016 1948. 0.027 8881. 0.041 6572. 0.083 12068.  63 58 89 09 59  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCKG ID2  29529.79 29471.16 27522.58 18640.68 12068.59  2 0 ' BLOCKS - WITHIN ORE ZONE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  OUNCES  OUTLINE  I N S I D E GRADE TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 421676. 390064. 203167. 84635.  31 31 44 75 50  0.041 0.041 0.043 0.057 0.080  17339.06 17329.31 16804.04 11615.26 6 7 7 6 . 16  1224.00 31611.87 186896.69 118532.25 84635.50  0.008 0.017 0.028 0.041 0.080  9. 525. 5188. 4839. 6776.  75 27 77 10 16  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 331589. 267338. 125305. 57234.  87 87 00 00 27  0.037 12473.97 0.038 12460.59 0.042 11353.40 0.060 7491.79 0.082 4697.12  1632.00 64251.87 142033.00 68070.69 57234.27  0.008 0.017 0.027 0.041 0.082  13. 1107. 3861. 2794. 4697.  38 20 61 67 12  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 753266. 657402. 328472. 141869.  25 25 50 75 81  0.039 0.040 0.043 0.058 0.081  2856.00 95863.75 328929.75 186602.94 141869.81  0.008 23. 0.017 1632. 0.028 9050. 0.041 7633. 0.081 11473.  13 46 39 77 29  29813.04 29789.91 28157.44 19107.05 11473.29  BLOCK MODEL: METHOE I: RESERVES  -  BENCH CUTOFF  BUCKG IDI  2 0 ' BLOCKS -• WITHIN ORE ZONE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0 .000 0 .010 0 .020 0 .035 0 .050  422900. 422900. 405405. 218443. 86414.  31 31 25 25 44  0.042 0.042 0.043 0.055 0.077  17612. 17612. 17311. 12027. 6658.  74 74 07 75 24  0.00 17495.06 186962.00 132028.81 86414.44  0.000 0.017 0.028 0.041 0.077  0 301 5283 5369 6658  .00 .67 .32 .51 .24  6860. 6860. 6860. 6860. 6860.  0 .000 0 .010 0 .020 0 .035 0 .050  333221. 333221. 281520. 130266. 52240.  87 87 12 25 34  0.037 12475. 0.037 12475. 0.041 11558. 0.057 7455. 0.080 4194.  58 58 16 49 58  0.00 51701.75 151253.87 78025.87 52240.34  0.000 0.018 0.027 0.042 0.080  0 917 4102 3260 4194  .00 .42 .67 .91 .58  TOTAL TOTAL TOTAL TOTAL TOTAL  0 .000 0 .010 0 .020 0 .035 0 .050  756122. 756122. 686925. 348709. 138654.  25 25 37 56 75  0.040 0.040 0.042 0.056 0.078  32 32 23 24 82  0.00 69196.87 338215.81 210054.81 138654.75  0.000 0 0.018 1219 0.028 9385 0.041 8630 0 . 0 7 8 10852  .00 .09 .99 .42 .82  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCKG IDO  30088. 30088. 28869. 19483. 10852.  2 0 ' BLOCKS -• WITHIN ORE ZONE lDUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0 .000 0 .010 0 .020 0 .035 0 .050  422900. 422900. 409436. 225428. 81600.  31 31 31 25 00  0.042 0.042 0.043 0.055 0.077  17770. 17770. 17530. 12298. 6306.  50 50 93 87 77  0.00 13464.00 184008.06 143828.25 81600.00  0.000 0.018 0.028 0.042 0.077  0 239 5232 5992 6306  .00 .57 .05 . 10 . 77  6860. 6860. 6860. 6860. 6860.  0 .000 0 .010 0 .020 0 .035 0 .050  333221. 333221. 286252. 134542. 54296.  87 87 87 12 66  0.037 12467. 0.037 12467. 0.041 11634. 0.056 7496. 0.077 4179.  73 73 94 50 58  0.00 46969.00 151710.75 80245.44 54296.66  0.000 0.018 0.027 0.041 0.077  0 832 4138 3316 4179  .00 .79 .44 .92 .58  TOTAL TOTAL TOTAL TOTAL TOTAL  0 .000 0 .010 0 .020 0 .035 0 .050  756122. 756122. 695689. 359970. 135896.  25 25 25 37 69  0.040 0.040 0.042 0.055 0.077  24 24 87 37 36  0.00 60433.00 335718.87 224073.69 135896.69  0.000 0.018 0.028 0.042 0.077  BLOCK MODEL: METHOD: RESERVES BENCH CUTOFF  BUCKG KRIGE  30238. 30238. 29165. 19795. 10486.  0 .00 1072 . 3 7 9370 . 5 0 9309 . 0 2 10486 . 3 6  2 0 ' BLOCKS -• WITHIN ORE ZONE lDUTLINE EXPLORATION KRIGED ESTIMATE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0 .000 0 .010 0 .020 0 .035 0 .050  422900. 422492. 397326. 195383. 84031.  31 31 87 12 69  0.041 0.041 0.043 0.058 0.080  17383. 17379. 16949. 11294. 6744.  05 32 30 77 56  408.00 25165.44 201943.75 111351.44 84031.69  0.009 0.017 0.028 0.041 0.080  3 .73 430 . 0 2 5654 . 5 3 4550 .21 6744 . 5 6  6860. 6860. 6860. 6860. 6860.  0 .000 0 .010 0 .020 0 .035 0 .050  333221. 333221. 272201. 123330. 51685.  87 87 37 25 46  0.036 12140. 0.036 12140. 0.041 11070. 0.057 7070. 0.079 4089.  83 83 59 83 89  0.00 61020.50 148871.12 71644.75 51685.46  0.000 0.018 0.027 0.042 0.079  0 .00 1070 .23 3999 . 77 2 9 8 0 , .93 4 0 8 9 .89  TOTAL TOTAL TOTAL TOTAL TOTAL  0 .000 0 .010 0 .020 0 .035 0 .050  756122. 755714. 669528. 318713. 135717.  25 25 25 37 12  0.039 0.039 0.042 0.058 0.080  88 15 90 61 45  408.00 86186.00 350814.87 182996.25 135717.12  0.009 0.017 0.028 0.041 0.080  3,.73 1500. .25 9 6 5 4 , .29 7531, .16 10834, .45  29523. 29520. 28019. 18365. 10834.  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCKG CPROB  2 0 ' BLOCKS - WITHIN ORE ZONE CONDITIONAL P R O B A B I L I T Y  ABOVE CUTOFF TONS  GRADE  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 416639. 346435. 189514. 99484.  31 12 31 06 50  0. 0. 0. 0. 0.  041 042 047 063 082  17383. 17330. 16212. 11947. 8206.  05 11 77 67 05  6261 70203 156921 90029 99484  .19 .81 .25 .56 .50  0 .008 0 .016 0 .027 0 .042 0 .082  52. ,94 1117, .34 4 2 6 5 , .10 3 7 4 1 , .62 8 2 0 6 , .05  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 324719. 242154. 119879. 62046.  87 50 87 06 67  0. 0. 0. 0. 0.  036 1 2 1 4 0 . 037 1 2 0 6 8 . 045 1 0 7 8 0 . 063 7510. 082 5106.  83 81 61 72 02  8502 82564 122275 57832 62046  .37 .62 .81 .39 .67  0 .008 0 .016 0 .027 0 .042 0 .082  72. ,02 1 2 8 8 . ,20 3 2 6 9 . ,89 2 4 0 4 . ,70 5 1 0 6 . ,02  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 741358. 588590. 309393. 161531.  25 62 19 19 12  0. 0. 0. 0. 0.  039 040 046 063 082  88 93 38 38 07  14763 152768 279197 147862 161531  .62 .44 .00 .06 . 12  0 .008 0 .016 0 .027 0 .042 0 .082  124, .95 2 4 0 5 , .55 7 5 3 5 . ,00 6 1 4 6 . .30 1 3 3 1 2 . ,07  29523. 29398. 26993. 19458. 13312.  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60 BH4  60* BLOCKS - NO ORE OUTLINE BLASTHOLE POLYGONS  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972.06 447315.06 316069.56 171588.50 100759.69  0.032 0.042 0.053 0.075 0.098  .41 .36 .51 .23 .07  163657.00 131245.50 144481.06 70828.81 100759.69  0. 0. 0. 0. 0.  004 015 027 042 098  688 1934 3848 2952 9877  .05 .85 .28 .16 .07  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076.37 357065.44 237374.50 127867.25 71024.62  0 . 0 2 6 14184 . 0 9 0 . 0 3 8 13504 . 8 2 0 . 0 4 9 11715 . 4 3 0.069 8809 .50 0.091 6457 . 7 0  187010.94 119690.94 109507.25 56842.62 71024.62  0. 0. 0. 0. 0.  004 015 027 041 091  679 1789 2905 2351 6457  .27 .39 .93* .80 .70  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 1 1 5 5 0 4 8 . 0 0 010 804380.50 020 553444.06 035 299455.81 050 171784.37  0.029 0.040 0.051 0.072 0.095  350667.50 250936.44 253988.25 127671.44 171784.37  0. 0. 0. 0. 0.  004 1367 . 3 0 015 3724 . 2 4 027 6754 . 2 0 042 5303 . 9 5 095 16334 . 7 9  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60 BH60  19300 18612 16677 12829 9877  33484 32117 28392 21638 16334  .47 .18 .94 .73 .79  6 0 ' BLOCKS •- NO ORE OUTLINE BLASTHOLE POLYGON WEIGHTED  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE:  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972.06 502901.00 385250.06 201062.44 99715.19  0 . 0 3 2 19300 . 1 7 0 . 0 3 7 18727 . 7 1 0 . 0 4 4 16893 . 5 4 0 . 0 5 9 11915 . 2 1 0.077 7687 . 0 4  108071.06 117650.94 184187.62 101347.25 99715.19  0. 0. 0. 0. 0.  005 016 027 042 077  572 1834 4978 4228 7687  .45 . 18 .32 . 17 .04  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076.37 401308.94 287901.19 143534.44 61200.03  0 . 0 2 6 14183 . 9 2 0 . 0 3 4 13493 . 18 0 . 0 4 1 11805 . 4 5 0.056 7975 . 0 7 0.075 4 6 1 4 . 79  142767.44 113407.75 144366.75 82334.37 61200.03  0. 0. 0. 0. 0.  005 015 027 041 075  690 1687 3830 3360 4614  .74 . 73 .37 .28 .79  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 1 1 5 5 0 4 8 . 0 0 010 904210.00 020 673151.31 035 344596.94 050 160915.25  0.029 0.036 0.043 0.058 0.076  250838.00 231058.69 328554.37 183681.69 160915.25  0. 0. 0. 0. 0.  005 1263 015 3521 027 8808 041 7588 076 12301  . 18 .91 .70 .45 .84  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60 BHKRIGE  33484 32220 28698 19890 12301  .07 .90 .99 .29 .84  6 0 ' BLOCKS - NO ORE OUTLINE BLASTHOLE K R I G I N G - " A C T U A L "  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972.06 521440.50 401896.50 209646.81 99715.19  0.033 0.037 0.044 0.060 0.079  .43 .30 .63 .84 .54  89531.56 119544.00 192249.69 109931.62 99715.19  0. 0. 0. 0. 0.  006 015 027 042 079  494 1808 5194 4652 7883  . 13 .67 .79 .30 .54  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076.37 410888.81 297954.31 134786.94 65851.19  0 . 0 2 7 14425 . 9 0 0 . 0 3 3 13763 . 9 5 0 . 0 4 1 12071 . 7 9 0.057 7659 . 8 7 0.073 4 7 9 9 .26  133187.56 112934.50 163167.37 68935.75 65851.19  0. 0. 0. 0. 0.  005 015 027 041 073  661 1692 4411 2860 4799  .96 . 16 .92 .61 .26  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 1 1 5 5 0 4 8 . 0 0 010 932329.37 020 699850.81 035 344433.75 050 165566.44  0.030 0.036 0.043 0.059 0.077  222718.62 232478.56 355417.06 178867.31 165566.44  0. 0. 0. 0. 0.  005 1156 .07 015 3500, .83 027 9606 .71 042 7512, . 90 077 1 2 6 8 2 , . 8 0  20033 19539 17730 12535 7883  34459 33303 29802 20195 12682  .32 .25 .42 .71 .80  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60 EX4  6 0 ' BLOCKS -• NO ORE OUTLINE EXPLORATION POLYGONS  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972.06 397620.62 278762.00 142897.94 78939.87  0.027 16613. 0.039 15594. 0.050 13894. 0.072 10350. 0.097 7620.  69 17 85 73 71  213351.44 118858.62 135864.06 63958.06 78939.87  0 .005 0 .014 0 .026 0 .043 0 .097  1019. 1699. 3544. 2730. 7620.  52 32 12 02 71  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076.37 307175.12 210397.50 114125.75 67515.81  0.025 13460. 0.041 12456. 0.053 11067. 0.074 8479. 0.098 6614.  14 24 75 98 96  236901.25 96777.62 96271.75 46609.94 67515.81  0 .004 0 .014 0 .027 0.040 0 .098  1003. 1388. 2587. 1865. 6614.  89 49 77 02 96  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048.00 704795.81 489159.56 257023.75 146455.69  0.026 0.040 0.051 0.073 0.097  80 41 60 71 67  450252.19 215636.25 232135.81 110568.06 146455.69  0 .004 0 .014 0 .026 0 .042 0 .097  2023. 3087. 6131. 4595. 14235.  39 81 89 04 67  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60 EX60  30073. 28050. 24962. 18830. 14235.  6 0 ' BLOCKS - NO ORE OUTLINE EXPLORATION POLYGON WEIGHTED  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972.06 460779.06 311108.25 145068.50 64545.63  0.027 16613. 0.034 15756. 0.044 13556. 0.063 9139. 0.090 5805.  35 59 84 47 59  150193.00 149670.81 166039.75 80522.81 64545.63  0 0 0 0 0  .006 .015 .027 .041 .090  856. 2199. 4417. 3333. 5805.  76 74 37 88 59  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076.37 384776.81 232152.06 113032.31 57544.34  0.025 13459. 0.033 12771. 0.045 10530. 0.065 7304. 0.085 4911.  68 87 01 92 15  159299.56 152624.75 119119.75 55487.97 57544.34  0 .004 0 .015 0 .027 0 .043 0 .085  687. 2241. 3225. 2393. 4911.  82 86 09 77 15  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 1 1 5 5 0 4 8 . 0 0 010 845555.87 020 543260.37 035 258100.87 050 122089.94  0.026 0.034 0.044 0.064 0.088  02 46 86 40 75  309492.12 302295.50 285159.50 136010.94 122089.94  0 .005 0 .015 0 .027 0 .042 0 .088  1544. 4441. 7642. 5727. 10716.  57 60 46 65 75  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60 IDIO  30073. 28528. 24086. 16444. 10716.  6 0 ' BLOCKS -• NO ORE OUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972.06 428334.87 310781.87 137838.75 64545.63  0.026 15911. 0.035 14907. 0.042 13167. 0.063 8704. 0.087 5623.  70 05 20 79 46  182637.19 117553.00 172943.12 73293.06 64545.63  0 0 0 0 0  .006 .015 .026 .042 .087  1004. 1739. 4462. 3081. 5623.  65 86 40 34 46  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076.37 330904.44 214134.81 94525.44 45157.46  0.023 12536. 0.035 11450. 0.046 9787. 0.070 6572. 0.099 4482.  46 12 45 90 46  213171.94 116769.62 119609.37 49367.98 45157.46  0 .005 0 .014 0 .027 0 .042 0 .099  1086. 1662. 3214. 2090. 4482.  34 68 55 43 46  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048.00 759239.37 524916.69 232364.25 109703.06  0.025 0.035 0.044 0.066 0.092  16 18 64 70 91  395808.62 234322.69 292552.44 122661.19 109703.06  0 .005 0 .015 0 .026 0 .042 0 .092  2090. 3402. 7676. 5171. 10105.  97 54 94 79 91  28448. 26357. 22954. 15277. 10105.  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60 ID5  6 0 ' BLOCKS - NO ORE OUTLINE INVERSE DISTANCE I N S I D E 1 GRADE:  ABOVE CUTOFF GRADE TONS  GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0 .000 0 .010 0 .020 0 .035 0 .050  610972. 450774. 344139. 156100. 68217.  06 87 94 81 62  0.027 16617. 0.035 15656. 0.041 14132. 0.060 9315. 0.084 5718.  16 65 25 15 74  160197. 106634. 188039. 87883. 68217.  19 94 12 19 62  0. 0. 0. 0. 0.  006 014 026 041 084  960 1524 4817 3596 5718  .51 .40 .10 .41 .74  6860. 6860. 6860. 6860. 6860.  0 .000 0 .010 0 .020 0 .035 0 .050  544076. 361210. 222147. 94525. 41485.  37 69 94 44 46  0.023 12448. 0.032 11485. 0.043 9522. 0.065 6157. 0.095 3961.  25 59 51 70 06  182865. 139062. 127622. 53039. 41485.  69 75 50 98 46  0. 0. 0. 0. 0.  005 014 026 041 095  962 1963 3364 2196 3961  .66 .08 .81 .64 .06  TOTAL TOTAL TOTAL TOTAL TOTAL  0 .000 0 .010 0 .020 0 .035 0 .050  1155048. 811985. 566287. 250626. 109703.  00 62 87 31 06  0.025 0.033 0.042 0.062 0.088  41 25 76 85 79  343062. 245697. 315661. 140923. 109703.  37 75 56 25 06  0. 0. 0. 0. 0.  006 014 026 041 088  1923 3487 8181 5793 9679  .16 .49 .91 .06 .79  BLOCK MODEL: METHOD:  BUCK60 ID3  RESERVES  -  BENCH CUTOFF  29065. 27142. 23654. 15472. 9679.  6 0 ' BLOCKS -• NO ORE OUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E I GRADE! BOUNDARIES  OUNCES  TONS  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0 .000 0 .010 0 .020 0 .035 0 .050  610972. 477033. 361292. 156247. 79233.  06 81 31 75 62  0.028 17326. 0.034 16447. 0.041 14754. 0.060 9445. 0.078 6219.  97 20 73 33 13  133938. 115741. 205044. 77014. 79233.  25 50 56 12 62  0. 0. 0. 0. 0.  007 015 026 042 078  879 1692 5309 3226 6219  .78 .46 .41 .20 .13  6860. 6860. 6860. 6860. 6860.  0 .000 0 .010 0 .020 0 .035 0 .050  544076. 383552. 226897. 86055. 48144.  37 75 00 37 02  0.023 12592. 0.030 11677. 0.042 9432. 0.065 5572. 0.084 4023.  44 05 75 69 38  160523. 156655. 140841. 37911. 48144.  62 75 62 36 02  0. 0. 0. 0. 0.  006 014 027 041 084  915 2244 3860 1549 4023  .39 .30 .05 .31 .38  TOTAL TOTAL TOTAL TOTAL TOTAL  0 .000 0 .010 0 .020 0 .035 0 .050  1155048. 860586. 588189. 242303. 127377.  00 62 37 12 62  0.026 0.033 0.041 0.062 0.080  41 25 49 02 51  294461. 272397. 345886. 114925. 127377.  37 25 25 50 62  0. 0. 0. 0. 0.  006 014 027 042 080  1795 3936 9169 4775 10242  . 16 .76 .46 .52 .51  BLOCK MODEL: METHOD:  BUCK60 ID2  RESERVES  -  BENCH CUTOFF  29919. 28124. 24187. 15018. 10242.  6 0 ' BLOCKS - NO ORE OUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E I GRADE1 BOUNDARIES  OUNCES  TONS  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0 .000 0 .010 0 .020 0 .035 0 .050  610972. 514863. 379423. 156247. 86577.  06 56 81 75 62  0.029 17832. 0.033 17185. 0.040 15270. 0.060 9372. 0.075 6513.  84 22 69 76 18  96108. 135439. 223176. 69670. 86577.  50 75 06 12 62  0. 0. 0. 0. 0.  007 014 026 041 075  647 1914 5897 2859 6513  .62 .53 .93 .58 .18  6860. 6860. 6860. 6860. 6860.  0 0 0 0 0  .000 .010 .020 .035 .050  544076. 396918. 237913. 92942. 49090.  37 87 06 44 58  0.024 12820. 0.030 11897. 0.040 9620. 0.060 5616. 0.078 3849.  79 27 65 09 69  147157. 159005. 144970. 43851. 49090.  50 81 62 86 58  0. 0. 0. 0. 0.  006 014 028 040 078  923 2276 4004 1766 3849  .52 .62 .55 .41 .69  TOTAL TOTAL TOTAL TOTAL TOTAL  0 .000 0 .010 0 .020 0 .035 0 .050  1155048. 911782. 617336. 249190. 135668.  00 44 87 19 19  0.027 0.032 0.040 0.060 0.076  62 50 34 86 86  243265. 294445. 368146. 113522. 135668.  56 56 69 00 19  0. 0. 0. 0. 0.  006 1571 014 4191 027 9902 041 4625 076 10362  .12 .16 .48 .99 .86  30653. 29082. 24891. 14988. 10362.  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60 IDI  6 0 ' BLOCKS - NO ORE OUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972.06 552677.00 400754.06 163591.75 84521.31  0.030 18457. 0.033 18093. 0.040 15853. 0.058 9569. 0.074 6278.  41 99 91 28 91  58295.06 151922.94 237162.31 79070.44 84521.31  0. 0. 0. 0. 0.  006 015 026 042 074  363 2240 6284 3290 6278  .42 .08 .63 .36 .91  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076.37 432659.69 245991.44 110355.87 37666.57  0.024 13224. 0.029 12511. 0.040 9846. 0.056 6157. 0.082 3093.  52 52 07 63 16  111416.69 186668.25 135635.56 72689.25 37666.57  0. 0. 0. 0. 0.  006 014 027 042 082  713 2665 3688 3064 3093  .00 .45 .43 .47 .16  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 1 1 5 5 0 4 8 . 0 0 010 985336.75 020 646745.56 035 273947.62 050 122187.87  0.027 31681. 0.031 30605. 0.040 25699. 0.057 15726. 0.077 9372.  93 51 98 91 07  169711.25 338591.19 372797.94 151759.75 122187.87  0. 0. 0. 0. 0.  006 014 027 042 077  1076 4905 9973 6354 9372  .41 .53 .07 .85 .07  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60 IDO  6 0 ' BLOCKS -• NO ORE OUTLINE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972.06 561245.00 416143.81 163575.37 73146.25  0.031 18924. 0.033 18604. 0.039 16338. 0.059 9622. 0.079 5774.  66 24 87 45 70  49727.06 145101.19 252568.44 90429.12 73146.25  0. 0. 0. 0. 0.  006 016 027 043 079  320 2265 6716 3847 5774  .41 .37 .43 . 75 .70  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076.37 437718.87 250642.62 103925.75 51408.02  0.025 13591. 0.029 12845. 0.041 10166. 0.059 6094. 0.076 3889.  05 43 66 39 53  106357.50 187076.25 146716.87 52517.73 51408.02  0. 0. 0. 0. 0.  007 014 028 042 076  745 2678 4072 2204 3889  .62 .77 .28 .86 .53  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 1 1 5 5 0 4 8 . 0 0 010 998963.94 020 666786.50 035 267501.19 050 124554.25  0.028 0.031 0.040 0.059 0.078  70 68 54 84 23  156084.06 332177.44 399285.31 142946.94 124554.25  0. 0. 0. 0. 0.  007 1066 . 0 2 015 4 9 4 4 . 14 027 10788 . 70 042 6052 . 6 1 078 9664 . 2 3  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60 KRIGE  32515. 31449. 26505. 15716. 9664.  6 0 ' BLOCKS - NO ORE OUTLINE EXPLORATION K R I G I N G  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972.06 533598.94 379864.44 172388.19 62587.23  0.030 18042. 0.033 17562. 0.040 15232. 0.057 9868. 0.084 5251.  68 14 35 54 24  77373.12 153734.50 207476.25 109800.94 62587.23  0. 0. 0. 0. 0.  006 015 026 042 084  480 2329 5363 4617 5251  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076.37 419407.81 251687.12 101706.25 37682.89  0.024 12860. 0.029 12072. 0.038 9653. 0.056 5744. 0.082 3075.  89 50 65 20 67  124668.56 167720.69 149980.87 64023.36 37682.89  0. 0. 0. 0. 0.  006 014 026 042 082  788 . 3 8 2418 . 8 6 3909 . 4 5 2668, .53 3075 .67  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 1 1 5 5 0 4 8 . 0 0 010 953006.81 020 631551.62 035 274094.50 050 100270.12  0.027 0.031 0.039 0.057 0.083  56 65 00 74 91  202041.19 321455.19 357457.12 173824.37 100270.12  0. 0. 0. 0. 0.  006 015 026 042 083  1268 .91 4 7 4 8 , .65 9 2 7 3 , .26 7285 .83 8 3 2 6 , .91  30903. 29634. 24886. 15612. 8326.  .54 . 79 .81 .30 .24  248 BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60 CPROB  6 0 ' BLOCKS - NO ORE OUTLINE CONDITIONAL P R O B A B I L I T Y  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  610972. 497144. 340912. 170150. 86274.  06 81 94 50 50  0. 0. 0. 0. 0.  030 18042 . 6 8 035 17409 . 6 2 044 15076 . 7 1 062 10512 . 0 4 081 7022 . 4 3  113827. 156231. 170762. 83876. 86274.  25 87 44 00 50  0. 0. 0. 0. 0.  006 015 027 042 081  633 2332 4564 3489 7022  .06 .91 .67 .61 .43  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  544076. 382812. 231804. 106763. 52001.  37 81 56 75 42  0. 0. 0. 0. 0.  024 12860 . 8 9 031 11976 . 1 2 042 9762 . 7 7 060 6443 . 9 5 080 4166 . 0 2  161263. 151008. 125040. 54762. 52001.  56 25 81 33 42  0. 0. 0. 0. 0.  005 015 027 042 080  884 2213 3318 2277 4166  .77 .35 .82 .93 .02  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  1155048. 879957. 572717. 276914. 138275.  00 69 56 31 87  0. 0. 0. 0. 0.  027 033 043 061 081  275090. 307240. 295803. 138638. 138275.  31 12 25 44 87  0. 0. 0. 0. 0.  006 015 027 042 081  1517 4546 7883 5767 11188  .82 .25 .49 .54 .45  30903 29385 24839 16956 11188  .56 .74 .49 .00 .45  249 BLOCK MODEL: METHOE I: RESERVES  -  BENCH CUTOFF  BUCK60G BH4  6 0 ' BLOCKS -• WITHIN ORE ZONE 1DUTLINE BLASTHOLE POLYGONS  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900.31 374397.25 287999.12 163934.44 97691.56  0.041 0.045 0.054 0.075 0.098  17212. 16965. 15665. 12337. 9568.  70 49 06 18 37  48503.06 86398.12 124064.69 66242.87 97691.56  0.005 0.015 0.027 0.042 0.098  247. 1300. 3327. 2768. 9568.  21 43 88 82 37  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221.87 290479.75 212845.50 120768.00 68886.75  0.037 0.041 0.051 0.070 0.091  12279. 12054. 10886. 8414. 6263.  08 28 00 78 66  42742.12 77634.25 92077.50 51881.25 68886.75  0.005 0.015 0.027 0.041 0.091  224. 1168. 2471. 2151. 6263.  80 28 22 11 66  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122.25 664877.06 500844.69 284702.50 166578.31  0.039 0.044 0.053 0.073 0.095  29491. 29019. 26551. 20751. 15832.  80 77 06 98 03  91245.19 164032.37 216142.19 118124.19 166578.31  0.005 472. 0.015 2468. 0.027 5799. 0.042 4919. 0.095 15832.  04 70 09 95 03  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60G BH60  6 0 ' BLOCKS -• WITHIN ORE ZONE 1DUTLINE BLASTHOLE POLYGON WEIGHTED  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900.31 409550.56 357718.19 191906.94 108674.87  0.041 0.042 0.045 0.061 0.076  17212. 17141. 16250. 11708. 8233.  47 68 20 68 92  13349.75 51832.37 165811.25 83232.06 108674.87  0.005 0.017 0.027 0.042 0.076  70. 891. 4541. 3474. 8233.  79 49 51 77 92  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221.87 324164.25 255701.81 143860.81 69637.44  0.037 12278. 0.038 12221. 0.044 11126. 0.056 8117. 0.073 5085.  81 14 71 33 44  9057.62 68462.44 111841.00 74223.37 69637.44  0.006 0.016 0.027 0.041 0.073  57. 1094. 3009. 3031. 5085.  66 43 38 89 44  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122.25 733714.87 613420.06 335767.81 178312.37  0.039 0.040 0.045 0.059 0.075  28 83 91 02 37  22407.37 120294.81 277652.25 157455.44 178312.37  0.006 128. 0.017 1985. 0.027 7550. 0.041 6506. 0.075 13319.  45 92 89 65 37  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60G BHKRIGE  29491. 29362. 27376. 19826. 13319.  6 0 ' BLOCKS -• WITHIN ORE ZONE 1DUTLINE BLASTHOLE K R I G I N G - " A C T U A L "  ABOVE CUTOFF GRADE TONS  GRADE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900.31 410121.75 375670.19 200850.31 104986.56  0.042 0.043 0.046 0.062 0.079  17779. 17696. 17125. 12362. 8275.  30 84 20 94 78  12778.56 34451.56 174819.87 95863.75 104986.56  0.006 0.017 0.027 0.043 0.079  82. 571. 4762. 4087. 8275.  46 64 26 16 78  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221.87 324768.12 270618.31 136663.69 70306.56  0.037 12403. 0.038 12344. 0.042 11481. 0.057 7848. 0.072 5076.  29 15 96 04 20  8453.75 54149.81 133954.62 66357.12 70306.56  0.007 0.016 0.027 0.042 0.072  59. 862. 3633. 2771. 5076.  14 18 92 85 20  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122.25 734889.87 646288.56 337514.06 175293.19  0.040 0.041 0.044 0.060 0.076  59 00 17 98 98  21232.37 88601.31 308774.50 162220.87 175293.19  0.007 0.016 0.027 0.042 0.076  141. 1433. 8396. 6859. 13351.  59 82 19 00 98  30182. 30041. 28607. 20210. 13351.  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60G EX4  6 0 ' BLOCKS - WITHIN ORE ZONE EXPLORATION POLYGONS  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  0.006 0 . 014 0 . 026 0 . 043 0 . 096  324. 1415. 3355. 2619. 7437.  36 63 19 04 31  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 366269. 267811. 138834. 77438.  31 87 31 25 37  0.036 0.040 0.050 0.072 0.096  15151. 14827. 13411. 10056. 7437.  52 16 53 34 31  56630.44 98458.56 128977.06 61395.87 77438.37  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 287933. 200018. 107206. 63109.  87 87 00 12 46  0.036 12055. 0.041 11818. 0.053 10562. 0.075 8069. 0.100 6294.  03 11 17 48 95  45288.00 87915.87 92811.87 44096.66 63109.46  0. 0. 0. 0. 0.  005 014 027 040 100  236. 1255. 2492. 1774. 6294.  92 94. 69 54 95  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 654203. 467829. 246040. 140547.  25 81 31 37 87  0.036 0.041 0.051 0.074 0.098  55 28 71 83 26  101918.44 186374.50 221788.94 105492.50 140547.87  0. 0. 0. 0. 0.  006 014 026 042 098  561. 2671. 5847. 4393. 13732.  28 57 88 57 26  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60G EX60  27206. 26645. 23973. 18125. 13732.  6 0 ' BLOCKS -• WITHIN ORE ZONE EXPLORATION POLYGON WEIGHTED  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 402532. 308741. 153538. 64839.  31 94 87 62 39  0.036 15151. 0.037 14986. 0.044 13577. 0.062 9475. 0.090 5835.  29 57 85 70 53  20367.37 93791.06 155203.25 88699.19 64839.39  0. 0. 0. 0. 0.  008 015 026 041 090  164. 1408. 4102. 3640. 5835.  72 72 15 17 53  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 328587. 230977. 109539. 55830.  87 00 06 87 74  0.036 0.037 0.046 0.066 0.087  12054. 12022. 10513. 7180. 4866.  71 81 14 96 56  4634.87 97609.94 121437.19 53709.13 55830.74  0. 0. 0. 0. 0.  007 015 027 043 087  31. 1509. 3332. 2314. 4866.  89 67 18 40 56  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 731120. 539718. 263078. 120670.  25 00 94 50 12  0.036 0.037 0.045 0.063 0.089  27206. 27009. 24091. 16656. 10702.  00 39 00 65 09  25002.25 191401.06 276640.44 142408.37 120670.12  0. 0. 0. 0. 0.  008 196. 015 2918. 027 7434. 042 5954. 089 1 0 7 0 2 .  61 39 35 55 09  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60G IDIO  6 0 ' BLOCKS -• WITHIN ORE ZONE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 404719. 319007. 140564. 67352.  31 81 12 19 62  0.035 14955. 0.037 14843. 0.042 13524. 0.063 8857. 0.086 5784.  87 20 34 14 12  18180.50 85712.69 178442.94 73211.56 67352.62  0. 0. 0. 0. 0.  006 015 026 042 086.  112. 1318. 4667. 3073. 5784.  66 86 20 03 12  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 313083. 231466. 98083. 51359.  87 00 62 19 06  0.035 11797. 0.037 11677. 0 . 0 4 5 10394. 0.069 6806. 0.094 4851.  02 21 92 46 53  20138.87 81616.37 133383.44 46724.12 51359.06  0. 0. 0. 0. 0.  006 016 027 042 094  119. 1282. 3588. 1954. 4851.  81 29 45 94 53  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 717802. 550473. 238647. 118711.  25 87 81 44 69  0.035 0.037 0.043 0.066 0.090  89 41 27 61 65  38319.37 167329.06 311826.37 119935.75 118711.69  0. 0. 0. 0. 0.  006 232. 016 2601. 026 8255. 042 5027. 090 1 0 6 3 5 .  48 14 66 96 65  26752. 26520. 23919. 15663. 10635.  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60G ID5  6 0 ' BLOCKS - WITHIN ORE ZONE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900.31 406710.87 354764.31 172894.12 74223.37  0.037 0.038 0.042 0.058 0.082  15764. 15642. 14815. 10059. 6068.  52 05 45 79 00  16189.44 51946.56 181870.19 98670.75 74223.37  0.008 0.016 0.026 0.040 0.082  122. 826. 4755. 3991. 6068.  47 61 66 79 00  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221.87 318256.44 240328.37 98638.06 47115.86  0.035 11749. 0.037 11653. 0.043 10355. 0.066 6537. 0.093 4366.  78 23 75 68 13  14965.44 77928.06 141690.31 51522.20 47115.86  0.006 0.017 0.027 0.042 0.093  96. 1297. 3818. 2171. 4366.  54 48 07 55 13  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122.25 724967.31 595092.69 271532.25 121339.25  0.036 0.038 0.042 0.061 0.086  30 29 20 48 14  31154.94 129874.62 323560.44 150193.00 121339.25  0.007 0.016 0.026 0.041 0.086  219. 2124. 8573. 6163. 10434.  01 09 71 35 14  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60G ID3  27514. 27295. 25171. 16597. 10434.  6 0 ' BLOCKS - WITHIN ORE ZONE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900.31 410382.87 373891.31 179112.06 84766.06  0.039 0.040 0.042 0.059 0.078  16487. 16381. 15794. 10499. 6594.  60 54 69 04 30  12517.44 36491.56 194779.25 94346.00 84766.06  0.008 0.016 0.027 0.041 0.078  106. 586. 5295. 3904. 6594.  06 85 65 74 30  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221.87 323903.12 258574.19 96271.69 51669.14  0.036 11894. 0.037 11834. 0.042 10738. 0.065 6261. 0.085 4405.  65 41 26 96 49  9318.75 65328.94 162302.50 44602.55 51669.14  0.006 0.017 0.028 0.042 0.085  60. 1096. 4476. 1856. 4405.  24 15 30 47 49  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122.25 734286.06 632465.56 275383.75 136435.25  0.038 0.038 0.042 0.061 0.081  26 96 96 01 80  21836.19 101820.50 357081.81 138948.50 136435.25  0.008 0.017 0.027 0.041 0.081  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60G ID2  28382. 28215. 26532. 16761. 10999.  6 0 ' BLOCKS -• WITHIN ORE ZONE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  1 6 6 . 30 1 6 8 3 . 00 9771 . 95 5 7 6 1 . 21 1 0 9 9 9 . 80  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900.31 419228.31 388889.44 187826.94 93464.62  0.040 0.040 0.042 0.058 0.075  16946. 16911. 16434. 10830. 7003.  35 39 25 75 05  3672.00 30338.87 201062.50 94362.31 93464.62  0.010 0.016 0.028 0.041 0.075  34. 477. 5603. 3827. 7003.  96 14 50 71 05  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221.87 328423.81 266619.94 117716.19 54117.14  0.036 12071. 0.037 12029. 0.041 10974. 0.059 6897. 0.081 4371.  93 16 40 91 73  4798.06 61803.87 148903.75 63599.05 54117.14  0.009 0.017 0.027 0.040 0.081  42. 1054. 4076. 2526. 4371.  77 77 49 18 73  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122.25 747652.12 655509.37 305543.12 147581.81  0.038 0.039 0.042 0.058 0.077  29 56 65 67 79  8470.12 92142.75 349966.25 157961.31 147581.81  0.009 77. 0.017 1531. 0.028 9679. 0.040 6353. 0.077 11374.  72 91 98 88 79  29018. 28940. 27408. 17728. 11374.  BLOCK MODEL: METHOD: RESERVES  -  BENCH CUTOFF  BUCK60G IDI  6 0 ' BLOCKS - WITHIN ORE ZONE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0 .000 0 .010 0 .020 0 .035 0 .050  422900.31 422900.31 402581.94 206856.06 95635.19  0.041 0.041 0.043 0.056 0.073  17483. 17483. 17144. 11518. 7026.  48 48 42 27 53  0.00 20318.37 195725.87 111220.87 95635.19  0.000 0.017 0.029 0.040 0.073  0. 339. 5626. 4491. 7026.  00 06 14 75 53  6860. 6860. 6860. 6860. 6860.  0 .000 0 .010 0 .020 0 .035 0 .050  333221.87 333221.87 295049.37 125713.00 44455.70  0.037 12375. 0.037 12375. 0.040 11726. 0.057 7162. 0.084 3725.  63 63 40 48 58  0.00 38172.50 169336.37 81257.25 44455.70  0.000 0.017 0.027 0.042 0.084  0. 649. 4563. 3436. 3725.  00 23 92 90 58  TOTAL TOTAL TOTAL TOTAL TOTAL  0 .000 0 .010 0 .020 0 .035 0 .050  756122.25 756122.25 697631.31 332569.06 140090.94  0.039 0.039 0.041 0.056 0.077  12 12 82 76 11  0.00 58490.94 365062.25 192478.12 140090.94  0.000 0. 0.017 988. 0.028 10190. 0.041 7928. 0.077 10752.  00 30 06 65 11  BLOCK MODEL: METHOE ): RESERVES  -  BENCH CUTOFF  BUCK60G IDO  29859. 29859. 28870. 18680. 10752.  6 0 ' BLOCKS -• WITHIN ORE ZONE INVERSE DISTANCE  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0 .000 0 .010 0 .020 0 .035 0 .050  422900.31 422900.31 406923.06 217643.56 73032.00  0.042 0.042 0.043 0.056 0.082  17864. 17864. 17577. 12104. 5965.  58 58 02 72 32  0.00 15977.25 189279.50 144611.56 73032.00  0.000 0.018 0.029 0.042 0.082  0. 287. 5472. 6139. 5965.  00 56 30 39 32  6860. 6860. 6860. 6860. 6860.  0 .000 0 .010 0 .020 0 .035 0 .050  333221.87 333221.87 294331.31 137365.50 59437.46  0.038 12671. 0.038 12671. 0.041 12000. 0.056 7714. 0.076 4501.  93 93 61 92 09  0.00 38890.56 156965.81 77928.00 59437.46  0.000 0.017 0.027 0.041 0.076  0. 671. 4285. 3213. 4501.  00 32 69 84 09  TOTAL TOTAL TOTAL TOTAL TOTAL  0 .000 0 .010 0 .020 0 .035 0 .050  756122.25 756122.25 701254.37 355009.06 132469.44  0.040 30536. 0.040 30536. 0.042 29577. 0.056 19819. 0.079 10466.  51 51 62 64 41  0.00 54867.87 346245.31 222539.62 132469.44  0.000 0.017 0.028 0.042 0.079  0. 958. 9757. 9353. 10466.  00 89 98 23 41  BLOCK MODEL: METHOE RESERVES  -  BENCH CUTOFF  BUCK60G KRIGE  6 0 ' BLOCKS - WITHIN ORE ZONE EXPLORATION K R I G I N G  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0 .000 0 .010 0 .020 0 .035 0 .050  422900.31 422900.31 400117.56 198810.31 80392.31  0.040 17120. 0.040 17120. 0.042 16766. 0.056 11184. 0.079 6358.  96 96 92 35 04  0.00 22782.75 201307.25 118418.00 80392.31  0.000 0.016 0.028 0.041 0.079  0. 354. 5582. 4826. 6358.  00 04 57 31 04  6860. 6860. 6860. 6860. 6860.  0 .000 0 .010 0 .020 0 .035 0 .050  333221.87 333221.87 268839.44 113146.56 38613.14  0 . 0 3 5 1 1 7 1 6 . 03 0 . 0 3 5 1 1 7 1 6 . 03 0 . 0 3 9 1 0 5 8 6 . 83 0.056 6 3 1 1 . 84 0.082 3 1 8 3 . 29  0.00 64382.44 155692.87 74533.37 38613.14  0.000 0.018 0.027 0.042 0.082  0. 1129. 4274. 3128. 3183.  00 20 99 55 29  TOTAL TOTAL TOTAL TOTAL TOTAL  0 .000 0 .010 0 .020 0 .035 0 .050  756122.25 756122.25 668957.06 311956.94 119005.44  0.038 0.038 0.041 0.056 0.080  0.00 87165.19 357000.12 192951.50 119005.44  0.000 0.017 0.028 0.041 0.080  0. 1483. 9857. 7954. 9541.  00 24 56 87 32  28837. 28837. 27353. 17496. 9541.  00 00 75 20 32  253 BLOCK MODEL: METHOD: RESERVES BENCH CUTOFF  BUCK60G CPROB  6 0 ' BLOCKS -• WITHIN ORE ZONE CONDITIONAL P R O B A B I L I T Y  ABOVE CUTOFF GRADE TONS  GRADE  OUTLINE  I N S I D E 1 GRADE  OUNCES  TONS  BOUNDARIES  GRADE  OUNCES  6840. 6840. 6840. 6840. 6840.  0. 0. 0. 0. 0.  000 010 020 035 050  422900. 418366. 353919. 191536. 93856.  31 31 12 87 37  0.040 0.041 0.045 0.061 0.081  17120. 17081. 16050. 11612. 7561.  96 02 83 12 16  4534. 64447. 162382. 97680. 93856.  00 19 25 50 37  0.009 0.016 0.027 0.041 0.081  39 1030 4438 4050 7561  .94 .20 .71 .96 . 16  6860. 6860. 6860. 6860. 6860.  0. 0. 0. 0. 0.  000 010 020 035 050  333221. 327608. 246707. 115476. 53390.  87 12 37 94 14  0.035 11716. 0.036 11667. 0.042 10390. 0.059 6869. 0.080 4295.  03 26 03 27 92  5613. 80900. 131230. 62086. 53390.  75 75 44 79 14  0.009 0.016 0.027 0.041 0.080  48 1277 3520 2573 4295  .77 .23 . 76 .35 .92  TOTAL TOTAL TOTAL TOTAL TOTAL  0. 0. 0. 0. 0.  000 010 020 035 050  756122. 745974. 600626. 307013. 147246.  25 44 56 87 56  0.038 0.039 0.044 0.060 0.081  00 28 87 39 09  10147. 145347. 293612. 159767. 147246.  81 87 69 31 56  0.009 88 0.016 2307 0.027 7959 0.041 6624 0 . 0 8 1 11857  .71 .41 .47 .31 .09  28837. 28748. 26440. 18481. 11857.  254  APPENDIX D  L I S T I N G OF CALCULATED SEMI-VARIOGRAM  note:  raw g r a d e s were m u l t i p l i e d  VALUES  by  100  LEGEND:  LAG  Lag d i s t a n c e .  N  Number o f p a i r s f o r a r i t h m e t i c r e l a t i v e variograms.  LN  Number o f  AR MEAN  A r i t h m e t i c mean g r a d e  LG MEAN  L o g n o r m a l mean g r a d e  VG  Calculated  variogram  LOG VG  Lognormal  variogram.  REL VG  Relative  samples  for  variogram.  and  lognormal of of  variogram,  samples. samples.  value.  255 FILE= ANGLE VERT ANG= LAG 30 57 105 137  N 831 5553 11622 6235  FILE= ANGLE VERT ANG= LAG 29 66 105 137  N 578 5289 9457 6758  FILE= ANGLE VERT ANG= LAG 31 57 105 139  N 527 5707 11524 4969  FILE= ANGLE l _ VERT ANG= LAG 32 66 106 137  N 554 5538 9010 6885  FILE= ANGLE VERT ANG= LAG 21 41 61 81 101  N 2020 1591 1185 825 530  BEX 90 0 LN 819 5410 11326 6104  AR MEAN LG MEAN 48.7 39.5 36.8 37.3  1.4211 1.3067 1.2981 1.2750  VG  LOG VG  REL VG  2476 . 1 2775. 8 2634. 6 2818. 6  0.1675 0.2186 0.2402 0.3011  1.0458 1.7757 1.9432 2.0308  VG  LOG VG  REL VG  2785. 0 2576 . 6 2791. 5 2595. 1  0.2100 0.2109 0.2416 0.2661  1.1516 1.6900 2.0173 1.9209  VG  LOG VG  REL VG  2578 . 0 2378. 7 2459. 2 2516 . 1  0 .1858 0.1881 0.2134 0.2395  1.2172 1 .5684 1.8283 1.8044  VG  LOG VG  REL VG  2556 . 0 2219. 3 2685. 9 2549 . 8  0.2498 0.2039 0.2285 0.2539  1.2367 1.5268 1.9704 1.8832  VG  LOG VG  REL VG  1134 . 7 1799. 8 1812. 1 2095. 1 2242. 3  0.0883 0.1421 0.1744 0.2117 0.2300  1.0778 1.6602 1.7701 2.0325 2.3290  BEX 45 0 LN 567 5166 9224 6625  AR MEAN LG MEAN 49.2 39.0 37.2 36.8  1.3704 1.3163 1.2911 1.2872  BEX 0 0 LN 524 5561 11230 4879  AR MEAN LG MEAN 46.0 38.9 36.7 37.3  1.3760 1.3176 1.2958 1.2816  BEX 135 0 LN 547 5417 8791 6746  AR MEAN LG MEAN 45.5 38.1 36.9 36.8  1.3027 1.3039 1.2848 1.2913  BEX 0 90 LN 1970 1547 1144 788 501  AR MEAN LG MEAN 32.4 32.9 32.0 32.1 31.0  1.2164 1.2200 1.2133 1.2107 1.1830  256 FILE= ANGLE= VERT ANG= LAG 29 56 105 137  N 329 2278 4759 2215  FILE= ANGLE VERT ANG= LAG 26 67 106 137  N 191 2172 3781 2586  FILE= ANGLE VERT ANG= LAG 27 55 106 140  N 167 2575 5067 1923  FILE= ANGLE VERT ANG= LAG 29 66 108 138  N 165 2408 3704 2681  FILE= ANGLE VERT ANG= LAG  N  21 41 61 81 101  759 530 337 179 55  BEXG 90 0 LN 327 2269 4730 2210  AR MEAN LG MEAN 49.8 46.8 44.8 46.2  1.5063 1.4751 1.4678 1.4765  VG  LOG VG  REL VG  2510 . 9 3665. 6 2984 . 2 3105. 2  0.1451 0.1523 0.1606 0.1819  1.0130 1.6755 1.4886 1.4520 •  BEXG 45 0 LN 190 2159 3769 2576  AR MEAN LG MEAN 47 . 3 45.4 45.3 45.5  1.4501 1.4727 1.4629 1.4742  VG  LOG VG  REL VG  2827 . 0 3070 . 3 3344. 6 2985. 6  0.1911 0.1475 0.1646 0.1631  1.2648 1.4878 1.6322 1.4431  VG  LOG VG  REL VG  2795. 7 2991. 9 3198. 2 3686 . 8  0.1403 0.1445 0.1608 0.1752  1 .0171 1 . 3695 1.5196 1.5318  VG  LOG VG  REL VG  2549. 7 2401. 2 3449 . 1 2899 . 3  0.1790 0.1425 0.1627 0.1732  0.7364 1.2486 1.6171 1.3868  VG  LOG VG  REL VG  0 .0741 0.1068 0.1203 0.1115 0.1200  0.8717 1. 3308 1.2622 1.0237 0 .6012  BEXG 0 0 LN 166 2559 5038 1914  AR MEAN LG MEAN 52.4 46 .7 45.9 49.1  1.5412 1.4829 1.4704 1.4947  BEXG 135 0 LN 164 2395 3676 2671  AR MEAN LG MEAN 58.8 43.9 46.2 45.7  1.5707 1.4626 1.4725 1.4799  BEXG 0 90 LN 755 526 332 174 53  AR MEAN LG MEAN 45.9 45.7 44.3 43.3 42.5  1.4864 1.4856 1.4741 1.4663 1.4773  1835. 2779. 2481. 1915. 1086.  2 5 4 6 8  257 FILE= ANGLE= VERT ANG= N  LAG 14 32 51 70 90 110 130 145  6891 43651 78256 105621 130096 155677 177403 96894  F I L Ei ANGLE= VERT ANG= 1  LAG  N 5854 41865 76334 104405 128193 152144 171886 92933  15 32 51 70 90 110 130 145  FILE — ANGLE= VERT ANG= l  1  LAG 14 32 51 70 90 110 130 145  N 6822 43712 77950 105823 129943 154452 172351 92854  BBH 90 0 LN 6874 43538 77990 105302 129677 155142 176798 96539  AR MEAN LG MEAN 36 39 39 39 40 40 39 39  .7 .5 .7 .9 .2 .1 .7 .7  1. 1. 1. 1. 1. 1. 1. 1.  3012 3139 3211 3288 3359 3363 3360 3375  LOG VG  REL VG  0 .0739 0 .1381 0 .1759 0 .2087 0 .2387 0 .2640 0 .2789 0 .2863  1 .1590 1 .6904 1 .8234 1 .9378 2 .0223 2 .0535 1 .9952 1 .9837  VG  LOG VG  REL VG  1610 . 8 2589 . 2 2800 . 5 2867 . 4 3121. 0 3131. 9 3054. 7 3086. 7  0 .0777 0 .1343 0 .1649 0 .1920 0 .2205 0 .2414 0 .2578 0 .2678  1 .2309 1 .6790 1 .7799 1 .8309 1 . 9812 2 .0054 1 .9953 2 .0241  VG  LOG VG  REL VG  1440 . 2 2475. 1 2546 . 9 2796. 7 2966 . 2 3052. 7 2995. 9 3070 . 2  0 .0638 0 . 1119 0 .1320 0 .1507 0 .1675 0 .1823 0 .1934 0 .2001  1 . 1043 1 .6283 1 .6533 1 .8070 1 .9287 1 .9721 1 .9977 2 .0443  VG 1560. 2636. 2872. 3084. 3261. 3302. 3140. 3126.  6 9 5 2 3 3 7 9  BBH 45 0 LN 5838 41743 76108 104079 127825 151671 171339 92630  AR MEAN LG 1 MEAN 36 .2 39 .3 39 . 7 39 .6 39 .7 39 .5 39 .1 39 .1  1. 1. 1. 1. 1. 1. 1. 1.  2780 3077 3177 3242 3261 3282 3271 3276  BBH 0 0 LN 6793 43571 77710 105514 129529 153922 171765 92510  AR MEAN LGI MEAN 36 .1 39 .0 39 .2 39 .3 39 .2 39 .3 38 .7 38 .8  1. 2619 1. 2983 1. 3086 1 . 3110 1. 3106 1. 3143 1. 3102 1. 3110  FILE= ANGLE= VERT ANG= N  LAG 15 32 51 70 90 110 130 145  5888 42168 76343 106062 130890 155512 177977 96231  F I L EI ANGLE= VERT ANG= 1  LAG 21 41 61 81 101  N 3257 2022 958 295 10  BBH 135 0 LN 5872 42053 76119 105723 130458 154958 177307 95874  AR MEAN LG - MEAN 36 .4 38 .9 39 .5 39 .6 39 .8 39 .7 39 .7 39 .6  1. 1. 1. 1. 1. 1. 1. 1.  2870 3021 3151 3191 3238 3265 3285 3300  VG  LOG VG  REL VG  0 .0660 0 .1202 0 .1470 0 .1713 0 .1927 0 .2124 0 .2282 0 .2381  1 .1097 1 .5528 1 .6824 1 .8756 1 .9705 1 .9832 2 .0628 2 .0345  VG  LOG VG  REL VG  2433. 6 3236. 9 3956. 4 2887 . 7 294. 9  0 .1048 0 .1615 0 .1824 0 .1425 0 .0377  1 .4742 1 .6928 1 .7098 1 .1376 0 .1580  1468. 2348. 2623. 2943. 3116. 3124. 3250. 3186.  5 8 4 9 9 7 2 5  BBH 0 90 LN 3248 2013 956 295 10  AR MEAN LG1 MEAN 40 43 48 50 43  .6 .7 .1 .4 .2  1. 1. 1. 1. 1.  3264 3672 4342 5066 6039  259 FILE= ANGLE= VERT ANG= LAG  N  BBHG 90 0 LN  14 4882 4889 32 29179 29148 51 50550 50478 66620 66515 70 90 79856 79708 92777 92611 110 130 102971 102784 55137 145 55029 FILE = ANGLE= VERT ANG= LAG  N  LAG  N  46 .3 51 .1 51 .2 50 .4 49 .8 49 .3 48 .6 48 .7  1 .4958 1 .5216 1 .5234 1 .5180 1 .5128 1 .5071 1 .5030 1 .5062  VG  LOG VG  REL VG  0 .0675 0 .1182 0 .1367 0 .1442 0 .1528 0 .1599 0 .1567 0 .1530  0 .9335 1 . 3529 1 .4523 1 .5272 1 .5707 1 .6081 1 .5734 1 .5644  LOG VG  REL VG  0 .0683 0 .1155 0 .1342 0 .1440 0 .1540 0 .1577 0 .1570 0 .1562  1 .0038 1 .3586 1 .4263 1 .4354 1 .5523 1 .5553 1 .5469 1 .5702  VG  LOG VG  REL VG  1989. 6 3430. 3 3536. 2 3868. 0 4102. 0 4106 . 9 3967 . 8 4012. 8  0 .0571 0 .1016 0 . 1170 0 .1314 0 .1441 0 .1517 0 .1546 0 .1561  0 .8858 1 .3028 1 . 3372 1 .4593 1 .5535 1 .5684 1 .5756 1 .5995  2003. 3533. 3800. 3879. 3891. 3916. 3714. 3716.  6 6 3 9 3 0 5 9  BBHG 45 0 LN  4030 15 4023 32 28023 27982 51 50309 50233 70 67296 67186 80422 80297 90 110 93246 93108 130 102624 102475 145 54439 54356 FILE ANGLE= VERT ANG=  AR MEAN LG MEAN  AR MEAN LG MEAN 46 51 51 50 50 49 48 48  .7 .1 .2 .5 .2 .4 .6 .6  1 .4896 1 .5209 1 .5240 1 .5215 1 .5176 1 .5119 1 .5056 1 .5051  VG 2193. 3552. 3739. 3663. 3915. 3802. 3658. 3703.  6 1 1 4 5 8 2 1  BBHG 0 0 LN  14 4664 4649 32 29092 29029 51 51551 51443 68941 70 68825 82601 82461 90 110 96665 96525 130 105743 105572 56167 145 56078  AR MEAN LG MEAN 47 51 51 51 51 51 50 50  .4 .3 .4 .5 .4 .2 .2 .1  1 .4878 1 .5204 1 .5272 1 .5274 1 .5273 1 .5265 1 .5199 1 .5182  260 FILE ANGLE= VERT ANG= LAG  N  BBHG 135 0 LN  15 4086 4079 32 27954 27921 51 49847 49780 70 67564 67466 90 81719 81592 110 94394 94257 130 106126 105939 145 56604 56511 FILE ANGLE= VERT ANG= LAG 21 41 61 81 101  N 2204 1397 743 241 10  AR MEAN LG1 MEAN 46.4 50.9 51.4 51.1 50.7 50.1 49 .6 49 .0  1. 1. 1. 1. 1. 1. 1. 1.  4894 5216 5247 5217 5194 5166 5137 5110  VG  LOG VG  REL VG  0.0589 0.1070 0.1266 0.1387 0.1473 0.1525 0.1546 0.1557  0 .8632 1 .2112 1 .3759 1 .5165 1 .5831 1 .5400 1 .5961 1 .5509  VG  LOG VG  REL VG  3445. 6 4013 . 2 4621. 7 3371. 3 294. 9  0.0951 0.1404 0.1399 0.1391 0.0377  1 .2278 1 . 3262 1 .5354 1 .1319 0 .1580  1858. 3142. 3635. 3959. 4073. 3860. 3930. 3730.  4 4 6 6 6 2 2 9  BBHG 0 90 LN 2200 1391 741 241 10  AR MEAN LG1 MEAN 53.0 55.0 54.9 54.6 43.2  1. 1. 1. 1. 1.  5384 5620 5644 5696 6039  261  APPENDIX E  L I S T I N G OF VARIOGRAMS  GENERATED BY MAXIMUM DIFFERENCE  METHOD  These variograms were c r e a t e d from the BEXG d a t a s e t . Any sample p a i r d i f f e r e n c e ( r e g a r d l e s s of grades), at a given l a g , was e x a m i n e d and i f t h e a b s o l u t e d i f f e r e n c e e x c e e d e d t h e maximum value shown for each variogram, it was not used in the computation of y(h). R e s u l t s show t h a t t h e o n l y v a r i o g r a m s w h i c h showed t h e 1 3 5 ° a n i s o t r o p y were t h e ones t h a t u s e d a l l sample pairs. T h i s was d e t e r m i n e d by examining the lowest f i r s t l a g value. I n most o f the other c a s e s , the lowest value of y at the first l a g was e i t h e r i n t h e 0 ° (N-S) o r t h e 4 5 ° d i r e c t i o n . N o t e t h a t a p p r o x i m a t e l y 50% o f a l l s a m p l e p a i r s had a b s o l u t e d i f f e r e n c e s o f l e s s t h a n 0.020 o p t . (raw g r a d e s were m u l t i p l i e d by 100. to produce these r e p o r t s ) . A l m o s t 90% o f a l l p a i r s had absolute differences of less than 0.080 opt. For horizontal d i r e c t i o n s , t h e l o w e s t v a l u e s o f y(l) f o r the v a r i o g r a m t h a t used a l l s a m p l e p a i r s was i n t h e 1 3 5 ° d i r e c t i o n for a c t u a l , lognormal and relative variograms. In the other cases, the lognormal variogram c o n s i s t e n t l y indicated that a n i s o t r o p y was i n the 4 5 ° direction. T h e a c t u a l and r e l a t i v e v a r i o g r a m s showed l o w e s t yd) i n the N-S d i r e c t i o n f o r the l o w e s t grade d i f f e r e n c e s and v a r i e d for the next 2 variograms. Only the a c t u a l variogram with maximum p a i r d i f f e r e n c e s o f 0 . 0 8 0 o p t . showed t h e 135° direction as l o w e s t . Lowest semi-variogram values at the f i r s t lag for each h o r i z o n t a l variogram are u n d e r l i n e d i n the listings. N o t i c e a l s o how much l o w e r the indicated variance o f the d a t a i s when t h e maximum p a i r d i f f e r e n c e s d e c r e a s e . The r e l a t i v e v a r i o g r a m s i l l s d e c r e a s e from about 1.5 to less than 0.4 f o r s a m p l e p a i r s w h i c h v a r y by l e s s t h a n 0 . 0 8 o p t . — t h i s represents n e a r l y 90% o f a l l p a i r s .  262 FILE= ANGLE VERT ANG= LAG 54 105 146  N 1122 2289 2123  FILE= ANGLE VERT ANG= LAG 67 106 145  N 1103 1827 2098  FILE= ANGLE VERT ANG= LAG 54 106 148  N 1283 2471 1992  FILE= ANGLE VERT ANG= LAG 66 108 145  N 1216 1768 2104  FILE= ANGLE VERT ANG= LAG 20 40 60  BEXG 90 0 LN 1117 2279 2114 BEXG 45 0 LN 1099 1820 2088 BEXG 0 0 LN 1276 2461 1984 BEXG 135 0 LN 1209 1762 2099 BEXG 0 90  N  LN  457 285 148  456 284 147  MAXIMUM  SAMPLE PAIR DIFFERENCE -  AR MEAN L G MEAN 27.3 27.4 27.5 MAXIMUM  1.3564 1.3605 1.3623  27.7 26.3 27.5 MAXIMUM  1.3612 1.3410 1.3603  MAXIMUM  1.3725 1.3507 1.3724  MAXIMUM  1.3581 1.3584 1.3769  58. 9 59. 7 61. 6  0.0409 0.0340 0.0391  0.0787 0.0793 0.0816  1.3597 1.3606 1.3057  2.0  VG  LOG VG  REL VG  59. 4 59. 1 61. 1  0.0363 0.0387 0.0401  0.0771 0.0857 0.0806 2.0  VG  LOG VG  REL VG  57 . 6 59. 2 58. 1  0.0397 0 .0403 0.0351  0.0699 0.0806 0.0727 2.0  VG  LOG VG  REL VG  60 . 8 60. 3 60. 3  0.0399 0.0396 0 .0362  0 .0798 0.0785 0.0734  SAMPLE PAIR DIFFERENCE -  AR MEAN L G MEAN 28.8 28.0 25.1  REL VG  SAMPLE PAIR DIFFERENCE =  AR MEAN L G MEAN 27.6 27.7 28.7  LOG VG  SAMPLE PAIR DIFFERENCE =  AR MEAN L G MEAN 28.7 27.1 28.3  VG  SAMPLE PAIR DIFFERENCE =  AR MEAN L G MEAN  2.0  2.0  VG  LOG VG REL VG  50.7 54.5 49.6  0.0276 0.0312 0.0363  0.0612 0.0693 0.0790  263 FILE= ANGLE VERT .ANG=  BEXG 90 0  LAG  N  LN  55 105 147  1564 3173 3013  1558 3158 2994  FILE= ANGLE VERT ANG= LAG 67 106 145  N 1495 2497 3007  FILE= ANGLE VERT ANG= LAG 54 106 148  N 1751 3353 2831  FILE= ANGLE VERT ANG= LAG 66 107 145  N 1706 2451 2997  FILE= ANGLE VERT ANG=  BEXG 45 0 LN 1485 2489 2989 BEXG 0 0 LN 1743 3336 2819 BEXG 135 0 LN 1698 2437 2982 BEXG 0 90  LAG  N  LN  20 40 60  593 372 222  591 370 220  MAXIMUM  SAMPLE PAIR DIFFERENCE =  AR MEAN L G MEAN 29.4 29.9 29.7 MAXIMUM  1.3783 1.3846 1.3839  MAXIMUM  1.3872 1.3678 1.3848  MAXIMUM  1.3901 1.3786 1.3926  MAXIMUM  1.3810 1.3828 1.3971  0.1700 0.1683 0.1761  VG 143 .8 146 .0 158 .4  VG 141 .5 143 .2 154 .2  VG 155 .0 149 .8 156 .9  1.4055 1.3934 1.3736  VG 124.2 134.5 166.9  3.5  LOG VG  REL VG  0.0610 0.0665 0.0705  0.1575 0.1778 0.1753 3.5  LOG VG  REL VG  0.0707 0.0633 0.0670  0.1490 0.1640 0 .1652 3.5  LOG VG  REL VG  0 .0743 0.0674 0.0674  0.1714 0.1674 0.1663  SAMPLE PAIR DIFFERENCE =  AR MEAN L G MEAN 32.8 30.7 30.0  0.0694 0.0641 0.0706  SAMPLE PAIR DIFFERENCE =  AR MEAN L G MEAN 30.1 29.9 30.7  REL VG  SAMPLE PAIR DIFFERENCE =  AR MEAN L G MEAN 30.8 29.5 30.6  147 .2 150 .0 155 .2  LOG VG  SAMPLE PAIR DIFFERENCE =  AR MEAN L G MEAN 30.2 28.6 30.1  VG  3.5  3.5  LOG VG REL VG 0.0407 0.0492 0.0552  0.1157 0.1423 0.1857  264 FILE= ANGLE VERT .ANG= LAG 55 105 146  N 1758 3717 3569  FILE= ANGLE VERT ANG= LAG 67 106 145  N 1710 2891 3530  FILE= ANGLE VERT ANG= LAG 54 106 148  N 2029 3889 3336  FILE= ANGLE VERT ANG= LAG 66 107 145  N 1944 2852 3521  FILE= ANGLE VERT ANG= LAG 20 40 60  N 652 425 260  BEXG 90 0 LN 1751 3695 3548 BEXG 45 0 LN 1697 2881 3507 BEXG 0 0 LN 2020 3866 3317 BEXG 135 0 LN 1935 2832 3500 BEXG 0 90 LN 649 422 256  MAXIMUM SAMPLE PAIR DIFFERENCE =  AR MEAN LG MEAN 31.4 32.0 31.9  1.3978 1.4034 1.4037  VG 231 .0 258 . 3 269 .7  LOG VG  REL VG  0.0814 0 .0854 0.0920  0.2347 0.2525 0.2647  MAXIMUM1 SAMPLE PAIR DIFFERENCE =  AR MEAN LG MEAN 32.2 30.7 32.1  1.4062 1.3871 1.4026  VG 239 .4 246 .2 267 .0  33.2 31.6 32.4 MAXIMUM  1.4124 1.3976 1.4087  REL VG  0.0767 0.0866 0.0920  0.2316 0.2610 0.2598  MAXIMUM  1.4004 1.3997 1.4143  REL VG  0.0872 0.0832 0.0911  0.2206 0.2460 0.2532  VG 247 .1 253 .4 267 .3  1.4249 1.4141 1.3926  VG 195 .4 232 . 3 277 .9  5.0  LOG VG  REL VG  0 .0912 0 .0878 0.0887  0.2375 0.2502 0.2499  SAMPLE PAIR DIFFERENCE =  AR MEAN LG MEAN 34.7 32.7 31.5  243 .0 245 .1 266 .3  5.0  LOG VG  SAMPLE PAIR DIFFERENCE =  AR MEAN LG MEAN 32. 3 31.8 32.7  VG  5.0  LOG VG  MAXIMUMI SAMPLE PAIR DIFFERENCE =  AR MEAN LG MEAN  5.0  5.0  LOG VG  REL VG  0.0493 0.0614 0.0716  0.1626 0.2174 0.2803  265 FILE= ANGLE VERT .ANG= LAG 55 105 146  N 1991 4184 4099  FILE= ANGLE VERT ANG= LAG 66 106 144  N 1924 3306 3993  FILE= ANGLE VERT ANG= LAG 55 106 148  N 2294 4429 3827  FILE= ANGLE VERT ANG= LAG 66 107 145  N 2175 3232 4014  FILE= ANGLE VERT ANG= LAG 20 40 60  N 703 475 295  BEXG 90 0 LN 1984 4157 4077 BEXG 45 0 LN 1911 3294 3969 BEXG 0 0 LN 2278 4402 3806 BEXG 135 0 LN 2165 3208 3990 BEXG 0 90 LN 700 471 290  MAXIMUM! SAMPLE PAIR DIFFERENCE =  AR MEAN LG MEAN 34.2 34.5 34.8  1.4196 1.4222 1.4248  VG 441 .0 462 .8 498 .8  LOG VG  REL VG  0.1057 0.1099 0.1199  0.3770 0.3895 0.4113  MAXIMUMI SAMPLE PAIR DIFFERENCE =  AR MEAN LG MEAN 34.9 33.8 34.8 MAXIMUM  1.4276 1.4121 1.4229  MAXIMUM  1.4340 1.4200 1.4321  MAXIMUM  1.4207 1.4222 1.4350  0.0990 0.1117 0.1155  0.3606 0.4095 0.3836  VG 453 .0 459 . 3 488 .1  VG 435 .7 461 .4 482 .8  1.4460 1.4371 1.4239  VG 321 .2 423 .4 478 .9  8.0  LOG VG  REL VG  0.1095 0.1103 0.1131  0.3488 0.3837 0.3912 8.0  LOG VG  REL VG  0.1122 0.1088 0.1125  0.3584 0.3872 0.3843  SAMPLE PAIR DIFFERENCE =  AR MEAN LG MEAN 37.5 35.8 35.0  REL VG  SAMPLE PAIR DIFFERENCE =  AR MEAN LG MEAN 34.9 34.5 35.4  438 .5 468 .9 463 .4  8.0  LOG VG  SAMPLE PAIR DIFFERENCE =  AR MEAN LG MEAN 36.0 34.6 35. 3  VG  8.0  8.0  LOG VG  REL VG  0.0587 0.0802 0.0865  0.2283 0.3310 0. 3900  266 FILE= ANGLE VERT ANG= LAG 56 105 137  N 2278 4759 2215  FILE= ANGLE VERT ANG= LAG 67 106 137  N 2172 3781 2586  FILE= ANGLE VERT ANG= LAG 55 106 140  N 2575 5067 1923  FILE= ANGLE i VERT ANG= LAG 66 108 138  N 2408 3704 2681  FILE= ANGLE VERT ANG= LAG 41 61 81  N 530 337 179  BEXG 90 0 LN 2269 4730 2210 BEXG 45 0 LN 2159 3769 2576 BEXG 0 0 LN 2559 5038 1914 BEXG 135 0 LN 2395 3676 2671 BEXG 0 90 LN 526 332 174  A L L SAMPLE  PAIRS  AR MEAN L G MEAN 46.8 44.8 46.2  1.4751 1.4678 1.4765  A L L SAMPLE  VG 3665. 6 2984. 2 3105. 2  1.4727 1.4629 1.4742  A L L SAMPLE  VG 3070. 3 3344. 6 2985. 6  1.4829 1.4704 1.4947  A L L SAMPLE  VG 2991. 9 3198. 2 3686. 8  1.4626 1.4725 1.4799  A L L SAMPLE  LOG VG  REL VG  0.1475 0.1646 0.1631  1.4878 1.6322 1.4431  LOG VG  REL VG  0.1445 0.1608 0.1752  1.3695 1.5196 1.5318  VG  LOG VG  REL VG  2401. 2 3449. 1 2899. 3  0 .1425 0.1627 0.1732  1.2486 1 .6171 1.3868  LOG VG  REL VG  0.1068 0.1203 0.1115  1.3308 1.2622 1.0237  PAIRS  AR MEAN L G MEAN 45.7 44.3 43.3  1.6755 1.4886 1.4520  PAIRS  AR MEAN LG MEAN 43.9 46.2 45.7  0.1523 0.1606 0.1819  PAIRS  AR MEAN LG MEAN 46.7 45.9 49.1  REL VG  PAIRS  AR MEAN L G MEAN 45.4 45.3 45.5  LOG VG  1.4856 1.4741 1.4663  VG 2779. 5 2481. 4 1915. 6  267  APPENDIX F  SCATTERGRAMS  LEGEND;  Block  Models  Method  BUCK  20' B l o c k s , outline.  BUCKG  20' B l o c k s , w i t h "ore zone" o u t l i n e ,  no  BUCK60  60' B l o c k s , outline.  no  BUCK60G  60' B l o c k s , w i t h " o r e zone" o u t l i n e ,  or  BHK  Blasthole Kriging - - "Actual".  EX20 EX60  E x p l o r a t i o n Polygon W e i g h t e d (20' & 6 0 ' )  ID10 ID5 ID3 ID2 IDI IDO  Inverse Distance to t h e i n d i c a t e d power,  KRIG  note:  Exploration Kriged Estimate.  results from conditional probability cannot be compared on a b l o c k by b l o c k b a s i s u s i n g s c a t t e r g r a m s .  268  ACTUAL  V S .  ESTIMATED  -  BLOCK  MODEL«  BUCK  0.240  O X 0.200 LU O " l—  0.160  <  or o ^  x  0.120  0.080  0.040  0.000 0.000  0.040  ACTUAL  — i 0.080  V S .  T~.  1 0-120 BHK  1 i 0-160 0.200 (ACTUAL)  ESTIMATED  Tr,  i  -  BLOCK  .  •  i 0.240  MODEL:  1 0.280  0-320  BUCK  r  0.280 .  0.240  D  •— 0-160 .  <  DC O 0.120 X LU  0-000 0.000  0.040  1 0.080  1 0.120 BHK  1 1 0.160 0.200 (ACTUAL)  1 0.240  1 0.280  0.320  269  ACTUAL  V S .  E S T I M A T E D  -  BLOCK  MODEL'  BUCK  0.240  O 0.200 .  < CC  o  _l  <^ 0.120 . UJ 0.080 .  0.000  — r 0.040  0.000  ACTUAL  1 0.080  V S .  1 0.120 BHK  i 0.160  1 0.200  (ACTUAL)  E S T I M A T E D  -  BLOCK  1 0.240  MODEL:  1 0.280  0.320  BUCK  0.240. r->  Q 0.200.  ,_ 0.160.  < or o  i  °j 0.120.  0.040  0.000  **1 0.040  1 0.080  1 0.120 BHK  I : 1 0-160 0-200 (ACTUAL)  1 0-240  1 0-280  0.320  270  ACTUAL 0.320  i  VS .  - BLOCK  ESTIMATED i  1  .  i  1  MODEL  1  i  BUCK i  0.280.  0.240 . <\l Q 0-200 .  -  Z  o  <  •  0.160 .  or o _i o_ 0.120.  *  X LU  •.:  0.080 .  •*&'::v S  -  0.040 .  0.000 B^^* -~; 1 i 0.r 000 0.040  ACTUAL 0.320.  1—  o. 080  VS.  i 0.120 BHK  i i 0.160 0.200 (ACTUAL)  ESTIMATED  -  BLOCK  i 0-240  MODEL'  0  BUCK  -r  T"  T  i 0.280  Q 0.200.  ,_ 0.160, < or o _i 0^ 0.120 LU  0.080  0.000 —I 0.000 0.040  1  0.080  1  0.120 BHK  1  I  0.160 0.200 (ACTUAL)  1  0.240  1  0.280  0  320  271  ACTUAL  V S .  E S T I M A T E D  -  BLOCK  MODEL'  BUCK  0.320.  0.240.  O Q  0.  z  o < or o  0. 160  120 .  UJ 0.080 .  0.000  ! 0.040  ACTUAL  1 0.080  V S .  1 0.120 BHK  1 1 0-160 0.200 (ACTUAL)  E S T I M A T E D  -  BLOCK  1 0.240  MODEL:  1 0.280  0.320  BUCK  0.2B0 .  0-240 UJ O — 0.200  or  2  0.160  < or o _j 0_ X UJ  0-080  0-040  o.ooo 0-000  — i 0.040  i 0.080  i 0.120 BHK  i 0-160  1 0.200  (ACTUAL)  i 0.240  i 0.280  0.320  272  ACTUAL  V S .  ESTIMATED  -  BLOCK  MODEL  1  BUCKG  0.320.  0.280.  0.240.  O X 0.200. LU  <  or o  a ! 0.120. x LU 0.080.  r. .•  0-000  0.040  ACTUAL  —I 0.080  V S .  I 0.120 BHK  1 I 0.160 0-200 (ACTUAL)  E S T I M A T E D  -  BLOCK  1 0.240  MODEL =  I 0-280  0.320  BUCKG  0-280 .  O —' 0.160 . i—  <  or o  r x o . 120 X  0.080  0-000 0.000  0.040  —i 0.080  1 0.120 BHK  i 1 0.160 0.200 (ACTUAL)  1 0.240  1 — 0.280 0.320  ACTUAL  V S .  ESTIMATED  -  BLOCK  MODEL  !  BUCKG  0.280 J  0.240 J  in Q 0.  < or o  0.160J  UJ  0.080  0.040J  0.000  0.040  I 0.080  I 0.120 BHK  ACTUAL n  V S .  1 0.160  1 0.200  I 0.240  1 0.280  0.320  (ACTUAL)  ESTIMATED  -  r  BLOCK i  MODEL:  BUCKG  r  0.240 J  ro Q  0-200  < or o  _i  Q- 0-120-1 0.080  0.040J:  0.000 0-000  1 0.040  1 0.080  1 0.120 BHK  1 0.160  1 0.200  (ACTUAL)  1 0.240  1 0.280  0.320  274  ACTUAL  V S .  ESTIMATED  -  BLOCK  MODEL-  BUCKG  0.240 .  CM  Q  0-200J  ,_ <  0.160 .  o  _1 ^ 0.120.  0.000 0.000  1 0.040  ACTUAL  ,  ,  0.080  V S .  0.120 BHK  ,  !  0.160 0.200 (ACTUAL)  ESTIMATED  -  BLOCK  p  0-240  MODEL"  1  !  0-280  0.320  BUCKG  0.280 .  Q  0.200 .  <  OC  o  _l ^  0.120  0.000  1 0.040  1 0.080  1 0.120 BHK  1 1 0.160 0.200 (ACTUAL)  1 0.240  1 0.280  . 0.320  275  ACTUAL  V S .  E S T I M A T E D  -  BLOCK  MODEL'  BUCKG  0.320.  0.240 . o Q 0.200 ,_ 0.160 < or o 0.120  0.080 0.040 . 0.000 0.000  I 0.040  ACTUAL  1 0.080  V S .  1 0. 120 BHK  1 1 0 . 1 6 0 0 . 200 (ACTUAL)  E S T I M A T E D  -  BLOCK  I  0.240  MODEL:  1 0.280  0.320  BUCKG  0.320  0.240  or  0.200 .  2 0.160. < or o — 0.120 . 1  Q_ X  0.080 0.040 .  .000  0.040  0-080  0.120 BHK  0.160  0.200  (ACTUAL)  0.240  0.280  0.320  276  A C T U A L  V S .  E S T I M A T E D  -  B L O C K  M O D E L  1  B U C K 6 0  0.280  0.240  O  <o X LL)  0-200  o *-•  0.160  i—  <  cr CD CL 0 . 1 2 0 . X  UJ  0.040.  0.000  I 0.040  1 0.080  1 0.120 BHK  A C T U A L  V S .  E S T I M A T E D  1 0-160  1 0.200  1 0.240  1 0.280  0.320  (ACTUAL)  -  BLOCK  MODEL»  B U C K 6 0  o 5  0.200.  — i—  0.160.  <  or o CL X  0.120 .  0.080 .  ••-v.".*j?5r--?-.-.; 0.000  — i 0.000  0.040  0.080  1 0.120 BHK  1 1 0.160 0.200 (ACTUAL)  1 0.240  1 0.280  0.320  277  ACTUAL  VS.  ESTIMATED 1  ~i  1  -  BLOCK  MODEL'  BUCK60  r  0.240 -  to O  0.200.  <  or o _i ^  0.120  LU  o.ooo 0.000  0.040  0.080  0.120 BHK  ACTUAL ~1  ro Q  < or o _i  VS.  0.160  ESTIMATED  -  I  1  I  0.200  0.240  0.280  0.320  (ACTUAL)  BLOCK I  MODEL'  BUCK60  T"  0.200  0.120  LU  0-080  0.040  0.000 0.000  0.040  0.080  0.' 120 BHK  0-160  0.200  (ACTUAL)  0.240  0.280  0.320  278  ACTUAL  V S .  ESTIMATED  "T  1  I  BLOCK 1  MODEL« I  BUCK60 r  0.280  CM  Q  0.200  < 0T o _l x  0.120.  LU 0.080  0-040 .  \^.vK>'.'  0.000  1 0-040  ACTUAL 0.320.  1 0-080  V S .  1 0.120 BHK  ESTIMATED  T  1 1 0.160 0-200 (ACTUAL)  -  BLOCK  1 0.240  MODEL'  1 0-280  0-320  BUCK60  r  0-280 J  Q  0.200.  z o  <  0.160.  or o _i 0j 0.120. UJ  0.040 J  0.000  1 0.040  1 0.080  1 0.120 BHK  1 0.160  1 0-200  (ACTUAL)  1 0.240  1 0.280  0.320  ACTUAL  V S .  ESTIMATED  -  BLOCK  MODEL'  BUCK60  0.280  0.240 J  O Q  0.200  ,_  0.160 _|  < K O _l  0.120  0.080.  0.040 J  0.000  0.040  0.080  0.120 BHK  ACTUAL  V S .  ESTIMATED  0.160  0.200  -  BLOCK  0.320  0.000 BHK  0.240  0.280  (ACTUAL)  (ACTUAL)  MODEL:  BUCK60  0.320  280  ACTUAL  V S .  E S T I M A T E D  -  BLOCK  MODEL'  BUCK60G  0.280.  o  CD X  0.200.  <  or o CL X  0.I20J  0.080.  0-000  1 0-040  ACTUAL  1 0.080  V S .  1 0.120 BHK  E S T I M A T E D  1 1 0.160 0.200 (ACTUAL)  -  BLOCK  1 0.240  MODEL«  1 0.280  0.320  BUCK60G  0-280.  O 5  0.200.  z o  -*  0.160.  •— < or o CL X  LU  0.120. 0.080-1  0.000 0.000  1 0.040  1 0.080  1 0.120 BHK  1 1 0.160 0.200 (ACTUAL)  1 0.240  1 0.280  0.320  281  ACTUAL  V S .  0.320  ESTIMATED  -  BLOCK  MODEL:  BUCK60G  1  1  1  1  r  i 0.120  i 0.160  1 0.200  1 0.240  \ 0.280  ~i  0.280  0.240  in Q  0.200  < CC  o  _1 CL 0.120 LU 0.080  0.000  i 0.040  i 0.080  BHK  ACTUAL  V S .  ESTIMATED "i  0.320  (ACTUAL)  -  BLOCK  MODEL:  1  i  r  1 0.160  I 0.200  1 0.240  BUCK60G  0.240  to Q  0.200  ,_ 0.160  < or o _i  0^ 0.120 LU 0.080  0.040 ,  0.000 0.000  1 0.040  I 0.080  1 0.120 BHK  (ACTUAL)  1 0.280  . 0.320  282  ACTUAL 0.320  VS.  ESTIMATED i  i  i  -  BLOCK  MODEL  i  i  1  i  BUCK60G i  0.280 .  0.240 .  ID  CM  0.200 .  z o t— 0 . 1 6 0 .  <  or o _ J  0- 0.120 . x UJ  *  0.080 .  0.040 . - JeJr >.'*' '  .: 0.000 0 000  1 0.040  1 0.080  1 0.120 BHK  ACTUAL  VS.  ESTIMATED "T"  1 0.160  1 0.200  1 0-240  1 0-280  0 320  (ACTUAL)  -  BLOCK  MODEL"  T  BUCK60G  ~T~  0.240 J  Q  0.200  , _ 0.160 < or o _ i  %  0.120-1  0.080 .  0-000 0.000  1 0.040  1 0.080  1 0.120 BHK  1 1 0.160 0.200 (ACTUAL)  1 0.240  1 0.2B0  0.320  283  ACTUAL 0.320  VS. ESTIMATED  i  i  i  -  BLOCK  i  i  MODEL'  i  BUCK60G  i  0.280 .  0.240 .  O Q  o  •  o  O Q  EXPLORATION  0.200 _  0.080 .  -  0.040 _  0.000 0.  1  000  0.040  ACTUAL 0.320  i  1  1  0.080  0.120  VS.  BHK  ESTIMATED  i  i  1  0.160  1 0.200  (ACTUAL)  -  BLOCK  i  i  1 0.240  MODEL' i  0.280  0. 320  BUCK60G i  0.280 .  -  0.240 . LU O — 0.200.  -  o  i  -  1  0  o o  EXPLORATION  or  -  0.080 _ **  0.040 .  *  v."••'"'j'i--  :"• • ••  -  0.000 0. 000  0-'040  0.080  0.'l20  BHK  0.'l60  0.'200  (ACTUAL)  0.240  0.280  0. 320  

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
China 26 18
Russia 13 0
United States 7 0
Japan 6 0
Argentina 5 0
Canada 4 0
Hong Kong 2 0
United Kingdom 2 0
Croatia 2 0
Romania 1 0
Brazil 1 0
France 1 0
Poland 1 0
City Views Downloads
Beijing 24 0
Unknown 14 0
Penza 8 0
Tokyo 6 0
Buenos Aires 5 0
Ashburn 5 0
Vancouver 3 0
Central District 2 0
Shenzhen 2 18
Calgary 1 0
Mountain View 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0052363/manifest

Comment

Related Items