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A geostatical evaluation of the southern tail zone of Equity Silver Mines, Limited, Houston, B.C. Giroux, Gary Henri 1984

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A G E O S T A T I S T I C A L EVALUATION THE  SOUTHERN  TAIL  OF  ZONE  OF EQUITY  S I L V E R MINES, HOUSTON,  LIMITED  B.C.  BY  GARY HENRI  B.A.Sc,  University  A THESIS OF  of B r i t i s h  SUBMITTED  THE OF  Columbia,  IN PARTIAL  REQUIREMENTS MASTER  GIROUX  OF  FOR  APPLIED  FULFILLMENT  THE  DEGREE  SCIENCE  IN THE  FACULTY  OF  GRADUATE  (DEPARTMENT OF  GEOLOGICAL  We  thesis  accept to  The  this  the peguired  University  of  May ©  Gary  as  STUDIES SCIENCES)  conforming  standard:  British  Columbia  1984  Henri Giroux,  1970  1 984  In p r e s e n t i n g  this thesis  r e q u i r e m e n t s f o r an of  British  it  freely available  in partial  advanced degree a t  Columbia,  understood that for  Library  s h a l l make  for reference  and  study.  I  for extensive copying of  h i s or  be  her  g r a n t e d by  shall  not  be  G&-OCO G Y  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3  Date  Columbia  §><^)j, / f f , I? 2 f  of  further this  thesis  head o f  this  my  It is thesis  a l l o w e d w i t h o u t my  permission.  Department o f  the  representatives.  copying or p u b l i c a t i o n  f i n a n c i a l gain  University  the  f o r s c h o l a r l y p u r p o s e s may by  the  the  I agree that  agree t h a t p e r m i s s i o n department o r  f u l f i l m e n t of  written  ii  ABSTRACT The  Southern T a i l  silver-copper for  deposit  global  and  maintaining grades  zone o f E q u i t y  Sam  p r e s e n t s an i n t e r e s t i n g c h a l l e n g e  local  ore  reserve  q u a l i t y c o n t r o l on  estimations,  sampling  and  Goosly not only  but a l s o f o r  assaying.  Silver  from b o t h stockwork and m a s s i v e g a l e n a - s p h a l e r i t e  v a r y a s much  as,  distances. minimize  the  orders  effects  of  of  magnitude  methods erratic  across  have  been  lenses  very  short  developed  mineralization  on  to  reserve  and q u a l i t y c o n t r o l .  Conditional reserves  3  Geostatistical  estimation  probability  estimation  exploration  i s demonstrated  method f o r t h e  diamond d r i l l  declustering,  structural  distributions  to block  are  S i l v e r Mines,  data.  Southern  as a g l o b a l o r e Tail  zone  The e n t i r e p r o c e d u r e ,  analysis  and  using  including  conditioning  raw  grade d i s t r i b u t i o n s i s o u t l i n e d .  data  Results  p r e s e n t e d a s a g r a d e t o n n a g e c u r v e and c o m p a r e d t o e s t i m a t e s  c a l c u l a t e d by i n v e r s e A statistical data  distance.  and g r a p h i c a l  i s presented  as  s a m p l i n g and a s s a y i n g . indicate large  a  bias  random e r r o r  blasthole  method  Results  in silver  possible  the  Southern  volume.  increase  of  paired  Tail  zone  a n a l y s e s b e t w e e n two l a b o r a t o r i e s , a  i n the standard tube sampling  improvement  significant  evaluating  of m o n i t o r i n g t h e q u a l i t y of  from  c u t t i n g s a n d an i n v e r s e  e r r o r and sample  better  a  approach t o  An  technique  r e l a t i o n s h i p between  idealized  sampling  calculation  method  i n metal recovery could  for  sampling based  indicates be a t t a i n e d  that  on a  through  sampling.  For  l o c a l block  estimation,  a v a r i e t y of k r i g i n g techniques  iii  have been e v a l u a t e d polygonal  and  estimates.  compared  Both  k r i g i n g e r r o r s showed  cross  only  marginally  is  superior  other  to  w h i c h method  metal content of a mine  methods,  methods,  grams o f s i l v e r  t h a n a l o g p a r t i t i o n e d method. W h i l e no c o n c l u s i o n s as  units  For a t e s t area of  by t h e v a r i o u s  1.4 m i l l i o n  and  and c o m p a r i s o n of  to  s o i n some c a s e s .  method p r e d i c t e d  distance  of s e l e c t i o n mining  100 b l o c k s on t h e 1310 N b e n c h e s t i m a t e d the p o l y g o n a l  inverse  validation  that log kriging  u s i n g p a r t i t i o n e d sample data although  with  c a n be drawn  i s c o r r e c t , the n e c e s s i t y of m o n i t e r i n g  from s p e c i f i c  i s stressed.  more  blocks e a r l y i n the production  the life  TABLE OF  CONTENTS  ABSTRACT  i  TABLE OF CONTENTS  i i i  L I S T OF TABLES  vi  L I S T OF FIGURES  v i i  ACKNOWLEDGEMENTS  x  CHAPTER 1 : INTRODUCTION  1  CHAPTER 2 : GLOBAL RESERVES OF SOUTHERN  T A I L ZONE  BY CONDITIONAL PROBABILITY  4  Abstract  5  Introduction  6  Data  12  Data E v a l u a t i o n  14  Structural  16  (Semivariogram) I n t e r p r e t a t i o n  Declustering Conditional  21 Probability  25  G r a d e and Tonnage E s t i m a t i o n . . .  28  Conclusions  33  Acknowledgements  35  References  36  CHAPTER 3 : PRODUCTION QUALITY CONTROL EXPERIMENTS  37  Abstract  38  Introduction  39  Procedure f o r E v a l u a t i n g Quality Control  Testing  Duplicate at Equity  (Paired)  Data...  S i l v e r Mine  41 47  Duplicate  A n a l y t i c a l Data  48  Duplicate  B l a s t h o l e Sampling  52  V  B l a s t h o l e Sampling Procedures at Equity  Silver  Mine  55  Evaluation  of Sampling T e s t R e s u l t s  59  I d e a l i z e d Economic A n a l y s i s  65  Conclusions  70  Acknowledgements  73  References  74  CHAPTER 4 : AN• • EVALUATION OF VARIOUS KRIGING TECHNIQUES AS A P P L I E D TO EQUITY SILVER MINES SOUTHERN T A I L ZONE  75  Abstract  76  Introduction  77  Data A c q u i s i t i o n  78  Structural Analysis  79  T r a d i t i o n a l Model  79  Lognormal Model..  83  P a r t i t i o n e d Model  86  Log P a r t i t i o n e d Model  89  Multi-Gaussian  91  Model  Back A n a l y s i s  92  Block K r i g i n g  96  Conclusions  102  Acknowledgements..  103  References  104  CHAPTER 5 ,: CONCLUSIONS  105  REFERENCES  109  APPENDIX I - C o m p a r i s o n o f E q u i t y L a b a n d a Check L a b on M i l l Sample A s s a y s APPENDIX I I - D u p l i c a t e B l a s t h o l e S a m p l i n g f o r C o p p e r and S i l v e r  111 113  vi APPENDIX I I I - R e s u l t s for Different T e c h n i q u e s f o r 42 B l o c k s  Sampling  APPENDIX IV - C a l c u l a t i o n o f Volumes f o r D i f f e r e n t Sampling Techniques  115 117  vii  LIST  CHAPTER  OF  TABLES  2  TABLE  1 - Lithological  TABLE  2 - General Procedure f o r Global Reserve E s t i m a t i o n by C o n d i t i o n a l P r o b a b i l i t y . . . .  11  3 - Parameters of 3-Dimensional S p h e r i c a l M o d e l S o u t h e r n T a i l Zone D i a m o n d D r i l l Data  20  TABLE  TABLE CHAPTER  4 - Grade  TABLE  TABLE  TABLE  TABLE  TABLE  TABLE  TABLE  and Tonnage  8  Curves  (Silver)  3  TABLE  CHAPTER  Units  1 - Summary o f R e s u l t s f o r P a i r e d t-Test on Three Sets of Paired Duplicate Analyses f o r Silver  51  2 - R e s u l t s f o r P a i r e d t - T e s t f o r Copper a n d S i l v e r o n 21 D u p l i c a t e Blasthole Samples  52  3 - Sample Volumes  58  Types with and Weights  Corresponding  4 - Comparison of Sampling Procedures C o m p a r i n g V o l u m e , ' Amount o f S c a t t e r (Sy) and R e g r e s s i o n P a r a m e t e r s ( y = A + Bx )  63  5 - Tabulation of Blastholes Misclassified by T u b e S a m p l i n g Assuming that a Best (Calculated) Bulk Estimate i s Correct, a n d C u t - O f f G r a d e i s 30 g . A g E / t o n n e  66  1 - A Summary Principal  81  4 o f t h e Ranges Directions  i n the Four  2 - A Summary o f P a r a m e t e r s f o r t h e F o u r Anisotropic Semivariogram Models Developed  89  3 - Mean S q u a r e d D i f f e r e n c e s o f E s t i m a t e d and True Blasthole Grades as a Function of 3 Grade C a t e g o r i e s for 5 Estimation Procedures  94  L I S T OF FIGURES CHAPTER 2 Figure  1 : L o c a t i o n of E q u i t y S i l v e r Goosly Deposit  Figure 2 :  M i n e s ' Sam ,  Plan v i e w o f t h e S o u t h e r n T a i l zone showing collar l o c a t i o n s o f 108 diamond d r i l l h o l e s  13  p l o t of Figure 3 : Cumulative l o g p r o b a b i l i t y 2235 s i l v e r a s s a y s from e x p l o r a t i o n d i a m o n d d r i l l h o l e s , S o u t h e r n T a i l zone,  15  vertical relative F i g u r e 4 : Average v a r i o g r a m f o r 3 m. c o m p o s i t e grades  17  semisilver  horizontal F i g u r e 5 : Average variogram f o r s i l v e r NW-SE d i r e c t i o n  relative semigrades i n the  horizontal F i g u r e 6 : Average variogram f o r s i l v e r NE-SW d i r e c t i o n  relative semigrades i n the  18  19  F i g u r e 7 : N a i v e mean s i l v e r v a l u e p l o t t e d f o r various c e l l s i z e s (s) i n order t o d e t e r m i n e t h e optimum c e l l s i z e f o r declustering  23  F i g u r e 8 : Unbiased histogram f o r Southern T a i l zone silver from 3 m. composites with h i s t o g r a m o f raw d a t a s u p e r imposed  24  F i g u r e 9 : Unbiased histogram f o r s i l v e r grades of 10 x 10 x 10 cu.m. b l o c k s , S o u t h e r n Tail zone, w i t h h i s t o g r a m from unb i a s e d 3 m. c o m p o s i t e s superimposed....  27  s l i c e ( i n c l u d i n g l e v e l s 1280 F i g u r e 10 : Upper to 1235), Southern T a i l zone, showing distribution o f 45 m. b l o c k s . B l o c k s within t h e double lines used t o calculate tonnage o f 48.8 m i l l i o n tonnes; blocks containing data are shaded  29  F i g u r e 11 : G r a d e - t o n n a g e c u r v e f o r S o u t h e r n T a i l zone showing two t o n n a g e curves : one based on a t o t a l mineralized t o n n a g e o f 59 m i l l i o n tonnes and a second based on 48.8 m i l l i o n t o n n e s . . . .  32  ix CHAPTER  3  Figure  1  : A  Figure  2  : A simple linear model e r r o r s in p a i r e d data  Figure  Figure  Figure  Figure  Figure  Figure  Figure  Figure  Figure  Figure  Figure  3  4a  4b  5a  5b  6  7  8  9  10  11  system  : Idealized exhibited analysis  for e v a l u a t i n g check to  assays....  42  describe 44  examples of on X-Y p l o t s o f  patterns duplicate 46  : Plot of comparison between two l a b o r a t o r i e s s h o w i n g 23 p o i n t s about an e q u a l v a l u e reference line (Y=X) for tailings (T), ore (0) and c o n c e n t r a t e s (C) s a m p l e s f o r c o p p e r  49  : Plot of comparison between two l a b o r a t o r i e s showing 23 p o i n t s a b o u t an e q u a l v a l u e reference line (Y=X) for tailings (T), ore (0) and c o n c e n t r a t e s (C) s a m p l e s f o r s i l v e r  49  : Paired results for copper d u p l i c a t e b l a s t h o l e samples  from  53  : Paired results for silver d u p l i c a t e b l a s t h o l e samples  from  21  21 53  : Plan view of blasthole cuttings showing l o c a t i o n s of the tube and c h a n n e l s a m p l e s ( C y r e t a l , 1980)  56  : Original estimate data  60  tube bulk  sample for 42  : Average channel sample estimate bulk for 42 data  versus best paired silver  versus best paired silver 61  : Bulk sample v e r s u s best estimate f o r 42 p a i r e d s i l v e r d a t a  bulk 62  : Plot showing the s c a t t e r about the regression line (Sy) versus sample volume w i t h a curve f i t t e d e m p i r i c a l l y . .  64  : Original tube estimate bulk equivalent data  68  sample for 42  versus best paired silver  C H A P T E R  4  Figure  Figure  1 : Average horizontal semivariograms f o r selected benches Southern T a i l zone, showing experimental curves for directions 1 to 4  80  2 : Structural ellipse of ranges i n the four p r i n c i p a l d i r e c t i o n s showing t h e direction o f minimum a n d maximum structure  82  Figure 3  Figure  Figure  Figure  Figure  84  4 : Average h o r i z o n t a l semivariogram i n the d i r e c t i o n o f minimum a n d maximum structure f o r l o g transformed s i l v e r g r a d e s , S o u t h e r n T a i l zone ,  85  5 : Lognormal cumulative distribution curve f o r 2773 silver grades from 1310 N, 1310 S a n d 1315 N b e n c h e s , S o u t h e r n T a i l zone  87  6 : Average horizontal semivariograms i n the direction o f minimum a n d maximum structure for partitioned lognormal s i l v e r g r a d e s , S o u t h e r n T a i l zone  90  7 : Scatter plot showing real silver grade versus s i l v e r grade e s t i m a t e d by l o g p a r t i t i o n e d k r i g i n g f o r 1510 b l a s t h o l e s , S o u t h e r n T a i l zone ,  93  Test area o f 1310 N b e n c h showing s i l v e r assays f o r blastholes w i t h an arbitrary g r i d o f 100 ( 5 x 5 x 5 c u . m.) b l o c k s s u p e r i m p o s e d ,  97  Graph•showing relative kriging error (using four d i f f e r e n t k r i g i n g models) for 25 a r b i t r a r i l y selected blocks f r o m t h e 100 e s t i m a t e d  99  10 : T e s t a r e a o f 1310 N b e n c h showing k r i g e d s i l v e r g r a d e f o r 100 ( 5 x 5 x 5 cu.m.) b l o c k s . Kriged silver grade calculated using log partitioned model  100  Figure 8  Figure 9  Figure  A r i thmet i c and l o g transformed h i s t o grams f o r 2575 s i l v e r grades from blastholes S o u t h e r n T a i l zone  xi  ACKNOWLEDGEMENTS  The and  author  indirectly First  would  concerned  special  like  t o thank  with  this  thanks  supervising  the research,  constructive  criticism  The  author  allowing completing Project  Thanks M r . W.  Technical Engineering  Special Montgomery  at  personal  with  the  problems  are  due  to  for  Mr.  his  group  Green  for help  i n preparing  support  and h e l p  h a s been  J . C y r , D. thanks  to  Fraser, D.  thanks  t o Anne,  support.  Silver  Mines  f o r help Colleen  for  Limited  for  assistance in  E.T.  Lonergan,  co-operation of Placer  and  and  in  data.  provided  P. B e a u d o i n  Walker  for  and p r o v i d i n g  Development  t o t h e computer  at Equity  directly  study.  and f o r f i n a n c i a l  Placer  a n d D.F. Symonds  Lastly and  Thanks  also  Department  Miller,  data  both  to Dr. A . J . S i n c l a i r  to Placer  the  Supervisor  particular  J.H.L.  to  t h e work.  assistance.  assisting  throughout  people  study.  are extended  i s grateful  access  many  by t h e M i n i n g  Ltd., a n d W.  drafting  most  notably  Myckatyn. and  J.H.  and encouragement. and Kevin  for their  patience  1  CHAPTER 1  INTRODUCTION  2  The Silver  Sam  Mines  southeast  Assay the  bodies, data  i s of  of  the  all  stages  forming  a  deposit,  central  The  the  deposit  Main  zone  and  the  several  Tail  form  the  interest  due  grades  of  mine  as  a  and  and  of  each  stages  the  subsequent  planning  series  chapter  the  to  of  of  development.  three  independent  dealing  with  a  study.  erratic  problems  and  zone.  development -  this  seeming  km.  principal  Tail  i n the  Equity 35  two  Southern  basis  by  Columbia  consists  from  zone  owned  British  collected  special  silver  organized  is in  Houston.  Southern  deposit  silver-copper  Limited,  of  mineralized  of  Goosly  that The  The  nature  arise study  sections,  particular  in is  each  set  of  global  or  problems. Chapter geological method  to  the data  estimation  of  with  The in  method in  outlined  of  duplicate  as  grade  simple  a method  of  :  comparison  reliability  of  several using  a In  sampling Chapter  examined  sampling  sampling  of  the  method  of  data.  A  results  problems  of  deposit  and  the  wrong  control  and  support  a  and The  high  block  data.  are  finally  the  financial  estimation  dealt  are  error  a  with  procedure  Several  presented  laboratories,  random  are  graphical  results  two  method  with  local  quality  and  procedures.  four  The  evaluating paired  to  a  distance.  statistical  are  a  drill  described with  portions  production  data  regards  diamond is  using  of  proposed.  of  three. A  is  inverse  reserves  solutions  estimation  probability of  geologic  the  exploration  high  problems  Chapter  with  from  conditional  clustered  covered  deals  reserves  of  compared  two  check  sets with  on  the  comparison  of  ramifications  of  are  discussed.  i s examined  at  the  3  Southern outlined of  good  with  Tail and  compared  geologic  several  zone.  Several with  empirical  c o n t r o l on  examples  different  given.  any  ore  kriging  procedures. reserve  procedures The  estimate  are  importance is  stressed  4  CHAPTER  GLOBAL  R E S E R V E S OF BY  THE  2  SOUTHERN  TAIL  CONDITIONAL P R O B A B I L I T Y  ZONE  5  ABSTRACT  The  Southern  deposit  of  Equity  mineralized  of  zone  global  procedure  for  geostatistical  a  assay a  histogram  . cut-off  variance  for  average  an  ore  Here  we  in  outline  reserves  to  and  erratically  difficulties  reserves.  mean  silver-copper  by  based  the  on  produce  an  dispersion)  of  of  semi-variogram  model  estimating  dispersion  grade  of  the  blocks  that  of  any  and an  affine  correction  of  block  for  10  that  grades  to  the  10  10  m  conditions  the  histogram  of  data.  histogram zone  as  a  grade  of  estimates  (and  means  histogram  presented  ore  procedure  the  Tail  presents  global  3-dimensional  size,  Southern  is  conditional probability  provides  raw  Goosly  data,  (2)  (3)  Sam  Limited  which  (in situ)  of  the  Mines  declustering  unbiased  The  of  estimating  method  (1)  zone  Silver  ore  establishment the  Tail  based  was  x  estimated  grade-tonnage 40 on  g.Ag/tonne the  method  of  x  i n the  3  block  grades  f o r g o i n g manner  curve.  Tonnage  agree  closely  inverse  estimates with  distance.  for  the  and above  is a  comparable  6  INTRODUCTION  Sam British  Goosly Columbia  The  deposit  the  north  contains grade  and  of  about  39  8.6  intrusions  and  dipping  /tonne  form  The erratic  two  ore  much  (Wetherell  larger  present  minerals  tetrahedrite  minerals rarer  include  and  galena-sphalerite more  exploratory different replacement zone,  two  grades units,  ore  by  cut-off rock  is a  striking  degrees  westerly  cut  by  younger by  gently  section  zones.  far  is  apparently  parts  the  most  exceeds Less  pyrrhotite  and a  i s  The  of  massive to  be  the results  space  and b r e c c i a  ore  variety  these  from  zone.  volume abundant  of near  shown  open  the  t h e main o r e  mineralization Both  of  abundant  zones  has  i n each  fracture  an  mineralized  anticipated of  by  both  greatly  mining  are evident  clearly  are  silver-rich  form  zone  a n d a l t h o u g h s e p a r a t e on  irregular is  than  to  rocks  stratigraphic  chalcopyrite.  and  a  underlain  characterized  sphalerite,  occur  the  A  zone  1979).  more  and  prevalent  i s  rocks.  Locally  features  however,  are  generally  d r i l l i n g . The in  rocks  Pyrite  galena,  sulphosalts.  somewhat  These  economic  on  1).  Tail  Country  45  but  sulphide  based  an a r e a  (Figure  t h e Main  sedimentary  within  in central  Southern  about  are  e t a l , 1979).  ore  and  of s i l v e r  of a r b i t r a r y  of  The  dipping  inlier  zones  zone.  equivalent.  1 (Wetherell,  distribution  basis  Tail  silver  1979). an  deposit  s e p a r a t e ore zones,  tonnes  and  silver  s o u t h e a s t of Houston  volcanic  in Table  bulk  pyroclastic  a l ,  Tertiary  presented  km.  million  degrees et  35  a  Southern  of Mesozoic 15  is  o f two  the  g  (Wetherell  same  about  consists  about  sequence  the  deposit  of  somewhat  filling  and  Southern  Tail  controlled  and  7  8  TABLE  1 - Lithological  Units  (from  P E R I O D o r EPOCH  FORMATION  MIOCENE  POPLAR B U T T E S V O L C A N I C ROCKS  MIOCENE EOCENE  AND  Wetherell,  o r INTRUSION  1979)  LITHOLOGY  Olivine  basalts  ENDAKO GROUP  B a s a l t s and a n d e s i t e flows and b r e c c i a s LAKE INTRUSIONS G a b b r o , m o n z o n i t e INTRUSIONS Quartz monzonite  GOOSLY NANIKA EARLY OLIGOCENE AND L A T E U P P E R CRETACEOUS  OOTSA  M I D D L E UPPER CRETACEOUS  T I P TOP H I L L V O L C A N I C ROCKS  Andesite breccias rhyolite  BULKLEY  INTRUSIONS  Porphyrite granodiorite quartz monzonite  KASALKA  GROUP  Welded t u f f s , breccias, latite-andesite flows, lahars, rhyolite, basal congloberate  KASALKA  INTRUSIONS  Porphyritic latitea n d e s i t e , d a c i t e and d i o r i t e dikes, sills and stocks Amygdaloidal basalts and intermediate marine sandstones and shales  E A R L Y UPPER CRETACEOUS  L A K E GROUP  LOWER C R E T A C E O U S  SKEENA  GROUP  UPPER J U R A S S I C AND L A T E M I D D L E JURASSIC  BOWSER L A K E GROUP  R h y o l i t e and d a c i t e flows and p y r o c l a s t i c s p l u s minor andesites and basalts and and  dacite flows,  Marine and non-marine shales, sandstones, and c o n g l o m e r a t e p l u s andesite breccias, t u f f s and flows  TABLE  1  (Cont.)  MIDDLE J U R A S S I C  FRANCOIS LAKE INTRUSIONS  Granite, granodiorite d i o r i t e and syenite batholi ths  EARLY MIDDLE J U R A S S I C AND LOWER J U R A S S I C  HAZELTON  Andesite and basalt flows, t u f f s , and breccias plus interc a l a t e d marine shale and conglomerate  LOWER J U R A S S S I C TOPLEY AND U P P E R T R I A S S I C LATE  TRIASSIC  TAKLA  GROUP  INTRUSIONS  GROUP  Quartz quartz  monzonite diorite  Andesite and basalt flows, b r e c c i a s , and tuffs with interbedded m a r i n e a r g i l l i t e , graywacke, and conglomerate  10  and  commonly  although  has  the  intensive  appearance replacement  -quartz-sericite  zones.  a  massive  dominance  layers but  of  pyroclastic  much  less  Global total  or  general  not  based  global  been  (Sinclair,  on  the  A  in  for  1978).  We  Tail  disseminated  ore  Mineralized than  i n the  to  both  e m p i r i c a l and  the  estimation  have  zone  of  been  earlier  such  i s provided  Equity  of  to  in Table  Mines  test and  2.  The  the  determined  in  global  zone.  of  mind  are Thus,  recoverable procedures  geological  reserves  reserves  Limited  using  probability.  for the Our  the  procedure  against  in  part  examine  grade-tonnage  procedures.  measure  with  develop  study,  Tail  theoretical  of  Silver  present  profitibility.  confused  to  shows  particular  commonly  conditional  part  empirical  advantage of  elected  of  in  be  along  viability  not  pyrite-  contrast,  a  although  economic  local  Southern  represent  and  stockwork  f r a c u t r e s are  c o n s i d e r a t i o n s of  approach  has an  of  produced in  deposit  are  used  product  study  a  number  potential  natural our  of  evidence  mineralixed  zone,  rock.  detailed  geostatistical  results  Main  c o n s i d e r a t i o n s of  Southern  motivation  and  a  has  geological reserves  reserves  reserves.  the  in  resource  with  have  of  The  of  curves  general  to  that  are  organization  a of  11  TABLE  2  - General Procedure for Global Conditional Probability  1.  Data  Evaluation  production  of  production uniform  plan of  Reserve  -  of  editing  drill  hole  composites  support  and  Estimation  of  of  by  data,  locations, approximately  determination  of  simple  statistics. 2.  Structural  hole  analysis  experimental  experimental  -  semi-variograms,  semi-variogram  3.  histogram  procedure 4.  volume-variance declustered Estimation of  and  point based  for declustering biased  Conditional  blocks  -  a  -  relationships  data of  Probability  and  the  specific  size.  down  a  3-  model. on  a  general  data. application  of  based  on  semi-variogram  grade-tonnage  of  horizontal  semi-variograms  dimensional Unbiased  determination  model.  relationships  for  1 2  DATA  Exploration was  obtained  the  1970's a l o n g  feet -45  from  degrees,  azimuth 47.6  mm)  feet  (3 m)  much were  89 o f w h i c h  grade  assayed  principal meaningful  high  were  was  mostly  at NA  -74  (1  of  17  inch core  in 100  drilled  degrees  7/8  a l lo b t a i n e d as s p l i t  intersections d i s t a n c e s than  for  Our  copper,  global  to  semi-variograms  grade  a manner  ore  lower  value.  support  at  were  with  an  d i a . or  of about  In  approximately  silver, with  order  10  size). adjacent  3 metre  over  Samples  gold silver,  to  histograms  with  sampled  sections.  only  (sample  combined  were  grade  antimony,  and unbiased  were  as to produce  were  commonly  i s concerned  t o a common samples  of core  zinc,  study  contributor  be c o m p o s i t e d  small  core  were  o f 090 d e g r e e s ,  plunged  zone  drilled  at intervals  of the holes  h a d an a z i m u t h one  holes  Tail  in length.  shorter  arsenic.  diamond d r i l l  2). Ninty  and  180. D r i l l  f o r the Southern  of c r o s s - s e c t i o n s  (Figure  and samples  High  such  a series  vertically of  information  108 e x p l o r a t i o n  (30 m e t r e s )  drilled  to  assay  and the  produce  the data had To t h i s  end,  samples  composites.  in  gure  2  : Plan view of the Southern T a i l showing collar locations of diamond d r i l l holes.  zone 108  14  DATA  Data level in  of  were  examined  errors  silver  in  grade  in  sampling  and  the  assay  values.  available  3  metre  assays  population the  grade  type,  values  represented  in  The  amount  of  check  %  two  important  local  of  errors  variability;  and  appears  to  into An  of  at  the  the  the  at  estimations.  grade  These  graph  of  showing  the  The  low  grade  represents  less  the  abundant  small  stage  ore  galena  were  and  was  recognized  led  to  in  the  not  data  i s , sampling  will  contoured  in metal  of  can  assumed  with  our  sampling  although  not  provide First,  with  sections  content.  premise  exploration  quality.  compared  early  a substantial  p r o p r i e t a r y data  variability,  basic be  single  mineralogical  noting  stages  sampling  reserve  stationarity,  of  regarding  ore  the  composites  common  negligible  trends  a  probability  production  various  grade  variations  than  s e c t i o n s . The  property  that  of  more  into  data.  property.  are  insight  a v a i l a b l e data  i s worth  random,  that  the  the  be  i n d i c a t e extreme  appears  of  secondly,  examination  is a  of  populations.  variability  conclusions  analytical  It  provide  systematic  3 metre  reflects  assaying  development  local  67  exploration  exploration  and  not  and  3  lognormal  identified  the  extreme  the  bias  Figure  pyrite-tetrahedrite. pods  to  assaying,  in mineralized  population  silver-rich  in  two  representing  background  high  of  detail  possible presence  of  existence  some and  population  probable  EVALUATION  large,  introduce  and  a  plans  did  Consequently,  i t  geostatistical  confidence.  study,  Figure  3  : Cumulative log probability plot of 2235 s i l v e r assays from exploration diamond d r i l l holes, Southern Tail zone.  16  STRUCTURAL  A pairs  (SEMI-VARIOGRAM)  semi-variogram of a  variable  i s 'half  the  mathematical  representation  referred formal to  to  commonly  values.  estimating a  later  The  dispersion  use  a  semi-variogram experimental  down-hole  of  difference'  the distance  determination the  a  structural 'zone  of  an  semi-variogram  of  analysis  influence'  (lag)  adequate is  and p r o v i d e s  concept  of  the semi-variogram  (variance)  of  block  grades  for  function  application  model  applied  model  i s discussed  for  (vertical  for  model data  Geological  four  based  a r e much  that  variograms  paralleling  The  the  on  Southern  on  3m  more  examined  and  45  in in  two sill  model  became  erratic  evident the  two  semi-variograms and  nugget  (Figure  the patterns  principal  weakness  determining  the  range  4)  to  in  the  a r e shown  the  ranges  5 and model  plunge  i n a NW-SE d i r e c t i o n  a  in Figures  data.  of  5  and  controlled been  4.  semi-  directions  have  The  pronounced  experimental  been  090  in Figure  down-hole  expect  Figure is  in  mathematical  a r e shown are  down-  directions.  fitted  principal  have  and  the  us  effect  in Figure in  than  a  Separate  for different  horizontal and  3-dimensional  zone.  degrees  composites  led  a  Tail  were  different  considerations  anisotropy  down-hole  the  to develope  experimental semi-variogram  Horizontal  deposit.  procedure  semi-variograms  and  (spherical)  based  function  of  the  standard  orientations  direction)  where  The  as of  a  squared  section.  We  hole  pairs.  quantification  assay  t h e mean  (grades) as  separating  INTERPRETATION  by  the 6 the  selected  6  respectively.  The  the  subjectivity  in  (Figure  5).  17  Figure  4  : Average vertical v a r i o g r a m f o r 3 m. grades.  relative composite  semisilver  18 .  a'=40m.  0  50  100  150  200  250  Lag h (m«tr«s)  Figure  5  : Average horizontal relative semivariogram f o r s i l v e r grades i n the NW-SE direction.  19  5.0»(340)  4.0-  1(404)  7(h)  3.0^  (370)  | FITTED  MODEL  7(h) = A/|*qC,  A =8.29 ,1 = 13.4 A/j = .62 C, = 2.83 a=7l.6  2.0-  I.OJ  /  V  — i —  50  —I—  100  —I—  150  l  200  I  " 250  lag h ( m t t r t s )  Figure  6  : Average horizontal r e l a t i v e semivariogram f o rs i l v e r grades i n t h e NE-SW d i r e c t i o n .  20  Never-the-less, global  estimation.  summarized  TABLE  t h e model  appears  Parameters  reasonable of  f o r purposes  t h e 3 - d i m e n s i o n a l model a r e  i n T a b l e 3.  3 - Parameters of 3-Dimensional S p h e r i c a l T a i l Zone D i a m o n d D r i l l Data  Nugget  Effect  Sill  (Co)  8.29/1  (C  2.83  )  Range Vertical  (av)  11 m  NE-SW  (aNE)  72  m  NW-SE  (aNW)  27  m  Anisotropy  of  Ratio  NE/vert.  6.54  NE/NW  2.07  Model  South  21  DECLUSTERING  Declustering of  biased  mineral  spatial  in  high  parts.  high  a  proportion  to  this  those  source  In  mean  basis  each  F o r example,  former of  total case  1/100  weight  The optimum  the  cell  is  be  each  will  extremes,  problem  size  in  for assigning  and the b i a s is  sample  be  of the data.  To  less  or  weight  abnormal  would case  by  weight  100 s a m p l e s 30  a  have  In  relative  3-  for  will  samples.  have the  Journel  superimposing a equal  containing  i n the l a t t e r  to  i s provided  involves  sample  leading  the  weight  individual  sample  1/30.  size  not accounted  data  individual  too  declustering.  containing  as another  t o low  contains  to apply  s e t and a s s i g n i n g  a cell  in  holes are  relative  clusters  t h e name  procedure  i f a l l the data  weight cell  cell,  each  principal  extremes: equal  weight  in  for declustering  on a d a t a  , whereas,  would  Commonly,  samples,  and d i s p e r s i o n  occur  the  grid  same  of a deposit  grade  the e f f e c t s  more d r i l l  i t i s necessary  of d a t a , hence,  dimensional  the  grade  that  brief,  cell.  data.  evaluation  high  of bias  samples  theoretical  (1983).  to minimize  sample  sections  of  of both  concentrations A  of  and p r o p e r t y grade  used  C o n s e q u e n t l y , *a h i s t o g r a m o f t h e d a t a  overestimates offset  t o methods  distributions  exploration  located grade  refers  so  will  variable  weights  then  i s not accounted small  have  high. weights  that  each  t h e same cases  For will  the  be  every  two has  for. Similarly,  i f  i s i n a separate  and, again,  weighted sizes  the  sample  sample  weight  cell  i s to define  to assays. Consider  a r e i n one c e l l  f o r . In both too  declustering  mean  between  assigned  such  the bias of  the  these  two  that  the  22  weighted cases.  mean  The  estimates through This  the  data  will  approximate  cell  size  of  a  size  illustrated  mean  by  Tail  between  two  3 m  composite  zone  (Figure  a l l drill  grade  of  sizes  the  Figure  7.  idealized  hole  7).  based  The  on  expectation  geometric  constraints  dimensions  of  each  the  sample  number  of  is  number  the A  shown  of  as  the  The  y-axis  accumulation has  a  deviation  of  164.2. As  also  on  Figure  the %.  shown  proportion raw This  data not  quantifies  of is  only the  a  8 as  data 18.2  of  points  and  hole  above. error  data  39.3  shaded  for  as the  zone a  chosen in  from  the  results one  from of  declustered , where  one  of  shown  results  1/Lni  least  the  series was  approaches  then  to  declustered  in  the area.  than  out  need  the  of  size  L  sample  the with  is  the  and  ni  a  40  the for  distribution  as  each  g  interval.  of  i s worth Ag/tonne  declustered  The  a  standard  raw  data  is  noting  that  cut-off  for  data  15.3  declustering  overestimation  is  proportion  with  histogram It  a  class  g.Ag/tonne  for  of  Tail  metres  error  size  at  weights  the  45  frequency  whereas  magnitude  passes  i .  shows  greater %  trial  each  cell  equal  reference a  of  were  unbiased  of  mean  data  block  Figure  i s an  m  containing in  for  and  cell  weight  the  8.  mean  mean  interpretation  trial 70  The  of  distribution  the  the a  samples  extreme  cited  Southern  dimension  beyond  blocks  the  idealized  of  deposit.  metre  the  cases  drill  two  unbiased  where  limiting  calculated  histogram as  which  45  occurs  from  cell  receiving a  the  7).  the  departure  in  obtaining  exploration  was  A  than  g r a p h i c a l l y by  data  deposit  (Figure  optimum  the  less  for  field  i s determined  the  be  mineralized  Using  cell as  a  minimum  cell  Southern  of  error  is  but  also  that  could  23  20  -I  '  25  1  I  50  75  I  |  100  125  S ( c t l l dimensions i n m s t r s s )  Figure  7  : N a i v e mean s i l v e r v a l u e p l o t t e d f o r various c e l l s i z e s (s) i n order to d e t e r m i n e t h e optimum c e l l s i z e f o r declustering.  24  .040  J  .033.  .030—1  RAW DATA DISTRIBUTION  .025J  n  DECLUSTERED UNBIASED DISTRIBUTION  >O  z  3  o  .020.  .013 _ l  .010 _l  .008  30  100 SILVER  ISO  (g./tonn«)  Figure 8 : Unbiased histogram f o r Southern T a i l z o n e s i l v e r f r o m 3 m. c o m p o s i t e s w i t h h i s t o g r a m o f raw d a t a s u p e r i m p o s e d .  200  25  arise  i f d e c l u s t e r i n g were  not  done.  CONDITIONAL  We or  have  true  support  mining and  not  size  therefore the  this  point  distribution  However,  block  at  same  of  silver  sample  increases  the  obtained  selection a  blocks  block  be  support.  will  the  made  It  produce  estimate in  a  of  the  Southern  on  stands  estimation  are  several  methods  distribution  the  basis  to  reason  variance  'tighter'  a l l based  block  distribution.  grade  which  we  use  the  block  here,  distribution, The  but,  affine the  blocks  the  grade  on  will  unbiased Tail  Zone.  of  block  a  that  as  decrease  and  distribution  In  the  about  course,  relationship  i s as  of  follows  as  with  the  of  form  sample  variance.  and (Z)  Huijbregts, and  the  1981)  distribution  :  a  y  i s the  variance  of  distribution  Y  a  z  i s the  variance  of  distribution  Z  2  2  m  i s the  and  z  declustered is  distribution  any Z.  mean  value  of of  of  grade  Y = a y / a z ( Z - m ) + m  where  the  procedure,  general the  the  sample  form  correction  smaller  grades  core  the  mirrors  (Journel  core  to  is that  estimating  the  affine  distribution of  for  from  assumptions  assumption  distribution  (Y)  available  (histogram)  distribution,  of  -grades  will  the  an  mean.  There  between  PROBABILITY  the the  data variable  in  26  The  only  seeking be  unknowns and  the  obtained  Huijbregts,  in this  variance  using 1981) o  2  where  =  D (v/G)  that  D (v/G) 2  v  is  the  2  grades  in  the  distribution  distribution.  The  Y  we  are  variance  relationship  can  (Journel  and  :  =  D (c/G)  -  2  D (c/v) 2  dispersion variance  units  D (c/G)  are  additivity  states  i s the  2  mining  of  Rrige's  which y  equation  in mining  volume  dispersion  volume  G  of  grades  of  G.  variance  of  (obtained  from  core the  hi stogram). and  D (c/v) 2  grades  in  variogram  The Figure  The  Ag/tonne  and  if  core  the  situ would  grade  a  standard  estimates  result.  of  blocks  sample  dispersion variance  mining  unit  v  (obtained  of  core  using  semi-  model).  distribution 9.  i s the  grades will  for  have  deviation  distribution a  serious  10 the  of  metre  same mean  143.6.  were  blocks  used  It  is  i s shown  grade  of  in  39.3  obvious  that  inadvertently for  overestimation  of  high  grade  g  in ore  0  SO  100  130  SILVER (g./tonna)  Figure  9  : Unbiased histogram for silver grades of 10 x 10 x 10 c u . m . blocks, Southern T a i l zone, with histogram from unbiased 3 m. c o m p o s i t e s superimposed.  ZOO  ZOO  28  GRADE  Using  i t i s a simple  of  a l l material  is to  to  shown  procedure above  as F i g u r e  below. Mines  since A  their  Limited,  i n Figure  to c a l c u l a t e the proportion  and grade  an  level  45 m e t r e  The  in situ  of  be  2.89 t o n n e s /  the  density  remaining  reserve  estimation  the  of the Southern  blocks  would  last  g r a v i t y of  3  Tail  no d a t a  present, to  blocks were  reach  was o b t a i n e d  used  zone i s  The  necessary m  material  outlined.  i n d i c a t e d , but with removal  as  blocks  cut-off.  and s p e c i f i c  The upper  10 w i t h  density  shown  i n producing  the boundaries  included  ESTIMATION  f o r 10 m e t r e  given  on t h e v o l u m e  estimated.  within  any  overcome  deciding be  TONNAGE  the d i s t r i b u t i o n  9  problem  AND  from  ore  Equity  in  previous  global  from  the three  45 m e t r e  estimations. The levels  total  tonnage  t o be c o n s i d e r e d  was  59,000,000  tonnes.  proportion  of tonnage  above  4).  The  tonnage  9,024,000 A  tonnes  more  periferal the 40  of  material  conservative  reduced  volume  g.Ag/tonne  this  averaging  blocks  F o r a c u t - o f f o f 40 g . A g / t o n n e t h e  with  c u t - o f f was above  125.1  was a r r i v e d  below  was 4 8 , 8 0 0 , 0 0 0  cut-off,  of  40 g . A g / t o n n e  (from  Table  i s therefore  g.Ag/tonne.  estimate data  .15296  cut-off. tonnes,  7,460,000  a t by  eliminating  The t o t a l  with  tonnes  tonnage of  a tonnage  above  averaging  a  125.1  g.Ag/tonne. It  i s  important  to  reserve  estimation  makes  occurs  within  given  geological on  a  ore reserve  a similar  note  that  no a t t e m p t volume.  this  to identify These  calculated prior  40 g . A g / t o n n e  cut-off  method  of i n situ ore where  results  compare  to production  f o r 10 m e t r e  the  blocks  and  ore  with  a  based  by t h e  29 Owl  K)  o cn  *  1 • •  8 o o  \  I  8||l||  o CM o I  ro  -  2  eg o  -  •  .  •  o •  ;  fllllj  1  oo  8  10  o  'V'.- • o co  »  o (0 -  IllSf  mm  •o o  §1111  o  <0 (0  o  •  o o t-<o CM  Figure  10  10  o  00  co 10  <M  CM  : Upper s l i c e (including levels 1280 to 1235), S o u t h e r n T a i l zone, showing d i s t r i b u t i o n o f 45 m. b l o c k s . Blocks within the double lines used to calculate tonnage of 48.8 million tonnes; blocks containing data are shaded.  o  10  CM  o  ~  I  30  TABLE  4 - Grade  and Tonnage Curves  CUT-OFF (g/tonne)  GRADE (g/tonne)  20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 1 00.0 110.0 1 20.0 1 30.0 1 40.0 150.0 160.0 170.0 180.0 1 90.0 200.0 210.0 220.0  89.9 114.1 125.1 1 35.8 1 49.0 1 56. 1 161.7 170.3 180.2 185.7 188.6 196.5 203.3 206. 1 210.0 212.7 218.3 218.7 220. 1 220.9 221 .4  (Silver)  TONNAGE USING ( T o t a l o f 59 m i l l i o n tonnes)  14 10 9 7 6 6 5 5 4 4 4 3 3 3 2 2 2 2, 2,  056 293 025 983 877 327 917 331 71 1 389 221 754 368 212 988 823 469 440 291 2, 1 62 2, 028  000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000  TONNAGE USING ( T o t a l o f 48.8 m i l l i o n tonnes)  11 8 7 6 5 5 4 4 3 3 3 3 2 3 2 2 2 2 1 1 1  626 513 465 603 688 233 894 409 897 630 491 1 05 786 657 471 335 042 018 895 789, 678,  000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000  31  inverse  distance  averaging  121.5  method  curve  is a  Thus,  an  various  Of  natural  cut-off  blocks mining  no  end  curves  cut-off  8,124,000  tonnes  to  the  of  i s an  of  ore  recovery  are  located. be  assays,  block  on  that a  it  selection.  on is  a  a  produce  more  block  global  for such  sizes.  estimates  volume,  selection  relatively  11).  provided  several  block  this  (Figure  to  such  of  grade-tonnage  is  mineralized  Precise  based and  matter  based  in  that  method  procedure  easy  selection  where  fact  the  re-emphasize of  probability  potential  It  will  blasthole lead  of  for  indication  l i e in  result  must  eventually  will  conditional  reserves  grades.  we  above  production that  the  indication  course,  provide  of  global  grade-tonnage  indicated  g.Ag/tonne.  Advantages estimating  which  tight  the during  grid  detailed  of  data  Figure  11  : Grade-tonnage c u r v e f o r Southern T a i l zone showing two tonnage curves : one based on a total mineralized tonnage of 59 m i l l i o n tonnes and a second based on 48.8 m i l l i o n t o n n e s .  33  CONCLUSIONS  Global Tail  zone  using  (in  of Equity  the  correction  method  ore  Silver  Mines  of block  histogram  of  conditioned  support.  grades  sample,  has  data,  t o t h e sample  relative  estimates  Limited  to  the that  sample  i s , the  grades  relationship  i n c o r p o r a t i n g the semi-variogram  based  on  case  results  10 m b l o c k  weighting. probability  The  estimates  compare  approach (1)  no  the  form  using  rigid  block  well  by a m e t h o d  principal  an a f f i n e  assumptions  of the histogram  conservation  (e.g.  of  blocks  are  unbiased  data.  with of  histogram of  using  global  inverse  of  the  Krige's  of e i t h e r  distance  conditional  regarding sample  lognormality  to  reserves  or and  Instead,  the  available  but  (2)  effects  of a u t o c o r r e l a t i o n a r e i n d i c a t e d i t  the  reserve  estimate  Krige's (3)  A  obtained costly  additivity complete for  v i a the semi-variogram  necessity  and  relationship. grade-tonnage  many  block of  is  block  are :  b e made  lognormality).  conditioned  the  geostatistical  correction must  as  function.  advantages  grades  block  data  that the  form  fundamental  affine  sample  assumes  i s estimated  relationship,  this  an  dispersion  additivity  In  a  of  general  The l e s s e r  generated  i n which  procedure  same  Southern  been  histogram  This  data.  f o r the  have  of c o n d i t i o n a l p r o b a b i l i t y  t o a common  histogram  reserve  i s a p p l i e d t o an u n b i a s e d  composited  grades  situ)  curve  sizes  regenerating  can  without new  be the  grade  estimates an  as  would  be  required  i n v e r s e d i s t a n c e model  interpolation  procedure.  or  any  i n the case other  of  exact  35  ACKNOWLEDGEMENTS  This Hillhouse  study  Myckatyn  has  been  W. for  of  provided  Engineering Green  of Placer  their  support  initiated  a n d Mr. E.T. L o n e r g a n  W.  the  was  Equity  Silver  at  the  of Placer Mines  suggestion  o f D r . N.  Development  L t d . and  Limited.  Technical  b y P. B e a u d o i n , J . C y r a n d  J.H.L.  Department  Mines  of E q u i t y  Development  cooperation  was p r o v i d e d  L t d . We  and involvement by P l a c e r  Silver thank in  Miller  Development L t d .  of  L t d . a n d Mr.  a l l of these  the  support  study.  people  Financial  36  REFERENCES  J o u r n e l , A.G. and Ch. H u i j b r e g t s (1981) M i n i n g Academic Press ( I n c . ) L o n d o n L t d . , 600 p.  geostatistics;  J o u r n e l , A.G. (1983) N o n - p a r a m e t r i c e s t i m a t i o n d i s t r i b u t i o n s ; Jour. I n t . Assoc. Math. Geol. p. 445-468  of s p a c i a l v.15, no. 3.,  Ney, C.S., geologic deposit, no. 723,  J.M. A n d e r s o n and s e t t i n g and s t y l e B r i t i s h Columbia; p 53-64.  A. P a n t e l e y e v (1972) Discovery, o f m i n e r a l i z a t i o n , Sam Goosly I n s t . Min. M e t a l l . B u l l . v. 65,  S i n c l a i r , A.J. (1978) S a m p l i n g a m i n e r a l d e p o s i t f o r f e a s i b i l i t y s t u d i e s and m e t a l l u r g i c a l t e s t i n g ; i n M u l a r , A.L. and R.B. B h a p p u , M i n e r a l P r o c e s s i n g P l a n t D e s i g n ; Am. Inst. Min. E n g . New Y o r k , p 115-134. W e t h e r e l l , D.G (1979) G e o l o g y and Ore G e n e s i s copper-silver-antimony Deposit, Unpublished D e p t . of G e o l o g i c a l S c i e n c e s , U n i v e r s i t y of V a n c o u v e r B.C., 208 p.  o f t h e Sam Goosley MSc Thesis, B.C.,  W e t h e r e l l , D.G., A . J . S i n c l a i r a n d T.G. Shroeter, (1979) P r e l i m i n a r y r e p o r t on t h e Sam Goosly copper-silver deposit; B.C. M i n i s t r y of E n e r g y , M i n e s and P e t r o l e u m R e s o u r c e s , P a p e r 1979-1, pp. 132-137.  CHAPTER  PRODUCTION  3  Q U A L I T Y CONTROL  EXPERIMENTS  38  ABSTRACT  Quality adequate  control  accuracy  particulary  in  Southern  Tail  analysis  and  procedures  and  precision  erratically  zone  of  1.  a  their  2.  a  large  sampling  a  results  blasthole recovery benefit  in excess  that  will  improved of  such  have  as  the  duplicate  demonstrated two  laboratories  in  the  used  standard  to  provide  relationship and  volume  grade  and  between  of  tube  grade  samples  from  cuttings.  indicate  through  assaying,  L t d . There,  between  error  systematic  cuttings  and  deposits  for production blastholes,  blasthole  maintain  analyses,  random  reproducibility  These  bias  to  sampling  Mines  tests  procedure  estimates 3.  sampling  silver  in  Silver  significant  in  essential  mineralized  Equity  duplicate  are  $  an  improved  provide block  1 million  a  sampling marked  selection, per  year.  technique  increase  perhaps  with  in  for metal  a  net  39  INTRODUCTION  Optimal  block  selection  i n mining  depends  o n two  critical  procedures, v i z . 1. o b t a i n i n g 2.  representative  weighting  appropriate block Here  we  blast  of error  holes.  for  efficient  mining  in  the  case  deposit  such  fashon  with  quality  optimal  in a  an  given  evaluate  values  and a n a l y t i c a l  and  waste  selection  to  of assay  sampling  as the Southern  assays estimate  designed  o p e r a t i o n s . Sampling  of block  a s s a y s and  1979).  tests  ore  of  to • best  i n the assignment  High  essential  selection  ( c f . Raymond,  are concerned  sources  a  sample  to production procedures are  discrimination  is  zone  of  i na l l  particularly  f o r an e r r a t i c a l l y  Tail  various  Equity  critical  mineralized  Silver  Mines  Ltd. The lies  within  volcanic inlier in  Southern  inlier  rocks i s  the  an  intruded by  ores  with  a  between  The  strike  50 d e g r e e s .  thought to  a  Southern  Goosly  sedimentary,  Wetherell  lesser Tail  degree,  zone  025 d e g r e e s mainly  a l ,  deposit  1978).  monzonite  complex.  t o be e p i g e n e t i c  silver  pyroclastic  et  by a q u a r t z  gabbro-monzonite  of about  breccia  the  i n t h e west  Sulphides occur  Sampling during  and  o f t h e Sam  of Cretaceous  a  are  structurally, controlled.  zone  ( W e t h e r e l l 1979;  east  antimony  Tail  and The  stock and  Silver-copper-  in origin  and  both  stratigraphically  i s crudely  tabular  i n form  and a w e s t e r l y d i p of  30  in a  cement  stockwork  or as a  to  fragments. tests  early  on p r o d u c t i o n b l a s t h o l e stages  of  mine  cuttings  development  by  were  begun  Equity's  40  Engineering  Department.  response  to the  deposit.  This  the  results  comparison  of  findings report  of  Additional  these  duplicate  of  deals  a  were  geostatistical  sequentially  studies, data.  studies  a l l  of  with  carried study  an  which  out of  evaluation involve  in the of the  41  A  PROCEDURE FOR  Quality involves  standard  to  Paired  by  the  procedures  interest  because  errors an  A  during  statistical quantify  procedure elements  to  as of  of  20th  both  or as  in i t  sample  production  duplicate  both  medium  of  which  Such  data  types  is  in  might  quality  that  or  is  (eg.  are  differences.  random  or  of The  systematic  fundamental  become  the  evaluation  1.  Parallel  the  Several  patterns of  use  of  order  of  errors  paired is  to  In  system  as  evaluation  of  duplicate quality  illustrated  graphical to  assay  required  apparent. are  is  simple  in  of  assay  production  utilized or  to  examination  decision-making  identify  that  might  data.  A  in applying  brief,  the  raw  of  as  a  multi-modal  v i s u a l check probability  and be  the  essential  follows: both  and  certain  and  log  on  the  data.  P r o b a b i l i t y graphs  possibility  example,  methods.  approach  for  1.  are  functions.  For  commonly  quality.  Figure  transformed  results  or  a  classed  d i f f e r e n t types  will  2.  be  evaluation  subjective  10th  or  DATA  a n a l y t i c a l method  similarities  can  classes  in  an  from  paired  routine  methods  various  represented of  in  of  different  evaluation  data  property  data.  every  or  their  and  assaying  paired  derive  a n a l y t i c a l ) data  schematically  amount  of  general  sample.(or  an  and  (PAIRED)  a n a l y t i c a l standards,  errors)  and  appreciation  may  lead  of  (or  (bias)  of  same  control  differences  or  DUPLICATE  sampling  analyze  data  cuttings)  analyzed  OF  reproducibility  procedure  blasthole  of  comparison  the  duplicate.  be  control  the  evaluating  EVALUATION  density  42  PAIRED DATA  Ili^Sw-^i  fmmmmmJ  RAW DATA  •  LOG TRANSFORM  :  PROBABILITY GRAPHS 2-  UNI MODAL  NON-PARAMETRIC TESTS  CHI SQUARE TEST 3-  PAIRED T-TEST  XY  PLOTS  4-  SUBJECTIVE EVALUATION  CURVE FITTING | Generally straight line !  5-  Figure  1 : A  system  for evaluating  check  assays.  43  3.  Paired  as  appropriate,  tests  t-test  (e.g.  indicated density 4.  concentration Curve  model,  error,  particular, fixed  ideal, be  bias  simple  necessary  the  simple  most  error  and  and  X  subjective of  error  especially  we  concerned  are  model  bias  in Figure but  provides  where  probability  of  and  log  evaluation  of  as  raw  a  function  a  simple  with  of  as  2.  linear  recognizing  random  illustrated  More  complex  experience  an  large  are  =  +  paired b  line  in y  a  adequate  the  by  an  models  may  indicates  that  representation  for  of  the  line  sample  subgroup  is treated  separately  as  should  a  rule,  e  a  according  y-intercept  of  bias)  (random  pairs to  i s the  slope  (proportional  subgroups  and  +  values,  is  about  numbers  bX  into  procedure  error  errors.  bias),  squares  Each  for  nature  plots  quantify  model  (fixed  divided  the  test)  patterns.  Y  Where  statistical  rank  x-y  i n d i v i d u a l cases  linear  of  data  level.  Y  where  form  proportional  linear  in  paired  of  fitting,  to  transformed  (histogram).  data in  log  non-parametric  the  Examination  5.  or  Wilcoxon  function  variation  raw  and  by  transformed  In  of  are  the and  is  available  throughout at  e  the  error).  identifiable  contain  least  least  time  the 30  they  are  periods.  evaluation to  40  pairs.  44  (d)  (c) x = approximation y = sample FIGURE  2  A  to true  value.  result  SIMPLE  LINEAR MODEL  TO D E S C R I B E  ERRORS IN  PAIRED DATA. (a)  Simple  random  error  (b) S i m p l e  random e r r o r  plus  proportional  (c)  Simple  random e r r o r  plus  fixed  (d) S i m p l e  random e r r o r  plus  proportional  biases  bias  bias and  fixed  45  In  this  fashon,  variation  in  duplicate  data  fluctuations standards each  new  procedure A  laboratory as a  f o r such  situations  not appear  2.  in  Figure  emphasis  science  multimodal  in error 3.  with  incorporated  in  For shorter  replicate  period  of  added  to  is  a n a l y s i s data f o r  graphs i s  and  to  data  t-tests  a data  placed  on  set,  but  as this  cases. a  scatter  recognize  error  subjective diagrams.  the  very  The  common  of :  histograms and  variations  in  the  type  of  error  as  a  concentration.  hypothetical  variations  to deal  t o be e s s e n t i a l i n most  an a p p r o a c h  function  Several  of time.  is  probability  i n earth 1.  methods  t o examine  pair  considerable of  attempts  by t h e l a b o r a t o r i e s i n s u c e s s i v e  analytical does  procedure  analysis  function  i t i s useful  analyzed  evaluation reason  the evaluation  as a  but  common  function  examples  of concentration  demonstrating are provided  46  (e)  (f)  FIGURE 3 IDEALIZED EXAMPLES OF PATTERNS EXHIBITED ON PLOTS OF DUPLICATE ANALYSES (a)  Random e r r o r p l u s  X-Y  outlier  (b) Two levels of random e r r o r as a f u n c t i o n of concentration ( a n a l y t i c a l e f f e c t a t low v a l u e s ) (c) P r o p o r t i o n a l high values  bias  a t low v a l u e s ,  random e r r o r a t  (d) Two l e v e l s o f random error as concentration (nugget e f f e c t at h i g h  a function values)  (e) Error component  effect  resulting  (f) proportional bias incorrect standard  from  arising  s.g.  from d i l u t i o n s  in of  of one an  47  QUALITY  Since  CONTROL T E S T I N G  the early been  stages  zone  has  thus,  p o t e n t i a l l y subject  Production  began  were  directed  and  sampling  appreciated at  Equity  four  recognized  in  towards  scoops  blasthole.  of This  cuttings sampling  in British  relatively  small  sample  a  Southern A  Tail  at  elements  zone  block tube  , common  to  Silver  (e.g.  the  Mines  analytical work  c a n be m ) 3  composed o f  centrally  located  to several  procedure  for  efforts  ( 5 x 5 x 5  open p i t  1968),  blasthole  subsequent  check  of  assay  Ewanchuck,  of the t o t a l  problems.  stages  of t h i s  sample  technique  in a  and  selection  single,  i s given  program  Equity  that  of  erratically,  of the q u a l i t y  a  proportion  Tail  the e a r l i e s t  importance  Columbia  Southern  analytical  The  from  description  general  errors  an e v a l u t i o n  on a c o m p o s i t e  operations  :  1980 a n d f r o m  and  MINES  the  mineralized  t o sampling  i f one i s aware  SILVER  of e x p l o r a t i o n , as being  procedures.  i s based  AT EQUITY  uses  cuttings  as applied  a  as a  to the  section.  analytical  and  L t d . contained  sampling  the following  : 1.  Duplicate  analysis  by E q u i t y  and a  second  laboratory. 2. 3.  Duplicate Test  blasthole of  sampling.  several  blasthole  sampling  procedures. 4. E v a l u a t i o n  Some in  of  the detailed  subsequent  sections.  of sampling  r e s u l t s of t h i s  results.  program  will  be  presented  48  DUPLICATE  The be  made  first by  standard third  and  comparing samples  a  an  Southern  Tail  zone  Mines'  results  from  and  exercise  both  no  which  results of  contrast,  a  of  for  data  can  (internal)  from  a  this  approach  second  comparison  a n a l y s e s because  Equity  reference  as  two  of  or  even  is  to  The  and  an  both The  Appendix  is  the  I.  i f the  labs  correct.  The  analytical  two  paired  the  4b).  be  a  bias  points  can  of  shows A  labs  t-tests  absence  results  a l l  bias  as  potential  from  (Figure  almost  by  Laboratory.  indicate  a  Equity's  alleviated.  verify  silver  as  of  from  silver  based  to which  4a),  labs  line.  o v e r e s t i m a t e or  be  and  only  copper  groups  for  value  can  can  (Figure  between  silver  samples  included  serve notice  for  grade  the  mill  are  i s given  recognized  results  low  24  a Vancouver  comparisons  difference  an  validity  analyzed f o r copper  however,  when  and  of  laboratories  agreement  grade  equal  on  results  purpose  total  indication  assay  reasonable  a  were  any  does,  The  In  duplicate  L a b o r a t o r y and  Unfortunately,  high  check  analytical  principal  example,  Equity  problem  The  DATA  bias.  As  differ,  easiest  routine  with  laboratory.  detect  perhaps  ANALYTICAL  for  any  the  bias.  significant is  plot  indicated  above  explained  underestimate  show  by  the  either  as  the  check  will  occur  laboratory. Here for  ( i ) ore  these the  we  groups fixed  demonstrate  assume  and  tailing  separately bias. an  that and by  Results  average  bias  different  levels  of  ( i i )concentrates, paired are of  t-test  tabulated 336  in  error and  order  in Table  g.Ag./tonne  for  treat to 1 and  each  of  quantify clearly  concentrates  n=23  • I -2 3 -4 5  14  16  IB  20  22  24  CHECK LABORATORY % Cu.  CHECK LABORATORY g. AgVlonne  F I G U R E 4 a PLOT OF COMPARISON BETWEEN TWO LABORATORIES  SHOWING 23 POINTS ABOUT  AN EQUAL VALUE R E F E R E N C E L I N E FOR T A I L I N G S CONCENTRATE  .  ( T ) , ORE  (0)  ( C ) SAMPLES  (Y=X)  AND  FOR  COPPER  F I G U R E 4 b PLOT OF COMPARISON BETWEEN LABORATORIES AN FOR  EQUAL  SHOWING  VALUE  TAILINGS  CONCENTRATE  23 P O I N T S  REFERENCE  ( T ) , ORE  LINE  (O)  ( C ) SAMPLES  TWO ABOUT (Y=X)  AND  FOR  SILVER  ^  50  with and  Equity tailing  line,  a  an  data  14 o f  situation  assuming the  overestimating  no b i a s  single outlier.  pronounced g.Ag./tonne This  with  relative  at q u a l i t y control  level  of  average  30  g  percent  discrepencies investigated well both  and c h i p  These constantly  concentrations, incorporated  than  .01,  indicated  and  interpreted  as  demonstrates  average  about  a  5.5  t h e need  of a n a l y t i c a l for  the  i s 5.5  g  that  for  analyses  tails,  cut-off  Ag,  the  replicate analysis  Replicate  a  repeated should  concentrates,  ie.  source  laboratories  standards  not only  At  s e l e c t i o n the indicated  clear  two  continued  results.  block  is  for considerable  an of  should  be  of samples  as  analyses  by  include a l l and  ore  but  samples.  results conduct  indicates  It  o f sample  value  t o the second l a b .  error.  through  is  For ore  equal  less  c a n be  on  laboratories  between  much  the o u t l i e r  analyzing  lab.  the  a bias  between  laboratories.  core  above  the line  excluding  /tonne  as use of l a b o r a t o r y  categories also  Ag  discrepancy  eighteen  below  study  effort  plot  probability  Equity  preliminary  t o the second  Consequently,  t-test  with  high  a  plotting  A paired bias  15 v a l u e s  exists.  value  relative  demonstrate internal  so  that  i n reported  the necessity  checks large  assay  against  a  standards  systematic  values.  that  errors  laboratory of are  known not  51  TABLE  1 - Summary o f R e s u l t s f o r P a i r e d t - T e s t o n T h r e e Sets of P a i r e d D u p l i c a t e Analyses f o r S i l v e r .  GROUP  n  AVERAGE  STANDARD  STANDARD  PAIRED  DEVIATION  ERROR  DIFFERENCE (g/tonne)  Ore  and  tailing  Ore  and  tailing  minus  outlier  Concentrates  15  3.76  8.24  2.13  1 4  5.53  4.75  1 .27  8  335.70  444.90  148.30  52  DUPLICATE  Twenty-one  duplicate  evaluate  the level  technique  utilized  for  copper  for  paired  in  also  Equity  block  the  Silver  a large  Mines  5  paired  and t h i s  random  (Table  error,  i s based  on s u c h  results  solely  indicates  and s i l v e r  to  by t h e t u b e - s a m p l i n g  evaluate  and a p a r t i c u l a r l y  s e l e c t i o n a t present  taken  u s e f u l l y on a n x - y p l o t  procedure  copper  were  I I ) . These  to  Figure  sampling  indicate  variability  are d i f f i c u l t  f o r both  samples  (Appendix  b u t c a n be v i e w e d  t-test  results at  by E q u i t y  qualitative evaluation.  unlikely  SAMPLING  blasthole  of sampling  and s i l v e r  tabulation  BLASTHOLE  as  a  (Figure  that  bias  i s verified  5) i s  by a  2 ) . However, t h e  an e x p e c t e d crucial  problem  one  individual  because  blasthole  results.  TABLE  2 - R e s u l t s f o r P a i r e d t - T e s t f o r Copper and S i l v e r o n 21 D u p l i c a t e B l a s t h o l e Samples.  GROUP  Ag  n  AVERAGE PAIRED DIFFERENCE  STANDARD DEVIATION  STANDARD ERROR  Copper  21  .001  .0473  .01 03  Silver  21  7.14  31.01  6.77  grades  i n g/tonne  a n d Cu g r a d e s  in %  0  I  2  3  -4  5  -6  ORIGINAL ASSAY % Cu.  10  30  50  *  70  ORIGINAL ASSAY  F I G U R E 5 a PAIRED RESULTS FOR COPPER 21 D U P L I C A T E BLASTHOLE  FROM  SAMPLES  90  110  130  150  (g. Ag./tonne)  F I G U R E 5b P A I R E D R E S U L T S FOR S I L V E R FROM 21 D U P L I C A T E BLASTHOLE  SAMPLES  ^  54  Even an  with  evident  function  difference of  duplicates tightly  the limited  about  about  the equal  than  greater  is  increased dramatically.  line  with  squared random off  sampling one  point  relative reduce  the equation  d e v i a t i o n about  grade  data  g Ag/tonne  plus  procedure.  the data y =  Where of  of F i g u r e  and g i v e s error.  (relative)  error  large  random  sampling error  plot  a general  30  procedures  inherent  samples  fitted  to a  i s t h e mean idea  percent. sampling  of the cutThese results  i n an e f f o r t  i n the  of  pair  A t t h e 30 g . A g / t o n n e is  a  fairly  of a  duplicate  5 c a n be  as  a pair  one v a l u e  .87x - 0 . 0 6 8 . T h e e r r o r  the line  potential  of  data  t o the n e c e s s i t y of e v a l u a t i n g tube  to other the  line.  the  5 there i s  variability  values  the scatter  analytical  standard  both  70 g . A g / t o n n e  70 g . A g / t o n n e  in Figure  of s i l v e r  Where  values  is  70  represented  i n the nature  concentration.  a r e below  Below  data  to  tube-sampling  55  TESTING  BLASTHOLE  Equity deposit from  SAMPLING  Silver  employ  'cones'  Mines  a  tube  of  Limited  procedure  application  by  completion  of  has  Bethlehem a  e x p e r i m e n t a t i o n has  from  the  diameter at  tube  four  portion i s then  individual  samples  one  form  bag In  to  view  analyses to  As ways  the and a  tube  bulk  test,  from  the  top  of  the  'overdrill'  cuttings  4  sites  sites  A  3  then  6).  four  in  the  and  3-inch  in  duplicate  section  procedure  the  against  tube  were  sampled  diameter  manner  described  combined  to  four  inch  channel  wide  Figure riffled  6.  track  in  decision two  sample was  tube  i n the  samples  previously  form  following  were  taken  (Figure  one  samples shovel  were  tube  from  The  four  channel  once  with  one  split  taken  6)  sample  with  locations samples kept  as  made  alternatives  (composite). b)  The  combined  : a)  inch  sample.  previous  blastholes  pile  successively  sampling. 42  a  material  (Figure  are  Upon  away  u n d e r l y i n g bench. the  errors  sampling  the  to i t s  1968).  scrapes  from  sample  'tube'  large  d i s c u s s e d i n the  test  channel  located  composite the  through  somewhat  regard  (Ewanchuk  zone samples  A  with  driller  next  Tail  cuttings.  represents  the  MINES)  for obtaining  Ltd.  cuttings  SILVER  Southern  described, Mines  shown  scooped  a  of  of  pushed  symmetrically  their  the  of  EQUITY  procedure  been  blasthole  which  (AT  blasthole  Copper  thickness  top  at  sampling  production  comparable  predetermined  PROCEDURES  a  5  shown  in  were the  each sample  :  56  CHANNEL 3  FIGURE 6 PLAN VIEW OF BLASTHOLE CUTTINGS SHOWING L O C A T I O N S OF THE T U B E AND CHANNEL SAMPLES (Cyr et a l (1980). 1  57  for  that  all  channel  four  and  channels  channel  sample.  riffled  until  the  remaining  combined This  one  to  splits  form  composite sample  a  from  composite  sample  bag  of  was  material  remained. c)  1  the  tube  until  one  remained.  This  sample  sample,  sample  and  results  f o r each  In possible single  the  any  estimate'  grade  weighting  each  were  listed  four  bulk  blasthole  pile  bag  represented  the  this  by  were  the  was  then  of  cuttings  a  residual  i t  is  particular  uniform  (see Appendix  IV  which  case  combining  ideal  channel with  the  III.  with  i t s corresponding a  assayed  convenient  answer  by  composite  then  i n Appendix  blasthole  assuming  3.  listed  correct In  sample  samples,  sample  study  for' each  cuttings,  in Table  sample  channel  residual  result.  calculated,  blasthole  the  have of  i n the  analysis.  comparative  to  type  material  riffled  bulk The  remaining  we  to  rarely  compare  formed  a  The  f o r the  for calculations)  a  'best  a l l results  volume.  shape  but  and  volumes cone  of  and  are  58  TABLE  3 - Sample Types Weights  with  C o r r e s p o n d i n g Volumes and  SAMPLE  VOLUME  Tubes  113  Channel 1  720 i n .  3  Channel  2  300 i n .  3  Channel  3  360 i n .  3  Channel  4  300 i n .  3  2447 i n .  3  Residual  *  Bulk  proportions  of t o t a l  in.  WEIGHTS *  .027  3  volumes.  .396  .577  59  EVALUATION  For  purposes  analytical economic  of  copper  and  grades  so  TEST  we  RESULTS  will  only  for  silver  because  of  copper  grades  in  much  more  importance silver  SAMPLING  demonstration  results  Furthermore,  OF  grades  are  produce  more  of  the  consider  relatively  block  minor  selection.  variable  significant  the  errors  than in  are  block  selection. Some  concern  separation  of  existed  material  Consequently  the  to  direction  was  see  i f one  b i a s e d . No The  accumulated use  the  sampling  relatively  is  to  sample  to 4.  to  h i g h . We  errors  the  samples  'tail'  samples  of  the  of  density cuttings.  were  examined  the  cuttings  although  attribute the  were  combined  corresponding  exist  sample  The  show  'best  composite  p r o v i d e d by  fitted  to  with  found  channel  the  provide a  tube  Table  data  composite  Consequently,  the  blasthole  channel  channel  channel  sample  relative  holes  of  possible  four  this  the  results  channel  dispersion  largely  individual for  in a  to  the  samples  and  comparison  of  methods.  Tube either  the  found.  was  sampling  cone  relative  compared  bias  composite  a  individual  was  and  No  v a l u e s was  in  individual  average  composites. of  bias  four  weighted  four  regarding  the  better  analytical  results  residual  or  estimate'  estimate One  scatter  plots  more  channel  results. the  considerably  of  of  grade  samples of  the  measure data  results  true  about  F i g u r e s 7, show  bulk  8,  this the and  clearly  7,8  and of  grade  relative  that  blast  than  do  lines  summarized the  9).  'goodness'  regression 9 and  do  results  samples  silver  than  bulk  (Figures  or  of  dispersion  quality  in of  60  Y=X  • CI  5?.  ,  Y = 75U 894X  ,a  •—, to .  or ~ o  area  GO  N= 42  A  a a  j a  BO. a  .0  BEST  :BO.D 240.0 ESTIMATE BULK  320.0  area 'W detail  Y=X  a a .  •  •  03 !Z)  — I  •  _l GC  or o  /  •^  a .  /  /  20  0.0  /  /  / m/ /  7 ORIGINAL  FOR  PAIRED  42  TUBE  SILVER  •  /Ag_ '  •  Y =75! + 894 • •  N= 42  •  •  0  40.0  BEST FIGURE  //  /  /  A  •  CD  SAMPLE  DATA  400 .0  60.0  80.0  100.0  ESTIMATE BULK VERSUS  BEST  ESTIMATE-  BULK  61  Y=X  m  ud°  (_) UJ (_3 a  Y=374 + 974X  X o  or^ •  UJ  -  >  X  a  CD  -I  N= 42  area A  see below  J .0  80.0  160.0  BEST  C3  240.0  ESTIMATE  3ULK  320.0  400.0  a .  area A detai M „ 11  Y=X  co  x" X (_)  3  UJ  .  x °  Y = 3.74+974 X M= 42  0.0  FIGURE BULK  FOR  8  AVERAGE 4 2 PAIRED  20.0  40.0  60.0  BEST  ESTIMATE  CHANNEL  SAMPLE  SILVER  DATA  80.0  100.0  BULK VERSUS  BEST  ESTIMATE  62  Y=X  o m  A g _  Y = -2.83+1.02 X N= 42  0.0  see below ,  I  80.0  ,  160.0 . BEST  ,  240.0  ESTIMATE  320 0  400.0  BULK  Area "A" detai Y=.:X  00  Ia -  ac  Ag_  5 ? -  •Z83+I.02X  CO  N= 42  a a t"NJ  C3  a *  o'.o  F I G U R E  9  B U L K  P A I R E D  S I L V E R  S A M P L E  D A T A  1  —I  20.0  40.0 BEST  V E R S U S  1 60.0  ESTIMATE  B E S T  -,— 80.0  !00.0  BULK  E S T I M A T E  B U L K  F O R  4 2  63  a in  sampling Table  TABLE  procedure  i s related  4 and F i g u r e  t o sample  volume,  as  evidenced  10.  4 - Comparison of Sampling Procedures Comparing V o l u m e , Amount o f S c a t t e r ( S y ) a n d R e g r e s s i o n Parameters ( Y= A + BX ) .  SAMPLING PROCEDURE  Tube  Channel  SAMPLE VOLUME ( a s a p r o p o r t i o n of total)  sy  A  B  sampling vs best  .027  43.37  7.510  0.894  sampling vs best  .396  23.37  2. 129  1 .022  Bulk vs best  .577  12.36  -2.834  1 .022  64  60. CO  co c  c o 40J 'to CO  AxTUBE SAMPLES  <D k_ CT)  or 3  o  A CHANNEL COMPOSITES  20J  Y =50-46^X~  o  "^BULK  o o CO I  .4  .2  .6  .8  ~i i.o  VOLUME (as proportion of total sample)  FIGURE  10  VERSUS  SAMPLE  PLOT  SHOWING VOLUME  S C A T T E R ABOUT THE  WITH A  CURVE  FITTED  REGRESSION  LINE  65  IDEALIZED  To  emphasize  estimates the  economic  42 b l a s t h o l e s  representing blocks  assumed  to define  conditions and  a part  contain  i s  selection  of accurate  must  2-dimensional  single  exactly  true  allow  analysis  which,  even  emphasizes  the importance  to  though of  Assay  Each  block  Neither  a  quality  m  3  is  size i s  of  b u t t h e assumed  conduct  as  of 5 x 5 x 5  these  geometry  simple  hypothetical,  high  data f o r  and the block  unit.  grade  considered  bench.  at Equity  us  be  array  blasthole,  the s e l e c t i v e mining  unit  can  of a production  a  blasthole  be e x a m i n e d .  were t e s t - s a m p l e d  a hypothetical  to  ANALYSIS  importance  implications that  simulating  assumed  the  ECONOMIC  economic  dramatically  sampling  in  block  select ion. The economic  following analysis (1)  quantitative  parameters  are specified  f o rthe  : a  selective  mining  unit  (block)  i s 341  tonnes. (2)  selection  assays  A  cut-off  experiments grade  (AgE)  (%)  / 0.04.  (3)  cut-off  will  of  be  30  were  g.AgE/tonne  to  ore c l a s s i f i e d  based  where  grades  AgE  on  silver-equivalent  (g/t)  = Ag  (g/t)  o f 3 0 , 70 a n d 90  + Cu  g.AgE/tonne  compared.  g.AgE/tonne conducted  i s 90 g . A g E / t o n n e .  30  i s  cut-off  whereas  Figure  imposed.  as waste,  prevailed  in  the present  11 s h o w s  classified  when  (1984)  the scatter  T h e two h a t c h e d  and waste  1980  areas as  plot  the  cut-off with  a  correspond ore.  Both  66  types  of  misclassifications  economically material should  i s  that  the grade  individual blocks)  TABLE  t h e grade  blastholes  i s shipped  at this  point  of a block  (and  are listed  t o t h e dump  that  the m i l l block  i s given  by  and  that waste  circuit. It  classification  their  by t h e o r i g i n a l  i n Table  in  by t h e b e s t  extension,  estimate of - these  corresponding  composite  tube  5.  5 - T a b u l a t i o n o f B l a s t h o l e s M i s c l a s s i f i e d by T u b e Sampling Assuming that a Best (Calculated) Bulk Estimate i s C o r r e c t , and C u t - o f f Grade i s 30 g . A g E / t o n n e .  O R I G I N A L T U B E SAMPLE M I S C L A S S I F I E D AS WASTE  TUBE  ORIGINAL TUBE SAMPLE M I S C L A S S I F I E D AS ORE  BEST  ESTIMATE  Cu  Ag  AgE  Cu  Ag  AgE  .02  16  16.5  .09  82  84.3  .05  28  29.3  .10  68  .03  28  28.8  .04  .02  27  27.5  .02  10  10.5  Cu  dearly  l o c a t e d b l a s t h o l e . Grades  are misclassified  method  mines  contaminating  of a c e n t r a l l y  which  sampling  metal  inadvertently  be r e - e m p h a s i z e d  assumes of  recoverable  cost  grades  TUBE  ESTIMATE  Cu  Ag  AgE  Ag  AgE  10  55  57.5  .06  28  29.5  70.5  06  51  52.5  .03  21  21.8  45  46.0  07  31  32.8  .06  27  28.5  .04  34  35.0  .06  30  31 .5  i n % , Ag g r a d e s  i n g/t,  Cu  BEST  AgE g r a d e s  in g/t.  67  The  data  balance that  of  Table  calculation.  original  From  tube  of  blocks  i d e n t i f i e d as (1023  blocks  ore.  through of  A  recoverable  In  over  per  is  cut-off  grade),  for  one  of  would more  ounce  be  If  The  27,211  the  (1705  64,006  as  to  The  5  the  ore tube  result  in  silver  at  tonnes)  of  of  whether  of  averaging  would  (682  5  waste  grams  tonnes  grams  offset  3  of  original  blocks  cost  more  than  than  1.0  a  total net  these  the  added  are  highly the  block may  estimates well  to  g  30 of  gain  in  costs  of  5000  resulting  tpd  grams  dollars  grams  of  (the  were  potential  days)  having  approximate  relatively  the  at  increased high  high  42  net a  Canadian  figures  demands  for  extended  $10.00  specific  of  improved  silver  silver  of  grams  from  of  are  warrant  AgE/tonne  300  and  obviously  the  for  (assuming  the  milling  20,460  same p r o p o r t i o n s  course,  magnitude  and  43,546  4,000,000  idealized  mining  cost  benefit  (say  million Of  of  equivalent  production  silver).  and  ore.  selection  to  (64,006-20,460)  of  improved  the  the  tonnes).  Never-the-less,  sampling  is  years  calculation  from  case  tonnes  (14,322  arises  evident  procedure.  particular  selection  block  sufficient  Consequently,  benefit value  is  by  2 additional  then  as  of  silver  additional  milling  682  silver.  blocks  an  question  metal  this  assumed  block  and  sampling  additional  mill  is  g.AgE/tonne).  waste  correct  i t  mass  misclassification  total  of  interesting  11  waste  26.6  to  grams  the  of  a  f o r an  Figure  in  blocks  averaging  Thus,  the  mining  3  used  5 and  contain  91,217  practical  improved  ore  be  result  assigned  g.AgE/tonne).  cost  and  tonnes  contain  sending a  waste  incorrectly  samples 53.5  as  can  Table  samples  blocks  silver  ore  5  in  this best.  revenue quality  levels  of  68  Y=X  PI  equiv.  CDS i  .—'CN  , , Cl (-3d  <'  -,co_| o  CO  area  7=765+ .903X N= 42  A  see  below  .3.0  80.0  160.0 BEST  c?  240 0  ESTIMATE  BULK  area A detai  320.0  400.0  Y=X  WASTE CLASSIFIED AS ORE  Ag. equiv  LTJ •  —1°  Y=7S5+9C3X ORE  T 20.0  0  F I G U R E  F O R  4 2  11  O R I G I N A L  P A I R E D  T U B E  S I L V E R  CLASSIFIED AS WASTE  T <K>.0 GO.O BEST E S T I M A T E SULK  S A M P L E  E Q U I V A L E N T  V E R S U S  D A T A  B E S T  N •  =  BO 0  ^XP '^ — C  100.0  E S T I M A T E  B U L K  69  expenditure  on  Similar of  70  year; is  mass  a  39,000  magnitude in  These  90  our  calculations  indicate  g.AgE/tonne  g.AgE. of  control.  balance  g.AgE/tonne with  error  sample  a  net  loss  by  a  hypothetical  calculations  saving  cut-off  Regardless  of  the  of  cut-off  3,500,000  g.AgE  the  with  for  is  per  saving general  large  procedure  need  grade  annual  grade  technique  the  a  calculated  selection  emphasize  on  cut-off  sampling block  based  random evident.  representative  samples. Figure of  a  10  demonstrates  blasthole  that  i s minimized  i f the  thoroughly  mixed  and  procedure  would  be  done  and  splitting  Sample  collection  drill  entered  resulting minimized.  from  the  subsampled  as  best  underlying  drilling  the  into  error entire a  while could  bench the  so  in  grade  volume  basis  be that  of  for  drilling  estimation cuttings  assays.  was  in  is This  progress.  stopped  before  sampling  variability  underlying  bench  would  the  be  70  CONCLUSIONS  The mineral  importance deposit  procedure stage  accuracy  analytical  an  laboratory program,  effective  problems  methods  assaying  must  graphical  Tail  zone  effectively  quality  The  be m o n i t o r e d approach  evaluate quality  quantifying  sampling  should  i n sampling  i n both  implementation in  continually. here  Mines  Ltd.  control errors  monitoring  such  the  a  from  that  the  by b o t h  might  and  statistical Southern  i s one example  results  check  sampling  The s i m p l e  to data  analyses  for isolating as  of  itself;  at every  and  as well  a  sampling  be e x e r c i s e d  procedure  programs,  applied Silver  Care  control  i s not an end  of Equity  precision  D u p l i c a t e sampling  i n sampling  precision.  however,  and  be o v e r e m p h a s i z e d .  of p r o p e r t y development.  potential  and  cannot  and  •represent  and  of  o f how  to  identifying  otherwise  go  unnot i c e d . At  Equity  laboratories results  showed  for  Duplicate  error  by  blasthole  assays,  sampling  sampling,  using methods  'best  estimate'  (tube,  channel,  volume  results bias  between  in  two  analytical  one o f t h e two l a b o r a t o r i e s .  samples,  using a tube-sampling  alternate  the  analytical  Follow-up  are obviously necessary.  for silver  sampling  of  a small but s i g n i f i c a n t  silver  investigations  collected  comparison  of  technique,  thereby  indicating  techniques.  tube was  f o r the  sampling,  undertaken  sample residual sample  channel  a  t h e need of  sampling were  by w e i g h t i n g  by t h e i r  increases  showed  program  and r e s u l t s  calculated bulk)  A  Southern  zone,  large  random  for testing comparative and  compared a l l sample  respective  t h e amount  Tail  bulk with  types  volumes.  o f random  a  As  sampling  71  error be  decreases  the  most  The  accurate  cost  per  the  higher  of  sample  entire  pile  8  of  block,  correct  64,000 but  mining In  a  and  terms  of  recovery  and  net  annual  It  i s worth  in  (weighting) has  mineralized  of  tube  'best  sample  to  samples  of  personnel sampling.  i t must  sampling  shows  each  is  grams  and Hence,  be  will  shown  offset  that  an  of  about  in  this a  that  effort  might  estimation shown  of  to  deposits.  be  a  has  result  8  42  the  a  being g  at  tonnes  its  been  made  to  from  the  use as  the  (2  blocks)  of  a  of in  of ore.  improved  excess  presented  of  1  are  single centrally  consider of  improvements  moving  Raymond  importance  in mill  cost  a l l results by  result  added  that  of  respective  through  well  are  each  the  benefit  grade  the  (selection  would  net  crucial  that  same p r o p o r t i o n  block  from  block  sent  cones  blastholes  Assuming  blocks  682  procedures, of  of  within  43,000  additional  re-emphasizing  No  the  silver  production  obtained  8  method.  r e s u l t s of  r e p r e s e n t i t i v e of  of  of  sampling  estimates'  sampling  estimation  sample.  recovery  others,  that  result  dollars.  located  tube  milling  the  bulk  by  bulk  tube  gained  with  benefit  could  on  for  Therefore,  classification  million  based  bulk  more  increase.  is centrally located  additional  having  total  needed  comparison  the  blastholes unit)  of  requires  than  cuttings  by  mining  total  costs.  cuttings,  misclassified the  however,  will  idealized  blasthole  cutting  precision  sampling  An  and  equipment  added  indicate.a  procedure.  cuttings,  sophisticated  that  a l l results  collection  blasthole  the  and  average  (1979), in  among  erratically  72  The conducted the  quality in  1980  Southern  continued procedures mining  control shortly  Tail  for  selection  after  zone.  examination  experiments production  R e s u l t s have and  improving  quality  ( e . g . S i n c l a i r and  was  served  development the  reported  of  Giroux,  as  here  were  initiated  from  a  of block  basis  for  the  geostatistical estimations for  1983).  73  ACKNOWLEDGEMENTS  This former  Mine  benefited Silver Ltd.  study  from  Mines  Financial  was  initiated  Engineer  at  in discussions  Equity  the contributions L t d . , and support  Silver  with Mines  b y D. F r a s e r  W.H.  L t d . and has  and J . Cyr  Mr. E . T . L o n e r g a n , P l a c e r  was p r o v i d e d  by P l a c e r  Myckatyn  Equity  Development  Development L t d .  74  REFERENCES  Cyr, J . , J . M i l l e r (1980) B l a s t h o l e S a m p l i n g P r o c e d u r e Study, P r i v a t e r e p o r t , E q u i t y S i l v e r M i n e s L t d . , N o v e m b e r , 11 p. E w a n c h u c k , H. (1968) Grade I n s t . Min. M e t a l l . Spec. M i l l e r , J . (1981) B l a s t h o l e Equity S i l v e r Mines L t d . , R a y m o n d , G., (1979) Ore m i n e r a l i z e d ore body, J u n e , pp. 90-97.  Control V o l . 9,  at Bethlehem Copper, pp. 302-307.  Sampling Procedure, May, 5 p.  estimation Can. Inst.  Private  Can.  report  p r o b l e m s i n an erratically Min. M e t a l l . Bulletin,  S i n c l a i r , A . J . , a n d G.H. G i r o u x , (1983) G e o l o g i c a l c o n t r o l s semi-variograms in precious metal deposits; G e o s t a t i s t i c s f o r N a t u r a l R e s o u r c e s C h a r a c t e r i z a t i o n , NATO ASI Series, D . R e i d e l P u b l i s h i n g Company, D o r d r e c h t , H o l l a n d , pp. 965978.  of  W e t h e r e l l , D. ( 1 9 7 9 ) G e o l o g y a n d O r e G e n e s i s o f t h e Sam Goosley copper-silver-antimony D e p o s i t , U n p u b l i s h e d MSc Thesis 1979, D e p t . of G e o l o g i c S c i e n c e s , U n i v e r s i t y of B r i t i s h C o l u m b i a , V a n c o u v e r , 208 p. W e t h e r e l l , D., A . J . S i n c l a i r and T . S c h r o e t e r , (1979) P r e l i m i n a r y r e p o r t on t h e Sam G o o s l y c o p p e r - s i l v e r d e p o s i t ; i n P a p e r 1 9 7 9 - 1 , B.C. M i n i s t r y of E n e r g y , M i n e s and Petroleum R e s o u r c e s , pp. 132-137.  CHAPTER  AN  E V A L U A T I O N OF  APPLIED  VARIOUS  TO E Q U I T Y S I L V E R  4  KRIGING TECHNIQUES  MINES'  SOUTHERN  TAIL  AS ZONE  76  ABSTRACT  A  variety  attempted and  f o r the  compared  squared  point  block).  among  estimation  errors  best  of  the  A  trial  several  by  metal  kriging  set  contents  of  extreme  results,  (lowest). metal a  Such  contents  mine  optimum  so  that  block  as  which  that  log  100  blocks  Ltd.  assigned  not  better the  to  distinguish  log  kriging For  than  of  block  empirical  availability  make c o m p a r i s o n s .  partition  from  differences 1,400,000  polygonal  kriging  of  blocks can  early be  of  silver a  of  Block is  the  in  the  estimated  estimated by  the  modified  emphasize  compared  estimation procedure  bench,  total  ( h i g h e s t ) and  differences  estimates  1310N  in  grams  extreme some  Mines  procedure.  await to  do  although  are  must  been  tested.  show  much  that  Silver  assay  methods  best  have  v i z . inverse distance  blasthole  the  with  suggest  of  techniques  procedures  procedures  amount  kriging  Equity  e s t i m a t i o n methods  contents  also  of  validation  kriging an  block  zone  (central  Cross  procedures  as  Tail  is marginally  purposes  block  to  empirical  a l l the  data  methods  known  two  polygonal  encompassing  partitioned  approaches  Southern  with  and  clearly  of  the  need  production with  attained.  log to  metal  two  most  kriging know  history  reality  by  and  of an  77  INTRODUCTION  Kriging as  the  "best  weights random  linear  for  an  error  variety clear  i s a moving  of  why  kriging  of  estimations  Tail  difficulty  selection  purposes  by  a  i n the  a  to  lesser  zone  occur  west  and  a  mainly  fragments.  of  provides squared  i t i s not  to another.  substantial or  to  i s minimized.  e v o l v e d and  preferred  A  always  Different  differences  b l o c k s and,  Equity  what  Clearly,  by  interest  in  i s more,  a l l  kriging  complex.  approaches. the  Sam  Goosly  in  from  stockwork  or  both  The  30  with to as  a  50 a  and  The  strike  is  i n the  east  ores  are  and  Southern of  degrees.  cement  silver  inlier  structurally,  controlled.  form  the  sedimentary,  1979). stock  bulk  Silver-copper-antimony and  and  estimates for  Cretaceous  monzonite  in origin  seemingly  deposit  in block  (Wetherell,  stratigraphically  a  of  a  1984b)  the of  provides  kriging  the  Sinclair,  quartz  tabular  in  of  Ltd.  because  confidence  rocks  a  Mines  several  inlier  w e s t e r l y d i p of in  the  block)  estimates.  zone  an  epigenetic  crudely  (or a  points  having  volcanic  degree,  is  degrees  be  mean  in  i s of  Tail  gabbro-monzonite  thought  that  such  variability  of  within and  points  have  ( G i r o u x and  Southern  pyroclastic  i t  compare  grade  attendant  intruded  zone  study  of  lies  because  result  opportunity to  The  referred  estimator"  be  error  commonly  "best".  preliminary  deposit  should  can  technique  point  particular  be  nature  a  procedures  different  Southern  erratic  data  estimating  for  cannot  practical  of  approach  substantially  This  array  procedures  methods  unbiased  kriging  one  average  about  to  Tail 025  Sulphides  between  breccia  78  DATA  During raw  data  zone. and of  The 1320  1:500,  hole at  a  visit  were data  bench  Vancouver  one  of  three  the  blasthole into were  a  showing  plans  then  and  data  merged  to produce and  of  September the  f o r the  numbers  and  locations  on  results  from  the assay silver,  1980  Southern  plans  for copper,  of  a  were a  and of  errors  edited.  data  and  sample  plots  location  assay  northern  The  by  Development  keypunched Check  also  digitized  Placer  levels.  assay  locations  in  bench  showing  were  of  computer.  produced  3 benches  of  sample  sheets  f o r each  were  from  Limited  antimony  1310,  and  Tail 1315  a  scale -blast  arsenic  location.  office  created,  Mines  consisted  analyzed  sample  The  base  assay  samples  each  to Equity  collected  levels and  ACQUISITION  base  information  the  writer  Ltd.  southern  number  both  sets  corrected.  of  f o r each  blast  files  were  for  each  assays f o r each  of  data  sample  entered locations  Listings  corrected sample  the  part  and  the d i g i t i z e d  The  Six  at  files  number, hole.  of  the  were  then  x  and  y  79  STRUCTURAL  The  Southern  assay  data  from  2  as  Tail  (Giroux  variability  t o 2000  block  makes  in geostatistical  sill  values  the of  and hence  variety  5 x 5 x 5 m  of l o c a l  terms large  leads  error  and thus  selective  3  f o rs e v e r a l v a r i a b l e s ,  because,  of  a l l metals  economically,  and  attempted  recovered,  also  i s  difficult  effects,  t o t r y and  the best  only  as small degree of  very  nugget  vary  high  errors.  units.  available  high  3  erratic  can  distances  m ). This  to large  make  mining  holes  estimation  estimation were  Blast  across  ( 5 x 5 x 5  of techniques  estimation  1984b).  g Ag/tonne  size  any form  and  A  i s c h a r a c t e r i z e d by l o c a l l y  and S i n c l a i r ,  g Ag/tonne  the estimation  zone  ANALYSIS  possible  Although  silver  silver  distributed  estimation  assays  results  were  a r e shown ,  i s t h e most by  minimize  far  important the  most  errat ically.  Traditional  To four six from  Model  determine  directional data  files  from  benches  semivariograms  and compared.  benches  apparent  the structure along  1310N,  with  the  and  (4) l a r g e r  and  with  a common  of  variability  sill (sill)  1315S  exception  a n i s o t r o p i c form than  produced  examples  of these  geometrical SW-NE  Four  1310S,  a comparison  were  with  the plane  and  of t h e benches,  f o r each  a r e shown 1320S.  as Figure 1  Two p o i n t s a r e  semivariograms.  of  1315S,  ranges  in directions  First, a l l  exhibit  in directions E-W  for a l l 4 directions.  of the  the  same  N-S ( l )  ( 2 ) a n d NW-SE Second,  i s p r o p o r t i o n a l t o t h e mean  the grade  (3), level  of  the  80  TO  Figure  1  20" Lag  (m)  30~~  40  °  !0  20 Lag  : Average h o r i z o n t a l semivariograms f o r s e l e c t e d benches Southern Tail zone, showing experimental curves for d i r e c t i o n s 1 t o 4.  (m)  30  40  81  samples. The mine  geologists  outside sites  discrepancies  the  on t h i s  included  Equity.  mineralized bench.  i n 1315S were  results  averaged  to  I t was d i s c o v e r e d  area  was b u l l d o z e d  As a r e s u l t  summarized  from  the  produce  semivariograms.  the data  a  The  in Table  remaining  single  ranges  these  with the  f i l l  i n t o prepare 1315S  from drill  were  not  North-South East-West  ranges  variograms  and were  of  segments  were  four-directional  four  directions  i n the Four  RANGE ( a )  (1)  (2)  20  m.  10  m.  (3)  10  m.  Southwest-Northeast  (4)  18  m.  i n the  minimum then  are  Principal  Southeast-Northwest  f i t t o determine  azimuth)  bench  1.  DIRECTION  ellipse  that  from  5  set  of  1 - A Summary o f t h e R a n g e s Directions.  The  discussed  i n the study.  The  TABLE  from  observed  four  directions  the directions (112.5  produced  degrees) f o r each  were  plotted  o f maximum ranges  and  an  (22.5 degrees  (Figure  of t h e 5 benches  2 ) . Semii n these  Figure  2  : Structural ellipse of ranges i n the four p r i n c i p a l d i r e c t i o n s showing the direction of minimum and maximum structure.  83  two  directions The  of  second  minimum  noteworthy  of  raw  data  (Figure  the  mean  grade  of  proportional in  any  the  By  effect  forcing  data were the  a  sets  South  Tail  Lognormal  Zone  converted  also  positively  to  Table account 4  must  five  of  be  sill  linear  equations  (C1)  =  a m  fitted  semivariogram in Table  silver  shows  of  model  a  account and  the  mean  to  points.  the  , and  2  with  (CO)  versus  average  CO  into  effects  model  the  level  indicates  taken  nugget  components  through  semivariograms  phenomenon  i s summarized  (Figure to  skewed  five  C1  =  0  for silver  m  2  in  2.  by  for  This the  indicate  proportional  and  a  to  shows  log histogram  that  semivariograms  each of  and  of  the  the  silver  non  effect.  The  minimum five  takes  logorithmic  model for  be  strongly  made w i t h of  Figure  grades  the  for log  the  the 3 is  are  not  log. values  and  model  stationarity model  fitted  in  effect  curves  addition  (Figure  summarized  proportional  t r a n s f o r m a t i o n . The  were  established  averaged.  are  we  transformed  directions,  benches  lognormal  approach  some  data  t r a n s f o r m a t i o n was  semivariogram  maximum  parameters 2.  3). A  the  Never-the-less, for comparitive purposes  develope  i n the  values  l o g v a l u e s . The  Experimental  previously, The  the  resulting  lognormal.  proceeded  4).  of  skewed  data  produced  which  a  the  fluctuation This  and  line  of  structure.  Model  positively  data.  the  of  (3 i n t h e  The  A histogram  exactly  Plots  produced  and  determined.  was  samples.  best-fit  average  characteristic  structural  were  the  maximum  i s present  d e v i s e d model.  squared  1)  the  corresponding  grade  and  to  i s for purposes  of  in into  Figure a  simple  of  local  84  80.0  _  LOG (bosel0) HISTOGRAM  12.5  >-  70.0 _  UJ  Ll_  60.0 _ 7.S  !.  N = 2576 HERN = 1.037 GM/T S.C. = .718 GM/T C.I. = .200 GM/T  t>5 50.0 _  >LJ LU  o UJ  L a . -.4000  30.0 _  I.4E  '»!  2.0000  1.2000 1.2E  2)  I.6E  4.4000 31  I.3E  SI  I  1  6.0000  7.6000  (.IE  7)  I.4E  SILVER .ARITHMETIC HISTOGRAM  20.0 -  N = 2576 MEAN = 49.200 GM/T 5.D. = 145.821 GM/T C. I. = 30.000 GM/T  ]0.0  LW .000  2*0.000  T '460. 000  720.000  SILVER  Figure  3  : A r i t h m e t i c and l o g transformed h i s t o grams f o r 2575 silver grades from b l a s t h o l e s , Southern T a i l zone.  960.000  1200.000  61  85  0.5-  "I  0  1 8.0  1 16.0 LAG  Figure  4  1 24.0 h  1 32.0  (metres)  : Average horizontal semivariogram i n t h e d i r e c t i o n o f m i n i m u m a n d maximum structure f o r l o g transformed silver grades, Southern T a i l zone.  1 40.0  1— 48.0  86  estimation  within  data  x  within  which  15  m  and  2  Partitioned  The  nugget  models,  caused  grades,  led to a A  indicates data.  g  not  local  =  3.5  =  55  very  low  grades,  but  340  g Ag/tonne  technique. the will  range send  Of 20  to  upper  major to  ore  100 to  of  at  1984a)  than  be  A  the  15  to  plot  similar the  the  selected  g Ag/tonne dump a n d  and  B  The of  i s not  as  the  ore  waste  or  Tail  stage,  based for  any  on  very  A  pit  of  340  the  is  the  blasthole high  mining  or  units  containing  sample  incorrect through  background  threshold  greater  local  blocks containing  where  diamond  silver-bearing  Blocks  by  bimodal  upper  selective  i.e. a  silver  stockwork  Southern A  5)  populations.  units,  grade.  population  are  i n the  for those  the  alteration  production  mining  the  represent  the  silver  structural  exploration  drilling. A  of  (Figure  to  respectively.  visible  forgoing  nature  approaches  and  and  cut-off  concern  the  of  erratic  from  estimation  rather  the  , will  both  represents lenses  selective  area  the  very  established  importance of  in  separates the  critical  from  are  in exploration  effectively  close  C)  data)  The  sample  less  three populations within  g Ag/tonne)  estimation  sill  g Ag/tonne)  the  intersected  grades  of  g Ag/tonne)  630  paramount  and  Sinclair,  data.  with  are  i s assumed.  cumulative d i s t r i b u t i o n  (B a n d  =  (2% of  Ag/tonne  stationarity  for alternative  silver  (mean  (mean  Of  two  ( G i r o u x and  population  but  search  of  (mean  galena  dimensions  tremendously  presence  lower  sulphides silver  the  lognormal  distribution drilling  local  effect  by  the  The  whose  Model  high  analysis.  fields  a  than  estimation samples  in  classification mill.  With  this  87  SILVER F R O M I3ION.I3IOSJ3I5N  CUMULATIVE  Figure  5  : .Lognormal c u m u l a t i v e d i s t r i b u t i o n c u r v e f o r 2773 s i l v e r g r a d e s f r o m 1310 N , 1310 S a n d 1 3 1 5 N b e n c h e s , Southern T a i l zone.  %  88  criterion set  for  i n mind,  the  To  purpose  account  in  directions Table was  2.  the  existed. ratio  By  of  our  model,  grade  will  use  local  minimum  erratic  four  was  reduced  partitioned  used  for  data  only  to  reiterate, local of  m  this  anisotropy the  from  the  0.5  in  whereas 22  m  approach  B  in  directions  from  estimation  populations  shown  population  model,  60  model  maximum  are  principal  grade  increased To  benches  high  sill  i n the  five  and  same d i r e c t i o n s f o r  range.  when  the  The  2  the  to  data  relative  (7(h)/m ).  the  was  that  model  effect,  for  influence maximum  this  established  that  the  modelling.  ellipse  0.25  of  from  of  to  direction  removed  proportional  for  effect  model  was  average  confirm  nugget  of  known  e l i m i n a t i n g the  traditional range  structural  previously the  to  population  used  structural  checked  high  the  were  for  A  of  for  semivariograms parameters  the  near and  C  in  the the  assumes  the  cut-off  of  Figure  5. Discussions models the  of  described  extreme  north  of  the  data  Dyke  the  of  the  maximum  example  and  of  south. East range  of  i n any  did the  had  others,  necessity  is possible  Equity  date,  end  East to  north  absolute as  the  of  to  north  data  azimuth This  with  f i t the The  different separate  Dyke 68  not  geologists  deposit.  a A  mine  degrees  discussed  s t r u c t u r e s observed mineralized  an  bulk  on  only  a n i s o t r o p i c model  with  in this  geostatistical  at  the  (Sinclair  i n c o r p o r a t i n g as  the  fractures  o r i e n t a t i o n from  semivariogram  produced  indicated  much study.  and  paper,  study  Giroux, point  geologic  1983). to  the  information  89  Log  Partitioned  Using  the assumptions  populations 3  of  were  (model  Table  used,  2 only  were  fourth  produced  summarized  anisotropic i n Table  model  populations  transformed  i n each  curves  to  As i n  (< 340 g log  values.  was  and then  in  Figure  fitted  to  6.  TYPE  SILL  CO  1  the  data,  RANGE  RANGE  22.5  112.5  C  metres  Traditional  2  4.13  m  2  8.26  m  2  metres  22  1 0  Log  0.75  2.25  30  1 2  Partitioned  0.80  3.10  60  1 2  Log  0.45  1 .55  33  1 5  Partitioned  1  See text  2  m  f o r d e t a i l s of each  i s t h e mean v a l u e applied  of data  model  type  t o which  files  Again  2 - A Summary o f P a r a m e t e r s f o r t h e Four A n i s o t r o p i c semivariogram Models Developed.  NUGGET  Semi-  averaged  2.  MODEL  model  Ag/tonne)  of the 5 acceptable data  shown  model  2) a n d m u l t i -  was d e v e l o p e d .  22.5 a n d 112.5 d e g r e e s  the experimental  geometrical  o f l o g n o r m a l i t y (model  t h e two l o w e r  the d i r e c t i o n s  produce  TABLE  3) a  but i n t h i s case  variograms along  Model  model i s  to a as  90  AVERAGE SEMI-VARIOGRAM (5 BENCHES) PARTITIONED LOGNORMAL SILVER  0 f  0  Figure  6  1 11  11  ' 11 i i i 11 i 1111 i i i 1 1 111111i 11111 i 1 1 i 111 i 111 11  10  LAG  20  30  h (metres)  : Average h o r i z o n t a l semivariograms i n t h e d i r e c t i o n o f m i n i m u m a n d maximum structure forpartitioned lognormal s i l v e r grades, Southern T a i l zone.  40  50  91  Multi-Gaussian  Still a  another  Gaussian  (Verly, of  Model  alternative,  (normal)  1983).  This  the distribution  distribution  method by  minimize  the- e f f e c t s  modelling  and l o c a l  a  strict  1983), was  An to  a  zone, in the  restraint  developed, added  was  towards  of  of  observed. t h e mean,  transformation.  does  in  f o r the high toward  grade  tail  mean  and  the  structural  The p r o c e d u r e ,  however,  requires  variables  question  (Verley  t o be  of applying  in  in Equity  data.  a Gaussian  model  transformation  as occurs  When  of the d i s t r i b u t i o n  the t a i l  A  unacceptable.  distribution,  an upper  to  transformation  m i n e r a l i z a t i o n on  not exist  and found  consequence  i t  erratic  the  t h e raw d a t a  by a g r a p h i c a l  account  bringing  that  tested  multinormal  would  estimation.  stationarity a  i s to transform  population  i n the Southern  Tail  i s brought  c a n be t o t a l l y  lost  in  92  BACK  To models bench and  try  and  evaluate  the  summarized  in Table  2,  was  used.  then  aureole was  The  of  Ag/tonne  the  ) was  in  were  distance  removed  not  of  significant,  manner.  The  for  bias  in  to used  each  grade.  is  isolated sample  high  from  estimate form log  of  of  the a  partitioned  in  the  of  by  1723  upper  a  different  upper  test  point  allow two  to  of  the  Inverse  showed with  with estimate  a  cause  an  overestimate.  are  shown  to  illustrate  high  a l l  the  low  high  for  each  value,  Results  this  a  scattered  Conversely,  neighborhood  g a  of  overestimating  areas  possible  340  point.  samples,  values.  ( >  methods  and  one  samples  population.  five  in  value  using  to  because  each  1310N  single  population  this  grade  on  kriging  will  model  the  blasthole  methods,  as,  low  removing  the  i t i s not  value  weighting  of  of  back-analysis  estimate  high  surrounding  low  to  unexpected  values,  of  for  the  estimating  underestimating not  data  different  techniques This  the  quality  point  Each  from  also  results  method  data.  the  was  a  removed  applicable  squared  The  the  this  relative  c o n s i s t s of  surrounding  comparison  models  method  estimating  calculated  fair  ANALYSIS  bias  for  any the  (Figure  7). To to  evaluate  use  mean  dispersion account in  for  three  100 shown  g  of  known range  Table  and 3  methods,  difference  "estimated"  Ag/tonne in  different  squared  the  assay  the  from  bias,  greater are  "true"  each  categories  far  as  i t was a  : less than from  measure  values.  method  was than  100  therefore  g  In  of  the  an  evaluated 20  g  relative  effort  but  to  separately  Ag/tonne,  Ag/tonne.  conclusive,  decided  The  20  to  results  the  log  93  •260.00  LU  210.00  _  140.00  _  N = I5I0  CT  O 70.00  .00 .00  70.00  140.00  210.00  REAL  EQUITY  Figure  POINT  RG  280.00  VALUE  KRIGING  7 : Scatter plot showing r e a l silver grade v e r s u s s i l v e r grade e s t i m a t e d by l o g p a r t i t i o n e d k r i g i n g f o r 1510 b l a s t h o l e s . Southern T a i l zone.  350.00  94  partitioned 100  model  g Ag/tonne  the  range  gives  where  the least  block  includes  scatter  selection  a l l cut-off  is  i n t h e range  most  grades  o f 20 t o  critical  because  f o r the f i r s t  years  of  production.  TABLE  3 - Mean S q u a r e d D i f f e r e n c e s o f E s t i m a t e d a n d B l a s t h o l e Grades as a Function of 3 Grade Categories for 5 Estimation Procedures.  POINT ESTIMATION METHOD  MEAN  SQUARED  VALUE<20  Inverse  Dist.Sq.  Traditional Log  Kriging  Partitioned Log  The model  back  estimation  i s of l i m i t e d  assigned  regardless note  comparable  24.47  36.73  125.87  1 5.00  35.47  146.79  27. 1 7  39.37  126.54  1 4.22  34.77  146.03  of which that  kriging  inverse  in quality  of  evaluating  situation,  with  which  distributed.  the  VALUE>100  122.76  use i n t h i s  to  20<VALUE<100  37.09  method  regularly  DIFFERENCE  22.00  the a v a i l a b l e data  fairly  factors  to  Kr.  Part. Kr.  estimated, are  Kr.  True  samples  to  where  semivariogram f o r each  make  the  be  i s used.  very  weighting different,  I t i s of  distance  squared  as a p o i n t  to various  kriging  procedures,  point  estimate  Consequently,  cannot  procedure  a  interest  estimator  is  despite the  95  fact  that  inverse  This . uniformity extend  to block  kriging of  ore  compared We  can  with  estimation  using log  a  estimation. be  surmised  followed  the  Any  estimation improvement  qualitatively  through  that  would  blocks  near  method  traditional  kriging.  of  the presence  the  mill  of  anisotropy.  certainly brought  until and  does  not  about  by  specific  blocks  estimates  can  be  production.  data of  ignores  quality  anticipated  transformed  although  of  only  are  distance  the  partitioning  provide  a  the c u t - o f f .  seems  kriging  t o be with  clear This  marginally  approach  on  improvement was  not  better  a proportional  i n the  the than  effect  log  case either  model  or  96  BLOCK  As  a  further  test  models,  a  section  of  estimation. kriging all  One  using  pertinent  erratic set  with  of  blast  The  of  blast  nature  of  hole  5  the  x  deposit  and  5 x  5 m  of  surrounding  aureole  to  estimate  The  partitioned  models,  on  the  from  the  than 340  340 g  g  the  grade block,  or  more radius  situation, local was would  of  A  the  a  being  compensate  case,  samples  from  surrounding  rather  than  A a  to  the  high  since  relative The  evaluate  to  various without  the  massive  block  population  and  8.  The data  Ag/tonne. data  in  ignore  values  assaying  greater  value  greater  than  Instead,  the  was  assigned  errors of  samples,  though  blocks.  occurs  where  selected within estimated.  the  high  the  In  those  the this  samples,  search  Undoubtedly, material  a  grades.  number  within  block.  grid  the  radius blocks  i n a d d i t i o n to  galena-sphalerite lenses  are  A  very  dimensions.  results the  grade C  ignore  by  block  block  be  assigned  g  g Ag/tonne)  grade  points  estimated  in this  kriging.  large  to  completely  and  a  block  Figure  1820  holes  such  a  high  on  hand,  block  remaining  B  that  for  The  individual  were  the  contain  (630  structural  a l l available  population  of  still  by  over  involving  to  contained  population  rational  0.5  other  estimated  2.  shown  i.e. blast  block  average  population thin  not  would  second  If  i t was  the  The  search  population,  Ag/tonne.  considerable,  one  (A)  Ag/tonne  average to  upper  Table  used  single two  were  demonstrated  from  l o g models  selected  are  is well  various  blocks  3  models  ranging  of  was  information  values  traditional  quality  bench  four  hole  the  the  1310N  hundred  each  KRIGING  from  b e n e f i t of  block a  kriging  correct value  are  difficult  with  which  to to  97  8360 E 5  ;838QE  9  •85  -4  '17  .134  >I6  .14  '100 -9  840QE -  5  .25  'is  *3  *I8  *883  *l 5  -II  *2I •2  o ID  i  2  V  'A  •I  .5  4*9  •|49  23*1  3 53  266  *88  2*41  57  • 3  *2  '5  39  78  5  •fe-  *3  11  8  72  31  11  81  •-4.6E  *I0  .250  :6l;3  II  *3  49  428  •  18  40  34  15  15*8  118  14  106  54  86  9  52  *I0  73  "3  : :  •2  18 2 0  •3  j  "'3  "is  1 1  I  29  5  8  I  13  49  *I2  18  87  2  :  8*2  5  81  •4  Figure  8  1*5  49  •5  84  '15  -4  "74  *4  'I  236 i|55  12  7*1  17  45  II.  13  *6  *2  II  ' 20  44  35  1677  27  •  3  OJ  2*0  •  O  o  58  -  V  •3  •9  210  137 33  4*0  7 '7  '3  : Test area of 1310 N bench showing s i l v e r a s s a y s f o r b l a s t h o l e s w i t h an a r b i t r a r y g r i d o f 100 ( 5 x 5 x 5 cu. m.) blocks superimposed.  -193  10  92  97 13b  55  119 •20*102  98  compare  block  estimates.  compared,  however,  selection  o f 25 b l o c k s  entire The  range  graph  of  shows  corresponding values have  percent.  silver  relative kriged  errors  highest  the  high  t o about  t h e same  ranging  38 t o 46  The  test  partitioned Ag/tonne  area  14,700  tonnes  located  blast  15,700  tonnes  these  additional (based  on  is,  on  estimated the  best  i s  were  the  to  1,403,215  used  blocks  as  Figure  would  averaging  50  percent).  the  silver  kriging  to  t o 175  relative  and  kriging The l o g  estimation  errors,  .estimated  43  145 g A g / t o n n e .  f o rmining  by  10. A p p l y i n g  select  averaging  log  a 30 g  blocks  or  If centrally  selection,  the d i f f e r e n c e s i n central grams  drill  of s i l v e r  46 b l o c k s o r  225 g  Ag/tonne,  metal  hole  content  estimation  worth  about  between  p r e d i c t s an  $  415,000.00  9.00 ) .  i t i s impossible  estimation  of  9.  (Figure 8 ) .  methods,  material  60  of  partitioning  relative  of m a t e r i a l , apparently  average,  range  from  improve  100  results  of material holes  or  the  as Figure  traditional  data  (50  full  ranging  both  shown  1 o z . A g =U.S.$  Since  the  representing  percent.  showing  one compares two  of  the lowest  to these  be p r e d i c t e d If  errors,  c a n be  arbitrary  proportions  the  indicate  extent  gives  kriging  cut-off  for  that  f o r an  a r e shown  e r r o r s as  population  model  from  estimated,  estimates  relative  factor  Errors  present,  kriging  The r e s u l t s  partitioned  would  values  common  error.  o f t h e 100  Log transformation  removing  one  i s the kriging  encountered. the  The  closest  t o prove to  through technique  which  reality,  the m i l l , remains  estimation  without the f i n a l  unresolved.  procedure  tracing  the  conclusion for If  however,  99  Figure  9 : Graph showing r e l a t i v e k r i g i n g error (using four d i f f e r e n t k r i g i n g models) for 25 arbitrarily selected blocks f r o m t h e 100 e s t i m a t e d .  100  B L O C K S WITH > 3 0 g . / t o n n e Ag. AVERAGE  Figure  10  GRADE =14 5 g./tonne A g .  : Test area of 1310 N bench showing k r i g e d s i l v e r g r a d e f o r 100 ( 5 x 5 x 5 cu.m.) blocks. Kriged silver grade c a l c u l a t e d using l o g p a r t i t i o n e d model.  101  one  consults  answer  studies  i s known,  methods  of  effect  blocks  kriging relative  the  material  regression grade  (Journel  assigning  volume  assigned problems Tail an  to  production  (e.g.  Royle  an  i n an  extent  encompassing erratically  estimation  of  knowledge  improvement  Southern  Tail  zone  through  the  mill  estimates. over  short  several  pit  Such  a  sites,  block,  and  the  studies  that  the  result  suggest  the  of  grade  of  some  of  must  blocks  production  difficult  in  can  be  practice,  the  methods. the  case  the  be  of  followed  compared  with  because  even  ore  for  as  from  stockpiled material.  as  kriging,  blocks,  intervals well  milling  Southern  significant  polygonal  group  are  estimation  over  In  which  data  a  uncertain.  high  polygonal  that  represents  true  in  of  as  of  1983).  serious  such  a  called  located  in  body  use  to  estimators  estimation the  data  exist  Khosrowshahi,  theory  utilize  so  block  centrally  mineralized  that  t e s t s are  time  conclude  remains  large so  and  correct  and  located  unbiased  procedure,  i n q u a l i t y of  without  give  the  overestimation  other  which  P r a c t i c e elsewhere  unbiased  However,  in  1981)  centrally  consistant  shown  must  where  estimates),  are  to  improvement  of  Numerous  one  deposits,  Huijbregts,  (polygonal  procedures,  zone.  and grade  results.  Consequently, estimation  simulated  p r e v a i l s and  procedures to  on  is derived  from  102  CONCLUSIONS  The compare on  a  Southern several  Tail  different  traditional  partitioned  data  were  and  devised Cross  blasthole  data.  Lognormal in  be  A  to  test  techniques silver  the  difference  of  a  local  of  part  of  a  estimator  and  log  history  Models  to  based  transform,  partitioned  of  than  any  of  a  data  set  can  be  estimates  in  selected.  the the  marginally  produce  the  estimated  by  to of  The  mine  lowest would  mill. several  1,400,000  know a  methods  i t  through  kriging.  life  of  better  the  however,  predicting  need  of  spacing  different  to  were  combination  cut-off.  the  grades  partitioned  early  near  for  individual  regular  comparison,  blocks  a  produced  values  block  again,  to  fairly  kriging  valid  100  log  the  results  actual  indicates, deposit  estimating due  kriging  range  kriging  For  of  inconclusive  polygonal  more  a  transformed  partitioned  set  of  case  techniques.  effect,  log  values  monitor  with  practical  kriging  procedures  critical  errors.  necessary  a  partitioned  lognormal  estimation  and  were  sample  the  block  a  tested.  Comparisons showed  set  assays  erratic  provides  proportional  validation  highly  results  zone  grams  magnitude  metal so  of  contents the  best  1 03  ACKNOWLEDGEMENTS  This  study  was  initiated  Hillhouse  and Mr.  E.T.  Computer  support  has  Placer  and  particular  Technical  support  Department  of Equity  Miller  and  J.B.  Development L t d .  and  at  Lonergan been  the  of  provided  suggestion  Placer  are  advice  was p r o v i d e d  Limited  Cyr.Financial  Development  by t h e c o m p u t e r  thanks  Mines  o f D r . N.  extended  and  support  in  to  Ltd.  group a t  Bill  Green.  by t h e E n g i n e e r i n g particular  was p r o v i d e d  J.H.L.  by P l a c e r  104  REFERENCES  G i r o u x , G.H. and A . J . S i n c l a i r , (1984a) G l o b a l R e s e r v e s of Southern T a i l z o n e by C o n d i t i o n a l P r o b a b i l i t y ; W e s t e r n M i n e r (in preparation). G i r o u x , G.H. and A . J . S i n c l a i r , (1984b) P r o d u c t i o n quality c o n t r o l experiments; Western Miner ( i n p r e p a r a t i o n ) J o u r n e l , A.G. and Ch. H u i j b r e g t s (1981) M i n i n g A c a d e m i c P r e s s ( I n c . ) L o n d o n L t d . , 600 p.  geostatistics;  R o y l e , A.G. a n d S. K h o s r o w s h a k i , ( 1 9 8 3 ) V a l u a t i o n o f a l l u v i a l t i n a n d g o l d d e p o s i t s ; T r a n s . I n s t . M i n . a n d M e t a l l . ( S e c . A, M i n e r a l I n d u s t r y ) , v o l . 92, p p . A 1 3 - A 1 8 . S i n c l a i r , A . J . a n d G.H. Giroux, (1983) G e o l o g i c a l c o n t r o l s of semi-variograms in precious metal d e p o s i t s ; G e o s t a t i s t i c s f o r N a t u r a l R e s o u r c e s 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 , D . R e i d e l P u b l i s h i n g Company, D o r d r e c h t , H o l l a n d , p p . 965978. V e r l y , G. ( 1 9 8 3 ) The m u l t i g a u s s i a n a p p r o a c h and to the e s t i m a t i o n s of l o c a l r e s e r v e s ; J o u r n a l G e o l o g y , V o l . 15, No.2, pp. 263-290.  its applications of Mathematical  W e t h e r e l l , D. ( 1 9 7 9 ) G e o l o g y a n d O r e G e n e s i s o f t h e Sam Goosley c o p p e r - s i l v e r - a n t i m o n y D e p o s i t , U n p u b l i s h e d MSc Thesis 1979, Dept. of G e o l o g i c S c i e n c e s , U n i v e r s i t y of B r i t i s h Columbia, V a n c o u v e r , 208 p.  CHAPTER  5  CONCLUSIONS  1 06  Geostatistical stages zone of  i n the development  have  estimation  of global  blasthole  procedures  grades.  reserves;  to determine  Conditional estimate  The study  sampling  and  probability  chooses 2)  3)  4)  the grade  mining grade 5)  volume  which  planning  Tail  Two  estimates  zone  were  by  inverse  40  g Ag/tonne The  dealt  with  approach  most  a  nature  three parts:  of q u a l i t y  an  control  geostatistical  with  geologic  volume  hole  ore  the following  familiar  on  with  reserve benefits:  the deposit  t o be e s t i m a t e d  patterns that  could  the  form  of  the  grade  a r e made distribution  i s conditioned  and t h e r e f o r e  to the  o v e r e s t i m a t i o n s of  are avoided  tonnage  curve  i s extremely  f o r the mineralized useful  in  resource  i s produced.  for in situ  made. T h e r e s u l t s  distance  silver  cut-off  i n Chapter  grade  was  predicted.  of  precision  3.  A  handling  reserves f o r the Southern  straddled  and an a v e r a g e  importance  for  zone  and tonnages grade  into  Tail  i n reserves are accounted f o r .  support  a  Southern  of d i f f e r e n t  provides  no a s s u m p t i o n s  distributions  various  block estimations.  drill  to a bias  at  by t h e e r r a t i c  i s divided  the mineralized  irregular  lead  caused  Mines'  an e x a m i n a t i o n  Tail  the geologist  applied  Silver  a test  local  f o r the Southern 1)  been  of Equity  a s an a i d t o h a n d l i n g p r o b l e m s  the s i l v e r  in  procedures  simple  duplicate  t h e tonnage  of  125 g A g / t o n n e  and a c c u r a c y statistical analysis  indicated  i s  at  a  i n sampling are and  graphical  presented  with  107  emphasis  placed  errors.  Applying  data  from  the  on  both  identifying  these  procedures  Southern  1)  Tail  finding  a  analytical  results used  2)  a  showing in  by  the  method  3)  proving  that  be  reduced  by  4)  showing  that  financial  million  Finally  a  Southern effect,  Tail a  log  transformed empirical A  need  into  two  have  a data  of  duplicate  :  one  bias  in  the  two  of  error  for  samples  silver  collected  sampling  the  size  error  of  cost  of  sampling,  attained could  be  by in  could  the  collecting larger  sample samples  the  net  lowering excess  the  of  1  year.  g e o s t a t i s t i c a l approaches  tested  Models  by  sampling  sampling  while  been  transform,  silver  increasing  d o l l a r s per  sets  significant  random  benefits  partitioned  on  based  blasthole  on  a  set  were  data  traditional  partitioned  data  devised  for for  the  proportional  set and  local  and  tested  a  log  against  methods.  for  structural analysis good  domains  semivariogram Cross assays  the  of  in  random  tube  the  several  blasthole  variability  zone.  detailed  the  of  variety  estimation  for  duplicate  increase  sampling  but  large  assays  to  quantifying  resulted  small  laboratories  would  block  zone  and  from  by  models  of  the  1310  bench  geologic  control.  When  the  geologic  mapping  two  distinctly  were  validation surrounding  bench  emphasized was  divided  different  obtained. prodecures  data  were  for  estimating  inconclusive,  individual  probably  due  to  108  a  combination  spacing  of  of b l a s t h o l e  A comparison showed  erratic  lognormal  estimation  errors.  of  kriging  The  results  with  polygonal estimates  importance the the  life  selected.  techniques  lognormal  most  the f a i r l y  cost  the  to  of e s t i m a t i n g  indicating  partitioned  so t h a t  for  kriging  developed,  of m o n i t e r i n g grade  of a mine  best,  results  partitioned  different  than  and  regular  data.  the  more  sample a s s a y s  1.4  effective,  produce 100  grams  This  of mining  metal  lowest using  descrepancy of  points  silver to the  blocks early  content  estimation  the  models  blocks,  a wide  million  kriging.  content  the true  showed  various  is  known  technique  can  in and be  109  REFERENCES  Cyr, J . , J . M i l l e r (1980) B l a s t h o l e S a m p l i n g P r o c e d u r e S t u d y , P r i v a t e r e p o r t , E q u i t y S i l v e r M i n e s L t d . , N o v e m b e r , 11 p. E w a n c h u c k , H. (1968) Grade I n s t . Min. M e t a l l . Spec.  Control V o l . 9,  at Bethlehem Copper, pp. 302-307.  Can.  G i r o u x , G.H. and A . J . S i n c l a i r , (1984a) G l o b a l R e s e r v e s of S o u t h e r n T a i l z o n e by C o n d i t i o n a l P r o b a b i l i t y ; W e s t e r n M i n e r (in press). G i r o u x , G.H. and A . J . S i n c l a i r , (1984b) P r o d u c t i o n q u a l i t y c o n t r o l experiments; Western Miner ( i n p r e p a r a t i o n ) . J o u r n e l , A.G. and Ch. H u i j b r e g t s (1981) M i n i n g Academic Press ( I n c . ) L o n d o n L t d . , 600 p.  geostatistics;  J o u r n e l , A.G. (1983) N o n - p a r a m e t r i c e s t i m a t i o n d i s t r i b u t i o n s ; Jour. I n t . Assoc. Math. G e o l . p. 445-468  of s p a c i a l v.15, no. 3.,  M i l l e r , J . (1981) B l a s t h o l e Equity S i l v e r Mines Ltd., Ney, C.S., geologic deposit, no. 723,  J.M. A n d e r s o n and s e t t i n g and s t y l e B r i t i s h Columbia; p 53-64.  R a y m o n d , G., (1979) Ore m i n e r a l i z e d ore body, J u n e , pp. 90-97.  Sampling Procedure, May, 5 p.  Private  report  A. P a n t e l e y e v (1972) Discovery, o f m i n e r a l i z a t i o n , Sam Goosly I n s t . Min. M e t a l l . B u l l . v. 65,  estimation Can. Inst.  p r o b l e m s i n an erratically Min. M e t a l l . B u l l e t i n ,  R o y l e , A.G. a n d S. K h o s r o w s h a h i , ( 1 9 8 3 ) , V a l u a t i o n o f alluvial t i n and g o l d d e p o s i t s ; T r a n s . I n s t . Min. and M e t a l l . ( S e c . A, M i n e r a l I n d u s t r y ) , v o l 92, p p . A13-A18. S i n c l a i r , A.J. (1978) S a m p l i n g a m i n e r a l d e p o s i t f o r f e a s i b i l i t y s t u d i e s and m e t a l l u r g i c a l t e s t i n g ; i n M u l a r , A.L. and R.B. B h a p p u , M i n e r a l P r o c e s s i n g P l a n t D e s i g n ; Am. Inst. Min. E n g . New Y o r k , p 115-134. S i n c l a i r , A . J . a n d G.H. G r i o u x , (1983) G e o l o g i c a l c o n t r o l s of semi-variograms in precious metal deposits; G e o s t a t i s t i c s f o r N a t u r a l R e s o u r c e s C h a r a c t e r i z a t i o n , NATO A S I Series, D. R e i d e l P u b l i s h i n g C o m p a n y , D o r d r e c h t , H o l l a n d , p p . 965978. V e r l y , G. (1983) The m u l t i g a u s s i a n a p p r o a c h and t o t h e e s t i m a t i o n s of l o c a l r e s e r v e s ; J o u r n a l G e o l o g y , V o l . 15, No.2, pp. 263-290.  i t s applications of M a t h e m a t i c a l  no W e t h e r e l l , D.G (1979) G e o l o g y and Ore G e n e s i s copper-silver-antimony Deposit, Unpublished Dept. of G e o l o g i c a l S c i e n c e s , U n i v e r s i t y of V a n c o u v e r B.C., 208 p.  o f t h e Sam Goosley MSc Thesis, B.C.,  W e t h e r e l l , D.G., A . J . S i n c l a i r a n d T.G. Shroeter, (1979) P r e l i m i n a r y r e p o r t on t h e Sam Goosly copper-silver deposit; B.C. M i n i s t r y of E n e r g y , M i n e s and P e t r o l e u m R e s o u r c e s , P a p e r 1979-1, pp. 132-137.  111  APPENDIX I  COMPARISON  OF  E Q U I T Y L A B AND  A CHECK  L A B ON  M I L L SAMPLE  ASSAYS  11 2  SAMPLE  NUMBER  Tail 6 g T a i l 6d T a i l 8g T a i l 8a Ta i 1 1 1 g T a i l 14g T a i l 14d CoF 6g CoF 6d CoF 8g CoF 8a CoF 11g CoF 14g CoF 14d CoF 14a Cone 6g Cone 8g Cone 8a Cone 1 1 g C o n e 14g C o n e 14d R/Gcon a Cone 2d C o n e 15n  CU CHECK  CU EQUITY  AG CHECK  AG EQUITY  . 1 2 .09 . 12 .09 .09 .07 . 1 2 .24 .26 .29 .33 .19 .21 .23 .29 14.8 17.8 19.4 20. 1 18.2 18.1 3.36 25.2 18.2  . 1 2 .10 .12 .08 .10 .08 . 1 2 .25 .26 .29 .34 .19 .22 .23 .24 15.5 18.8 19.4 18.9 19.0 18.2 3.30 26.7 18.4  44.0 36.0 38.0 31.0 52.0 28.0 53.0 86.0 82.0 82.0 98.0 98.0 88.0 93.0 1 04.0 4840 4800 5446 9040 7480 7200 1 340 7360 5920  54.0 43.7 44.0 35.9 56.9 29.0 57.5 97.0 90.9 94.0 1 07.0 100.0 67.0 98. 1 104.0 571 5 5440 631 0 851 5 7735 7285 1 361 7800 6286  APPENDIX I I DUPLICATE  BLASTHOLE  SAMPLING  FOR  COPPER  AND  SILVER  11 4  ORIGINAL CU  CHECK CU  .17 .07 .09 .04 .06 .31 .22 .30 .51 .33 .03 .05 .02 .03 .08 .05 .04 .02 .07 .12 .03  . 1 5 .07 . 1 6 .06 .06 .34 .17 .23 .54 .48 .03 .02 .02 .02 .07 .05 .03 .02 .02 .06 .02  Mean.difference Cu S =  =  .0295 .0364  % %  DIFF. CU  ORIGINAL AG  .02 .00 .07 .02 .00 .03 .05 .07 .03 .15 .00 .03 .00 .01 .01 .00 .01 .00 .05 .06 .01  1 67 85 61 43 53 53 77 62 40 87 7 5 17 38 1 1 7 24 8 1 30 58 54  CHECK AG  DIFF. AG  11 7 73 1 24 35 54 62 48 49 22 1 29 8 7 10 50 8 7 10 9 32 40 43  Mean Ag  50 1 2 63 8 1 9 29 13 18 42 1 2 7 1 2 3 0 14 1 98 18 1 1  difference =  19.62  S = 24.73  g/tonne g/tonne  APPENDIX I I I RESULTS  FOR  D I F F E R E N T SAMPLING  TECHNIQUES  FOR  42  BLOCKS  EQUITY ORIGINAL  TUBE  • H  CU  AG  46840 113070 49760 112920 49820 50710 51150 52540 1 16380 55710 118000 1 17380 1 17320 1 17820 1 17810 117830 85260 85480 85670 85910 86110 1 17670 73260 136570 83870 84780 84950 87451 98680 146350 146580 146750 153840 154070 153340 153350 153560 155070 210410 205840 156450 21 1850  .14 .06 .02 .08 .03 .69 .69 . 12 .06 . 1 1 .03 .02 .28 .07 .09 .06 .47 .56 .0 . 14 .33 .07 .04 .04 .04 .42 . 18 .02 .24 .02 . 19 .24 . 15 .06 .02 .03 .07 .05 . 10 .20 .04 .0  5. 20. 11 . 123. 36. 274. 148. 10. 76. 85. 28. 27. 108. 76. 126. 42. 11. 325. 0. 78. 199. 31 . 19. 11 . 29. 220. 52. 3 0 1 .• 43. 10. 15. 4. 141 . 51 . 16. 22. 6. 28. 55. 68. 9. 2.  CHANNEL  H 3050 3170 31 1 0 3230 3350 3410 3470 3540 3600 3660 3840 3780 3720 3960 4020 3900 4540 4600 4660 4720 4780 4080 4240 4300 4360 4420 4480 4910 5220 5100 5040 5160 5400 5340 5460 5520 5280 7240 7300 7360 5570 7420  CU .21 .04 .01 .05 .07 .89 !58 . 11 .05 . 1 1 .03 .03 .05 .08 . 13 .04 .79 . 16 .02 .04 .22 .07 .04 .03 .06 .44 . 13 .86 .25 -. 16 .11 .20 .26 ;02 .22 .02 .01 . 12 .05 . 12 .04 .01  4  CHANNEL AG  12. 13. 3. 54. 85. 335. 161 . 9. 42. 95. 30. 28. 55. 99. 157. 32. 14. 44. 4. 16. 105. 36. 17. 7. 44. 268. 29. 204. 88. 92. 27 . 4. 260. 14. 218. 14. 5. 83. 25. 45. 7. 4.  H 3020 3140 3080 3200 3320 3380 3440 3510 3570 3630 3810 3750 3690 3930 3990 3870 4510 4570 4630 4690 4750 4050 4210 4270 4330 4390 4450 4880 5190 5070 5010 5130 5370 5310 5430 5490 5250 7220 7280 7340 5550 7400  1  CHANNEL  CU  AG  .21 .04 .02 . 13 . 13 .73 .76 . 11 .07 . 16 .07 .03 .0 . 14 .08 .07 .65 .46 .02 .05 .25 .06 .03 .04 .02 .38 . 15 .70 .31 .15 . 17 .21 .23 .02 .03 .02 .01 . 10 .07 .12 .05 .01  15. 15. 10. 206. 149. 395. 168. 8. 69. 142. 77. 34. 0. 105. 107. 55. 19. 234. 7. 15. 118. 32. 20. 15. 13. 231 . 24. 155. 90. 31 . 28. 4. 245. 9. 23. 14. 5. 49. 36. 40. 9. 3.  # 3030 3150 3090 3210 3330 3390 3450 3520 3580 3640 3820 3760 3700 3940 4000 3880 4520 4580 4640 4700 4760 4060 4220 4280 4340 4400 4460 4890 5200 5080 5020 5140 5380 5320 5440 5500 5260 7250 7310 7370 5580 7430  SOUTH T A I L 2  ZONE  CHANNEL  DUPLICATE 3  ANALYSIS  CHANNEL  CU  AG  -H  CU  AG  .30 .03 .02 .07 .05 .78 .43 . 13 . 13 . 15 .06 .03 .03 .09 .07 .06 .40 .51 .01 .05 .42 .05 .25 .03 .01 .40 .06 .23 . 16 .07 . 14 .20 .29 .02 .05 .03 .01 .06 .07 .33 .06 .01  21 . 13. 13. 90. 54. 380. 102. 21 . 46. 143. 65. 35. 42. 95. 80. 40. 9. 11 . 6. 19. 223. 32. 50. 12. 8. 222. 13. 96. 93. 56. 36. 5. 310. 16. 44. 19. 13. 34. 14. 108. 9. 2.  3040 3160 3100 3220 3340 3400 3460 3530 3590 3650 3830 3770 3710 3950 4010 3890 4530 4590 4650 4710 4770 4070 4230 4290 4350 4410 4470 4900 5210 5090 5030 5150 5390 5330 5450 5510 5270 7230 7290 7350 5560 7410  .30 .03 .04 .09 .03 .86 .97 . 13 .06 . 15 .03 .03 .03 .05 . 12 .06 .32 .41 .05 . 10 .39 .07 .04 .02 . 11 .47 .53 .45 .35 .02 .20 . 19 .31 .05 .02 .01 .04 .06 .08 .20 .09 .01  35. 13. 18. 132. 40. 394. 387. 18. 62. 136. 22. 28. 44. 59. 233. 20. 10. 203. 16. 48. 180. 32. 16. 11. 95. 297. 269. 133. 163. 10. 20. 4 . 315. 50. 19. 10. 18. 27. 45. 67. 25. 2.  » 3060 3180 3120 3240 3360 3420 3480 3550 3610 3670 3850 3790 3730 3970 4030 3910 4550 4610 4670 4730 4790 4090 4250 4310 4370 4430 4490 4920 5230 51 10 5050 5170 5410 5350 5470 5530 5290 7260 7320 7380 5590 7440  COMPOSITE  CU  AG  .25 .05 .02 .07 .06 .97 .60 .10 .06 . 15 .03 .03 .07 .09 .09 .07 .44 .43 .02 .09 .24 .07 .04 .03 .02 .39 . 1 1 .76 .27 .02 . 15 .19 .25 .03 .06 .01 .03 .08 .03 . 19 .06 .01  18. 22. 6. 103. 70. 393. 163. 8. 62. 142. 32. 27. 55. 98. 160. 35. 131 . 217. 5. 45. 123. 28. 18 . 10. 18. 233. 21 . 175. 89. 9. 26. 4. 240. 22. 57. 10. 12. 45. 17 . 68 . 18. 2.  BULK  H 3070 3190 3130 3250 3370 3430 3490 3560 3620 3680 3860 3800 3740 3980 4040 3920 4560 4620 4680 4740 4800 4100 4260 4320 4380 4440 4500 4930 5240 5120 5060 5180 5420 5360 54B0 5540 5300 7270 7330 7390 7210 7450  BEST  CU  AG  .26 .04 .01 .07 .04 .87 .52 . 16 .05 . 14 .04 .04 .03 .09 . 12 .06 .38 .45 .03 .08 .30 .05 .03 .03 .03 .43 .09 .79 .21 .02 . 16 .23 . 17 .03 .07 .02 .01 . 1 1 .05 . 16 .04 .01  22. 15. 4. 101. 54. 389. 151 . 20. 46. 117. 47. 37. 50. 86. 178. 48 11 226. 7 . 40. 147. 23. 14. 10. 21 . 268. 16 181 . 74 11. 24. 3. 167. 21 . 66. 13. 7. 78. 26. 54. 8. 2,  ESTIMATE  cu - 0 . 25 0 . 04 0 . 01 0. 07 0. 05 0. 85 0 . 58 0 . 14 0. 06 0 . 14 0 . 04 0. 04 0. 04 0. 09 0. 1 1 0. 06 0. 47 0 . 41 0. 03 0. 07 0. 30 0. 06 0. 05 0. 03 0 . 04 0 . 43 0 . 13 0 . 73 0 . 23 0. 06 0 . 15 0 . 22 0 . 21 0. 03 0. 09 0 . 02 0 . 01 0 . 10 0. 06 0 . 17 0. 05 0 . 01  AG 20 14 6 102 65 377 166 17 49 1 18 45 34 48 88 164 43 12 179 7 34 148 27 18 10 29 262 37 176 85 30 25 4 210 21 82 14 8 68 28 57 9 2  APPENDIX CALCULATION  OF VOLUMES  FOR  IV  DIFFERENT  SAMPLING  TECHNIQUES  118  Volume  of Tube  inch  Samples  -  3  -  sample  length  -  volume  of  -  sample composite  -  therefore  Volume  diameter assumed  sample  total  of Channel  -  4 separate  -  height  -  refer  -  Direction  of  t o be  i s 28.3  4  cu.in.  i s composed tube  inches  sample  of  4 tube  samples  volume  =  5  wide  113  cu.in.  720  cu.in.  Samples  channels sample  to Figure  using  cone  inch  assumed  6 Chapter  1 - Volume  a  3  t o be  8  shovel  inches  for directions  = 3 6 x 5 x 8 x . 5 =  -  Direction 2 -  Volume  == 15 X  5 X  8 X  .5  =  300  c u . in..  -  Direction 3 -  Volume  == 18 X  5 X  8 X  .5  =  360  cu. i n .  -  Direction 4 -  V o l u m e == 15 X  5 X  8 X  .5  =  300  cu. i n .  Volume  of Bulk  Sample  -  assume  a  -  height  of cone  -  volume  of t o t a l  the  uniform  shaded area  cylindrical  assumed sample  t o be will  i n diagram  pile 8  of  inches  equal  chips as  volume  above of  119  1  (0,13.3)  1.  y = .67 x + 1 3 . 3 x= 1 . 4 9 y - 1 9 . 9 x= C-^y : + d ^  2.  y = - 2 . x - 8.0 x = - 5 . y - 4.0 x^ C y + d 2  V  (-8,8)  2  1  Integrate between these limits.  (-20,0)  ^  B •LASTHOLE  Volume to be estimated  .  ^(0,-8)  V =  v 2 2 J(TTx - Tlx ) d y u 1 2  u  {(C  1  2 2 + d ) - (C y + d )}dy 1 2 2  y  Y2 2 2 2 2 = IT J) { ( C - C ) y + 2 ( C d -C d ) y + ( d - d ) } d y u 1 2 1 1 2 2 1 1  = TT u{ v  2 2 3 2 2 2 ( C - C ) y + (C d - C d ) y + ( d - d ) y } 1 2 11 2 2 1 2  2  2  = {(1,49-(-.5)*(8) 3 4243.19  say  3  +((1.49*  4220 c u .  in.  2 2 2 -l9.9)-(-.5*-4)*(8)+(l9.9-4)*8  x  120  -  Volume  of bulk  sample  = t o t a l volume and c h a n n e l s 4240 -  - volume 1793  =  of  tubes  2447  cu.in.  


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