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Ore reserve estimation, Silver Queen vein, Owen Lake, British Columbia Nowak, Marek Stanislaw 1991

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C. 2_. ORE RESERVE ESTIMATION SILVER QUEEN VEIN OWEN LAKE BRITISH COLUMBIA By Marek Stanislaw Nowak M.Sc, The U n i v e r s i t y of Mining and Me t a l l u r g y , Cracow, Poland, 1979 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Mining and Mine r a l Process Engineering) We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA JANUARY 1991 Copyright Marek Stanislaw Nowak, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of MI«I\* J> f<A*e/*i# -£oce*3 The University of British Columbia Vancouver, Canada Date DE-6 (2/88) i i ABSTRACT The S i l v e r Queen p o l y m e t a l l i c v e i n system south of Houston, B.C., can be t r e a t e d as a 2-dimensional problem f o r purposes of reserve/resource e s t i m a t i o n . Complexities i n o b t a i n i n g reserve/resource estimates a r i s e from ( i ) u n c e r t a i n t i e s i n g e o l o g i c a l i n t e r p o l a t i o n and e x t r a p o l a t i o n of the v e i n system, ( i i ) u n c e r t a i n t i e s i n the d i s t i n c t i o n between v e i n and h i g h l y a l t e r e d w a l l r o c k i n some o l d d r i l l l o g s , ( i i i ) complex and m u l t i v a r i a b l e g e o l o g i c a l c h a r a c t e r of the v e i n , ( i v ) a l i m i t e d number of e x p l o r a t i o n d r i l l holes and (v) a d i f f e r e n t support f o r d r i f t and d r i l l hole data. Each of these problems has been considered i n d e t a i l . The study comprises g e o l o g i c a l a n a l y s i s , data a n a l y s i s , p o i n t k r i g i n g ( a n a l y s i s of t h i c k n e s s and metal d i s t r i b u t i o n ) b l o c k k r i g i n g and comparison of reserve/resource e s t i m a t i o n by v a r i o u s procedures i n c l u d i n g o r d i n a r y k r i g i n g , inverse squared d i s t a n c e w e i g h t i n g , and polygonal methods. A novel component of the i n v e s t i g a t i o n i s the use of correlograms ( i n r e a l i t y , 1 minus the correlogram) as a s u b s t i t u t e f o r the variogram i n g e o s t a t i s t i c a l estimates. This procedure was t e s t e d as a means of d e f i n i n g c o n t i n u i t y of DDH and D r i f t assay data of d i f f e r i n g support. Ordinary k r i g i n g of l a r g e polygonal blocks provides metal contents more or l e s s comparable t o but l o c a l l y more con s e r v a t i v e than polygonal r e s u l t s reported i n a recent f e a s i b i l i t y study. D i f f e r e n c e s are i n p a r t due t o the use of somewhat d i f f e r e n t data f o r the two procedures. The e f f e c t of the volume of the s e l e c t i v e mining u n i t on the recovered tonnage and grade i s described and l i m i t a t i o n s of the i n d i r e c t lognormal method are presented. i i i TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES v i LIST OF FIGURES v i i i ACKNOWLEDGMENT XV CHAPTER I INTRODUCTION 1 CHAPTER II GEOLOGY, MINERALIZATION AND STRUCTURE IN THE SILVER QUEEN MINE 3 I I . 1 Regional Geology 3 11.2 Property Geology 3 11.3 M i n e r a l i z a t i o n 4 I I . 4 S t r u c t u r e 7 CHAPTER III THEORETICAL BACKGROUND OF RESERVE/RESOURCE ESTIMATION 10 III. l I n t r o d u c t i o n 10 111.2 Var i o g r ams 11 111.3 R e l a t i v e variograms 13 I I I . 4 Correlograms 14 I I I . 5 I n d i c a t o r variograms 16 I I I . 6 K r i g i n g 16 I I I . 7 Support of data 19 I I I . 8 Volume-Variance r e l a t i o n s h i p 19 CHAPTER IV DATA 25 IV. 1 I n t r o d u c t i o n 25 IV. 2 Basic assumptions 30 CHAPTER V METHODOLOGY AND DATA EVALUATION 32 V. l I n t r o d u c t i o n 32 V.2 Vein thi c k n e s s 33 V.2.1 E x p l o r a t i o n d r i l l holes 33 V.2.2 Underground workings 36 V.3 S p a t i a l d i s t r i b u t i o n of grades 40 i v TABLE OF CONTENTS cont'd page CHAPTER VI STRUCTURAL ANALYSIS-YARIOGRAPHY 46 VI. 1 C o n t i n u i t y functions of th i c k n e s s 46 VI. 1.1 Var iograms 46 VI. 1.2 R e l a t i v e var iograms 49 VI. 1.3 Correlogram f u n c t i o n s 53 VI. 1.4 I n d i c a t o r variograms 56 VI.2 C o n t i n u i t y functions of accumulations... 59 VI.2.1 Correlogram f u n c t i o n s 59 VI.2.1.1 Gold accumulations....59 VI.2.1.2 S i l v e r accumulations..61 V I . 2 .2 I n d i c a t o r variograms 61 CHAPTER VTI DISCUSSION OF SUPPORT OF DATA 67 CHAPTER VIII CROSSVALIDATION 71 CHAPTER IX ANALYSIS OF VARIABILITY OF THICKNESS AND ACCUMULATIONS 78 IX.1 P o i n t k r i g i n g of thic k n e s s and accumulations 78 IX.2 V a l i d i t y of k r i g i n g v a r i a n c e 91 CHAPTER X BLOCK KRIGING 95 CHAPTER XI ANALYSIS OF CHANGE OF SUPPORT 103 CHAPTER XII ESTIMATION OF RESERVES FOR MINIMUM MINING WIDTH 110. X I I . 1 B a s i c assumptions 110 XII.2 Choice of modified correlogram models I l l XI I . 3 Ore reserve e s t i m a t i o n 115 XII.4 Comparison of r e s u l t s w i t h unpublished Cominco estimates 117 CHAPTER XIII CONCLUSIONS 121 V TABLE OF CONTENTS cont'd page BIBLIOGRAPHY 126 APPENDIX I Examples of Assignment of Some D r i l l Hole M i n e r a l i z e d I n t e r s e c t i o n s to No. 3 Vein 129 APPENDIX II A n a l y s i s of Bimodal D i s t r i b u t i o n of Thickness of No. 3 Vein 134 APPENDIX III S t a t i s t i c a l A n a l y s i s of Metal Grades i n Wallrock and w i t h i n the No. 3 Vein 138 APPENDIX IV Data F i l e s Used i n the A n a l y s i s 143 APPENDIX V Comparison of Correlogram Functions f o r D i f f e r e n t Sections of the No. 3 Vein and of the 2600 L e v e l D r i f t 165 APPENDIX VI M o d i f i e d Correlogram Models of Copper, Lead, and Zinc accumulations 167 APPENDIX VII C r o s s v a l i d a t i o n of Gold Accumulations Based on D r i f t Data 170 APPENDIX VIII Contour Maps of Copper and Lead Accumulations Based on Ordinary P o i n t K r i g i n g 177 APPENDIX IX Ordinary Block K r i g i n g of Thickness and Copper, Lead, and Zinc Accumulations i n the C e n t r a l and Southern Section of No. 3 Vein..180 APPENDIX X Further Notes on I n d i r e c t Lognormal C o r r e c t i o n Model of Blocks 25x25 f t 2 and of Blocks 30x7 f t 2 187 APPENDIX XI A n a l y s i s of D i s t r i b u t i o n of Copper Grades and i t s i n f l u e n c e on the Variogram 190 APPENDIX XII Examples of Increases of Quantity of Metals when M i n e r a l i z a t i o n i s Found Outside the No. 3 v e i n 193 APPENDIX XIII M o d i f i e d Correlograms of Accumulations of S i l v e r , Copper, and Zinc based on minimum mining widths 4.0 f t 195 APPENDIX XIV Estimates of No. 3 Vein Thickness and Average Grade of Blocks 200x150 f t 2 f o r C e n t r a l and Southern Section 197 v i LIST OF TABLES page TABLE 1.1 Comparison of B r i t i s h and M e t r i c U n i t s 2 TABLE V . l Simple s t a t i s t i c s f o r metal accumulations w i t h i n 15 f e e t of No. 3 v e i n . . . . 41 Table VI.1 M o d i f i e d correlogram and i n d i c a t o r variogram models f o r d i f f e r e n t v a r i a b l e s and c u t o f f s 66 TABLE X . l Estimated i n s i t u resources 98 TABLE X.2 P o s s i b l e minable resources 98 TABLE XI.1 C o e f f i c i e n t s c a l c u l a t e d f o r t r a n s f o r m a t i o n of o r i g i n a l data values by i n d i r e c t lognormal method 105 TABLE XI.2 Examples of the tranformation of the o r i g i n a l v e i n t h i c k e n s s hole data v a l u e s , y, i n t o Zf values 105 TABLE XI.3 Estimated p r o p o r t i o n of tonnage and grade due t o change of support c a l c u l a t e d by ILN i n the C e n t r a l S e c t i o n of the v e i n 107 Table XI.4 Comparizon of p o s s i b l e minable resources f o r d i f f e r e n t c u t o f f s performed on block s i z e 200xl50xthick i n C e n t r a l s e c t i o n 108 Table X I I . 1 D i l u t e d i n s i t u Resoures 115 Table X I I . 2 D i l u t e d P o s s i b l e Minable Resources 116 Table XII.3 Estimated f u l l y d i l u t e d tonnage, average grade, and gross value of metals recovered from the No. 3 v e i n 117 TABLE XII.4 Comparison of estimates of average thi c k n e s s and grade of a polygon (POL2) i n C e n t r a l s e c t i o n of No. 3 v e i n 119 TABLE XII.5 Comparison of estimates of average thickness and grade of a polygon (P0L2) where stope averages (Cominco) and low grade d r i l l holes (Author) are excluded 119 Table AX.l Estimated resources f o r the s e l e c t i o n mining u n i t 25x25 f o r d i f f e r e n t c u t o f f s , C e n t r a l s e c t i o n of No. 3 v e i n 188 v i i LIST OF TABLES cont'd page Table AX.2 C a l c u l a t i o n of p o s s i b l e gains r e s u l t i n g from a s e l e c t i o n mining u n i t of one days's p r o d u c t i o n 188 Table AXI.1 Comparison of average copper grades f o r d i f f e r e n t areas i n the C e n t r a l s e c t i o n of No. 3 v e i n 190 Table AXI.2 Comparison of r e l a t i v e variogram values of Copper accumulations f o r d i f f e r e n t subsets of data, f i r s t two lags taken, C e n t r a l s e c t i o n of No. 3 v e i n 192 Table A X I I . l Examples of increases of metal accumulations when minimum mining width 4.0 f t i s assumed and m i n e r a l i z a t i o n of i n t e r e s t i s found outside the v e i n 193 . v i i i LIST OF FIGURES page Figure IV.1 L o n g i t u d i n a l s e c t i o n of No.3 v e i n : C e n t r a l p a r t 26 Southern p a r t 26A Figure IV.2 S t r u c t u r a l contour map of the No. 3 zone 27 Figure IV.3 L o n g i t u d i n a l s e c t i o n , p o s i t i o n of DDH a f t e r transformation of southern p a r t of v e i n 28 Figure V . l D i s t r i b u t i o n of v e i n t h i c k n e s s ( f t ) - C e n t r a l 34 Figure V.2 Cumulative d i s t r i b u t i o n of v e i n t h i c k n e s s ( f t ) - C e n t r a l 34 Figure V.3 D i s t r i b u t i o n of v e i n t h i c k n e s s ( f t ) - South 35 Figure V.4 Cumulative d i s t r i b u t i o n of v e i n t h i c k n e s s ( f t ) - South 35 Figure V.5 D i s t r i b u t i o n of v e i n t h i c k n e s s ( f t ) - D r i f t 37 Figure V.6 Quantiles of thickness from d r i l l hole vs. d r i f t data 37 Figure V.7 D i s t r i b u t i o n of v e i n t h i c k n e s s - subset 1.8-5.9 f t 37 Figure V.8 D i s t r i b u t i o n of v e i n t h i c k n e s s i n d r i f t , subset 1.8-5.9 f t 37 Figure V.9 S e c t i o n of a 2600 l e v e l d r i f t where v e i n thickness i s l a r g e r than the width of the d r i f t 39 Figure V.10 P r o f i l e s t o demonstrate the p o t e n t i a l importance of m i n e r a l i z e d w a l l r o c k as a source of ore. D r i l l hole i n t e r s e c t i o n s are l o c a t e d near 27000 E a s t i n g 42 Figure V . l l S c a t t e r p l o t of uppermost v e i n assays versus hangingwall assays: a) z i n c (%), b) s i l v e r (oz/st) 43 Figure V.12 S c a t t e r p l o t of lowermost v e i n assays versus f o o t w a l l assays: a) z i n c (%), b) s i l v e r (oz/st) 44 Figure V I . 1 Variogram of t h i c k n e s s - C e n t r a l 47 i x LIST OF FIGURES cont'd page Figure VI.2 Variogram of t h i c k n e s s , h o r i z . d i r e c t i o n - C e n t r a l 47 Figure VI.3 Variogram of t h i c k n e s s , v e r t . d i r e c t i o n - C e n t r a l 47 Figure VI.4 Variogram of thickness - South 47 Figure VI.5 Variogram of thickness f o r both zones, South and C e n t r a l 49 Figure VI.6 R e l a t i v e variogram of t h i c k n e s s - Central....51 Figure VI.7 R e l a t i v e variogram of t h i c k n e s s - South 51 Figure VI.8 R e l a t i v e variogram of t h i c k n e s s - C e n t r a l and South 51 Figure VI.9 R e l a t i v e variogram of t h i c k n e s s measured on l e v e l 2600 51 Figure VI.10 S c a t t e r p l o t of variance versus squared mean of t h i c k n e s s f o r blocks (DDH) and s e c t i o n s of the d r i f t 52 Figure VI.11 a) Correlogram of v e i n t h i c k n e s s , C e n t r a l and South, b) Correlogram of a l l d r i f t data ( l a r g e l a g s ) , c) Correlogram model of t h i c k n e s s of the v e i n 54 Figure VI.12 a) Correlogram model of t h i c k n e s s f o r subset of data 1.8-5.9 f t . d e r i v e d from d r i f t and d r i l l hole data, b) Correlogram of t h i c k n e s s f o r subset of data 1.8-5.9 f t . from d r i l l holes i n South and C e n t r a l \ s e c t i o n s of the v e i n 55 Figure VI.13 I n d i c a t o r variograms of t h i c k n e s s from South and C e n t r a l s e c t , c a l c u l a t e d from d r i l l hole data: a) cut-off=2.5 f t . ; b) cut-off=3.5 f t . ; c) cut-off=4.5 f t . d) c u t - o f f = 5.5 f t 57 Figure VI.14 I n d i c a t o r variograms of t h i c k n e s s from d r i f t data: a) cut-off=2.5 f t . ; b) cut-off=3.5 f t . ; c) cut-off=4.5 f t . d) cut-off=5.5 f t - 58 Figure VI.15 Range of i n d i c a t o r variograms of t h i c k n e s s as a f u n c t i o n of the c u t - o f f chosen; Co represents nugget e f f e c t 60 X Figure VI.16 LIST OF FIGURES cont'd a) I n d i c a t o r variogram of t h i c k n e s s f o r cut-off=4.0 f t . c a l c u l a t e d from a l l d r i l l hole data; b) i n d i c a t o r variogram model of c o n t i n u i t y of t h i c k n e s s based on d r i f t and d r i l l hole data page 60 Figure VI.17 Figure VI.18 Figure VI.19 a) Correlogram of gold accumulations from d r i l l hole data; b) Correlogram of gold accumulations from d r i f t assays; c) D i r e c t i o n a l h o r i z o n t a l correlogram of g o l d accumulations from d r i l l hole assays, d) Correlogram model of g o l d accumulations based on d r i f t and d r i l l hole assays 62 a) Correlogram of s i l v e r accumulations based on a l l d r i l l hole assays; b) Correlogram of s i l v e r accumulations from d r i f t assays; c) Correlogram model of s i l v e r accumulations based on d r i f t and d r i l l hole assays 63 I n d i c a t o r variogram model f o r a) g o l d accumulations, cut-off=0.85 o z * f t / s t ; b) z i n c accumulations c u t - o f f = 3 0 % * f t ; c) s i l v e r accumulations, cut-off=40 o z * f t / s t 65 Figure VII.1 Correlogram of z i n c accumulations from underground d r i l l holes 68 Figure VI1.2 Variogram of gold grades from a) d r i l l h ole assays; b) d r i f t assays 70 Figure VII.3 Correlogram of gold grades from a) d r i l l h ole assays; b) d r i f t data 70 Figure V I I I . 1 C r o s s v a l i d a t i o n of gold accumulations from d r i l l h o les, search r a d i u s 200x200 f t a) Histogram of known data; b) Histogram of estimates; c) Histogram of r e s i d u a l s ; d) S c a t t e r p l o t of estimates versus tr u e values 72 Figure V I I I . 2 C r o s s v a l i d a t i o n of gold accumulations from d r i l l h oles, polygons method: a) Histogram of known data; b) Histogram of estimates; c) Histogram of r e s i d u a l s ; d) S c a t t e r p l o t of estimates versus t r u e values 74 x i LIST OF FIGURES cont'd page Figure V I I I . 3 C r o s s v a l i d a t i o n of gold accumulations from d r i l l h o les, i n v e r s e squared d i s t a n c e weighting method: a) Histogram of estimates; b) Histogram of r e s i d u a l s ; c) S c a t t e r p l o t of estimates versus t r u e values 75 Figure IX.1 P o s t i n g of DDH which were used i n a n a l y s i s of v a r i a b i l i t y of t h i c k n e s s and accumulations of metals 79 Figure IX.2 Contour map of th i c k n e s s of v e i n No. 3, c a l c u l a t e d by o r d i n a r y p o i n t k r i g i n g 80 Figure IX.3 Contour map of th i c k n e s s i n d i c a t o r f o r cut-off=4.0 f t 82 Figure IX.4 Contour map of k r i g e d estimate of thic k n e s s f o r p r o b a b i l i t y g r e a t e r than 0.5 th a t the thickness i s l a r g e r than 4.0 f t 83 Figure IX.5 Contour map of gold accumulations, c a l c u l a t e d by o r d i n a r y p o i n t k r i g i n g 84 Figure IX.6 Contour map of gold accumulation i n d i c a t o r , cut-off=0.85 o z * f t / s t 85 Figure IX.7 Contour map of s i l v e r accumulations c a l c u l a t e d by o r d i n a r y p o i n t k r i g i n g 87 Figure IX.8 Contour map of s i l v e r accumulations i n d i c a t o r , cut-off=40 o z * f t / s t 88 Figure IX.9 Contour map of zi n c accumulations c a l c u l a t e d by o r d i n a r y p o i n t k r i g i n g 89 Figure IX.10 Contour map of zi n c accumulations i n d i c a t o r , cut-off=30 % * f t 90 Figure IX.11 Contour map of k r i g i n g v a r i a n c e of e s t i m a t i o n of Au accumulations w i t h the search r a d i u s 600 f t . t o estimate variance i n the neighbourhood 93 Figure X . l D r i l l holes used f o r reserve e s t i m a t i o n , Southern s e c t i o n 96 Figure X.2 Estimates of average t h i c k n e s s and Au grade of blocks 200x150 f t ^ , by o r d i n a r y k r i g i n g method, C e n t r a l s e c t i o n of No. 3 v e i n 99 x i i LIST OF FIGURES cont'd page Figure X.3 Estimates of average thickness and Au grade of blocks 200x150 f t 2 , by o r d i n a r y k r i g i n g method, Southern s e c t i o n of No. 3 v e i n 100 Figure X.4 Estimates of average thickness and Ag grade of blocks 200x150 f t 2 , by o r d i n a r y k r i g i n g method, C e n t r a l s e c t i o n of No.3 v e i n 101 Figure X.5 Estimates of average thickness and Ag grade of blocks 200x150 f t 2 , by o r d i n a r y k r i g i n g method, Southern s e c t i o n of No. 3 v e i n 102 Figure X I I . l Correlogram of v e i n thickness from: a) d r i l l hole data, minable widths, b) d r i f t data, minable widths 112 Figure XII.2 Correlogram of gold accumulations: a) d r i l l hole assays, minable widths, b) d r i f t assays, minable widhts 112 Figure XII.3 Correlogram of Lead accumulations: a) d r i l l hole assays, minable widths, b) d r i f t assays, minable widths 114 Figure A . I I . l Cumulative frequency d i s t r i b u t i o n of t h i c k n e s s from C e n t r a l s e c t i o n represented by two normal component popul a t i o n s 136 Figure A.II.2 Cumulative frequency d i s t r i b u t i o n of t h i c k n e s s from Southern s e c t i o n represented by two normal component p o p u l a t i o n s . 137 Figure A . I I I . l S c a t t e r p l o t of lowermost v e i n assays versus f o o t w a l l assays: a) gold ( o z / s t ) , b) l e a d (%), c) copper (%) 139 Figure A . I I I . 2 S c a t t e r p l o t of lowermost v e i n assays versus f o o t w a l l assays: a) gold ( o z / s t ) , b) l e a d (%), c) copper (%) 140 Figure A . I I I . 3 S c a t t e r p l o t of adjacent v e i n assays: a) g o l d ( o z / s t ) , b) s i l v e r ( o z / s t ) , c) copper (%), d) lead (%), e) z i n c (%) 141 Figure A.V.I Correlogram of thickness from d r i l l hole data: a) South, b) C e n t r a l 166 x i i i LIST OF FIGURES cont'd Figure A.V.2 Figure A . V I . l Figure A.VI.2 Figure A.VI.3 Correlogram of thi c k n e s s from s e c t i o n of a d r i f t : a) 114 data, b) 251 data 166 Correlogram of copper accumulations: a) d r i l l hole assays, b) D r i f t assays, c) Correlogram model 168 Correlogram of l e a d accumulations: a) d r i l l hole assays, b) d r i f t assays, c) Correlogram model 168 a) Correlogram of z i n c accumulations from d r i l l hole assays, b) Correlogram of z i n c accumulations from d r i f t assays, c) Correlogram model of z i n c accumulations 169 Figure A . V I I . l F i g u r e A.VII.2 Figure A.VII.3 Figure A.VII.4 Figure A.VII.5 C r o s s v a l i d a t i o n of gold accumulations from d r i l l h o l e s , search r a d i u s 150x150 f t : a) Histogram of known data; b) Histogram of estimates; c) Histogram of r e s i d u a l s ; d) S c a t t e r p l o t of estimates versus t r u e values 172 C r o s s v a l i d a t i o n of gold accumulations from d r i f t assays, correlogram model used: a) Histogram of t r u e v a l u e s ; b) Histogram of estimates; c) Histogram of r e s i d u a l s ; d) s c a t t e r p l o t of estimates versus t r u e values 173 C r o s s v a l i d a t i o n of gold accumulations from d r i f t assays, pure nugget e f f e c t model: a) Histogram of estimates; b) Histogram of r e s i d u a l s ; c) S c a t t e r p l o t of estimates versus t r u e values , 174 C r o s s v a l i d a t i o n of gold accumulations from d r i f t assays, i n v e r s e square d i s t a n c e weighting method: a) Histogram of estimates; b) Histogram of r e s i d u a l s ; c) S c a t t e r p l o t of estimates versus t r u e values 175 C r o s s v a l i d a t i o n of gold accumulations from d r i f t assays, polygonal method: a) Histogram of estimates; b) Histogram of r e s i d u a l s ; c) S c a t t e r p l o t of estimates versus t r u e values 176 Figure A.VIII.1 Contour map of Cu accumulations c a l c u l a t e d by o r d i n a r y p o i n t k r i g i n g 178 x i v LIST OF FIGURES cont'd page Figure A.VIII.2 Contour map of Pb accumulations c a l c u l a t e d by o r d i n a r y p o i n t k r i g i n g 179 Figure A . I X . l Estimates of average th i c k n e s s and Cu grade of blocks 200x150 f t 2 , by o r d i n a r y k r i g i n g method, C e n t r a l s e c t i o n of No. 3 v e i n 181 Figure A.IX.2 Estimates of average t h i c k n e s s and Cu grade of blocks 200x150 f t 2 , by o r d i n a r y k r i g i n g method, Southern s e c t i o n of No. 3 v e i n 182 Figure A.IX.3 Estimates of average v e i n t h i c k n e s s and Pb grade of b l o c k s 200x150 f t 2 , by o r d i n a r y k r i g i n g method, C e n t r a l s e c t i o n of No. 3 v e i n 183 Figure A.IX.4 Estimates of average v e i n t h i c k n e s s and Pb grade of bl o c k s 200x150 f t 2 , by o r d i n a r y k r i g i n g method, Southern s e c t i o n of No. 3 v e i n 184 Figure A.IX.5 Estimates of average t h i c k n e s s and Zn grade of blocks 200x150 f t 2 , by o r d i n a r y k r i g i n g method, C e n t r a l s e c t i o n of No. 3 v e i n 185 Figure A.IX.6 Es t i m a t i o n of average v e i n thickness and Zn grade of blocks 200x150 f t 2 , by o r d i n a r y k r i g i n g method, Southern s e c t i o n of No. 3 v e i n 186 Figure A.XIII.1 Figure A.XIII.2 Figure A.XIII.3 Correlogram of s i l v e r accumulations, minable widths: a) d r i l l hole assays; b) d r i f t assays 196 Correlogram of copper accumulations, minable widths: a) d r i l l hole assays; b) d r i f t assays 196 Correlogram of z i n c accumulations, minable widths: a) d r i l l hole assays; b) d r i f t assays 196 XV ACKNOWLEDGMENT My t h e s i s would be impossible without the work and encouragement of the f o l l o w i n g . F i r s t l y I am very g r a t e f u l f o r the c o n s t r u c t i v e c r i t i c i s m , the r e v e a l i n g i n s i g h t s , and the u n s t i n t i n g help of Dr. A l a s t a i r S i n c l a i r . Without h i s i n t e r e s t and support t h i s work would simply not have been p o s s i b l e . I am a l s o indebted t o Mohan S r i v a s t a v a , who guided me throughout the process, c h e e r f u l l y l e n d i n g from h i s great r e s e r v o i r of knowledge and experience without the l e a s t i n h i b i t i o n . Mohan's patience and w i l l i n g n e s s t o l i s t e n t o some of my more e r r a t i c remarks has been g r e a t l y appreciated. My whole-hearted thanks are given, of course, t o Houston Metals Inc., who allowed me access t o t h e i r data f i l e s on the S i l v e r Queen Deposit. My t h e s i s has b e n e f i t e d g r e a t l y from the comments of Dr. Margaret Thomson, Dr. C r a i g L e i t c h and C h r i s Hood. T h e i r s p e c i a l i z e d knowledge of the geology and the m i n e r a l i z a t i o n of t h i s p a r t i c u l a r d eposit has been of great help. Dr. Andy Mular and Dr. A l l a n H a l l a l s o r e c e i v e my s p e c i a l thanks f o r t h e i r help i n s t e e r i n g my work through the appropriate academic channels. I cannot f i n i s h without mentioning Z o f i a Radlowski, P.Eng., computing expert i n the G e o l o g i c a l Sciences Department. She has my deepest thanks f o r the hours spent on my behalf e n t e r i n g data from o l d r e c o r d s , and g e n e r a l l y g u i d i n g me through the m i n e f i e l d of software a p p l i c a t i o n . F i n a n c i a l support was provided from a Science C o u n c i l of B.C. core research grant t o Dr. A.J. S i n c l a i r w i t h the support of The M i n e r a l Deposits Research U n i t , Department of G e o l o g i c a l Sciences, UBC. 1 CHAPTER I INTRODUCTION The goal of t h i s study i s t o a r r i v e a t estimates of both i n s i t u resources and minable reserves f o r the S i l v e r Queen p o l y m e t a l l i c v e i n d e p o s i t . The a n a l y s i s i s concerned w i t h the thorough i n t e g r a t i o n of g e o l o g i c a l knowledge i n t o the e s t i m a t i o n process, w i t h the v a r i a b i l i t y of v e i n t h i c k n e s s and w i t h d i s t r i b u t i o n of grades of f i v e elements (Ag, Au, Zn, Pb, Cu) i n the s o - c a l l e d No. 3 zone. "Change of support" ( e s t i m a t i n g recoverable grade i n mining s e l e c t i o n u n i t s from w i d e l y spaced e x p l o r a t i o n data) w i l l be evaluated i n terms of the volume-variance r e l a t i o n although assessment of reserves w i l l depend on a r b i t r a r i l y chosen c u t - o f f grades t o i l l u s t r a t e methodology. The de p o s i t and data w i l l be examined from the mining p o i n t of view: where both the tenors of m i n e r a l i z a t i o n and minimum mining width w i l l govern the choice of the minable widths. In some cases minable widths w i l l be i n f l u e n c e d by m i n e r a l i z a t i o n adjacent t o the v e i n . During the course of the a n a l y s i s a v a r i e t y of g e o s t a t i s t i c a l t o o l s w i l l be used t o estimate the q u a l i t y and qu a n t i t y of reserves/resources and the p r o b a b i l i t y t h a t the estimated value i s above the c u t - o f f chosen. Results f o r a v a r i e t y of e s t i m a t i o n techniques ( p o l y g o n a l , o r d i n a r y k r i g i n g , i n verse squared d i s t a n c e weighting) w i l l be compared; the a n a l y s i s w i l l be based on data c o l l e c t e d and described throughout the years i n B r i t i s h u n i t s . A comparison of B r i t i s h 2 u n i t s used i n the a n a l y s i s w i t h M e t r i c u n i t s i s given i n Table I . l : B r i t i s h Units Metric Units lbs 454.0 g oz 31.1 g f t 30.47 cm St 0.907 t oz/st 34.28 g/t oz • f t / s t 10.45 g • m/t % . f t 0.33 % • m TABLE I.1 Comparison of B r i t i s h and M e t r i c U n i t s The q u a n t i t a t i v e computerized and q u a l i t a t i v e g e o l o g i c a l data set on which the a n a l y s i s i s based was created w i t h the ass i s t a n c e of Z. Radlowski and g e o l o g i c a l c o n t r i b u t i o n from C. L e i t c h , M. Thomson, and C. Hood. The software used i n t h i s a n a l y s i s was GEOSTAT TOOLBOX developed by R. Froidevaux (1988), and STATPAC programs developed by USGS (1987). The l a t t e r programs were p a r t i a l l y m odified t o s u i t the author. 3 CHAPTER II. GEOLOGY, MINERALIZATION AND STRUCTURE IN THE SILVER QUEEN MINE TT.1 REGTONAT, GEOT.OGY S i l v e r Queen depo s i t i s i n the Buck Creek B a s i n near Houston i n the B u l k l e y v a l l e y r e g i o n of c e n t r a l B r i t i s h Columbia. The Buck Creek b a s i n has been i n t e r p r e t e d as a resurgent c a l d e r a , w i t h the important nearby E q u i t y S i l v e r mine l o c a t e d w i t h i n the eroded c e n t r a l u p l i f t e d area (Church, 1985). The S i l v e r Queen mine l i e s on the c a l d e r a r i m or perimeter of the b a s i n , which i s roughly d e l i n e a t e d by a s e r i e s of r h y o l i t e o u t l i e r s and s e m i c i r c u l a r alignment of Upper Cretaceous and Eocene v o l c a n i c centres s c a t t e r e d between Francois Lake, Houston and Burns Lake. A prominent 30 km long lineament, t r e n d i n g e a s t - n o r t h e a s t e r l y from the S i l v e r Queen mine towards the c e n t r a l u p l i f t h o s t i n g the E q u i t y mine, appears t o be a r a d i a l f r a c t u r e c o i n c i d i n g w i t h the e r u p t i v e a x i s of Upper Cretaceous v o l c a n i c s and a l i n e of syenomonzonite stocks and feeder dykes t o an assemblage of T e r t i a r y "moat v o l c a n i c s " (Church, 1985). Block f a u l t i n g i s common i n the b a s i n , l o c a l l y j u x t a p o s i n g the va r i o u s ages of v o l c a n i c rocks. TT.3 PROPERTY KEPT-OKY S i l v e r Queen depo s i t has had a long h i s t o r y of e x p l o r a t i o n and produced a s u b s t a n t i a l amount of s i l v e r (168,000 o z ) , z i n c (11.1 m i l l i o n l b s ) , l e a d (1.55 m i l l i o n l b s ) , copper (893,000 4 l b s ) , and gold (3160 oz) from 210,000 tons of ore d u r i n g 1972 and 1973 ( L e i t c h et a l , 1990). There are f i v e major rock u n i t s and three dyke types i n the immediate v i c i n i t y of the S i l v e r Queen and as s o c i a t e d p o l y m e t a l l i c veins ( L e i t c h e t a l , 1990) as f o l l o w s : "A b a s a l r e d d i s h purple p o l y m i c t i c conglomerate i s o v e r l a i n by fragmental rocks ranging from t h i c k c r y s t a l t u f f t o coarse l a p i l l i t u f f and b r e c c i a or l a h a r , and t h i s i s succeeded upwards by a t h i c k f e l d s p a r p o r p h y r i t i c andesite flow u n i t i n t r u d e d by m i c r o d i o r i t e s i l l s and other f e l d s p a r porphyry and quartz porphyry dykes and sto c k s . A l l the u n i t s are cut by dykes t h a t can be d i v i d e d i n t o three groups: amygdaloidal dykes, bladed f e l d s p a r porphyry d i k e s , and diabase dykes. The succession i s unconformably o v e r l a i n by b a s a l t i c t o p o s s i b l y t r a c h y a n d e s i t i c v o l c a n i c s . M i n e r a l i z e d veins were emplaced a f t e r the amygdaloidal, f i n e grained p l a g i o c l a s e r i c h dykes which are s t r o n g l y a l t e r e d . The dykes w i t h bladed p l a g i o c l a s e c r y s t a l s represent l a t e r stage of events and are u n a l t e r e d . These d i k e s , some of which a l s o c o n t a i n pyroxene phenocrysts, are p o s s i b l y c o r r e l a t i v e w i t h the Ootsa Lake Group Goosley Lake v o l c a n i c s . " TT.3 MTNERAT.T7ATTDN This study i s confined t o the s o - c a l l e d No. 3 zone ( p r e v i o u s l y No. 3 vein) which has been the focus of the past production and recent e x p l o r a t i o n . The zone crops out over a dis t a n c e of one thousand metres and i s the o n l y v e i n on the property which has been explored by d r i l l i n g , underground sampling, and sto p i n g (from 2880 and 2600 l e v e l ) . W i t h i n t h i s s t r u c t u r e i n d i v i d u a l veins range from 0.1 t o 3.0 m i n thickness and c o n s i s t g e n e r a l l y of the assemblage c a r b o n a t e - b a r i t e -specular hematite as gangue w i t h disseminated t o l o c a l l y massive 5 p y r i t e , s p h a l e r i t e , galena, c h a l c o p y r i t e , t e n n a n t i t e , and argentian t e t r a h e d r i t e . Native gold (as electrum grains w i t h i n the galena) has been recognized s p o r a d i c a l l y throughout the No. 3 s t r u c t u r e (Hood et a l , 1991). M i n e r a l s of i n t e r e s t are present i n v e i n No. 3 i n f o l l o w i n g r e l a t i o n s h i p s (C. Hood, personal communications, 1990): galena: mostly coarse grained, may i n c l u d e c h a l c o p y r i t e , t e t r a h e d r i t e , or p y r i t e and may be locked i n s p h a l e r i t e and c h a l c o p y r i t e ; s p h a l e r i t e : may i n c l u d e c h a l c o p y r i t e , t e t r a h e d r i t e , galena, or p y r i t e and i n places a l l the foregoing sulphides are i n c l u d e d . I t has been found locked i n galena i n small amounts; c h a l c o p y r i t e : can be locked w i t h p y r i t e , s p h a l e r i t e , and t e t r a h e d r i t e . > In places c h a l c o p y r i t e contains i n c l u s i o n s of s u l f o s a l t s and galena; and T e t r a h e d r i t e : l a r g e l y f i n e grained and locked w i t h c h a l c o p y r i t e . C e r t a i n assemblages dominate i n d i f f e r e n t segments of the No. 3 zone. Hood e t a l (1991) document four p a r t s of the No. 3 s t r u c t u r e , each c h a r a c t e r i z e d by m i n e r a l o g i c a l features t h a t complicate simple s t a t i s t i c a l i n t e r p r e t a t i o n based on the e n t i r e data s e t . For example, although Ag seems to be c o r r e l a t e d w i t h Cu, from the s t a t i s t i c a l a n a l y s i s of d r i l l hole assays i t shows that o v e r a l l c o r r e l a t i o n i s weak (Pearson c o r r . c o e f f . = 0.41; 6 Spearman c o r r e l a t i o n c o e f f i c i e n t = 0.55). P a r t of the expl a n a t i o n of t h i s low c o r r e l a t i o n i s t h a t there are s e v e r a l s i l v e r bearing minerals which are not a s s o c i a t e d s p a t i a l l y w i t h c h a l c o p y r i t e . I n d i v i d u a l v e i n s w i t h i n the No. 3 zone are h i g h l y v a r i a b l e i n c h a r a c t e r , ranging from massive or banded gangue-rich veins w i t h w e l l - d e f i n e d f o o t w a l l and hangingwall through i r r e g u l a r discontinuous massive sulphide pockets of v e i n m i n e r a l i z a t i o n t h a t has a g r a d a t i o n a l contact w i t h h i g h l y a l t e r e d w a l l r o c k , t o i l l - d e f i n e d stockwork and b r e c c i a zones. In general the v e i n and i t s t h i c k n e s s i s defined by the tenor of m i n e r a l i z a t i o n , p a r t i c u l a r l y precious metal values, as measured by assay composites, and t o a l e s s e r extent i s based on a l t e r a t i o n and v e i n mineralogy ( L e i t c h e t . a l . 1990). In a few cases (DDH UG-88-30, DDH UG-88-31) m i n e r a l i z a t i o n can be found i n the hangingwall of the No. 3 v e i n i n m i c r o d i o r i t e w i t h up t o 30% banded p y r i t e and some s p h a l e r i t e present. This l a t t e r type of m i n e r a l i z a t i o n contains up t o 4.5 oz / s t Ag and 5.4%/st z i n c . A t r a n s i t i o n a l zone from l o c a l l y massive sulphides i n the v e i n t o barren w a l l r o c k can be a l s o found i n the f o o t w a l l i n the form of s i l i c i f i e d and p y r i t i z e d rock c o n t a i n i n g minor s p h a l e r i t e (DDH UG-88-24). In some cases a m i n e r a l i z e d zone occurs i n a l t e r e d w a l l r o c k c o n t a i n i n g s t r i n g e r s of p y r i t e and s p h a l e r i t e ; such zones can c a r r y values of economic i n t e r e s t (DDH UG-88-30 0.09 o z / s t Au, 4.52 oz / s t Ag along 4.52 f t ) . This f a c t suggests c e r t a i n d i f f e r e n c e s i n g e o l o g i c a l and mining i n t e r p r e t a t i o n of v e i n t h i c k n e s s which, 7 from the mining p o i n t of view, can be wider than the v e i n s t r u c t u r e i t s e l f . TT.4 STKTTCTTTRF. The s t r u c t u r e of rocks i n the S i l v e r Queen mine area i s dominated by a g e n t l y west t o northwest-dipping homocline. There i s no f o l d i n g apparent at the property s c a l e ; the sequence appears t o have been t i l t e d 20 t o 30 degrees from the h o r i z o n t a l by block f a u l t i n g . Two prominent s e t s of f a u l t s are present i n the area; a nor t h w e s t e r l y - t r e n d i n g s e t and a n o r t h e a s t e r l y - t r e n d i n g s e t . The former predates or i s contemporaneous w i t h m i n e r a l i z a t i o n , and the l a t t e r i s mainly p o s t - m i n e r a l i z a t i o n . The NW f a u l t s d i p 60 t o 80 degrees t o the northeast and the NE set appears t o be s u b v e r t i c a l . Most of the m i n e r a l i z e d veins and the dykes f o l l o w the NW f a u l t s , and i n places v e i n s are cut o f f and d i s p l a c e d by the NE s e t . The l a t e r a l displacements appear t o be small t o n e g l i g i b l e i n d r i f t s and from the mining p o i n t of view are not very important (maximum displacements of s e v e r a l f e e t have been observed). One exception i s the f a u l t recognized at the southern end of the No. 3 zone which might be r e s p o n s i b l e f o r s h i f t i n g the southern e x t e n s i o n of the v e i n t o the northeast. The new v e i n found south of the f a u l t probably c o r r e l a t e s w i t h the No. 3 zone and i s known as NG-3 v e i n . The No. 3 zone can be d i v i d e d i n t o Northern, C e n t r a l and the Southern s e c t i o n s . These d i f f e r mainly by s t r i k e d i r e c t i o n . The North zone s t r i k e s about 116° and the C e n t r a l 8 about 138° and dips approximately 59° t o 64° t o the east. For our purpose here, mainly geometric, the northern and c e n t r a l segments can be considered as one. The southern p a r t of the v e i n s t r i k e s about 93° and dips 60° e a s t e r l y . The abrupt change i n s t r i k e d i r e c t i o n , which was the ba s i s f o r d i s t i n g u i s h i n g the Southern segment, has been suggested by L e i t c h e t a l . (1990) to be caused by a zone of c r o s s f a u l t i n g . I t i s the w r i t e r ' s o p i n i o n based on v i s u a l i n s p e c t i o n of the outcrop of the v e i n as w e l l as on underground g e o l o g i c a l maps from d r i f t s , t h a t c r o s s f a u l t i n g i s not r e s p o n s i b l e f o r the abrupt change i n v e i n o r i e n t a t i o n . This problem.has s e r i o u s i m p l i c a t i o n s f o r the p h y s i c a l c o n t i n u i t y of the v e i n and consequently f o r tonnage and grade es t i m a t i o n s . Judging from the v e i n outcrop and from g e o l o g i c a l maps from 2600 l e v e l , there i s no f i r m evidence to support the presence of cross f a u l t s . The vein's sinuous character might e q u a l l y w e l l be r e s p o n s i b l e f o r the dramatic change i n s t r i k e at the south end of the No. 3 zone. Recent work by Thomson & S i n c l a i r (1991) may provide a p o s s i b l e model f o r the s t r u c t u r a l c o n t r o l of m i n e r a l i z a t i o n . Based on the presence of b r e c c i a and s t e e p l y d i p p i n g s l i c k e n s i d e s w i t h i n the f o o t w a l l , the No. 3 v e i n i s i n t e r p r e t e d as a normal, e x t e n s i o n a l f a u l t plane. F a u l t i n g i s r e l a t e d t o a process of seismic-pumping as described by Sibson (1975). P r i o r t o seismic f a i l u r e , i n c r e a s i n g t e c t o n i c shear s t r e s s r e s u l t s i n f r a c t u r i n g of the surrounding rock mass normal to the l e a s t compressive s t r e s s , inducing the m i g r a t i o n of f l u i d from the surrounding rock mass toward the f r a c t u r e s . At the 9 onset of d i l a t a n c y , the drop i n the f l u i d pressure causes a r i s e i n the f r i c t i o n a l r e s i s t a n c e t o shear along the f a u l t . The m i g r a t i n g f l u i d f i l l s the c r a c k s , the f l u i d pressure r i s e s and seismic f a i l u r e occurs when the shear s t r e s s equals the f r i c t i o n a l r e s i s t a n c e . The f l u i d i n the d i l a t e n c y zone i s e x p e l l e d upward through the f a u l t and interconnected f r a c t u r e s , d e p o s i t i n g s i l i c a and metals upon c o o l i n g . I t i s the w r i t e r ' s o p i n i o n t h a t there i s s t r u c t u r a l c o n t i n u i t y between the C e n t r a l and Southern p a r t s of the No. 3 zone. This i n t e r p r e t a t i o n i s c o n s i s t e n t w i t h the above-des c r i b e d model by Thomson & S i n c l a i r (1991) and i s i n disagreement w i t h the " c r o s s - f a u l t model" of L e i t c h et a l (1990). The No. 3 v e i n was created i n an environment where the maximum p r i n c i p a l s t r e s s was v e r t i c a l . I t appears t h a t the maximum p r i n c i p a l s t r e s s switched t o h o r i z o n t a l g i v i n g r i s e t o the c r e a t i o n of shears oblique t o the d i r e c t i o n of the v e i n . This environment was r e s p o n s i b l e f o r sudden openings along what l a t e r became No. 3 v e i n . Abrupt changes i n thickness are known t o e x i s t and are discussed l a t e r i n the chapter on s t r u c t u r a l a n a l y s i s . 10 CHAPTER I I I . THEORETICAL BACKGROUND OF RESERVE/RESOURCE ESTIMATION I I I . l INTRODUCTION Es t i m a t i o n of the d i s t r i b u t i o n of grades w i t h i n mineral deposits has been a c o n t i n u i n g problem f o r g e o l o g i s t s and mining engineers faced w i t h c r i t i c a l and c o s t l y d e c i s i o n s through the e x p l o r a t i o n and prod u c t i o n h i s t o r y of a mi n e r a l d e p o s i t . G e o s t a t i s t i c a l a n a l y s i s represents an approach to es t i m a t i o n based on a theory of r e g i o n a l i z e d v a r i a b l e s (Matheron, 1971). Though g e o s t a t i s t i c a l a n a l y s i s i s more complicated mathematically than t r a d i t i o n a l reserve e s t i m a t i o n methods (polygons, i n v e r s e distance weighting, e t c . ) , more accurate estimates and the b e t t e r understanding of fu t u r e problems t h a t r e s u l t may w e l l warrant such e f f o r t . Where c l a s s i c a l s t a t i s t i c a l a n a l y s i s assumes t h a t a v a r i a b l e (e.g. grade) i s independent from one l o c a t i o n t o the next ( i . e . d i s t r i b u t e d randomly), g e o s t a t i s t i c s i n t e r p r e t s v a r i a b l e s as " r e g i o n a l i z e d " , t h a t i s i n c o r p o r a t i n g an element of a u t o c o r r e l a t i o n t h a t t r a n s l a t e s t o a "zone of i n f l u e n c e " of a sample (David, 1977; Jou r n e l & H u i j b r e g t s , 1978). The d i s t r i b u t i o n of grades w i t h i n a depo s i t i s p a r t l y s t r u c t u r e d and p a r t l y random. I f the v a r i a b i l i t y of grades were only random, c l a s s i c a l s t a t i s t i c a l a n a l y s i s would always remain the best t o o l i n e s t i m a t i o n . Both the s t r u c t u r a l and random components of v a r i a b i l i t y can be described by a mathematical model c a l l e d the variogram, the t r a d i t i o n a l t o o l of g e o s t a t i s t i c a l a n a l y s i s . I I I . 2 Vflrlograms The g e o s t a t i s t i c a l approach to e s t i m a t i o n i s based on a p r o b a b i l i s t i c model i n which the data are viewed as the r e s u l t of some random process d e f i n e d i n space by a random f u n c t i o n . A v a i l a b l e sample values are viewed as a p a r t i c u l a r r e a l i z a t i o n of the random f u n c t i o n . In mining p r a c t i c e o n l y one r e a l i z a t i o n i s a v a i l a b l e (e.g. a l l assayed samples). To estimate the random f u n c t i o n we need s e v e r a l r e a l i z a t i o n s of the f u n c t i o n . To bypass t h i s problem the i n t r i n s i c hypothesis i s introduced, which s t a t e s t h a t the variogram f u n c t i o n 2 r ( x , h ) , which represents the v a r i a n c e of the increment (Z(x+h)-Z(x)), depends o n l y on the s e p a r a t i o n v e c t o r 'h' (modulus and d i r e c t i o n ) and not on the l o c a t i o n 'x'. Thus, E(Z(x+h)-Z(x))=0 Var(Z(x+h)-Z(x))=E((Z(x+h)-Z(x)) 2)=2r(h) where: 2T(h) - i s the t r u e variogram f u n c t i o n ; Z(x) - i s a random v a r i a b l e at p o i n t 'x'; and Z(x+h) - i s a random v a r i a b l e at p o i n t 'x+h'. The theory i s based on p o i n t support ( i . e . zero volume) f o r a v a r i a b l e , a c o n d i t i o n o n l y approximated i n nature where 12 d i s c r e t e sample s i z e i s e s s e n t i a l f o r o b t a i n i n g grade measurements. Regardless of the problem of v a r i a b l e support, the e x p e c t a t i o n at a p o i n t remains the mean value ( i . e . s t a t i o n a r i t y e x i s t s ) except i n cases where a d r i f t (trend) can be shown to e x i s t . Such a t r e n d destroys the " s t a t i o n a r i t y " and complicates g e o s t a t i s t i c a l a n a l y s i s (Myers, 1989). In p r a c t i s e o n l y a l i m i t e d data, based on v a r i a b l e supports, i s a v a i l a b l e a l l o w i n g f o r a d i s c r e t e approximation of the t h e o r e t i c a l f u n c t i o n : r*(h)=l/2n E ( z ( x ) - z ( x + h ) ) 2 where: z(x) - i s the grade at any l o c a t i o n x; z(x+h) - i s the grade at a distance 'h'; and n i s the number of sample p a i r s separated by 'h'. The e s t i m a t i o n of the t r u e variogram f u n c t i o n through the sample variogram can be crude when there i s not enough data, the data are h e t e r o s c e d a s t i c or the samples are p r e f e r e n t i a l l y c l u s t e r e d (David, 1988; S r i v a s t a v a and Parker, 1989). The covariance f u n c t i o n can be defined i n terms of gamma values as: Cov(h)=r (oo) _ r(h) where: 13 r ( o o ) - i s the s i l l l e v e l of r value beyond the range; and T(h) - i s the T value f o r d i s t a n c e 'h'. The l i t e r a t u r e i s somewhat sloppy i n usage of the terms "variogram" and "semivariogram". Here we accept the now t r a d i t i o n a l usage of "variogram" f o r one h a l f the t r u e variogram, t h a t i s f o r the T(h) f u n c t i o n . TIT..1 Relative, Variograms S t a t i o n a r i t y of the mean, one of the assumptions i n many g e o s t a t i s t i c a l a p p l i c a t i o n s , i s not s t r i c t l y t r u e over an e n t i r e d e p o s i t where mining data commonly d e f i n e r i c h and poor p a r t s . Wherever there are zones of higher grade the v a r i a n c e w i t h i n these areas i s generaly a l s o higher. Changes i n the l o c a l v a r i a b i l i t y c o n t r a d i c t the assumption t h a t the v a r i a n c e of the d i f f e r e n c e s i s independent of l o c a t i o n l e a d i n g t o the so c a l l e d p r o p o r t i o n a l e f f e c t . I t w i l l be shown t h a t t h i s p r o p o r t i o n a l e f f e c t i s present i n the S i l v e r Queen de p o s i t . I f we d i v i d e the deposit i n t o l a r g e panels or c e l l s of equal s i z e and p l o t v a r i a n c e f o r each panel versus the mean f o r each panel i t i s p o s s i b l e t o show a f u n c t i o n a l r e l a t i o n s h i p : s 2 = f(m) Once such a r e l a t i o n s h i p i s e s t a b l i s h e d a r e l a t i v e variogram i s p r e f e r r e d t o an absolute variogram, where r * r e l = r*(h)/f(m) 14 Commonly, a general r e l a t i v e variogram i s adequate, which d i r e c t l y s c a l e s the value i n each l a g by a f u n c t i o n of the mean of the sample values t h a t c o n t r i b u t e t o t h a t l a g ( S r i v a s t a v a & Parker, 1988; David, 1988). This type of r e l a t i v e variogram w i l l be analyzed i n the s t r u c t u r a l a n a l y s i s of the deposit i n question. I t i s worth n o t i n g t h a t some of the g e o s t a t i s t i c a l software packages a u t o m a t i c a l l y assume a f u n c t i o n a l r e l a t i o n s h i p between variance and mean of data as: s 2 m2 which should be viewed w i t h c a u t i o n as i t may be an o v e r s i m p l i f i c a t i o n of the t r u e f u n c t i o n a l r e l a t i o n s h i p . R e l a t i v e variograms represent a somewhat i n d i r e c t approach to s c a l i n g the absolute variograms by a f u n c t i o n of the mean, where i n f a c t i t i s the variance we should be usi n g d i r e c t l y without i n t r o d u c i n g a d d i t i o n a l e r r o r from r e g r e s s i o n ( S r i v a s t a v a and Parker, 1988). The f o l l o w i n g a n a l y s i s i s concerned w i t h a second t o o l f o r c h a r a c t e r i z i n g the a u t o c o r r e l a t i o n of a v a r i a b l e as a f u n c t i o n of 'h', i . e . the correlogram. I I I . 4 f!orrplnqrams The correlogram may be considered a r e l a t i v e variogram w i t h d i r e c t a p p l i c a t i o n of the variance as s c a l i n g f a c t o r i n s t e a d of the mean. 15 G r a p h i c a l l y , a correlogram represents the r e l a t i o n s h i p between the c o r r e l a t i o n c o e f f i c i e n t of v a r i a b l e Z(x) and a v a r i a b l e Z(x+h) separated by distance 'h' p l o t t e d versus the dist a n c e 'h'. In other words the correlogram i s the covariance f u n c t i o n s t andardized by standard d e v i a t i o n s of two v a r i a b l e s (Agterberg, 1970). Cor(h) = Cov(h)/a(x)*a(x+h) In the case of o m n i d i r e c t i o n a l correlogram or the presence of s t a t i o n a r i t y and no p r e f e r e n t i a l data c l u s t e r i n g present cr(x) and a(x+h) are eq u i v a l e n t so t h e i r product i s the variance of v a r i a b l e considered. The correlogram i s g e n e r a l l y a f u n c t i o n t h a t decreases from a maximum of one when h=0. Because the correlogram decreases w i t h i n c r e a s i n g d i s t a n c e the r e l a t i o n s h i p 1 - cor(h) w i l l be used here to show v a r i o g r a m - l i k e d i s p l a y s . In f u r t h e r a n a l y s i s when t h i s modified correlogram i s r e f e r r e d to i t w i l l represent t h i s v a r i o g r a m - l i k e r e l a t i o n s h i p . A u t o c o r r e l a t i o n f u nctions such as variograms, covariances, and correlograms are not r e s i s t a n t t o o u t l i e r s ; furthermore, they don't provide enough informa t i o n f o r a complete d i s t r i b u t i o n (Krige and Magri, 1982). They are appropriate f o r the e s t i m a t i o n of the mean value. The e s t i m a t i o n of the d i s t r i b u t i o n can be accomplished by c a l c u l a t i n g the p r o p o r t i o n of values above or below a c e r t a i n c u t - o f f . The implementation of the c u t - o f f as a d e l i m i t e r t o what i s waste and what i s not, i s very appealing t o a mining engineer. The t o o l which helps to assess the d i s t r i b u t i o n s i s the i n d i c a t o r variogram. 16 TTT.5 T n r i i c a t o r VariograniR I n d i v i d u a l grade values from a continuous d i s t r i b u t i o n f u n c t i o n can be transformed t o an i n d i c a t o r v a r i a b l e (1 or 0) r e l a t i v e t o an a r b i t r a r i l y d e f i n e d c u t - o f f v a l ue z c as fol l o w s ( J o u r n e l , 1983): I ( z ( x ) / z c ) = l when z(x)<cut o f f grade z c and l ( z ( x ) , z c ) = 0 when z(x)>cut o f f grade z c Experimental variograms can be computed and modelled on t h i s new i n d i c a t o r v a r i a b l e I ( z ( x ) , z c ) , and t h e i r shape w i l l be determined by the c u t - o f f grade z c chosen.Although t h i s type of a n a l y s i s r e q u i r e s the assumption of s t a t i o n a r i t y , i t i s very robust; the presence of " o u t l i e r s " does not a f f e c t a u t o c o r r e l a t i o n f u n c t i o n as much as i t does f o r variograms. Further, i t does not concern i t s e l f w i t h d e f i n i n g the d i s t r i b u t i o n of values which i s addressed i n some g e o s t a t i s t i c a l methods l i k e lognormal or d i s j u n c t i v e k r i g i n g . TTT.fi KRTKTNtt K r i g i n g i s a l o c a l e s t i m a t i o n technique which provides the best l i n e a r unbiased e s t i m a t o r of a v a r i a b l e . I t i s "best" because i t i s c a l c u l a t e d i n such a way to ensure a minimum e s t i m a t i o n v a r i a n c e (Matheron, 1963). The experimental data used c o n s i s t of a set of d i s c r e t e measurements. The es t i m a t o r Zk* i s a l i n e a r combination of the n data v a l u e s : 17 Zk* = (Elambdai*Zi) The weights are c a l c u l a t e d t o ensure t h a t the e s t i m a t o r i s unbiased and t h a t the e s t i m a t i o n variance i s minimal by s o l v i n g the k r i g i n g system: Slambda )3*C(v a /v i8) — yi = C(v a,v) Elambdap = 1 where: }i - Lagrange m u l t i p l i e r lambda^ - weights (optimal) C(va,v£) - average covariance between the data i n neighborhood C ( v a / v ) - average covariance between data and unknown value being estimated The minimum e s t i m a t i o n v a r i a n c e , known as the k r i g i n g v a r i a n c e , can a l s o be c a l c u l a t e d from the formula: o^kj- = o 2 v - Slambda a * C(v a,v) - pi where: a 2 v - var i a n c e of v a r i a b l e s t u d i e d dependent on support of sample I f the k r i g i n g technique uses i n d i c a t o r variograms (see s e c t i o n I I I . 5 ) the estimated value of I ( z ( x ) , z c ) represents p r o b a b i l i t y t h a t unknown z(x) i s smaller than or equal t o the chosen c u t - o f f , c o n d i t i o n e d by data i n the neighborhood: I ( z ( x ) , z c ) = P r o b ( z ( x ) < z c / s u r r o u n d i n g d a t a ) . I f we c o n s i d e r an area, r a t h e r than a p o i n t value then the estimated p r o p o r t i o n of grades z ( x ) < z c i n area A i s a f u n c t i o n : 18 $( A , z c ) = Z l a m b d a a * I ( z ( x a ) , z c ) where: lambda a - optimized weight c a l c u l a t e d by o r d i n a r y k r i g i n g method This f u n c t i o n can be c a l c u l a t e d p r o v i d i n g the i n d i c a t o r variogram models of I ( z ( x ) , z c ) f o r d i f f e r e n t c u t - o f f s z C / can be determined ( J o u r n e l , 1983). The k r i g e d estimates can be i n t e r p r e t e d as the e s t i m a t i o n of v a r i o u s q u a n t i l e s of the l o c a l cumulative d i s t r i b u t i o n f u n c t i o n c o n d i t i o n e d on the data i n the neighborhood. A s i n g l e estimated value i s the p r o p o r t i o n of data i n an area, equal t o or l e s s than the c u t - o f f grade f o r which i t was c a l c u l a t e d . In common w i t h t r a d i t i o n a l parametric s t a t i s t i c s i t i s o f t e n assumed f o r g e o s t a t i s t i c a l treatment t h a t the data are normally d i s t r i b u t e d or can be transformed t o a normal d i s t r i b u t i o n . Under the assumption of no r m a l i t y o r d i n a r y k r i g i n g provides an optimal estimator of an unknown value and the k r i g i n g v ariance can be used as a parameter of the e r r o r d i s t r i b u t i o n . That i s , the e r r o r Z(x)-Zk* i s assumed t o be normally d i s t r i b u t e d and, i t s d i s t r i b u t i o n i s f u l l y c h a r a c t e r i z e d by i t s mean (zero i f the estimates are unbiased) and i t s v a r i a n c e . For non-Gaussian d i s t r i b u t i o n s , a common case i n mining, the k r i g i n g variance provides a mere ranking of data c o n f i g u r a t i o n . Furthermore i t i s not the d i s t r i b u t i o n of e r r o r Z(x)-Z] c* which i s important but ra t h e r the c o n d i t i o n a l d i s t r i b u t i o n of the e r r o r given the data values used f o r e s t i m a t i o n at the p a r t i c u l a r l o c a t i o n x. The variance of t h i s c o n d i t i o n a l d i s t r i b u t i o n i s l i k e l y t o be 19 h e t e r o s c e d a s t i c t h a t i s dependent on data values (A. J o u r n e l , 1986). In t h i s paper ( S e c t i o n IX.2), the attempt w i l l be made to show t h a t u s i n g the k r i g i n g variance may not provide the best answer t o the problem of how mistaken one might be i n the assessment of average grades. I I I . 7 SUPPORT OF DATA VALUES Experimental variograms must be cons t r u c t e d u s i n g a d d i t i v e v a r i a b l e s ( J o u r n e l and H u i j b r e g t s , 1978). A grade expressed i n g/t i s an a d d i t i v e v a r i a b l e as long as i t i s de f i n e d on a constant support(sample s i z e ) . The theory of r e g i o n a l i z e d v a r i a b l e s assumes the p o i n t data being a v a i l a b l e . In p r a c t i c e the data are d e f i n e d on a c e r t a i n support (volume), so i n f a c t , we r e a l l y c a l c u l a t e r e g u l a r i z e d variograms. D r a m a t i c a l l y d i f f e r e n t supports can generate very d i f f e r e n t variograms f o r the same v a r i a b l e . I f the support i s small w i t h respect t o the domain analyzed(e.g. d r i l l core) the r e g u l a r i z e d variogram can be assumed t o approximate a p o i n t variogram. I I I . 8 VOT.TTMR - VARIANCE RETiATTONSHTP I t has been w i d e l y recognized t h a t the d i s t r i b u t i o n of grades of core samples i s d i f f e r e n t than the d i s t r i b u t i o n of grades of mining u n i t s on which s e l e c t i o n i s made (e.g. Parker, 1979). I f the d i s t r i b u t i o n of p o i n t ( d r i l l core) samples has experimental mean m; d i s p e r s i o n v a r i a n c e a 2(p,A) (Journel and H u i j b r e g t s , 1978); a c e r t a i n shape, f o r example asymmetric; then d i s t r i b u t i o n of s e l e c t i v e mining u n i t s i s considered t o have: mean equal t o the mean of po i n t samples m v = m d i s p e r s i o n v a r i a n c e a 2(v,A)<a 2(p,A) a d i f f e r e n t shape, more symmetric than t h a t of the po i n t s ( L a n t u e j o u l , 1988). To be able t o estimate recovered tonnage and q u a n t i t y of metal, the d i s t r i b u t i o n of small mining u n i t s should be assessed. D i s p e r s i o n v a r i a n c e a 2(v,A) can be estimated from formula (Journel and H u i j b r e g t s , 1978): a 2 (v,A)=Cov(v,v) -Cov(A,A) where: Cov(v,v) - average covariance between p o i n t s w i t h i n block v; Cov(A,A) - average covariance between p o i n t s i n the area of i n t e r e s t I f the area of i n t e r e s t i s l a r g e w i t h respect t o the range of experimental variogram, Cov(A,A)=0 and 21 a 2(v,A)=Cov(v,v)=l/v 2 Cov(x-y)dxdy So, as long as the u n d e r l y i n g covariance i s known, and i n our case i t can be c a l c u l a t e d from the variogram model chosen, the block va r i a n c e can be estimated. The two moments, mean and v a r i a n c e , are u n f o r t u n a t e l y not enough to des c r i b e the d i s t r i b u t i o n f u l l y . I t can be shown t h a t s t o c h a s t i c processes which have the same p o i n t d i s t r i b u t i o n and the same covariance f u n c t i o n can have completely d i f f e r e n t behaviour as the support increases ( L a n t u e j o u l , 1988). To overcome t h i s problem change-of-support models have to be added. The most w i d e l y used are a f f i n e c o r r e c t i o n and i n d i r e c t lognormal c o r r e c t i o n models (Isaaks and S r i v a s t a v a , 1989). The a f f i n e c o r r e c t i o n model assumes the p r e s e r v a t i o n of the d i s t r i b u t i o n shape on the assumption t h a t (Buxton, 1985): Based on t h a t , ore tonnage (T) and metal q u a n t i t y (Q) can be d e r i v e d : (Z(v)-m)/a v = (Z(x)-m)/a (1.7) T v ( z c ) = T ( y ) where: c u t - o f f grade chosen; y c u t - o f f grade f o r p o i n t support d i s t r i b u t i o n c a l c u l a t e d from formula (1.7); d e n s i t y f u n c t i o n of p o i n t support 22 T 0 - tonnage f o r c u t - o f f grade y=0 r Qv(Zc)=T(T z X ' f ( z X ) d z x From formula (1.7), i t appears t h a t the model i s a p p l i c a b l e o n l y f o r c u t - o f f z c >= m * ( l - a v / a ) . Otherwise c u t - o f f grade y becomes negative. Whenever sample grade d i s t r i b u t i o n has a spike at the o r i g i n c u t - o f f grade z c may be too small t o show the above r e l a t i o n s h i p . I f l a r g e supports are considered t h i s model does not appear to be proper because of the a r t i f i c i a l minimum which may not be r e a l i s t i c and because of l a c k of symmetrization (not compatible w i t h c e n t r a l l i m i t theorem). An example i s provided by Giroux and S i n c l a i r (19 ). f o r the E q u i t y S i l v e r Mines Deposit. I n d i r e c t lognormal c o r r e c t i o n model i n t u r n preserves skewness, and allows convergence t o n o r m a l i t y f o r l a r g e supports. In order t o estimate d i s t r i b u t i o n of block v a l u e s , p o i n t data are transformed by the formula (Isaaks and S r i v a s t a v a , 1989): CV - c o e f f i c i e n t of v a r i a t i o n ; f=a 2(v,A)/a 2(p,A) - v a r i a n c e adjustment f a c t o r . In our case study the variance adjustment f a c t o r i s small enough to suggest l a r g e r e d u c t i o n i n v a r i a n c e , and because of t h i s the a f f i n e c o r r e c t i o n model i s considered as i n a p p r o p r i a t e . where: b = V l n ( f • C V 2 + l ) / l n ( C V 2 + l ) a = m/Vf.CV 2+l (V(CV 2+l)/m) b (1.7a) (1.7b) Large r e d u c t i o n i n variance i s always present i n cases where s h o r t - s c a l e v a r i a b l i t y , represented by high nugget e f f e c t on a variogram, of considered assay values i s l a r g e . A histogram of transformed data values can be used to estimate tonnage and q u a n t i t y of metal above a c e r t a i n c u t - o f f . To a r r i v e at the f i n a l estimate two approaches can be considered: 1. Based on t h e o r e t i c a l d i s t r i b u t i o n e.g. normal or lognormal, recovery f u n c t i o n s can be c a l c u l a t e d . 2. Density f u n c t i o n f ( z ) can be given through a d i s c r e t e form of a histogram: T ( z 0 ) = T 0 - j ' f ( Z ) d z = T 0 - S f ( z ) Zc In the case analysed i n t h i s paper S f ( z ) represents p r o p o r t i o n of blocks above the c u t - o f f weighted by the average thickness of blocks above c u t - o f f : Sf(z)=Nbi(ZQ)»AvThick(ZQ)/Nfc,l(ZQ=0)«AvThick(ZQ=0) Metal q u a n t i t y i n the d i s c r e t e case i s c a l c u l a t e d as: Q(ZQ)=TQ» j z*f(z)dz=To»Sz»f(Z) Because the volume of blocks which w i l l be considered i s not constant due t o v a r y i n g t h i c k n e s s , Q(ZQ)=TQ »Sz« f ( z ) • A v t h i c k ( Z Q ) / A v t h i c k ( zrj=0) and Q(zo)=Qo/ m Sz»Nbi(z0)•Avthick(z0)/(Avthick(z0=0)•Nbl(zo=0)) 24 based on t h i s : Q(zo)=Qo-Sacc(z 0)«N b l(z 0)/(acc(zo)»N b l(z 0=0)) Thus u s i n g a histogram of metal accumulations of cor r e c t e d 'block' data, q u a n t i t y of metal co n d i t i o n e d on chosen c u t - o f f can be c a l c u l a t e d . Based on the above, volume-variance r e l a t i o n s h i p and i t s i n f l u e n c e on f i n a l reserve e s t i m a t i o n w i l l be s t u d i e d i n Chapter X I . 25 CHAPTER IV DATA TV.1 INTRODUCTION Three a v a i l a b l e data sets are a v a i l a b l e from the products of c l o s e t o twenty years of e x p l o r a t i o n of the v e i n : - 1) surf a c e d r i l l holes w i t h logs and assays, s i z e AQ, BQ, NQ; - 2) underground d r i l l holes w i t h logs and assays, s i z e AQ, BQ; and - 3) d r i f t c h i p samples w i t h assays and l i m i t e d g e o l o g i c a l maps. D r i f t assays f o r f i v e metals were entered from two s e c t i o n s of the 2600 l e v e l d r i f t ; 1400 f t and 550 f t long separated by a di s t a n c e of 500 f t (see F i g . IV.1). In a d d i t i o n 89 readings of the v e i n t h i c k n e s s based on v i s u a l r e p r e s e n t a t i o n were taken by the author i n the l i m i t e d area i n the v i c i n i t y of 27600-28000 s e c t i o n . A t o t a l of 169 d r i l l holes ( 49 d r i l l e d from surface) are in c l u d e d i n the a n a l y s i s . Of these 113 are from the C e n t r a l s e c t i o n of the v e i n (three of the d r i l l holes from 1974 where not i n c l u d e d i n the s t r u c t u r a l a n a l y s i s ) , and the remainder are from the southern s e c t i o n of the v e i n , ( F i g . IV.1). Although d r i f t assays ( t o t a l 365) were not taken i n t o account when reserve estimates were c a l c u l a t e d they were i n c l u d e d i n the a n a l y s i s of s p a t i a l d i s t r i b u t i o n of thickness and accumulations. No i n f o r m a t i o n on sampling and assaying procedures and p r e c i s i o n of data values i s a v a i l a b l e (W. Cummings, 1991, person a l communications) 26 FT. 0.0 200.0 Scale. I : 2400 400.0 F i g . IV.1 L o n g i t u d i n a l s e c t i o n , C e n t r a l p a r t of No. 3 v e i n , showing d r i l l hole i n t e r s e p t s . D r i l l numbers are coded as S or U (surface or underground), year d r i l l e d and a s e q u e n t i a l d r i l l i n g number. Lines A-A', B-B' on 2600 l e v e l r e f e r t o l o c a t i o n s of d r i f t samples used i n the study. 26A o o in 00 CM o o o O) CM O CM I to CO (M e S88j031© S73-BSH9 I \ 6 e l e s ya -B s i s o " 7 2 -™ ' 3 S88-032 SURFACE e S74-001 \ © U87-008 TZZZZTotZZZL \ _ U87-008 © U81-013 0 , U81-0& U81-015 U87-007 © U87-009 © U81-027 ©I " © © S73-$W30 y////y>y>///// /. PI L L DRIFT e 1)87-022 © % © U81-019 SAMPLES Q U81-021 B' o '-018 0 U87-O05 0 U87-006 U81-026 U81-020 © I A PU -Q U88-051 \ L A S K I T E ^ ® . DYKE U8H>24--_? §4-003 U88-052 © U88-t§66 U88-065 © U88-073 Q S88-057 © Q U89-001 S88-058 © U89-005 © © U89-003 U8S"008 0 U89-004 0 U88-071 069 U88-070 e 0 U88-072 U88-075 © U88-074 © U89-007 3 0 0 0 L E V E L O G U87-fl»-003 © U87-012 0 U87-010 © U87-013 2500 L E V E L 0 U87-014 2 0 0 0 L E V E L 0.0 200.0 Scale : I : 2400 FT. 400.0 F i g . IV.1 L o n g i t u d i n a l s e c t i o n , Southern p a r t of No 3 v e i n , see legend on l o n g i t u d i n a l s e c t i o n Centra? par^ F i g . IV.2 Structural contour map of the No. 3 zone (C. Leitc h , 1990, personal communications), HW=hangingwall, FW=footwall, numbers such as #3 2280' r e f e r to l e v e l 2880 f t of the No. 3 structure, mine coordinates are given by northings and eastings i n feet (recent exploration g r i d 1988-1989). Q S88-044 e S88-045 1° S73-BS168 Q e S88-042 S73-BS169 e S73-BS166 e S73-BS162 Q 0 U«8-02i88-054 e U88-0S7 0 U88-053 0 U88-0S9 e 0 IU88-058 U88-055 O J U88-06; 0 S72-NGV5 0 O 0 S73-BS154 C E N T R A L S73-BS167 0 S73-0 S88-043 -040 O S88-041 © U88-033 0 S88-039 0 3 0 1^88-034 UB8-061 060 0 U88-063 0 U88-035 O U88-056 0 . 0 0 U88-064 O U81-008 0 U81-007 Scale : I : 2400 2 0 0 . 0 S O U T H 0 S73-B156 S88-036 0 S88-037 0 S73-0 0 S88-035 0 S73-BS149 O S73 .. S88-I el U73-BU191 150 O U72-BU013 0 UtU6J09 U81-001 m - 0 0 4 0 — U81-016 O 0 U81-013 U81-012 O — O U87-008 e U87-007 o U87-00© U8I-027 3 0 0 0 L E V E L 0 S74-001 © Q S 7 3 _^|4030 0 U87-022 0 0 0 U87-MB- 018 0 U8/-0OJ 0 U81-019 O U81-021 0 I U87-006 a 5 0 0 L E V E L 0 ^ 0 U81-003 0 U81-005 0 U81-006 0 U81-011 0 U81-010 U81-g4 U81-015 I O U81-025 0 U88-047 Q U88-050 U88|051 O 0 U81-026 U81-020 0 U81-023 0 U81-024 0 gS74-003 U88-052 0 U88-049 0 U88-048 e U88-065 -069 0 U88-071 0 U88-073 0 S88-057 0 01 U89-001 S88-0S8 0 U89-005 0 0 U89-003 m ~ m 0 U89-004 0 U89-007 O U88-076 0 S74-002 0 58-068 © U88-067 FT. U88-0/0 g O U88-0/2 U88-075 0 U88-074 DDH from South used for r e se r ve estimation of Centra l section 4 0 0 . 0 Fig. IV.3 Longitudinal section, position of DDH after transformation of Southern part of the vein. oo 29 The attitude of d r i l l holes varies, r a i s i n g the question of true thickness of the vein. True thickness of the vein was calculated by assuming an average "uniform" s t r i k e d i r e c t i o n and average dip separately for both the Central and Southern segments. In the Central part the average attitude of the vein was taken as 138°/64°NE and i n the Southern part the attitude was assumed to be 093°/60°N. Vein thickness was determined on the basis of d r i l l hole attitude and the average vein attitude i n segments of the vein. The fact that a number of d r i l l holes were not d r i l l e d perpendicularly to the s t r i k e d i r e c t i o n was recognized. For some purposes (variogram modelling, contour maps on longitudinal projection) i t was adventageous to have the two vein segments rotated into a common plane. The plane chosen has the attitude of the Central section. A f t e r the rotation of Southern section around l i n e 60° N48°E i n section 28320 and further r o t a t i o n of 200 within the plane, horizontal distances between the assays from two sections are larger than i n r e a l i t y (see F i g . IV.1 vector 'a'). In order to calculate a variogram these distances should represent approximately the true distances between the pairs of values considered. This w i l l be achieved by tr a n s l a t i o n of coordinates of vein assays from southern zone towards the cen t r a l zone by vector: a = EL x tan 20° (Fig- IV.1) where: 30 EL - represents d i f f e r e n c e between the e l e v a t i o n of S88-031 and t r a n s l a t e d p o i n t . By those means, the h o r i z o n t a l distances between the points from two d i f f e r e n t planes w i l l represent approximately t r u e d i s t a n c e s measured. The drawback of such t r a n s l a t i o n i s t h a t r e l a t i v e v e r t i c a l p o s i t i o n s and distances between the assays i n the southern s e c t i o n are changed. This f a c t may be the reason f o r q u e s t i o n i n g the v a l i d i t y of variograms c a l c u l a t e d on such a data s e t . I t was f e l t t h a t i t was more important t o preserve the h o r i z o n t a l d i r e c t i o n , predominant d i r e c t i o n along which the variograms were c a l c u l a t e d . Furthermore, as i t appears i n our case study, the c o n t i n u i t y can be e s t a b l i s h e d o n l y at distances l e s s then 200 f t , there are no a n i s o t r o p i e s present, and the nugget e f f e c t f o r a l l v a r i a b l e s considered i s high. For t h a t reason even from the e s t i m a t i o n p o i n t of view (po i n t k r i g i n g ) , the e f f e c t on estimates w i l l be n e g l i g i b l e . Figure IV.3 shows the d r i l l holes a f t e r t r a n s l a t i o n . IV. 2, WAS TP. ASSUMPTIONS Eleven of the d r i l l h o l e s , marked w i t h t h i c k n e s s 0.01 (see Appendix I , I V ) , a v a i l a b l e t o us apparently d i d not i n t e r s e c t a v e i n . The most r e l i a b l e t o o l f o r a s s i g n i n g the l i m i t s of the v e i n i s the tenor of m i n e r a l i z a t i o n as measured by assay composites, e s p e c i a l l y Au and Ag assays (C. L e i t c h , personal communications, 1990). Other i n d i c a t o r s of the v e i n are a l t e r a t i o n (always present i n the v i c i n i t y of the v e i n ) , m i n e r a l i z a t i o n , and presence of shearing. There are some cases where the v e i n has been d e l i m i t e d , but assays are recorded across greater i n t e r v a l s . In such cases o n l y the v e i n t h i c k n e s s i s used f o r reserve e s t i m a t i o n and the assay values are ignored because they underestimate the v e i n m i n e r a l i z a t i o n . I f there are two veins very c l o s e t o each other, they are considered as one v e i n and assay values are not d i l u t e d by the i n t e r v e n i n g barren s e c t i o n ; the barren s e c t i o n i s taken i n t o account when a mining approach i s considered. I f there are two or three w i d e l y separated veins recognized, o n l y one of them has been i n t e r p r e t e d as the main No. 3 v e i n based on tenor of m i n e r a l i z a t i o n , a l t e r a t i o n and v e i n t h i c k n e s s . In a few d r i l l holes where the v e i n was not recognized, t h i c k n e s s was recorded as 0.01 at the p o s i t i o n determined by e x t r a p o l a t i o n from nearby d r i l l h oles. Appendix I describes i n d e t a i l d r i l l hole i n t e r s e c t i o n s which were assigned as v e i n subject t o the foregoing q u a l i f i c a t i o n s . At present the en echelon c h a r a c t e r of the v e i n i s not proven, nor i s there enough i n f o r m a t i o n t o def i n e a p h y s i c a l en echelon model t h a t could be inc o r p o r a t e d i n t o the reserve/resource model. Consequently we assume t h a t the No. 3 s t r u c t u r e c o n t a i n s planar v e i n , reducing our problem t o a two-dimensional reserve/resource e s t i m a t i o n procedure. 32 CHAPTER V METHODOLOGY AND DATA EVALUATION V.I INTRODUCTION S t a t i s t i c a l a n a l y s i s of a v a i l a b l e data p l a y s an important r o l e i n as s e s s i n g p o t e n t i a l problems d u r i n g the course of reserve/resource e s t i m a t i o n and i n a s s i s t i n g i n the choice of the g e o s t a t i s t i c a l procedure. A p r e l i m i n a r y data a n a l y s i s w i l l examine the form of cumulative d i s t r i b u t i o n and the p o s s i b i l i t y of trends i n the data. This w i l l be fo l l o w e d by a d e t a i l e d s t r u c t u r a l a n a l y s i s t o c h a r a c t e r i z e each v a r i a b l e i n terms of an appropriate a u t o c o r r e l a t i o n f u n c t i o n . At the e a r l y stages of an a n a l y s i s the C e n t r a l and Southern segments of the No. 3 zone w i l l be analysed s e p a r a t e l y . Where appro p r i a t e , the two data sets w i l l be t r e a t e d as one. A u t o c o r r e l a t i o n f u n c t i o n (model) w i l l be used i n k r i g i n g and other e s t i m a t i o n processes to develop estimates of g l o b a l reserves i n areas of p o t e n t i a l mining. This w i l l n e c e s s a r i l y i n c l u d e e s t i m a t i o n of the mean grade and mean thic k n e s s of i n d i v i d u a l mining blocks chosen (block k r i g i n g ) . Once.the i n s i t u and minable reserves are e s t a b l i s h e d , the volume-variance r e l a t i o n s h i p w i l l be stu d i e d i n order t o analyze the s e n s i t i v i t y of s i z e of s e l e c t i o n mining u n i t s on the estimates. The second p a r t of the a n a l y s i s w i l l concern i t s e l f w i t h mining r e s e r v e s . I t w i l l be assumed t h a t the minimum stope width i s 4.0 f t . I f the v e i n i s narrower than 4.0 f t , the composite d i l u t e d assay w i l l be c a l c u l a t e d . The mining reserves 33 w i l l be c a l c u l a t e d based on g e o s t a t i s t i c a l models deri v e d from d i l u t e d data. These models may not n e c e s s a r i l y be d i f f e r e n t from those chosen e a r l i e r . V.2.1 R y p l n r a t i n n d r i l l holps Estimates of v e i n t h i c k n e s s are a v a i l a b l e from 106 d r i l l holes c u t t i n g the C e n t r a l segment of the No. 3 zone, and 49 values from the Southern segment. Eleven cases of d r i l l holes where v e i n m a t e r i a l was not recorded are not i n c l u d e d i n the s t a t i s t i c a l a n a l y s i s . I t was f e l t t h a t they would unduly lower the average v e i n t h i c k n e s s . Seven of them are coming from the boundaries of the v e i n . Furthermore, i t was f e l t t h a t zero values are not p a r t of the p o p u l a t i o n whose v a r i a n c e and c o n t i n u i t y i s of i n t e r e s t t o us. S t a t i s t i c s of v e i n t h i c k n e s s are compared f o r the two data s e t s : d r i l l hole and d r i f t data. The p o s s i b l e causes f o r variance d i f f e r e n c e are analyzed. Further, d i s t r i b u t i o n of grades i n the neighborhood of the v e i n as w e l l as comparison between the hangingwall, f o o t w a l l , and v e i n assays w i l l be done i n order t o a s s i s t w i t h estimates of the q u a n t i t y of metal i n w a l l r o c k . The histogram of t h i c k n e s s f o r the C e n t r a l s e c t i o n ( F i g . V . l ) c l e a r l y shows a skewed d i s t r i b u t i o n w i t h a mean of 4.48 f t . A p l o t of the cumulative d i s t r i b u t i o n ( F i g . V.2) shows a p a t t e r n reminiscent of a mixture of two or more subpopulations 34 each of which could be normal ( S i n c l a i r , 1976). I f we assume t h a t the upper s i x values ( t h i c k n e s s > l l . 0 f t ) represent a unique p o p u l a t i o n (these l a r g e values do not appear t o be c o r r e l a t e d w i t h a s p e c i f i c rock type and are assumed t o be v a l i d ) then the remainder can be viewed as a mixture of two normal p o p u l a t i o n s , s l i g h t l y o verlapping w i t h means 1.7 f t and 5.8 f t (see Appendix I I ) . N h 1 8 -1 5 -12-9 -6 -N Min Max Mean Variance Standard dev. Coef. variat ion Med I st Q 3 r d Q - 106 - 0.33 - 1439 - 4.48 - 11.03 - 3.32 - 75.0 - 3.42 - 1.92 - 6.41 Jirfl. 0.0 Fig. V.I 3.5 7.0 10.5 I4J0 THICK Distribution of vein thickness (ft.) Central 16 .0 H 15.0 -12.0 -9 . 0 -6 J0 3 .0 -OJO 0 . Fig. V.2 X -I—I I -I— I 1 2 5 10 2 0 3 0 4 0 5 0 6 0 7 0 6 0 9 0 9 3 9 8 9 9 99.9 Cumulative distribution of vein thickness (ft) - Central -i—r —i—i—r—i—i—i i i i 0 S O  S O 0 TO 9 0  5 6  T The histogram of t h i c k n e s s i n the Southern zone (Fig.V.3) s i m i l a r l y shows th a t these data cannot be considered as a s i n g l e normal d i s t r i b u t i o n . The cumulative d i s t r i b u t i o n (Fig.V.4) suggests again the p o s s i b i l i t y of a mixture of subpopulations. 35 I f we exclude one extreme value the two normal populations d e r i v e d have the means 1.7 f t and 4.8 f t . N 12-10-8 -6 -« -2 -N Min Max Meon Variance S tandard dev. Coet. var iat ion Med I st Q 3 rd Q r-1 aO 2 . 5 5 .0 7.5 THICK 49 0.24 8.85 2.77 3.57 1.90 68.2 2.13 1.24 3.73 Fig.V.3 Distribution of vein thickness (ft.) - South I O A -8 . 0 -6.0 -4 J 0 -2XJ-OJO- I 0.1 Fig. V.4 1 2 5 10 Cumulative j I i i 3 — i — i — i — n — i — i 1 — i 1—r— 2 0 9 0 4 0 5 0 8 0 7 0 8 0 9 0 9 5 9 8 9 9 99.9 distribution of vetn thickness (ft.) - South The two normal populations from both s e c t i o n s do not appear t o be present i n two d i f f e r e n t rock types. I t i s i n t e r e s t i n g to note t h a t the narrow t h i c k n e s s populations from the C e n t r a l and Southern s e c t i o n s have the same mean and comparable standard d e v i a t i o n s (see Appendix I I ) , sugesting t h a t they may represent the same p o p u l a t i o n and t h e r e f o r e the same process of development. A rig o r o u s d i s c u s s i o n of the p o s s i b l e processes r e s u l t i n g i n t h i s s i m i l a r i t y i s beyond the scope of t h i s t h e s i s . 36 V.2.2 Underground workings In order t o b e t t e r describe the v a r i a b i l i t y of t h i c k n e s s , data from an a d d i t i o n a l 365 sample s i t e s from the 2600 l e v e l d r i f t were evaluated (see F i g . IV.1) . The assays were taken from assay plans drawn i n the e a r l y seventies during e x p l o r a t i o n by Bradina J o i n t Venture. I t was assumed t h a t the samples describe approximately t r u e thickness of the v e i n . This assumption i s based on the s i m i l a r i t y of th i c k n e s s w i t h readings taken by the author from the same area. S t a t i s t i c a l a n a l y s i s of the data ( F i g . V.5) revealed t h a t the v a r i a n c e of th i c k n e s s i n the d r i f t i s much lower than the variance of the same v a r i a b l e from d r i l l h o l e s , and tha t the d i f f e r e n c e i n v a r i a n c e c o u l d not be expl a i n e d w i t h the p r o p o r t i o n a l e f f e c t (see Chapter V I ) . Further a n a l y s i s w i l l attempt t o show t h a t f o r c e r t a i n subsets of data the sample s t a t i s t c s of thic k n e s s measured i n the d r i f t are comparable t o the sample s t a t i s t i c s of thickness measured from d r i l l h oles. Although i n f a c t we are d e a l i n g w i t h two d i f f e r e n t data s e t s , the s i m i l a r i t i e s when e s t a b l i s h e d w i l l a l l o w us t o use the two data sets t o model experimental variogram f u n c t i o n . P o s s i b l e e x p l a n a t i o n f o r the d i f f e r e n c e i n variance i n c l u d e : we have introduced v a r i a b i l i t y i n t o the e x p l o r a t i o n data because of the n e c e s s i t y of i n t e r p r e t i n g v e i n thickness from d r i l l and assay records; 37 N I 66-5 5 -4 4 3 3 2 2 Fig 0 . 0 2.5 . V.5 N - 3 6 5 Min - 0.40 Max - 13.0 Mean - 4.15 Variance - 3.47 Standard dev - 1.86 Coef. var iat ion - 44.9 Med - 4.0 I st Q - 2.70 3 rd Q - 5.60 0 - ~i— 5.0 7.5 10.0 Distribution 12.5 of THICK vein thickness (ft.) Drift * 0 . 9 5 dr i f tq 4 5 6 7 Fig. V.6 Quantiles of thickness from drill hole vs. drift data N 1 0 -8-6 4 -2 -0 N - 79 Min - 1.8 Max - 5.90 Meon - 3.40 Variance - 1.24 Standard dev. - M l Coef. var iat ion - 32.7 Med - 3.29 1 st Q - 2.34 3 rd Q - 4.20 -THICK 1.8 2 . 8 3.8 4 .8 5.8 Fig.V.7 Distribution of vein thickness subset 1.8 - 5.9 ft. 4 9 -4 2 -3 5 -2 8 • 21 -14 • 7 4 1.8 Fig.V.8 N M i n Max Mean Variance Standard dev. Coef. var iat ion Med st rd 2 .8 3.8 4 . 8 5.8 Distribution THICK 259 1.8 5.90 3.58 1.18 1.08 30.6 3.50 2.70 4 .50 of vein thickness in drift.subset 1.8-5.9 ft. 38 we may, i n a d v e r t e n t l y , have introduced v a r i a b i l i t y i n t o our data through our e f f o r t s t o c a l c u l a t e t r u e t h i c k n e s s from i n t e r p r e t e d d r i l l hole i n t e r s e c t i o n s ; g r eater v a r i a b i l i t y of t h i c k n e s s f o r e l e v a t i o n s below the 2600 l e v e l , where most of the d r i l l holes were known to have been d r i l l e d ; g r e ater v a r i a b i l i t y down d i p (where the d r i l l hole data predominate) than along the s t r i k e d i r e c t i o n due t o the f a u l t i n g mechanism; and d i f f e r e n t i n t e r p r e t a t i o n of the v e i n i n the d r i l l hole data and the d r i f t data s e t , where samples were taken w i t h a mining p o i n t of view, and o f t e n l i m i t e d t o the width of the d r i f t . The author b e l i e v e s t h a t the f i n a l e x p l a n a t i o n above i s most c o n s i s t e n t w i t h the a v a i l a b l e data. I f we p l o t t h i c k n e s s corresponding to a p a r t i c u l a r q u a n t i l e f o r one data s e t , versus the t h i c k n e s s f o r the same q u a n t i l e of the second data s e t , and repeat t h i s procedure f o r v a r i o u s q u a n t i l e s , we generate a s e r i e s of p o i n t s t h a t p l o t along the x=y l i n e i f the two d i s t r i b u t i o n s are i d e n t i c a l . I n creasing departure from the x=y l i n e i n d i c a t e s i n c r e a s i n g d i f f e r e n c e s i n the two p o p u l a t i o n s . In our case the underground and d r i l l hole data correspond reasonably w e l l i n the range 1.8-5.9 f t but d i f f e r d r a m a t i c a l l y on the t a i l s ( F i g . V.6). Further, i f we c a l c u l a t e histograms of the 1.8-5.9 f t subset of the data f o r both d r i l l hole and d r i f t v a l u e s , we n o t i c e t h a t sample s t a t i s t i c s are very s i m i l a r w i t h c o e f f i c i e n t s of v a r i a t i o n 32.7 and 30.6 f o r DDH and d r i f t data r e s p e c t i v e l y 39 ( F i g . V.7, V.8). The other s t a t i s t i c s i n the two subsets are al s o comparable which can be checked by c l a s s i c a l F and t t e s t s . These t e s t s , i t i s assumed, can be used i f the domain stud i e d represents the s i z e much l a r g e r than the d i s t a n c e at which c e r t a i n c o n t i n u i t y of v a r i a b l e s can be shown. The d i f f e r e n c e s between the two data s e t s are evident o n l y f o r the low values (below 1.8 f t ) and f o r the high values (above 5.9 f t ) . The l a c k of low values f o r d r i f t data i s understandable since only widths g r e a t e r than 1.8 f t were considered minable. As f o r the high v a l u e s , these were chopped wherever the v e i n thickness was g r e a t e r than the width of the d r i f t and only on rar e occasions was i t d i f f e r e n t ( F i g . V.9). F u r t h e r , the average width of the d r i f t i s approximately 6.4 f t supporting the upper l i m i t found i n F i g . V.6. Note t h a t the high frequency of thickness values c l o s e t o 6.0 f t i n F i g . V.5, f u r t h e r i n d i c a t o r t h a t the s i z e of the d r i f t was a l i m i t i n g f a c t o r . Fig.V.9 Section of o 2600 level drift where vein thickness is larger than the width of the drift. Shaded area represents the vein. The v a r i a n c e d i f f e r e n c e between the two populations w i l l l a t e r make i t d i f f i c u l t t o co n s t r u c t a s i n g l e variogram model f o r the two data s e t s . 40 The f u n c t i o n which w i l l accommodate the two data sets and w i l l enable s t r u c t u r a l modelling i s , as i t w i l l be shown, a correlogram. Y^J SPATTAT. DTSTRTRTTTTON DF The d i s c u s s i o n thus f a r has concentrated on the d i s t r i b u t i o n of thickness of the main No. 3 v e i n . I t i s known t h a t base and precious metals are present e x t e r n a l t o the v e i n i n the v i c i n i t y of the main zone i n the form of hangingwall and f o o t w a l l v e i n s as w e l l as zones of f r a c t u r e i n f i l l i n g . U n c e r t a i n t y i n d e f i n i n g hangingwall and f o o t w a l l contacts of the v e i n f u r t h e r emphasizes the importance of determining how much mi n e r a l t h e r e i s i n the w a l l r o c k . I t has a l s o been noted ( s e c t i o n IV.2) t h a t m i n e r a l i z a t i o n can be found i n w a l l r o c k adjacent t o the v e i n ; d r i l l holes U88-030 and U88-031 are examples. P r o f i l e s of these two holes are shown i n f i g . V.10. From a p u r e l y q u a n t i t a t i v e p o i n t of view these p o t e n t i a l sources of ore adjacent t o the main v e i n of the No. 3 zone are d i f f i c u l t t o use as a base f o r determining l o c a l r eserves. However, we w i l l i n v e s t i g a t e t h e i r p o t e n t i a l i n a more general way, as a p o s s i b l e added but u n c e r t a i n b e n e f i t t h a t w i l l occur d u r i n g mining. In order t o evaluate the p o t e n t i a l of w a l l r o c k m i n e r a l i z a t i o n we have a r b i t r a r i l y s e l e c t e d a l l assays w i t h i n 15 f t . t r u e d i s t a n c e from the v e i n , and have concentrated on metal accumulations. Table V . l summarizes the simple s t a t i s t i c s t h a t r e s u l t e d from t h i s a n a l y s i s . 41 VARIABLE n AVERAGE VALUE STANDARD DEVIATION METAL AVER. VALUE Length 339 2.4 1.8 AccAu 321 0.039 0.069 Au 0.016 AccAg 337 1.62 3.38 Ag 0.675 AccCu 339 0.13 0.34 Cu 0.054 AccPb 339 0.41 1.02 Pb 0.17 AccZn 339 2.14 4.72 Zn 0.89 TABLE V . l Simple s t a t i s t i c s f o r metal accumulations w i t h i n 15 f e e t of No. 3 v e i n . U n i t s are as f o l l o w s : length i n f e e t , Au and Ag i s i n o z / s t , other assays are i n %, a l l accumulations are length*corresponding assay The average values quoted i n Table V . l are much greater than the ve r y low values encountered away from the v e i n and w i t h the d i s p e r s i o n s , i n d i c a t e the l i k e l i h o o d t h a t l o c a l l y some metal could a t t a i n ore grade. Next, uppermost v e i n assays were compared w i t h the adjacent hangingwall assays. Up t o 1.0 o z / s t of s i l v e r and 0.8 % z i n c can be p i c k e d up i n the hangingwall i f mining includes w a l l r o c k m a t e r i a l j u s t beyond the l i m i t s of the v e i n (see F i g . V . l l ) . 42 DDH 1)88-30 M 111 1111155 Y////////////////////A I = = = Dyke S i l - Vein Md. Alt . Md. MD Md - microdlorite Sil.- si l iceous Alt.- altered Fig. V. 10 Profiles to demonstrate the potential importance of mineralized wallrock as a source of ore. Drill hole intersections are located near 27000 Easting. 43 ZN-Vn 2 5 -2 0 . 15-> ZN-Vn ZN-Hr Mean 7.53 0.79 Correlation (Spearman) 0.49 a) 6 ZN-Hr AG-Vn A 50-Fig. V. I 4 0 -3 0 ' 20-T lo-t*1. AG-Vn AG-Hr Mean 10.18 0.99 Correlation (Spearman) 0.59 i ' i 1 i 10 12 14 b) 16 18 AG -Hr Scatterplot of uppermost vein assays versus hangingwall assays: a) z inc(%) , b) silver (oz/st.) Vn-ve in ; Hr - hangingwall assay I f we compare the lowermost v e i n assays w i t h the adjacent f o o t w a l l assays i t turns out tha t the same happens w i t h s i l v e r values which are somewhat lower than i n the hanging w a l l ( F i g . V.12). Appendix I I I shows the s c a t t e r p l o t s and s t a t i s t i c s i n a fash i o n g iven above f o r remaining three analysed metals. 44 Z n - V n k 50-40 JO 20-10 AG-Vn A 40 30 -20 -10 -ZN-Vn Mean 8.52 Correlation (Spearman) ZN-F.r 0.80 0.50 a) Z N - F r AG-Vn A G - F r Mean 8.98 0.53 Correlation (Spearman) 0.44 b) AG-Fr Fig. V.I2 Scatterplot of lowermost vein assays versus footwall assays: a) zinc (%) b) silver (oz/st.) Vn - vein ; Fr - footwall assay The f a c t t h a t more s i l v e r can be found i n the hanging w a l l may help i n the choice of where necessary d i l u t i o n from mining would come from. P r a c t i c a l l y then, as mining i s planned f o r a p a r t i c u l a r p a r t of the v e i n , v e i n p r o f i l e s should be examined to evaluate the p o s s i b i l i t y of a d d i t i o n a l reserves beyond the geometric boundaries of the v e i n . 45 In order t o gain an i n s i g h t as t o how d i f f e r e n t are the adjacent grades w i t h i n the v e i n , the s c a t t e r p l o t s f o r these grades were co n s t r u c t e d (see Appendix I I I ) . I t turns out t h a t even at the s c a l e where distances between assays approach zero, the v a r i a b i l i t y of grades i s very l a r g e and there i s no c o r r e l a t i o n between the assay valu e s . S u r p r i s i n g l y , d e s p i t e the l a c k of c o r r e l a t i o n between assays w i t h i n the v e i n , there i s some weak c o r r e l a t i o n between assays i n the v e i n and the adjacent w a l l r o c k ( i . e . t h i s probable c o r r e l a t i o n appears t o be s i g n i f i c a n t f o r Ag assays between the uppermost v e i n and hangingwall f o r hangingwall assays > 2.0 o z / s t , F i g . V . l l b ) . A p o s s i b l e reason f o r i t c o u l d be the e x i s t e n c e of the a l t e r a t i o n zone on the margins of the v e i n : t h i s a l t e r a t i o n zone c a r r i e s m i n e r a l i z a t i o n which l o c a l l y c o u ld be of i n t e r e s t t o a miner. The above a n a l y s i s shows t h a t ore reserve e s t i m a t i o n must in c l u d e a d e t a i l e d knowledge of metal d i s t r i b u t i o n w i t h i n both the v e i n and adjacent a l t e r e d m i n e r a l i z e d w a l l r o c k . 46 CHAPTER VI STRUCTURAL ANALYSIS-VARICOGRAPHY VT.1 HONTTTJTTTTV FTINCTTONS OF THE THTCKNESS VT.1.1 Varinc/raniR Examination of f i g u r e s IV.1 and IV.2 showing the s p a t i a l d i s t r i b u t i o n of c o n t r o l p o i n t s f o r a s t r u c t u r a l a n a l y s i s i n d i c a t e s no excessive c l u s t e r i n g of data. We proceeded t o c a l c u l a t e the variogram of v e i n t h i c k n e s s s e p a r a t e l y f o r the C e n t r a l and Southern s e c t i o n s ( F i g . VI.1-VI.4). A l l d e l t a (A) denote fewer than 30 p a i r s . V e r t i c a l and h o r i z o n t a l variograms are s u f f i c i e n t l y s i m i l a r t h a t we have c a l c u l a t e d o m n i d i r e c t i o n a l variograms i n most cases. This approach i s adequate f o r the r e l a t i v e l y w i d e l y spaced d r i l l hole i n t e r s e c t i o n s t h a t provide our p r i n c i p a l data base. A n a l y s i s of the C e n t r a l s e c t i o n ( F i g . VI.1) i n d i c a t e s t h a t apart from the f i r s t l a g which contains o n l y 27 p a i r s , there i s v i r t u a l l y no c o r r e l a t i o n between any of the t h i c k n e s s data. The same holds t r u e i n the southern s e c t i o n of the v e i n ( F i g . V I . 4). As i t can be no t i c e d the variograms e x h i b i t an apparent hole e f f e c t which might i n d i c a t e some degree of r e g u l a r i t y i n the p o s i t i o n of t h i c k zones i n a t h i n n e r background f i e l d . Note th a t the s i l l values d i f f e r s u b s t a n t i a l l y between the two zones. For the southern zone, the plateau i s reached at 3.8 which represents o n l y approximately 30% of the s i l l found i n the C e n t r a l zone. The d i f f e r e n c e i s caused by a p r o p o r t i o n a l e f f e c t discussed i n S e c t i o n V.1.2. 47 1 5 -x x x x x X x 9 " X 6 -3 -o4 1 1 1 1 0 110 220 330 440 Fig. VI. I Variogram of thickness -—r~ 550 T 660 Central 18 15 H 12 9 -6 " 3 " 0 ^ 1 1 1 1 1 1 ~~ 100 2 0 0 300 400 500 600 Fig. VI.2 Variogram of thickness, horiz. direction - Central 12-10-8-6-4 -2-0- . I I I I I I 100 200 300 400 500 600 Fig. VI.3 Variogram of thickness, vert, direction - Central y n 5.4 -4.5 -3.6 -2.7 -1 .8 -0.9 -0.0 X X 0 110 220 330 440 Fig. V1.4 Variogram of thickness — i — 220 350 South —I— 660 A-denotes less than 30pairs 48 I t i s q u i t e common t h a t c o n t i n u i t y of analyzed v a r i a b l e i s dependent on d i r e c t i o n along which i t i s analyzed; t h a t i s , an a n i s o t r o p y e x i s t s . Despite somewhat l i m i t e d data h o r i z o n t a l and v e r t i c a l variograms were c a l c u l a t e d t o t e s t f o r p o s s i b l e a n i s o t r o p y . These d i r e c t i o n a l variograms (Figs VI.2 and VI.3) are very s i m i l a r and support the i n t e r p r e t a t i o n of an i s o t r o p i c s t r u c t u r e f o r S i l v e r Queen th i c k n e s s data. P o s s i b l e explanations of the remarkably poor c o n t i n u i t y e x h i b i t e d by variograms f o r t h i c k n e s s are: the d i s t a n c e s between samples should be s m a l l e r i f we want to c r e a t e a r e l i a b l e variogram model f o r short d i s t a n c e s ; the r e are too few data and r e s u l t i n g variograms are p o o r l y estimated; presence of o u t l i e r s ; and p r o p o r t i o n a l e f f e c t . In order t o t e s t the p o s s i b i l i t y t h a t a d d i t i o n a l data may help i n m o d e l l i n g , a l l 155 data values r e p r e s e n t i n g the two zones were analyzed as a s i n g l e data s e t . The variogram of t h i c k n e s s e x h i b i t s a pure nugget e f f e c t w i t h the t o t a l v a riance s l i g h t l y lower than the s i l l of variogram f o r C e n t r a l s e c t i o n ( F i g . V I . 5 ) . That d i f f e r e n c e i n the s i l l value i s due t o the p r o p o r t i o n a l e f f e c t . Fig.VI.5 HO 2 2 0 Voriogrom of 3 3 0 thickness - 1 — 4 4 0 for — i — 5 5 0 both 6 6 0 h zones, South and Central The presence of o u t l i e r s may be analyzed s t a t i s t i c a l l y ( C r e s s i e & Hawkins, 1980) or i t can be s t u d i e d w i t h the help of a variogram and s c a t t e r p l o t s . O u t l i e r s are defined here as very l a r g e values whose v a l i d i t y cannot be determined w i t h c e r t a i n t y . I t i s f e l t t h a t a few l a r g e values which are known t o represent n a t u r a l phenomena should not be considered as o u t l i e r s and by those means should not be c o r r e c t e d . VI. 1.2. R e l a t i v e varinqrflffls. One of the reasons f o r the s u b s t a n t i a l d i f f e r e n c e i n the shape of variograms from two zones i s the p r o p o r t i o n a l e f f e c t which i s q u i t e common i n mi n e r a l d e p o s i t s . To prove the p o i n t , general o m n i d i r e c t i o n a l r e l a t i v e variograms f o r both areas were c a l c u l a t e d ( F i g . VI.6 and VI.7), on the assumption th a t a 2 ©Cm 2. For each l a g (h=n*50 f t where n i s the l a g number) the variogram value i s d i v i d e d by the squared mean of sample values t h a t c o n t r i b u t e to t h i s l a g : r r e l ( h ) = r ( h ) / m 2 . To a r r i v e at the S i l l values f o r both areas 50 were found t o be 0.55 f o r the C e n t r a l zone and 0.52 f o r the Southern zone. The two variograms are very much s i m i l a r f o r the f i r s t few lags i n d i c a t i n g t h a t one variogram model can be de r i v e d f o r both areas. I f we c a l c u l a t e a r e l a t i v e variogram on a l l data from both zones, the outcome shows th a t the C e n t r a l and the Southern zones represent the same pop u l a t i o n ( F i g . VI.8). Because of the d i f f i c u l t y d e s c r i b i n g s h o r t - s c a l e v a r i a b i l i t y below 100 f t d i s t a n c e s , a t o t a l of 89 measurements of v e i n widths were taken from the 2600 l e v e l at an average distance of 6.6 f t between readings (Appendix IV shows the data c o l l e c t e d ) . The r e l a t i v e variogram of th i c k n e s s of the v e i n appears t o have the range A=56 f t ( F i g . VI.9) and no nugget e f f e c t . This variogram cannot be compared d i r e c t l y w i t h the variogram d e r i v e d from d r i l l hole data. When the two r e l a t i v e variograms ( F i g . VI.8 and F i g . VI.9) are analyzed, i t appears t h a t the s i l l of the r e l a t i v e variogram c a l c u l a t e d from DDH i s at l e a s t t w ice the s i l l c a l c u l a t e d from d r i f t samples. The f a c t t h a t the general r e l a t i v e variogram f a i l s t o e x p l a i n the d i f f e r e n c e i n s i l l v alue f o r d i f f e r e n t variograms may be caused by the v a r i a n c e of data values not being equal to the square of the mean. To f i n d the f u n c t i o n a l r e l a t i o n s h i p between the variance and the mean, the d r i f t data (read from l e v e l maps) were d i v i d e d i n t o s i x t e e n 150 f t s e c t i o n s and the var i a n c e and the mean were 51 X rel. 0.6 -0.5 -0.4 -0.3 -0.2 0.1 0 X X X X —I 1 1 800 1000 h 0 200 400 600 Fig.VI.6 Relative variogram of thickness - Central Srel. 0.68-0.57-0.45-0.34-0.22-0.11 -0 x x x X X x X X X X —I 1 1— 400 600 Fig.VI.7 Relative variogram of thickness T 1 1 0 200 -I 1 1 800 1000 h South 0.58-0.48 0.39-0.30-0.21-0.12-0 -I X X X X X X X X X 0 200 400 600 800 1000 h Fig. VI.8 Relative variogram of thickness - Central and South Xrel. 0.20. 0.17 • 0.13-0.10 • 0.06-0.03 H 0 X X X X X X X X X X X —r— 28 I— 56 84 112 140 160 h Fig. VI.9 Relative variogram of thickness measured on level 2600 A - denotes less than 30 pairs — i — 140 —I 160 52 c a l c u l a t e d f o r each s e c t i o n . In a d d i t i o n , the v e i n was subdivided i n t o seven blocks and sample s t a t i s t i c s c a l c u l a t e d f o r each block from DDH data. The a n a l y s i s showed t h a t variance of d r i f t data i s much lower r e g a r d l e s s of mean values ( F i g . VI.10). The reasons f o r the d i f f e r e n c e were found t o be mainly the width of the d r i f t which l i m i t e d the widths of samples taken (see S e c t i o n V.1.2). In a d d i t i o n , i t i s apparent t h a t the r e g r e s s i o n l i n e e x p l a i n i n g f u n c t i o n a l r e l a t i o n s h i p between the var i a n c e and the mean c a l c u l a t e d from DDH data can not be descr i b e d as a 2=m 2 w h i c h i s the r e l a t i o n s h i p o f t e n f o r c e d i n software packages. Fig.VI.10 Scatterplot of variance versus squared mean of thickness for blocks (DDH) and sections of the drift. Summarizing, we were able t o show the l a c k of c o n t i n u i t y of the t h i c k n e s s f o r d i s t a n c e s between data from d r i l l h o l e s . F u r t h e r , we showed t h a t , i n f a c t , the d i v i s i o n of the v e i n i n t o C e n t r a l and Southern s e c t i o n i s mainly based on geometry and a l l data may be used i n c o n s t r u c t i n g the model. This approach may i n f a c t be modified i n f u t u r e i f we attempt t o d i v i d e the No. 3 53 v e i n i n t o f o u r d i s t i n c t i v e m i n e r a l o g i c a l zones and group the data i n t h i s r e s pect (Hood, 1991). Unfortunately, variogram from the d r i f t c o u l d not be used to d e s c r i b e small s c a l e s t r u c t u r e . To overcome t h i s problem, correlograms w i l l be introduced. VI • 1 • 3 • r n r r p l o g r a n i f u n c t i o n s The correlogram, Cor(h), f u n c t i o n i s : Cor(h)=Cov(x,x+h)/a(x)*a(x+h) where: Cov(x,x+h) - i s the average covariance of samples separated by v e c t o r h, and a(x) and a(x+h) - are standard d e v i a t i o n s of the v a r i a b l e and i t s s p a t i a l t r a n s l a t i o n . For our purposes we w i l l d eal w i t h C o r m ( h ) = l - C o r ( h ) , or what we w i l l c a l l the "modified" correlogram because i t r e t a i n s the same general c h a r a c t e r as the variogram. I n i t i a l l y , C or m(h) f u n c t i o n s were c a l c u l a t e d on values from C e n t r a l and Southern s e c t i o n s of 2,600 l e v e l d r i f t . P o s s i b l e changes of c o n t i n u i t y c l o s e t o the o r i g i n and d i f f e r e n t apparent v a r i a b i l i t i e s of d r i f t data were examined. This p r e l i m i n a r y a n a l y s i s revealed no apparent d i f f e r e n c e i n nugget e f f e c t and the range i n d i c a t i n g no reason not to use a l l values i n order t o a r r i v e at the f i n a l model. Appendix V shows the experimental f u n c t i o n s . I f we c a l c u l a t e correlograms f o r a l l d r i l l hole (155 values) and d r i f t data (365 v a l u e s ) , the two can 54 both be modelled by nested exponential models w i t h small nugget e f f e c t and a range a i = 50 f t and a2 = 300 f t ( F i g . VI.11). Mod.Cor A 1.03 0.92 0.77-0.61 -0.46-0.30-0.16-X X X X X XX X X X X X X X X X X X A - denotes less than 30pairs a ) T — i — i — i — i — i — i — i — i — i — i 0 200 40O 600 800 1000 h Mod. Cor A 1.01 -0.84-0.67-0.31 0.34-0.17 X X X X X X x x X XX X X X X X b) —r— 60 —I— 120 - 1 — 180 - i 1 r 240 —I 300 Mod.Cor J t 1.2 1.0-0.8-0.6- X 0.4 0.2-' OX) Cor(h) = 0.I7+0.45X E x p 5 0 ( h) +0.38x E x p 3 Q 0 ( h ) X-K-X-*'* X x x C ) 60 -1 1 1 1 1 120 180 240 300 360 h Fig. VI. II a ) Correlogram of vein thickness, Central and South b ) Correlogram of all drift data (large lags) c ) Correlogram model of thickness of the vein The same f u n c t i o n c a l c u l a t e d on the 1.8-5.9 f t subset of the thickness data, which as i t was shown i n S e c t i o n V.1.2 can be considered as coming from the same p o p u l a t i o n f o r two data s e t , r e v e a l s a v e r y s i m i l a r p a t t e r n of the s p a t i a l v a r i a b i l i t y . The only d i f f e r e n c e i s s l i g h t l y higher nugget e f f e c t and 55 undoubtable poor c o n t i n u i t y at distances l a r g e r than 80 f t i f d r i l l hole data are considered ( F i g . VI.12). Mod. Cor 1.2 1.0-0.8-0J6- / X 0 4 - I 0 . 2 -OJO C o r ( h ) = 0 .25+0.45 » Exp 5 0 (h ) + 0 .3xExp 3 0 0 ( h ) . „ -* x x-x-*"x** x x x x a) — i 1 1 1 1 1— 0 60 120 180 240 300 360 M o d . C o r " 1 . 0 0 -0 . 9 1 -0 .72 0 . 5 4 -0 . 3 6 0 . 1 8 -A X X X X X X X X X X X X X X X X X A - denotes less than 30pairs b) 200 —I 1 1 1 1 ' 1 400 600 800 1000 Fig.VI.12 a) Correlogram model of thickness for subset of data t.8-5.9ft. derived from drift and drill hole data b) Correlogram of thick-ness for subset of data 1.8 - 5.9 ft. from drill holes in South and Central sections of the vein. The higher nugget e f f e c t i s f e l t to be due t o the absence of low values which might be considered more continuous than data from higher ranges. In view of the s i m i l a r i t y of Cor m(h) f u n c t i o n f o r the two data sets we conclude t h a t the use of a l l data f o r developing a mathematical model ( F i g . VI.11c) i s j u s t i f i a b l e . The nugget e f f e c t r e t a i n e d i n the model of c o n t i n u i t y i s f e l t t o be j u s t i f i e d by the nature of the v e i n , which appears t o have the width which can change d r a m a t i c a l l y at the very s m a l l d i s t a n c e s , and one of the reasons f o r t h i s may be the conjugate shears o b l i q u e t o the d i r e c t i o n of the v e i n which 56 c o u l d have allowed sudden openings along the f a u l t a c t i n g as a conduit f o r m i n e r a l i z e d f l u i d s . VT .1 .4. T n r i i r a t n r variograms I n d i c a t o r k r i g i n g i s one of the means of as s e s s i n g the p r o p o r t i o n of grades below a c e r t a i n c u t - o f f i n a block o r , i n the case of p o i n t e s t i m a t i o n , the p r o b a b i l i t y t h a t the p o i n t t o be estimated has the value below the c u t - o f f . Assessment of p r o b a b i l i t i e s can a l s o be used t o assess the u n c e r t a i n t y of e s t i m a t i o n of the p o i n t or block mean. I n d i c a t o r variograms c a l c u l a t e d on thickness of the v e i n ( F i g . VI.13) from d r i l l holes show no s t r u c t u r a l r e l a t i o n s h i p between the lags w i t h the p o s s i b l e exception of cut-off=3.5 f t ( F i g . VI.13b). I f we proceed w i t h the s i m i l a r a n a l y s i s on d r i f t d ata, i t appears t h a t the range increases from A=18 ( c u t -o f f =1.5) t o A=39 (cut-off=4.5) and again decreases t o A=12 (cut-off=6.5). These can be viewed on F i g . VI.14. I f we p l o t range versus c u t - o f f ( F i g . VI.15), a b e l l - l i k e shaped curve shows tha t the g r e a t e s t c o n t i n u i t y i s i n the mid-range values 3.5-4.5 f t . This f a c t suggests, t h a t s t o p i n g on the v e i n w i t h the average width 4.0 f t w i l l l e a d t o more p r e d i c t a b l e output i n terms of the tonnage moved. Based on the above, models of variograms f o r d i f f e r e n t c u t -o f f s can be used i n the o r d i n a r y k r i g i n g system t o c a l c u l a t e p r o b a b i l i t i e s . 57 0.50 -0.29 -0.18 -0.12 " 0.06 -0.00 —|— 130 1— 2 6 0 a) 3 9 0 520 650 X ind.4 0.30 0.29 -\ 0.18 0.12 0.06 0.00 x x x x x X x x 130 1— 260 1— 390 520 b) 550 K ind 0.24 -\ 0.20 0.16 0.12 0.08 0.04 0.00 -\ —I— 130 260 390 1— 520 c ) 650 indA 0.18 -1 0.15 0.12 -0.09 -0.06 -0.03 -0.00 130 260 390 520 d ) 650 Fig. VI.13 Indicator variograms of thickness from South and Central Sect, calculated from drill hole data: a ) cut-off = 2.5 ft.; b ) cut-off = 3.5 ft.; c) cut-off = 4.5 ft. ; d ) cut-off = 5.5 ft. 58 * X X * X X x x 12 — r -24 36 — r 48 — n 60 a) i nd . A 0.24 0.20 -0.16 -0.12 -0.08 -0£>4 -0.00 - r 12 — r 24 —r~ 36 48 — T 1 60 b) 12 — r 24 36 — r 48 — H 60 c) ind 0.18 x x x x 0.00 , , , 1 pH 0 12 24 36 48 60 d) VI. 14 Indicator variograms of thickness from Drift data a) cut-off = 2.5ft. ; b) cut-off = 3.5ft. ; c) cut-off = 4.5ft. : d) cut-off = 5.5ft. One such model f o r the c u t - o f f = 4.0 f t was d e r i v e d i n order t o de f i n e the p r o b a b i l i t i e s t h a t the v e i n t h i c k n e s s i s grea t e r than the minimum mining width assumed. The model def i n e d i s based on DDH ( F i g . VI.16a) and d r i f t data ( F i g . VI.16b). VT.2 C-ONTTNTITTY FUNCTIONS OF ACCUMULATIONS With t h i c k n e s s v a r i a t i o n s throughout the v e i n causing changes i n support, a n a l y s i s of the raw grades may be d i f f i c u l t . One s o l u t i o n t o t h i s problem i s to create a new v a r i a b l e t h a t accommodates the changing volumes. This new a d d i t i v e v a r i a b l e (accumulation) i s v e i n thickness*metal grade. The correlogram w i l l again be used t o analyze s p a t i a l c o n t i n u i t y . The a n a l y s i s w i l l be based on d r i l l hole data from both the C e n t r a l and the Southern zones as w e l l as from d r i f t assays taken from the 2600 l e v e l . VI. 2. 1 Corre Ingram F i i n r t i nns VI.2.1.1 Gold Accumulations Although c o n t i n u i t y f u nctions f o r t h i c k n e s s f a i l e d t o i n d i c a t e c o r r e l a t i o n a t the s c a l e considered, the correlogram of gold accumulation c a l c u l a t e d on d r i l l holes suggest a range of 270 f t (Fig.VI.17a). The same f u n c t i o n c a l c u l a t e d f o r d r i f t data (note l a r g e lags entered) again shows t h a t t h i s range i s appropriate (Fig.VI.17b). The well-pronounced hole e f f e c t at 160 f t i n d i c a t e s the presence of m i n e r a l i z e d zones about 80 f t wide. This hole e f f e c t seems to be present o n l y i n the 60 Range 3 9 -33 -22 IS Co = 0.05 o Co:0.01 -i r— 1.5 2.5 3.5 —I 4.5 —!— 5.5 6.5 Cut - O f f Fig.VI. 15 Range of indicator variograms of thickness as a function of the cut-off chosen; Co represents nugget effect "6 ind 0.25 0.20 0.15 o.io 0.05 0.00 — r — 110 220 1— 330 440 550 a) 660 h X ind 0.24 -0.20 -0.16 0.12 0.08 -0.04 4 0.00 x--x / 'X X' —I-12 ind = 0O2-t-0.llx E x p | 2 (h) +0.09x Exp 6 Q (h ) X y , _ x _ _ x _ x — x--* b) —I— 24 —I— 36 —r— 48 —r— 60 Fig.VI.16 a) Indicator variogram of thickness for cut-off = 4.0ft., calculated from all drill hole data j b) Indicator variogram model of continuity of thickness based on drift and drill hole data. 61 correlogram based on d r i f t data. D i r e c t i o n a l correlogram ( F i g . VI.17c) based on d r i l l holes do not seem to i n d i c a t e such a s t r u c t u r e ; one might argue, though, t h a t correlogram f o r h=200 f t represents the hole e f f e c t . Although the model chosen does not take i n t o account t h i s f e a t u r e , t h i s p o s s i b l e zoning should be considered, at l e a s t i n the v i c i n i t y of 2600 l e v e l once more data are a v a i l a b l e . The f i n a l model chosen i s a nested e x p o n e n t i a l s t r u c t u r e w i t h a nugget e f f e c t ( F i g . VI.17d). VI.2.1.2. S i l v e r Accumulations The correlogram model f o r s i l v e r accumulations i s based on both ddh and d r i f t data sets and was estimated as e x p o n e n t i a l w i t h a range a=90.0 f t ( F i g . VI.18). Note the high nugget e f f e c t which f a r exceeds the nugget e f f e c t from gold values due i n p a r t t o i r r e g u l a r d i s t r i b u t i o n of s i l v e r bearing minerals which are l a t e i n paragenetic sequence. The outcome of a n a l y s i s of accumulations of copper, l e a d , and z i n c and the r e s u l t i n g correlogram models are given i n Appendix VI. VI. 2 . 2 . Tndinat.nr Varinqrams As w i l l be shown l a t e r , some of the estimates c a l c u l a t e d from models given above appear t o be o v e r l y o p t i m i s t i c . The undue i n f l u e n c e of l a r g e values on estimated p o i n t s may r a i s e q u e s tion of v a l i d i t y of the estimates. We f e l t t h a t i n our case the apparently e r r a t i c values are l e g i t i m a t e due t o n a t u r a l v a r i a b i l i t y of the thickness i n the s t u d i e d v e i n system discussed i n S e c t i o n V . l . 62 Mod. Cor l t i .01 -0.84-0.67 -0.50-0.34-0.17-x X X X X X X X X X X X X X X X X X X 1 1 1— 0 200 —I 1—I—I 1—I 1— 400 600 800 1000 a) M o d . C o r 0.93-0.79-0.63-0.47-0.32-0.16-X X i 1 1 1 1 1 1 1 1 1 r~ 0 60 120 180 240 300 b) Mod.Cor 0.96-0.80-0.64-0.48-0.32-0.16 -X A X X X X X XX XX X X 0 200 400 600 A - denotes less than 30 pairs —I r — i — 800 1000 C ) Mod. Cor 1.2-1.0-0.8-0.6-0.4 0.2 0.0-• Cor ( h ) = 0.25*0.35x E x p 8 0 ( h) +0.4 x E x p 2 0 Q ( h) , 5 x x - -''X 'X ?x XX d ) I I I I I I-" 40 80 120 160 200 240 Fig.vl.17 a) Correlogram of gold accumulations from drill hole data b) Correlogram of gold accumulations from drift assays c) Directional horizontal correlogram of gold accumulations from drill hole assays d ) Correlogram model of gold accumulations based on drift and drill hole assays. 63 Mod.Cor 4 I.OZ 0.85 0.68-0.51 0.34-0.17-X X X X X X X X X X X X X X X X X X i r— 0 zoo —1 1 —I 1— 400 600 800 1000 a) Mod. Cor 1.04-4 0.87 0.69-0.52-0.34-0.17 X X X X X XX X X X X X X X X X X X —1 1 1 1 1 • 1 1 1 60 120 180 240 300 b) Mod.Cor i 1.2-i.o-0.8-0.6 0.4 0.2 0.0 Cor (h) = 0 . 4 5 + 0 . 5 5 x E x p g o ( h ) , x x ' x x x x x «-x-x x X.X" -I— 19 —r— 38 -1 r-57 76 95 - 1 — 114 c) Fig. VI.18 a) Correlogram of silver accumulations based on all drill hole assays b) Correlogram of silver accumulations from drift assays c) Correlogram model of silver accumulations based on drift and drill hole assays. A - denotes less than 30 pairs Other approach might i n v o l v e applying the system which discounts the weight f o r a l a r g e value. I n d i c a t o r variograms a l l o w us to model c o n t i n u i t y of accumulation i n a manner which may p i n p o i n t those o p t i m i s t i c estimates. The c u t - o f f values chosen were approximately t h i r d q u a n t i l e f o r g o l d , s i l v e r , and z i n c . As i t i s shown i n F i g . VI.19a g o l d accumulations represent a good c o n t i n u i t y w i t h a range 130.0 f t . S i l v e r accumulations ( F i g . VI.19c) i n t u r n appear t o represent a very short range of c o n t i n u i t y (a=50.0 f t ) and high nugget e f f e c t . The models chosen w i l l be a p p l i e d i n o r d i n a r y i n d i c a t o r p o i n t k r i g i n g and the outcome w i l l be compared w i t h estimates from o r d i n a r y k r i g i n g . M o d i f i e d correlogram models chosen f o r d i f f e r e n t v a r i a b l e s and i n d i c a t o r variogram models are given i n Table VI.1. 65 2f i nd 0.20 0.16 0.12 0.08 0.04 -0.00 8 (h ) = 0.06 + O.I2«Exp|30 (h) i— 30 60 90 120 1 ISO a) - i — 180 g ind 0.25 0.20 -0.15 0.10 0.05 0.00 • Jf ( h ) = 0.1 + O.I2»Exp360(h) V-x x - - - - * " - x " X b) i 120 -1 240 360 480 600 cf ind 0.25 -0.20 -0.15 -| x ' 0.10 0 .05-0.00 y (h) =0.12 + 0.1 *Sph50 (h) x x x X I 34 I 68 102 136 c) -I— 170 204 Fig.VI.19 Indicator variogram model for a ) gold accumulations, cut-off = 0.85 oz/st.x ft. b) zinc accumulations, cut-off = 3 0 % x ft c) silver accumulations, cut-off = 40 oz/st. x ft. 66 VARIABLE CORRELOGRAM MODEL Thickness Cor m(h) = 0. 17 + 0. 45Exp 5 0(h) + 0 .38Exp3Q0(h) Gold Accum. Cor m(h) = 0. 25 + 0. 35Exp 8 0(h) + 0 .40Exp200( h) S i l v e r Accum. Cor m(h) = 0. 45 + 0. 55 Expgo(h) Zinc Accum. Cor m(h) = 0. 26 + 0. 45 Sph 3 0(h) + 0.29Sph 4 00(h) Copper Accum. Cor m(h) = 0. 60 + 0. 40Sph 250(h) Lead Accum. Cor m(h) = 0. 50 + 0. 50Sph 1 8 0(h) Thickness -cut-off=4.0 V a r i n d ( h ) = 0. 02 + 0.11Expi2(h) + 0.09Exp 6 0(h) Gold Accum. cut-off=0.85 V a r i n d ( h ) = 0. 06 + 0.12Exp 1 3 0(h) Zinc Accum. cut-off=30 V a r i n d ( h ) = 0. 10 + 0.12Exp 3 6o(h) S i l v e r Accum. cut-off=40 V a r i n d ( h ) = 0. 12 + 0.10Sph 5 0(h) Table VI.1 M o d i f i e d correlogram and i n d i c a t o r variogram models f o r d i f f e r e n t v a r i a b l e s and c u t o f f s . 67 CHAPTER V I I DISCUSSION OF SUPPORT OF DATA A r e g i o n a l i z e d v a r i a b l e i s d e f i n e d on a s p e c i f i c support, t h a t i s , a p a r t i c u l a r o r i e n t a t i o n , shape and volume of a sample. This guarantees t h a t a l l l i n e a r combinations of i t s values r e t a i n the same meaning. Grade of a sample define d on a constant support i s an " a d d i t i v e " r e g i o n a l i z e d v a r i a b l e . The same grade d e f i n e d on v a r i a b l e supports i s - h o longer a d d i t i v e , meaning t h a t the average grade of two samples of d i f f e r e n t supports i s not the a r i t h m e t i c mean of t h e i r grades. Where assays are taken over d i f f e r e n t supports (e.g. d i f f e r e n t lengths of d r i l l c o r e ) , the a d d i t i v e v a r i a b l e t o be considered i s metal accumulation ( i . e . assay value * l e n g t h of sample). The d i f f e r e n c e i n volume of a sample based on the d i f f e r e n c e of a v e i n t h i c k n e s s i s q u i t e obvious and w i l l not be discussed here. There are p o s s i b l e more s u b t l e d i f f e r e n c e s due to d i f f e r e n t sampling programs. In our case study, the f o l l o w i n g should be taken i n t o account: d i f f e r e n t d r i l l i n g campaigns spreading throughout the l a s t twenty years; underground c h i p samples do not n e c e s s a r i l y represent the same volume as d r i l l core samples; and s p e c i f i c g r a v i t y may d i f f e r from one sample t o another. Although i t i s p o s s i b l e t o co n s i d e r s e p a r a t e l y data from d i f f e r e n t time p e r i o d s , i t would not be p r a c t i c a l because there are too l i t t l e data a v a i l a b l e from any one p e r i o d of sampling. 68 However, i t i s p o s s i b l e to examine three set of data i n d i v i d u a l l y : s u r f a c e d r i l l h o les; underground d r i l l h oles; and d r i f t samples. The i n f o r m a t i o n on the volume of samples taken underground i s not a v a i l a b l e (Cummings, personal communications) so the on l y means of checking the d i f f e r e n c e s i s the a n a l y s i s of variograms and correlograms of raw grades and accumulations based on these three s e t s . I f th e r e are no apparent d i f f e r e n c e s between the estimated nugget e f f e c t s and the s i l l v a l u e s , they might be considered a d d i t i v e v a r i a b l e s (although the volumes are undoubtedly d i f f e r e n t ) . To determine the i n f l u e n c e of underground d r i l l hole samples on the s p a t i a l c o n t i n u i t y , the correlogram of ZN*THICKNESS was c a l c u l a t e d f o r underground d r i l l holes and compared w i t h the correlogram of a l l data. Figure V I I . 1 i n d i c a t e s t h a t t h e r e i s no d i f f e r e n c e i n the s p a t i a l c o n t i n u i t y of the underground values when compared t o the correlogram f o r a l l data (see Appendix V I ) . M o d . Cor ,, x x 1.06- x x x x x x x x x x 0.«7 - x x X * X X * 0.70 -0.53 -035 -0.17 -—1 1 1 1 1 1 1 1 1 200 400 600 600 1000 Fig.VII.I Correlogram of zinc accumulations from underground drill holes. The problem of combining underground c h i p samples w i t h the core samples i n t o one variogram or modified correlogram model must be addressed i n a much more d e t a i l e d manner. We decided to look at the raw grades i n s t e a d of at accumulations. A d d i t i o n a l v a r i a b i l i t y coming from v e i n t h i c k n e s s obscures the v a r i a b i l i t y of grades which c e r t a i n l y would be lower i f the d i f f e r e n c e i n support was s u b s t a n t i a l w i t h r e s p e c t t o d r i l l hole data. Figure VII.2 represent the variogram f u n c t i o n f o r AU grades from two d i f f e r e n t data s e t s . I t appears t h a t there i s a very good s i m i l a r i t y between the two: the same holds f o r the modified correlogram ( F i g . V I I . 3 ) . A d d i t i o n a l m o d i f i e d correlogram f u n c t i o n s c a l c u l a t e d f o r both AG and ZN confirm t h a t , indeed, the two data sets can be combined f o r the purposes of d e s c r i b i n g s p a t i a l c o n t i n u i t y . The problem of d i f f e r e n t s p e c i f i c g r a v i t i e s i n d i f f e r e n t p a r t s of a d e p o s i t remains unsolved due t o the l a c k of data i n t h i s respect. The working assumption at t h i s stage i s t h a t the s p e c i f i c g r a v i t y i s roughly constant. Composites of the three bulk samples taken from the v e i n on the 2600 f t . l e v e l and a bulk sample from the v e i n i n t e r s e c t i o n i n the d e c l i n e were analyzed by L a k e f i e l d Reasearch (1988). The average of two determinations gave a s p e c i f i c g r a v i t y 3.21 or a tonnage f a c t o r of 10.0 f t 3 / s t . 70 5 4 0.019 0.016 H 0.013 0.010 -0.007 -0J0O5-X X X X X X X X XXX X XX o X XX o - var iogram values from drift data — i 1 1 1 1 1 1 1 1 — 200 400 600 800 1000 a) 8 0.012 -0.010 -0.008-0.006 0.004-1 0.002-1 X X X X X X X X X X X X X X X - 1 — I 1 1 1—I 1 — I— I 60 120 180 240 300 b) Fig.VII.2 Variogram of gold grades from a) drill hole assays b)drift assays. Mod. Cor A 0.99 -( 0.83 0.66 0.50-0.33-0.17-*3 X X X * Jx x xO x x n , . x x x x x x o - correlogram of grades from drift data a) I — i 1 1 — i — i — i — i — i — i i 0 200 400 600 800 1000 h Mod. Cor 0.79-| 0.66 0.52-0.39-0.26 0.13-1 X XX X X X X X X X X X X X X X X X b) 1 1 1 1 1 1 1 1 1 1 1 *~ 0 60 120 180 240 300 h Fig.VII.3 Correlogram of gold grades from a) drill hole assays b ) drift data A - denotes less than 30 pairs 71 CHAPTER V I I I CROSSVALIDATION C r o s s - v a l i d a t i n g of the models chosen may i n our case pose c e r t a i n problems. With the average spacing between the holes being approximately 100 f t i t i s u n l i k e l y t h a t k r i g i n g w i l l be able t o make much use of the s h o r t - s c a l e c o n t i n u i t y . N evertheless, the attempt was made t o perform p o i n t k r i g i n g of the g o l d accumulations. The major o b j e c t i v e was to determine the best search r a d i u s f o r f u t u r e block k r i g i n g . The r a d i u s chosen was 150 and 200 f t w i t h minimum three data values i n the neighborhood. In both cases the estimates were unbiased w i t h the average e r r o r c l o s e t o zero (see Appendix V I I , and F i g . V I I I . 1 ) . Variance of e s t i m a t i o n e r r o r , which can be compared t o the mean squared d i f f e r e n c e between the estimate and the r e a l value i f the average of the d i f f e r e n c e i s c l o s e to zero, i s s l i g h t l y lower f o r the search radius 200 f t . I f we compare the c o r r e l a t i o n c o e f f i c i e n t s between the r e a l and the estimated values f o r the two cases, again, the l a r g e r search r a d i u s appears to be b e t t e r . This l a r g e r search r a d i u s of 200 f t w i l l be used i n f u r t h e r c a l c u l a t i o n s . In order t o compare the r e s u l t s from k r i g i n g w i t h other e s t i m a t i o n methods polygonal estimates and i n v e r s e square d i s t a n c e w e i g h t i n g method were used f o r e s t i m a t i n g known data from samples i n the neighborhood. 72 N i 42-35-28-22-14-7 -N = 112 Mean - 0.59 Variance = 0.40 Coef. var. = 106.6 a) 0.0 1.0 2.0 3.0 ACCAU N 16 14-12-10-8--6-4-2-Mean - 0.61 Var iance = 0.12 Coef. var. = 57.3 b) a07 0.42 0.77 1.12 1.47 ACCAU Mean - 0.01 Var iance : 0.37 C ) -2JS -1.6 -0.6 0.4 1.4 ACCAU 1.5 *k ERR (ACCAU) i.o -0.5 Correlation ( Pearson) : 0 .34 * Correlation (Spearman) 0.46 d ) — i — ' i • 1 i — • — i — 0.5 1.0 1.5 2.0 £ 5 3.0 TRUE Fig.Vlll.l Crossvalidation of gold accumulations from drill holes, search radius 200x200ft:a) Histogram of known data; b) Histogram of estimates; c) Histogram of residuals; d ) Scatterplot of estimates versus true values. s By polygonal estimate i t i s understood t h a t the estimated value equals the c l o s e s t value i n the data s e t . Figure V I I I . 2 shows t h a t the histogram of estimates i s as skewed as the histogram of the tru e v a l u e s , w i t h the variance of estimates being much higher than the var i a n c e from other e s t i m a t i o n methods (see F i g . V I I I . 1 and V I I I . 3 ) ; but the variance of r e s i d u a l s c l e a r l y shows how poor an e s t i m a t i o n method i t i s . Inverse squared d i s t a n c e weighting method appears t o be much b e t t e r than the polygonal procedure w i t h v a r i a n c e of r e s i d u a l s comparable w i t h the variance from k r i g i n g r e s i d u a l s ( F i g . V I I I . 3 ) . I f we compare s c a t t e r p l o t s of tr u e versus estimated values f o r d i f f e r e n t methods i n Figures V I I I . I d , V I I I . 2 d , and V I I I . 3 c , i t appears t h a t c o r r e l a t i o n c o e f f i c i e n t s are e q u a l l y low f o r a l l of them. One must remember t h a t t h i s type of c r o s s - v a l i d a t i o n represents a very severe t e s t where data are so w i d e l y spaced, and the c o r r e l a t i o n c o e f f i c i e n t s become almost meaningless. Further, r e l a t i v e l y short range and hig h nugget e f f e c t of c o n t i n u i t y f u n c t i o n (which represents a n a t u r a l phenomenon) makes i t d i f f i c u l t t o app r e c i a t e the b e n e f i t s of the g e o s t a t i s t i c a l a n a l y s i s f o r such l a r g e d i s t a n c e s . To make sure t h a t the modified correlogram model chosen may improve the e s t i m a t i o n , d r i f t data was c r o s s - v a l i d a t e d using known nested s t r u c t u r e model and pure nugget e f f e c t model. 74 N 42-35 28-21 -14-7 -lUlkL 0.0 1.0 2.0 3.0 T R U E N 36-30 24-18 -12 -6 -Tf r fh lh l r f l i 0.0 0.5 1.0 1.5 2.0 2.5 N 28-2 4 -12 a 4 0 N Mean Va riance Coef. var. Mean Var i ance Coef. var. -: k . . . T i l l — POLEST Mean Variance 112 0.59 0.40 106.6 a) 0.617 0.37 98.6 b) -0.02 0.51 C ) -1.8 -0.8 0.2 1.2 RESPOL POLEST 25 2.0 1.5 -1.0 0.5 Correlation ( Pearson ): 0.331 Correlation ( Spearman ):0.444 d) 0.3 1.0 —I— 1.5 2.0 25 3.0 T R U E Fig.vlll.2 Crossvalidation of gold accumulations from drill holes, polygons method : a) Histogram of known data ; b) Histogram of estimates; c) Histogram of residuals; d) Scatterplot «f estimates versus true values. 75 N n 16 -14 -12 10-8-6 4 2-JUT . r 0.00 045 0.90 1.35 1.80 N - 112 Mean = 0.607 Var iance = 0.14 Coef. var. = 62.8 a) INVEST N 42-36-3 0 -24-18 " 12 6 0 • ll-fVrfl -1.4 -0.4 0.6 1.6 2.6 M e o n = -0.01 Va r i ance = 0.38 b) RES INV INVEST 1.5 -Correlation ( Pearson) : 0.35 Correlation ( Spearman ): 0.49 i.o -0.5 c) 0.3 1.0 1.5 2.0 2 5 3.0 T R U E .VIII.3 Crossvalidation of gold accumulations from drill holes, inverse square distance weighting method: a) Histogram of estimates! b) Histogram of residuals c) Scatterplot of estimates versus true values. S t a t i s t i c s of the a n a l y s i s and s c a t t e r p l o t s are given i n Appendix V I I . Using a pure nugget e f f e c t model amounts to simple averaging of the data i n the neighborhood. In t h i s case a d e f i n i t e improvement i n e s t i m a t i o n from mo d i f i e d correlogram model i n comparison w i t h pure nugget e f f e c t model can be n o t i c e d . I f we t r y a s i m i l a r procedure w i t h the c l a s s i c a l methods mentioned above, the outcome i s very s i m i l a r t o the r e s u l t s from d r i l l hole c r o s s v a l i d a t i o n . Polygonal method of e s t i m a t i o n on d r i f t data r e t u r n s worse estimates than the i n v e r s e distance weighting or p o i n t k r i g i n g . This f a c t once again shows the importance of samples which are f u r t h e r away from the estimated p o i n t even i n cases where the distances are very s m a l l . I t i s i n t e r e s t i n g t o n o t i c e t h a t the p o i n t k r i g i n g method produces i n t h i s case r e s u l t s very much comparable w i t h the inverse squared d i s t a n c e weighting procedure. A l l f i g u r e s supporting the above and more d e t a i l e d d i s c u s s i o n are given i n Appendix V I I . C r o s s - v a l i d a t i o n procedure described here show tha t e s t i m a t i n g unknown p o i n t s by o r d i n a r y k r i g i n g method w i l l produce b e t t e r r e s u l t s f o r a search r a d i u s 200 f t r a t h e r than 150 f t . F u r t h e r , the r e s u l t s of e s t i m a t i n g by the inverse squared d i s t a n c e method (ISD) are very much comparable w i t h the g e o s t a t i s t i c a l procedure. I t i s e v i d e n t , though, t h a t ISD does not give any i n f o r m a t i o n about the s t r u c t u r a l c o n t i n u i t y of v a r i a b l e s . In g e o s t a t i s t i c a l terms, ISD assumes no nugget e f f e c t though our variogram a n a l y s i s makes i t c l e a r t h a t a nugget e f f e c t does e x i s t . The method does not alow any q u a n t i f i c a t i o n of the u n c e r t a i n t y w h i l e g e o s t a t i s t i c a l methods can accomplish t h i s w i t h the k r i g i n g v a r i a n c e o r by i n d i c a t o r k r i g i n g . In view of t h a t , i t i s s t i l l f e l t t o be advantageous t o use g e o s t a t i s t i c a l methods i n assessment of r e s e r v e s . 78 CHAPTER IX ANALYSIS OF VARIABILITY OF THICKNESS AND ACCUMULATIONS TX.1 POT NT TCRTKTNn OF THICKNESS AND ACrTTMTTT.ATTONS Having shown the appropriateness of the correlogram model, point k r i g i n g of d i f f e r e n t variables along the vein i s the next l o g i c a l step towards ore reserve estimation. In t h i s case the two sections, Central and Southern, are considered i n one plane. The k r i g i n g plan at the boundary of the two sections includes data from both areas, shown i n Figure IX. 1. Point kriging of true thickness where the g r i d chosen i s 50x50 f t 2 and search radius i s 200 f t , reveals two large areas of i n t e r e s t below the 2600 l e v e l at the section 27,000 and 28,000 (Fig. IX.2) where thickness exceeds 4.0 f t . The review of points kriged reveals, though, that some of the o u t l i e r s seem to a f f e c t the estimates which could otherwise be much lower. To overcome t h i s possibly overoptimistic r e s u l t , indicator ordinary point k r i g i n g for a cutoff of 4.0 f t . was done on the same points. The outcome r e f l e c t s the p r o b a b i l i t y that the estimated value i s below 4.0 f t . These calculated p r o b a b i l i t i e s seem to be low i n the northern shoot (section 27,000) and much higher i n the southern, suggesting that as we approach the southern section the p r o b a b i l i t i e s of exceeding minimum mining width are low (Fig. IX.3). A contour map of thickness for p r o b a b i l i t i e s less than 0.5 suggests that we can be reasonably sure of the estimate approaching the true value, and suggests o o in L E V E L 2 6 0 0 C E N T R A L S O U T H E R N 3 0 0 0 L E V E L 2 5 0 0 L E V E L • —«- -O 2 0 0 0 L E V E L 0 150 M O 1r>0 S c a l e : I : 3 6 0 0 3 I M P E R I A L ( f I ) Fig. IX. I Posting of DDH which were used in analysis of variability of thickness and accumulations of metals. ^ - j _ L 1' j I M I' K RI A L ( I I ) 150 300 150 S c a l e : I : 3 6 0 0 Fig. IX.2 Contour map of thickness of vein No.3, calculated by ordinary point kriging. 81 that the area of i n t e r e s t i s su b s t a n t i a l l y lower (Fig. IX.4). If we would l i k e to be at least 70% c e r t a i n that the vein i n the area i s at l e a s t equal to minimum mining width, where d i l u t i o n with wallrock would not be substantial, the outcome would reveal that the area of i n t e r e s t around section 28,000 becomes very small (see F i g . IX.3). Point k r i g i n g of gold accumulations shows low values i n the north and elevated values as we go further south (Fig. IX.5). The immediate area of in t e r e s t which represents the values higher than 0.8 o z * f t / s t (approx. t h i r d q u a r t i l e ) covers the area 1300x250 f t . The estimated area of t h i s ore shoot i s much less optimistic i f we krige indicators for a cutoff of 0.85 o z * f t / s t . The i n d i c a t o r model used i s given i n Section VI.2.2. and the outcome of point in d i c a t o r kriging can be viewed on a contour map i n Figure IX.6. If we assume that we can be reasonably sure of the estimate i f the p r o b a b i l i t y of exceeding the cut-off i s greater than 0.6 (or less than 0.4 on the map), the area of i n t e r e s t becomes much smaller with an area of 600x150 f t between the sections 27900 and 28400 (please note t h i s area covers both Central and Southern sections) and somewhat disputable area of 300x200 f t further south. In fac t then, we have been able to define only less than a half of the area of in t e r e s t as carrying values greater than 0.85 o z * f t / s t . 3 0 0 0 L E V E L 2 0 0 0 L E V E L Scole : I : 3 6 0 0 Fig. IX.4 Contour mop of kriged estimate of thickness for probability greater thon 0.5 that the thickness is larger than 4.0 ft. Sca le : I : 3600 Fig IX 6 Contour map of gold accumulation indicator, cut-off = 0.25 oz* ft/st 86 The same holds t r u e f o r s i l v e r accumulations ( F i g . IX.7). Large values cover approximately the same area w i t h higher values f u r t h e r south. I f we perform o r d i n a r y k r i g i n g on i n d i c a t o r s f o r a c u t o f f of 40.0 o z * f t / s t (see F i g . IX.8), i t appears t h a t : f i r s t - high values between s e c t i o n 26600-27200 can be described as r e p r e s e n t i n g considerable u n c e r t a i n t y ( p r o b a b i l i t i e s l e s s than 0.5 t h a t they r e a l l y are higher than the c u t - o f f ) ; second - l a r g e values (higher than 40.0) which are present between s e c t i o n 27900-29200 appear to be l e s s probable as we go f u r t h e r south. Note t h a t the highest accumulations i n the v i c i n i t y of s e c t i o n 28300 do not c a r r y l a r g e s t p r o b a b i l i t i e s of exceeding the c u t - o f f . On the c o n t r a r y , they appear to be q u i t e weak, w i t h p r o b a b i l i t i e s of approximately 0.5. The reason f o r t h i s i s t h a t the very h i g h values i n d r i l l holes U81-11,13,14,15,16 are i n very c l o s e p r o x i m i t y t o d r i l l holes U87-09,07,12 and U81-23,26,27 which c a r r y low v a l u e s . Further, the i n d i c a t o r model chosen allows l a r g e weights f o r data away from the estimated p o i n t , p r a c t i c a l l y then a l l data i n the v i c i n i t y of 200 f t (low values are at l a r g e r distances) bear c e r t a i n i n f l u e n c e on the estimate. Zinc accumulations are the o n l y ones f o r which the highest values are between s e c t i o n 26600-27500. Further south the areas of i n t e r e s t are much s m a l l e r ( F i g . IX.9). The contour map of i n d i c a t o r s f o r a c u t o f f of 30.0 % * f t (approximately t h i r d S U R F A C E ^< » . 4 I M P E R I A L ( f l ) 150 300 4 50 Sca le . I : 3600 2 0 0 0 L E V E L .8 Contour map of silver accumulations indicator, cut- off = 40oz x ft/st. q u a r t i l e ) suggests once again t h a t as we go f u r t h e r south the l a r g e values are much l e s s probable ( F i g . IX.10). Other metal accumulations are described i n Appendix V I I I . The above a n a l y s i s i n d i c a t e s a d e f i n i t e area of i n t e r e s t around s e c t i o n 27000 f o r z i n c accumulations. Precious metal accumulations i n t u r n are much stronger as we go f u r t h e r south. Note a good l e v e l of c o n t i n u i t y of accumulations f o r gold and s i l v e r at the boundary between C e n t r a l and Southern s e c t i o n which supports the assumption t h a t they represent the same u n f a u l t e d v e i n . I t i s f e l t t h a t o v e r l a y i n g i n d i c a t o r k r i g i n g on e a r l i e r r e s u l t s gives a good i n s i g h t i n t o the e r r o r s committed during e s t i m a t i o n . Though we have used i n d i c a t o r k r i g i n g t o analyze such e r r o r s , t h i s i s more commonly attempted through the k r i g i n g v a r i a n c e . IX .2 VATiTDTTY OF KKTKTNn VARIANCE K r i g i n g variance represents minimum e s t i m a t i o n variance d e r i v e d when weights f o r samples i n the neighborhood of an estimated p o i n t are c a l c u l a t e d by the k r i g i n g system. I t does not depend on p a r t i c u l a r values of data, but o n l y on s t r u c t u r a l model chosen and on the p o s i t i o n of p o i n t s w i t h respect t o the estimated datum and w i t h respect t o each other. To be able t o b u i l d 95% confidence i n t e r v a l from the v a r i a n c e of e r r o r of e s t i m a t i o n , the a v a i l a b l e sample data have t o be assumed t o be normally d i s t r i b u t e d . Otherwise, and most commonly t h i s i s the case, the k r i g i n g v ariance represents a mere ran k i n g of data c o n f i g u r a t i o n . The f a c t t h a t i t i s not dependent on data values may be considered as a u s e f u l feature e s p e c i a l l y when a new d r i l l i n g campaign i s t o be undertaken. Thus, when a pseudo-regular g r i d of data i s present the k r i g i n g v a r i a n c e i s approximately constant throughout i f a p r o p o r t i o n a l e f f e c t i s not present. In our case when modified correlogram model i s used the v a r i a b l e a 2 c o r r e p r e s e n t i n g k r i g i n g v a r i a n c e i s : °2cor = °2}zr/°2 where: a 2 - a p r i o r i variance of data considered. In order t o c a l c u l a t e k r i g i n g v a r i a n c e f o r each estimated p o i n t on a g r i d 50x50 f t the f o l l o w i n g formula was used: ° 2krp = a 2 c o r p * °2p where: a 2p - v a r i a n c e of po i n t s w i t h i n the search radius 600 f t . This type of k r i g i n g v ariance i s c o r r e c t e d by la r g e values present i n the neighborhood, or i n other words i s i n some way co n d i t i o n e d on the data present. Figure IX.11 shows how t h i s type of k r i g i n g v a r i a n c e v a r i e s throughout the deposi t . I t i s not as constant as one might have expected, mainly because of the v a r i a n c e of data values c o n s t a n t l y i n c r e a s i n g as we go South. 2000 L E V E L I—- i Lfc- I M P E R I A L ( f t ) 0 150 300 4 50 Sca le : I : 3600 Fig. IX.II Contour map of kriging variance of estimation of Au accumulations with the search radius 600f t to estimate variance in the neighbourhood. I n d i c a t o r k r i g i n g introduces a p r o b a b i l i s t i c measure (J o u r n e l , 1988) d i r e c t l y r e l a t e d to data values from which the estimate i s c a l c u l a t e d r e t u r n i n g r e s u l t s more u s e f u l i n p r a c t i c a l a p p l i c a t i o n s . 95 CHAPTER X BLOCK KRIGING Using the a u t o c o r r e l a t i o n models described i n Chapter 5 block k r i g i n g of thickness and f o r f i v e metals was performed on the C e n t r a l and Southern v e i n segments se p a r a t e l y . I t should be noted here t h a t the problem of necessary d i l u t i o n due t o minimum mining width w i l l be addressed i n Chapter 11. Because of the w r i t e r ' s b e l i e f t h a t the v e i n i s continuous from the C e n t r a l to the Southern segment a narrow band of data (150 f t wide) adjacent but i n the C e n t r a l segment was used f o r k r i g i n g the southern segment, and v i c e v e r s a . Thus, 21 composite values from the Southern segment were used i n k r i g i n g the C e n t r a l segment (see F i g . IV.3) and 12 values from the C e n t r a l segment were used f o r k r i g i n g the Southern segment ( F i g . X . l ) . Furthermore, s e v e r a l d r i l l holes i n which the v e i n was not recognized, thus no assays, (four i n C e n t r a l and seven i n South) were a l l assigned a th i c k n e s s of 0.01 f t w h i l e the grade was assumed t o be unknown. I t was f e l t i t would be u n j u s t i f i a b l e to assume zero grade values i n those cases bearing i n mind s u b s t a n t i a l v a r i a b i l i t y of th i c k n e s s at small d i s t a n c e s as w e l l as the presence of m i n e r a l i z a t i o n greater than zero i n w a l l rock (see Chapter V). The 2-d block s i z e s e l e c t e d 200x150 f t 2 was chosen t o approximate f u t u r e mining stope s i z e . I t was f e l t t h a t stopes higher than 150 f t . may cause v e n t i l a t i o n problems and 200 f t along s t r i k e c ould be a p o s s i b l e minimum f o r any type of S73-BS1, l M$3S8W83lQ O S73-BS149 S88-035 Q 0 S73W* 1 5 0 S88-032 U73-BU191 0 ©U81-013 U81-012 _ a 0 U72-BU013 O 1)87-008 0 U87-007 0 U87-OO9 0 S U R F A C E 0 S74-001 0 Q S73-BKW130 0 G U81-027 U81-019 U81-021 U 8 7 - 0 2 4 U 8 7 - 0 2 5 / Q U 8 7 - 0 2 0 \ \U87-022 0 ® © r ' © e w-wi-y%fom]-ow us7-oo5 0 U87-006 U 8 7 - 0 2 I U 8 1 - 0 g ° „ U81-015 1)81-011 O U81-010 0 0 U81-026 U81-020 0 0 S88-057 0 U81-025 U 8 1 - ° 2 3 0 S88-058 e U88-050 0 U88-051 U88-048 O U81-024 0 §4-003 U88-052 0 U88-065 0 U88-073 0 m-00] e U89-005 0 0 im-tm 0 im-m o U88-067 9 0 U 8 8 # 9 U88-071 U88-070 © © 0 U88-0/2 U88-074 U88-0/5 0 U89-007 U 8 7 - 0 0 4 0 U87-0B7-003 0 U87-012 0 U87-013 0 U87-010 2 5 0 0 L E V E L O U8/-014 O D D H F R O M C E N T R A L S E C T I O N 2 0 0 0 L E V E L 150 3 0 0 S c a l e : I i) IMPERIAL ( ft.) 450 3600 Fig X.I Drill holes section used for reserve estimotion, Southern mechanization i n t r o d u c e d . Only the blocks which could be estimated w i t h at l e a s t f o u r d r i l l holes (search radius was 200 f t ) were estimated. Average t h i c k n e s s and accumulations f o r each block were c a l c u l a t e d by o r d i n a r y k r i g i n g . Average grade f o r each block then was c a l c u l a t e d according to the formula: Avgr=Avacc/Avth where: Avacc - average accumulation f o r a b l o c k , and Avth - average t h i c k n e s s of the same block. Figures X.2-X.5 show blocks w i t h the v a r i o u s average Au and Ag grade and t h i c k n e s s c a l c u l a t e d by o r d i n a r y k r i g i n g . Other metals are given i n Appendix IX. T o t a l i n s i t u reserves were estimated, t a k i n g i n t o account the P u l a s k i t e dyke c u t t i n g through the v e i n (see F i g . IV.1), and the mined out p o r t i o n of the v e i n . A constant s p e c i f i c g r a v i t y of 10 f t - V s t was assumed. Table X . l shows the outcome of the a n a l y s i s . F urther these reserves were r e d e f i n e d by t a k i n g i n t o account the m i n e a b i l i t y of the v e i n : 1. Only reserves below P u l a s k i t e dyke between s e c t i o n 26625-27600 are considered; 2. Crown p i l l a r s f o r #2600 and #2880 l e v e l and surface are taken i n t o account (20 f t . wide); and 3. Blocks which are above the stoped out area are excluded; s t a r t i n g from s e c t i o n 27700 no blocks above 2600 l e v e l are taken i n t o account. 98 Table X.2 shows the p o t e n t i a l l y minable i n s i t u resources f o r a c u t o f f of zero. CENTRAL SOUTH METAL SHORT GRADE THICK- SHORT GRADE THICK TONS NESS TONS NESS Au 43,647 0.110 4.71 130,615 0.271 2.79 Ag 519,890 6.32 4.34 130,615 14.48 2.79 Cu 519,890 0.24 4.34 130,615 0.93 2.79 Pb 519,890 1.06 4.34 130,615 1.60 2.79 Zn 519,890 6.87 4.34 130,615 10.07 2.79 TABLE X .1 Estimated i n s i t u resources U n i t s are as f o l l o w s : t h i c k n e s s i n f e e t , Au and Ag i n o z / s t , other metals are given i n % CENTRAL SOUTH METAL SHORT GRADE THICK- SHORT GRADE THICK TONS NESS TONS NESS Au 403,679 0.110 4.95 122,785 0.285 2.76 Ag 441,233 6.00 4.75 122,785 14.54 2.76 Cu 441,233 0.21 4.75 122,785 0.90 2.76 Pb 441,233 1.05 4.75 122,785 1.67 2.76 Zn 441,233 7.11 4.75 122,785 10.38 2.76 TABLE X.2 P o s s i b l e minable resources. U n i t s are as f o l l o w s : t h i c k n e s s i n f e e t , Au and Ag i n o z / s t , other metals are given i n % Sca le : I : 3 6 0 0 Fig X.2 Estimates of average thickness and Au grade of blocks 200x150ft by ordinary kriging method, central section of No. 3 vein. Fig. X.3 Estimates of average thickness and Au grade of blocks 200 x 150 ft?, by ordinary kriging method, southern- section of No. 3 vein Sca le : I 3600 Fig. X. 4 Estimates of average thickness and Ag grade of blocks 200x 150 ft 2 , by ordinary kriging method, Central section of No. 3 vein. 3 0 0 0 L E V E L 2 5 0 0 L E V E L 2 0 0 0 L E V E L t i \ T j I M P E R I A L ( f t ; 0 150 300 450 Scale : I : 3600 Fig. X 5 Estimates of average thickness and Ag grade of blocks 200x|50ff by ordinary kriging method, Southern section of No. 3 vein. 103 CHAPTER XI ANALYSIS OF CHANGE OF SUPPORT S e l e c t i v e mining i s ve r y o f t e n based on volumes d i f f e r e n t than volumes of blocks on which reserves were c a l c u l a t e d . I f the s e l e c t i o n i s based on mining blocks which on average represent the s i z e of the stope the recovered average grade and tonnage can be compared w i t h the i n i t i a l estimates (see Chapter X ). This i s not the case i f the s e l e c t i v e mining u n i t i s much sm a l l e r than blocks chosen f o r c a l c u l a t i o n of re s e r v e s . An attempt t o estimate the reserves based on a block s i z e 25x25 f t ^ by k r i g i n g w i t h d r i l l holes 100 f t apart, would y i e l d r e s u l t s comparable t o reserves as given i n Chapter X. D i f f e r e n t approach, i n f e r i o r t o o r d i n a r y k r i g i n g , has t o be used t o estimate the reserves based on t h i s new support. The technique chosen, i n d i r e c t lognormal method (ILN), i s used by a d j u s t i n g the histogram of p o i n t data v a l u e s , namely d r i l l h o l e s . Assume, f o r example, a s e l e c t i o n mining u n i t (SMU) 25x25xthick f t ^ , which corresponds roughly to one day's pr o d u c t i o n f o r a 300 tpd c a p a c i t y operation. I f we d i s r e g a r d the t e c h n o l o g i c a l c o n s t r a i n t s t h i s s i z e of SMU might be considered, i f we assume t h a t one day production can be s t o c k p i l e d and e i t h e r sent t o a m i l l or to a waste dump. In the w r i t e r ' s o p i n i o n three stopes mined out at the same time would be capable of ma i n t a i n i n g d a i l y production at such a r a t e . I f c u t and f i l l mining method i s introduced where the average t h i c k n e s s of the v e i n i s 4.7 f t . and the average breast 104 height 7.0 f t a block 30x7 f t . w i l l be mined out from each stope. I n case the stopes are at the di s t a n c e s from each other l a r g e enough t o assume independence of estimates the variance adjustment f a c t o r i s : - one 30x7 block f l = a 2 ( b l o c k , a r e a ) / a 2 ( . , a r e a ) - three 30x7 blocks f 3 = f l / 3 Based on t h a t , d r i l l hole data from C e n t r a l s e c t i o n were transformed by the formula: z = a * y b where: y - represents o r i g i n a l p o i n t data values ( d r i l l h o l e s ) ; and z - represents transformed data coming from the " t h e o r e t i c a l " histogram of average th i c k n e s s or accumulation of SMU considered. C o e f f i c i e n t s a and b are c a l c u l a t e d according to the formula 1.7a and 1.7b (page 22). This type of transformation does not n e c e s s a r i l y preserve the mean m and r e q u i r e s r e s c a l i n g by a f a c t o r c=m/m', where m' i s the mean of transformed data. Table XI.1 shows the values of c o e f f i c i e n t s from which Zf=z*c can be c a l c u l a t e d . 105 Coeff. Thick. AccAu AccAg AccCu AccPb AccZn f l 0.72 0.68 0.49 0.37 0.45 0.51 *3 0.24 0.23 0.16 0.12 0.15 0.17 cv 0.76 1.05 1.09 2.25 1.13 1.18 m 4.42 0.48 26.60 1.10 4.83 28.99 a 2.11 0.78 6.16 1.31 2.58 6.13 b 0.53 0.54 0.47 0.51 0.46 0.49 c 1.02 1.04 1.07 1.05 1.06 1.09 TABLE XI.1 C o e f f i c i e n t s c a l c u l a t e d f o r t r a n s f o r m a t i o n of o r i g i n a l data values by i n d i r e c t lognormal method Based on the above, the transformed Zf (see examples i n Table XI.2.) data represents d i s t r i b u t i o n of d a i l y production data coming from three stopes where from each stope a block 30x7x4.7 ft-3 i s mined out. y Z f y z f y Z f 1.60 2.70 14.60 9.0 5.38 5.3 2.07 3.10 9.84 7.3 1.29 2.4 7.98 6.50 0.91 2.0 6.62 5.9 6.41 5.80 0.01 0.2 5.02 5.1 1.52 2.70 3.73 4.4 2.89 3.9 TABLE XI.2 Examples of the tranformation of the o r i g i n a l v e i n t h i c k n e s s hole data values y, i n t o Z f transformed data v a l u e s . As i t can be n o t i c e d from above examples,the extreme values get pushed towards the mean and the r e s u l t of i t i s increased symmetry of the d i s t r i b u t i o n . Furthermore, i n order t o a r r i v e at the r e l a t i v e change of reserve e s t i m a t i o n w i t h respect t o the estimates based on 200xl50xthick f t ^ b l o c k s i z e as c a l c u l a t e d by k r i g i n g , the same 106 ILN method was used t o c a l c u l a t e the reserves e s t i m a t i o n s f o r the same block s i z e . Table XI.3 shows the r e l a t i v e change of reserves and the average grade f o r d i f f e r e n t c u t o f f s as: S t=tonnage(by ILN from 30x7)/tonnage(by ILN from 200x150) S g r=avgrade(by ILN from 30x7)/avgrade(by ILN from 200x150) Thus, t o t a l estimated recoverable reserves are: TlLN=S t*T 0.K. Av g r a d e I L N = S g r * A v g r a d e 0 . K . where: TO.K. - i s the estimated tonnage by o r d i n a r y k r i g i n g ; Avgraderj # £. - i s the estimated average grade from o r d i n a r y k r i g i n g f o r d i f f e r e n t c u t - o f f s chosen. The c u t o f f values chosen are approximately the f i r s t q u a r t i l e , the median, and the t h i r d q u a r t i l e . 107 Aver. Metal Cutoff Thick. ST Sgr T(ILN) Aver.gr(ILN) Au o z / s t 0.00 4.7 1.00 1.00 403,679 0.110 0.07 4.9 1.09 0.07 380,048 0.115 0.10 4.5 1.04 0.97 167,834 0.159 0.30 4.5 0.93 0.97 82,336 0.197 0.00 4.7 1.00 1.00 441,233 6.00 3.50 4.7 1.09 0.94 382,521 6.43 Ag o z / s t 5.70 4.7 1.14 0.92 170,742 8.99 8.60 3.7 0.93 0.94 63,800 12.37 0.00 4.7 1.00 1.00 441,233 0.21 0.12 4.7 1.17 0.91 370,268 0.24 Cu % 0.20 4.8 1.12 0.91 171,477 0.33 0.30 4.8 0.95 0.95 59,065 0.53 0.00 4.7 1.00 1.00 441,233 1.05 0.70 4.7 0.97 1.02 366,415 1.16 Pb % 1.10 4.4 1.07 0.96 223,075 1.32 1.6 3.9 1.04 0.92 35,215 1.70 0.00 4.7 1.00 1.00 441,233 7.11 3.70 4.9 0.97 1.01 395,055 7.58 Zn % 6.20 5.0 1.07 0.98 301,407 8.53 9.20 4.6 0.93 0.97 124,026 10.01 TABLE XI.3 Estimated p r o p o r t i o n of tonnage and grade due t o change of support c a l c u l a t e d by ILN i n the C e n t r a l S e c t i o n of the v e i n . The change i n c a l c u l a t e d contained metal i s n e g l i g i b l e f o r gold copper and l e a d , and s u b s t a n t i a l l y higher f o r s i l v e r and z i n c . The q u a n t i t y of estimated z i n c increases 5% and of esimated s i l v e r 4.5%. At t h i s stage the mining company must decide i f the a d d i t i o n a l p r o f i t warrants i n c r e a s e d costs of handling the ore. Note t h a t i f we d i s r e g a r d the f a c t t h a t production i s going t o take p l a c e from a few stopes and analyze volume-variance r e l a t i o n s h i p based on 25x25 f t ^ mining u n i t the outcome w i l l be more o p t i m i s t i c . This type of a n a l y s i s should not o n l y take i n t o account g e o l o g i c a l data but should a l s o concern i t s e l f w i t h the t e c h n o l o g i c a l process of mining. Appendix X shows the recovered 108 tonnage and grade f o r the mining blocks 25x25 f t , and i t a l s o attempts t o estimate the gross p r o f i t i n d o l l a r values when three 30x7 bl o c k s are considered. R e l i a b i l i t y of ILN method i n asse s s i n g g l o b a l estimates i s somewhat que s t i o n a b l e i f we c a l c u l a t e the reserves f o r d i f f e r e n t c u t o f f s and compare them w i t h k r i g i n g r e s u l t s on blocks 200xl50xthick f t ^ . Table XI.4 shows the outcome of a n a l y s i s . METAL CUT OFF ESTIMATES BY ILN METHOD ON SUPPORT 200X150 ESTIMATES BY ORD. KRIGING OF BLOCKS 200 X 150 TONNAGE (SHORT) AVERAGE GRADE TONNAGE (SHORT) AVERAGE GRADE Au 0.00 0.07 M 0.10 0.13 403,679 302,759 189,729 117,066 0.110 0.130 0.159 0.185 403,679 348,668 161,379 88,534 0.110 0.119 0.164 0.203 Ag 0.00 3.50 M 5.70 8.60 441,233 300,038 194,142 66,184 6.00 7.68 9.25 12.97 441,233 350,937 149,774 68,603 6.00 6.85 9.78 13.16 Cu 0.00 0.12 M 0.20 0.30 441,233 308,863 225,028 97,071 0.21 0.26 0.308 0.40 441,233 316,469 153,105 62,174 0.21 0.26 0.37 0.56 Pb 0.00 0.70 M 1.10 1.60 441,233 304,450 198,554 72,017 1.05 1.29 1.52 2.08 441,233 377,748 208,482 33,861 1.05 1.14 1.38 1.85 Zn 0.00 3.7 M 6.2 9.2 441,233 357,398 247,090 123,545 7.11 8.16 9.52 11.17 441,233 407,274 281,689 133,362 7.11 7.51 8.71 10.32 Table XI.4 Comparison of p o s s i b l e minable resources f o r d i f f e r e n t c u t o f f s performed on block s i z e 200xl50xthick i n C e n t r a l s e c t i o n . U n i t s are as f o l l o w s : Au and Ag i s i n o z / s t , other metals represent %. 109 I f we compare the estimates f o r the c u t o f f equal t o median (marked w i t h l e t t e r M i n the t a b l e ) , i t becomes apparent t h a t the i n d i r e c t lognormal c o r r e c t i o n method performs w e l l f o r lead and z i n c and t o a l e s s e r extent f o r gold but i t overestimates the tonnage and q u a n t i t y of metal f o r s i l v e r and copper. A c l o s e r look a t the copper m i n e r a l i z a t i o n i n C e n t r a l zone re v e a l s t h a t higher values are concentrated i n one area i n the v i c i n i t y of 28300 s e c t i o n . I t i s p o s s i b l e then, t h a t there w i l l be a small number of blocks which w i l l have higher average grade. Based on the modified correlogram model chosen the i n d i r e c t lognormal c o r r e c t i o n method assumes t h a t because of the high nugget e f f e c t higher values are more or l e s s evenly s c a t t e r e d throughout and the d i s t r i b u t i o n of block values becomes symmetric around the mean w i t h small v a r i a n c e . In r e a l i t y , the d i s t r i b u t i o n of block values i s s t i l l q u i t e skewed and o n l y a s m a l l number of blocks have hig h v a l u e s . The i n a b i l i t y of the method to recognize the high grade area and t o a d j u s t the outcomes based on s p a t i a l r e l a t i o n s h i p not revealed by the variogram i s a drawback worth a c l o s e r look. Appendix XI shows how the copper accumulation changes along the v e i n . 110 CHAPTER XII ESTIMATION OF RESERVES FOR MINIMUM MINING WIDTH XTT.1 BASTC ASSUMPTIONS As shown i n Chapter IV the m i n e r a l i z a t i o n of i n t e r e s t i s not n e c e s s a r i l y c o n f i n e d t o the v e i n . There are cases where m i n e r a l i z a t i o n can be found both i n the hangingwall and the f o o t w a l l . Appendix X I I shows a few examples of m i n e r a l i z a t i o n found o u t s i d e the v e i n . Furthermore, from the mining p o i n t of view narrow i n t e r s e c t i o n s have t o be d i l u t e d t o some predefined minimum mining width. Based on the above one can expect an increase i n the q u a n t i t y of metal considered f o r mining, as w e l l as an increase i n tonnage. In order t o c a l c u l a t e mining reserves i t was assumed t h a t : 1. Minimum mining w i d t h i s 4.0 f t ; 2. Grade across the minimum width i s a composite of best assays found i n the neighborhood of the v e i n , or i t i s d i l u t e d by 0 grade i f there are none; 3. The tenor of g o l d , s i l v e r , and zi n c m i n e r a l i z a t i o n as measured by assays i s the b a s i s f o r the choice of best i n t e r s e c t i o n i n the above order; 4. Even i f the v e i n exceeds 4.0 f t the mining width can be increased i n case there i s good m i n e r a l i z a t i o n present i n the f o o t w a l l or hangingwall of the v e i n (see Appendix X I ) ; 5. I f there i s a d d i t i o n a l v e i n present separated from the major v e i n by the low grade waste m a t e r i a l which would s u b s t a n t i a l l y d i l u t e the grade, i t i s omitted; 6. In places were v e i n was not found, the minimum mining width i s r e t a i n e d w i t h 0.00 grade f o r gold and 0.01 f o r other metals f o r reserve e s t i m a t i o n ; I l l 7. DDH S72-NGV3 w i t h composite grade entered as unknown i n the previous a n a l y s i s where v e i n thickness i s much l e s s than the assay i n t e r v a l was entered w i t h known va l u e s . In a d d i t i o n three i n t e r s e c t i o n s (U74-4, U74-5, U74-6) which were not considered so f a r were added and included i n reserve e s t i m a t i o n . X T T.3 PHOTCE OF M O D I F I E D f!OR'RF.TiO(TRAM MODELS Thickness The m o d i f i e d correlogram of thickness based on d r i l l hole i n t e r s e c t i o n s appears, at the s c a l e considered, t o represent pure nugget e f f e c t w i t h the e x c l u s i o n of the f i r s t two lags ( F i g . X I I . l a ) . I f we analyze d r i f t data d i l u t e d to the minimum mining width the modified correlogram ( F i g . X I I . l b ) does not d i f f e r from the f u n c t i o n c a l c u l a t e d i n Chapter VI. Thus, the model chosen i n previous a n a l y s i s w i l l again be used i n e s t i m a t i o n of mining r e s e r v e s . I t may be s u r p r i s i n g t h a t the m o d i f i e d correlogram of thickness of the v e i n where a l l v a r i a b l e s l e s s than 4.0 are considered as 4.0 does not show b e t t e r c o n t i n u i t y f o r s m a l l e r d i s t a n c e s . N a t u r a l l y the r e l a t i v e v ariance i s much sm a l l e r but i t does not show i n the s i l l of the modified correlogram which s c a l e s a l l covariances f o r d i s t a n c e s greater than range t o zero, or i n our case t o one. Otherwise at the s c a l e considered the s t r u c t u r a l r e l a t i o n s h i p i s s t i l l not present. 112 Mod. Cor A 0.96-0.80-0.64-0.48-j A 0.32-0.16-X X X X X X X X XX X X X X X X X a ) 1 1—I— I 1 1—I— I— I— I— I 0 200 4 0 0 600 800 1000 h Mod.Cor i 0.85-0.71 -0.56-0.42-0.26-0.14-X X X X X X X X X XX X X X X X b) i — i — i — i — i — i — i — i — i — i — i — 0 32 64 96 128 160 Fig.XII. I Correlogram of vein thickness from a) drill hole data, minable widths b) drift data, minable widths. Mod. Cor J> 1.03-0.83- X X 0.68-0.51 0.34-0.17-x x x x x X X X X X X X X X X X a ) 1 1 1 1 1 1 1 1 1 1 1 *~ 0 200 400 600 900 1000 h Mod.Cor A 0.95 0.79. 0.63. 0.47 0.32-0.16-X X X X b) T — i — i — i — i — i — i — i — i — i — i » -0 60 120 180 240 300 h Fig.XII.2 Correlogram of gold accumulations, a) drill hole assays, minable widths b) drift assays, minable widths. A - denotes less than 30 pairs 113 Gold accumulation M o d i f i e d correlograms of gold accumulation f o r d r i l l hole i n t e r s e c t i o n s ( f i g . XII.2 a) and f o r d r i f t data ( f i g . XII.2 b) do not appear t o d i f f e r from the modified correlograms c a l c u l a t e d f o r the v e i n . Therefore the model given i n Chapter 5 i s going t o be used i n f u r t h e r c a l c u l a t i o n s . Lead accumulation The m o d i f i e d correlogram of l e a d accumulation as given i n f i g . XII.3a r e t u r n s lower values f o r the f i r s t few lags than the ones encountered when the v e i n was analyzed. S u r p r i s i n g l y , t h i s s t r u c t u r a l behavior i s not evident when the c l a s s i c a l variogram i s c a l c u l a t e d . One must bear i n mind t h a t the correlogram i s a f f e c t e d by the covariance f u n c t i o n which f o r the f i r s t lags i s s u b s t a n t i a l . The covariance f u n c t i o n i n t h i s case i s a f f e c t e d by a few aberrant l a r g e value p a i r s . To check f o r the behavior of the f u n c t i o n the covariance was c a l c u l a t e d on a subset of data and i t turned out not t o d i f f e r so much when compared w i t h other l a g s . The m o d i f i e d correlogram of d r i f t data again i s comparable w i t h the same f u n c t i o n f o r the v e i n accumulations ( f i g . XII.3b). Although the model chosen i n Chapter VI returns s l i g h t l y higher values than given i n f i g u r e XII.3a i t was f e l t t h a t the d i f f e r e n c e i s n e g l i g i b l e f o r the purpose of e s t i m a t i o n , and t h i s model i s going t o be used i n f u r t h e r a n a l y s i s . 114 Mod. Cor 1.02 0.83 0.68 - O 0.51 -0.34-0.17 X X x x x x x o o o o x x o x 2 0 0 o Vein model — i — 400 600 8 0 0 1000 a) Mod. Cor 1.03-0.87-0.70-0.32-j x 033-0.17-X X X X X X X X X —r— 60 —1 120 ISO " I 1 2 4 0 - I 1 3 0 0 b) Fig.XII.3 Correlogram of lead accumulations, a) drill hole assays, minable widths b) drift assays, minable widths. A — denotes less than 30 pairs M o d i f i e d correlograms of accumulations of other metals as given i n appendix X I I I are not d i f f e r e n t from experimental f u n c t i o n s given i n Chapter VI. Therefore, the models d e r i v e d f o r these v a r i a b l e s from v e i n a n a l y s i s are going t o be used again. 115 XTT.3 ORE RESERVE ESTIMATION The approach towards the mining ore reserve e s t i m a t i o n i s e x a c t l y as described i n Chapter X when the reserves were based on the v e i n m i n e r a l i z a t i o n . The o n l y d i f f e r e n c e i s i n a s s i g n i n g the 0.00 values f o r gold and 0.01 f o r other metals were the v e i n was not found and the assays were not given i n the i n t e r v a l of i n t e r e s t . Table XII.1 shows the i n s i t u mining resources and Table XII.2 gives minable resources: METAL CENTRAL SOUTH SHORT TONS GRADE THICK-NESS SHORT TONS GRADE THICK-NESS Au 592,467 0.086 6.33 220,266 0.152 4.6 Ag 708,134 4.78 5.95 220,266 8.15 4.6 Cu 708,134 0.19 5.95 220,266 0.54 4.6 Pb 708,134 0.82 5.95 220,266 0.89 4.6 Zn 708,134 5.43 5.95 220,266 5.67 4.6 Table XII.1 D i l u t e d i n s i t u resources. Units are as f o l l o w s : t h i c k n e s s i n f e e t , Au and Ag i s i n o z / s t , other metals are given i n %. 116 METAL CENTRAL SOUTH SHORT TONS GRADE THICK-NESS SHORT TONS GRADE THICK-NESS Au 530,607 0.088 6.54 202,106 0.163 4.6 Ag 583,137 4.71 6.31 202,106 8.33 4.6 Cu 583,137 0.18 6.31 202,106 0.53 4.6 Pb 583,137 0.84 6.31 202,106 0.94 4.6 Zn 583,137 5.81 6.31 202,106 5.93 4.6 Table XII.2 D i l u t e d P o s s i b l e Minable Resources. U n i t s are as f o l l o w s : t h i c k n e s s i s i n f e e t , Au and Ag i s i n o z / s t , and other metal are given i n %. D i l u t e d p o s s i b l e minable resources are based on minimum width 4.0 f t . , somewhat i d e a l i z e d approach, w i t h no c o n s i d e r a t i o n t o a d d i t i o n a l d i l u t i o n from the s t r o n g l y a l t e r e d and o f t e n incompetent w a l l r o c k . Previous production data d u r i n g the p e r i o d January-June 1973 i n d i c a t e a d d i t i o n a l d i l u t i o n averaging approximately 20% (Cominco, 1988). Furthermore, the recovery of precious and base metals has been known t o be q u i t e low due t o the complex metallurgy averaging 29% f o r Au, 56% f o r Ag, Cu, and Pb, and 81% f o r Zn. Based on L a k e f i e l d Research t e s t work (1988) the re c o v e r i e s of paying metals by the process of f l o t a t i o n , b i o l e a c h i n g , and r o a s t i n g , were found t o be much higher. Table XII.3 shows the estimated value of recovered metals. 117 V a r i a b l e Short Tons 20% d i l . i n c l . Aver. Grade % * Recov. Spot Metal P r i c e s Oct. 24/90 $ US Value of Metal Au 879,255 0.086 63 371.10/oz 18,597,185 Ag 942,291 4.66 90 4 .23/oz 16,877,069 Cu 942,291 0.22 85 1.24/lb 4,431,311 Pb 942,291 0.71 87 0.35/lb 4,143,098 Zn 942,291 4.79 96 0.61/lb 53,728,649 TOTAL 97,777,312 Table XII.3 Estimated f u l l y d i l u t e d tonnage, average grade, and gross value of metals recovered from the No. 3 v e i n . Metal p r i c e s are quoted from The Northern Miner * Based on l a b o r a t o r y t e s t s by L a k e f i e l d Research XIT.4 COMPART RON OF WFRTTT.TS WTTH TTNPTIRTiTSHF.D POMTNCO F R T T M A T F f i In order t o check the estimated mining reserves w i t h the estimates from the past, two areas i n C e n t r a l s e c t i o n were compared. These areas of polygonal shape given i n the unpublished re p o r t by Cominco, were estimated o n l y by the data w i t h i n t h e i r boundaries. The f i r s t polygon w i t h a t o t a l of 22 d r i l l holes i n c l u d e d , between s e c t i o n 26250 and s e c t i o n 27250 (see F i g . IV.1, P0L1) returned average t h i c k n e s s 0.8 f t . higher and the q u a n t i t y of metals up t o 10% gr e a t e r (zinc) than t h a t given by Cominco. Larger t h i c k n e s s appears t o show because of two d r i l l h oles: U88-027 and U88-028 which show the t r u e m i n e r a l i z e d t o be 10 f t . wider. The d i f f i c u l t y of determining the l i m i t s of the v e i n has 118 been w e l l recognized i n t h i s area and some of the d r i l l holes l i k e U88-027 were cut t o 15.0 f t by Cominco. The s i l v e r accumulation i s o n l y 95% of the Cominco estimates. The main reason appears t o be the i n t e r p r e t a t i o n of v e i n a t t i t u d e i n the area. There are a few d r i l l holes (U88-20, U88-21, U88-22, U88-31) which show the v e i n t o be narrower than estimated by Cominco. Average s i l v e r grade w i t h i n considered i n t e r s e c t i o n s i s s i m i l a r but the q u a n t i t y of metal i s l a r g e r . Because a number of d r i l l holes were not d r i l l e d p erpendicular t o the s t r i k e d i r e c t i o n the assumed a t t i t u d e of the v e i n w i l l have an e f f e c t on the c a l c u l a t e d t r u e t h i c k n e s s of the v e i n and i n t u r n on the q u a n t i t y of metal. The f a c t t h a t c l o s e t o 10% more q u a n t i t y of z i n c was estimated when wider s e c t i o n s were i n c l u d e d may suggest the p o s s i b i l i t y of some k i n d of mechanization f o r wider stopes. The second polygon i n c l u d e d 13 d r i l l holes (see F i g . IV.1, P0L2). Estimated average t h i c k n e s s i s approximately the same i n both cases. There are l a r g e d i s c r e p a n c i e s though i n the estimate of average grade e x c l u d i n g g o l d . Table XII.4 compares the c a l c u l a t i o n s . 119 VARIABLE AUTHOR COMINCO THICKNESS Au Ag Cu Pb Zn 5.36 f t 0.176 o z / s t 8.49 o z / s t 0.20 % 1.11 % 8.15 % 5.40 f t 0.178 o z / s t 10.21 o z / s t 0.283 % 1.48 % 9.07 % TABLE XII.4 Comparison of estimates of average t h i c k n e s s and grade of a polygon (POL2) i n C e n t r a l s e c t i o n of No. 3 v e i n . These l a r g e d i s c r e p a n c i e s are because of the f o l l o w i n g : averages from four stopes as w e l l as U81-17 and U81-18 are i n c l u d e d i n Cominco e s t i m a t i o n ( t o t a l 17 data i n c l u d e d i n e s t i m a t e s ) ; Two d r i l l holes BU-191 and U81-09 of very low grade (BU-191 c a r r i e s o n l y t r a c e values) are inc l u d e d i n the present a n a l y s i s . I f we exclude the stope data and two low grade holes the estimates w i l l be as given below: AUTHOR COMINCO VARIABLES GRADE ACCUMULATION GRADE ACCUMULATION Ag 9.41 51.60 f t * o z / s t 8.98 51.9 f t * o z / s t Cu 0.222 1.22 f t * % 0.249 1.43 f t * % Pb 1.23 6.76 f t * % 1.38 7.97 f t * % Zn 8.94 49.00 f t * % 9.23 53.30 f t * % THICKNESS = 5.48 THICKNESS = 5.78 TABLE XII.5 Comparison of estimates of average t h i c k n e s s and grade of a polygon (P0L2) where stope averages (Cominco) and low grade d r i l l holes (Author) are excluded. U n i t s are as f o l l o w s : t h i c k n e s s i s i n f e e t , Ag i s i n o z / s t , other metals are i n %. As noted, the d i f f e r e n c e s are not t h a t l a r g e any more although l e a d and copper s t i l l represent o n l y 85% of the q u a n t i t y of metal c a l c u l a t e d by Cominco. 120 I t i s concluded t h a t i n g e n e r a l , t r u e thickness of the v e i n i s s l i g h t l y l a r g e r i n Cominco estimates due t o probably d i f f e r e n t assumption of the d i p of the No. 3 zone which may a f f e c t a l s o the estimates of accumulations. 121 CHAPTER X I I I CONCLUSIONS Vein type d e p o s i t s , although known t o represent u s u a l l y l a r g e v a r i a t i o n s of metals i n space, can and should be viewed by means of g e o s t a t i s t i c a l a n a l y s i s . Before any e s t i m a t i o n procedures can be u t i l i z e d the importance of g e o l o g i c a l c o n t r o l cannot be overestimated. The study of metal p r o f i l e s from e x p l o r a t i o n d r i l l i n g data, as w e l l as e s t a b l i s h i n g c o n t i n u i t y of the v e i n e s p e c i a l l y at the boundary between C e n t r a l and Southern s e c t i o n s was necessary before any e s t i m a t i o n procedure was t o take p l a c e . During the process of a n a l y s i s the f o l l o w i n g problems, p r e v i o u s l y unnoticed, were revealed: v a l i d i t y of data, i . e . importance of e x p l o r a t o r y data a n a l y s i s ; v e i n boundaries ( L e i t c h e t . a l . , 1990); nature and complexity of m i n e r a l i z a t i o n (Hood & S i n c l a i r , 1991); d i s t r i b u t i o n of grades i n w a l l r o c k . These problematic features when ex p l a i n e d through i n t e r a c t i o n between g e o l o g i c a l assessment of depo s i t and s t a t i s t i c a l and variogram a n a l y s i s should, i f p o s s i b l e , be incor p o r a t e d w i t h i n the f i n a l mathematical model chosen. High nugget e f f e c t r e f l e c t e d i n the model of thickness can be ex p l a i n e d w i t h the s t r u c t u r a l a n a l y s i s of the v e i n . 122 P a r t i c u l a r problems arose i n d e f i n i n g the a u t o c o r r e l a t i o n f u n c t i o n . C l a s s i c a l estimate of c o n t i n u i t y by variogram f u n c t i o n , as i t turned out, was inadequate f o r e s t i m a t i o n of u n d e r l y i n g c o n t i n u i t y f u n c t i o n throughout the whole of the s t u d i e d domain. I t was found t h a t the m o d i f i e d correlogram f u n c t i o n (presented as an i n v e r t e d correlogram) allows combining i n f o r m a t i o n from two se t s of data (DDH and d r i f t data) f o r which a common variogram model c o u l d not be determined. Furthermore, l a c k of s t a t i o n a r i t y i s the other reason t o consider the correlogram f u n c t i o n as one d e s c r i b i n g c o n t i n u i t y of s t u d i e d v a r i a b l e s i n the most robust manner. Not only does the modified correlogram approach perform b e t t e r w i t h respect to the c l a s s i c a l variograms but i t a l s o seems t o be more s t a b l e than the r e l a t i v e variogram. One may argue t h a t t h i s type of a f u n c t i o n i s b i a s e d because the covariance r e q u i r e s an e s t i m a t i o n of the unknown mean, but the same c r i t i c i s m must apply to r e l a t i v e variograms s i n c e they a l s o r e q u i r e estimates of the means of values f o r p a r t i c u l a r l a g s . The assumption of the known mean i s then necessary i n order t o produce the model a p p l i c a b l e throughout. In the course of a n a l y s i s d i f f e r e n t e s t i m a t i o n techniques such as i n v e r s e squared d i s t a n c e weighting, polygonal estimates method, simple averaging of data i n the neighborhood, or o r d i n a r y k r i g i n g were compared through a c r o s s v a l i d a t i o n procedure. The a n a l y s i s i n d i c a t e d t h a t the o r d i n a r y k r i g i n g procedure was s u p e r i o r w i t h respect t o other methods. One may argue t h a t comparisons on p o i n t data showed t h a t ISD method 123 performs e q u a l l y w e l l , but t h i s does not t r a n s l a t e t o estimates of u n i t s which have much d i f f e r e n t support e.g. 200x150 f tP-. Ordinary k r i g i n g technique takes i n t o account the support of a bl o c k estimated which i s not the case w i t h any more c l a s s i c a l methods. I t was shown a l s o t h a t the i n d i c a t o r k r i g i n g technique may be p a r t i c u l a r l y u s e f u l i n cases where very l a r g e values i n the neighbourhood tend t o unduly i n f l u e n c e the estimated area. Comparisons of r e s u l t s from both k r i g i n g techniques may i n d i c a t e the areas of p o t e n t i a l i n t e r e s t f o r mining being much s m a l l e r than given from o r d i n a r y k r i g i n g . . Problems of assessment of u n c e r t a i n t y of e s t i m a t i o n are approached by comparing c l a s s i c a l o r d i n a r y k r i g i n g w i t h the i n d i c a t o r k r i g i n g . The outcomes of these two a n a l y s i s when o v e r l a i d may serve as a good i n d i c a t i o n of e r r o r s committed when e s t i m a t i n g average t h i c k n e s s and grade at p o i n t x. In t u r n , k r i g i n g v a r i a n c e as i t i s shown does not desc r i b e e r r o r s of e s t i m a t i o n c o n d i t i o n e d on data values and appears t o be i n f e r i o r i n comparison w i t h i n d i c a t o r a n a l y s i s . The w e l l known phenomenon of volume-variance r e l a t i o n s h i p addressed i n our a n a l y s i s c a l l s f o r the knowledge of change-of-support model which does not always p r o p e r l y d e s c r i b e s p a t i a l v a r i a b i l i t i e s s t u d i e d . 124 The i n d i r e c t lognormal c o r r e c t i o n model proposed here, as i t i s shown, can be q u i t e l i m i t e d when l o c a l high grade ore shoots are present. I t s dependence on the c o n t i n u i t y f u n c t i o n model chosen which does not r e v e a l l o c a l p e c u l i a r i t i e s , as i s the case w i t h copper grades i n our a n a l y s i s , may be the cause of l a r g e e r r o r s when e s t i m a t i n g recovery f u n c t i o n s . I t i s f e l t t h a t change-of-suport models which would take i n t o account t h i s not so r a r e phenomenon warrant f u r t h e r research. The correlogram f u n c t i o n used i n t h i s paper, although mentioned i n the l i t e r a t u r e , has not been u t i l i z e d elswere as an a l t e r n a t i v e t o o l t o the variogram. I t appears t h a t i t can be used s u c c e s s f u l l y i n nonstationary cases. I t s behavior and shortcomings should be s t u d i e d i n other case s t u d i e s before any general conclusions can be drawn. I t would a l s o be advantageous t o develop a procedure which allows comparisons and uses j o i n t l y o r d i n a r y k r i g i n g and i n d i c a t o r k r i g i n g t o estimate ore rese r v e s . I t would c e r t a i n l y help mining engineers to design t e c h n o l o g i c a l processes t h a t take i n t o account n a t u r a l v a r i a b i l i t i e s o f t e n obvious o n l y t o a g e o l o g i s t . Based on very l a r g e v a r i a b i l i t e s of both t h i c k n e s s and metals i n the No. 3 v e i n i t i s f e l t t h a t f u t u r e sampling programs should be undertaken mainly underground. R i g i d sampling procedures where samples are of approximately the same volume i f taken across s i m i l a r widths, s t r i c t d e f i n i t i o n of what 125 i s sampled ( i . e . v e i n and a l t e r a t i o n zone) as w e l l as notes of any s t r u c t u r a l d i s c o n t i n u i t i e s should help i n c r e a t i o n of b e t t e r models f o r ore reserve e s t i m a t i o n . Sampling of core from underground d r i l l i n g should adhere t o methods developed i n d r i f t sampling. I t i s f e l t t h a t other g e o s t a t i s t i c a l procedures such as c o k r i g i n g ( i . e . e s t i m a t i o n of gold grade by s i l v e r grades) or i n t e g r a t i o n of s o f t i n d i r e c t i n f o r m a t i o n w i t h the help of Markov-Bayes procedure should be t r i e d . I t i s hoped t h a t recovery of l a r g e blocks w i l l be monitored i n the f u t u r e so t h a t the e f f e c t i v n e s s of v a r i o u s e s t i m a t i o n procedures can be compared i n a production s i t u a t i o n . The probable en echelon c h a r a c t e r of the No. 3 v e i n should a l s o be pursued, f o r i t would add t o the estimated resources due to o v e r l a p p i n g en echelon v e i n s . 126 BIBLIOGRAPHY Agterberg, F.P., 1970, A u t o c o r r e l a t i o n Functions i n Geology, i n G e o s t a t i s t i c s , D.F., Merriam ed., Proceedings of a Colloquium on G e o s t a t i s t i c s , U n i v e r s i t y of Kansas, Lawrence, Kansas, June 7-9, 1970, Plenum P r e s s , New York, p. 113-141. Buxton, B.E., 1985, G e o s t a t i s t i c a l Determination of the P r e c i s i o n of Gl o b a l Recoverable Reserve Estimates, Ph.D. T h e s i s , Department of A p p l i e d E a r t h Sciences, Stanford U n i v e r s i t y , p. 314. Church, B.N., 1985, Update On the Geology and M i n e r a l i z a t i o n i n the Buck Creek Area - the E q u i t y S i l v e r Mines R e v i s i t e d , B.C. 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E l s e v i e r Science P u b l i s h e r s B.V., Amsterdam, p.216 Davis, John C , 1973, S t a t i s t i c s and Data A n a l y s i s i n Geology., John Wiley & Sons, Inc, Canada, p. 645 Giroux, G.H., and A.J. S i n c l a i r , 1986, G e o s t a t i s t i c s at E q u i t y S i l v e r Mines L t d . : Global reserves i n the Southern T a i l Zone by volume-variance r e l a t i o n , Proc. Symp. of the Geology Div., Can. I n s t . Min. M e t a l l . , Montreal, P.Q., May 10-11, p. 218-237 Hood, C , S i n c l a i r , A., and L e i t c h , C, 1991, Min e r a l o g i c V a r i a t i o n Observed at the S i l v e r Queen Mine, Owen Lake West-Central B r i t i s h Columbia, B.C. M i n i s t r y of Energy Mines and Petroleum Resources, Report 1991-1. 127 Isaaks, E.H., S r i v a s t a v a , R.M., 1989, A p p l i e d G e o s t a t i s t i c s . Oxford U n i v e r s i t y Press: New York J o u r n e l , A.G., 1983, Common Problems Seen i n Variograms, Math, Geol., V o l . 16, No. 3, p. 305-313 J o u r n e l , A.G., 1986, G e o s t a t i s t i c s : Models and Tools f o r the Earth Sciences, Math. Geol., V o l . 18, No. 1, p.119-140. J o u r n e l , A.G., 1988, New Distance Measures: The Route Toward T r u l y Non-Gaussian G e o s t a t i s t i c s , Math, Geol., V o l . 20, No. 4, P. 459-475. J o u r n e l , A.G., and H u i j b r e g t s , Ch., 1978, Mining G e o s t a t i s t i c s . Academic Press: London. J o u r n e l , A.G., 1990, " A Markov-Bayes Formalism f o r I n t e g r a t i n g Seismic Data Accounting f o r C a l i b r a t i o n U n c e r t a i n t y " , SCRF Annual Meeting, May 16-17, Stanford U n i v e r s i t y K r i g e , D.G., and Magri, E.J., 1982, Studies of the E f f e c t s of O u t l i e r s and Data Transformation on Variogram Estimates f o r a Base Metal and a Gold Ore Body, Math. Geol., V o l . 14, No. 6, p.557-564. L a k e f i e l d Reserach, Laboratory I n v e s t i g a t i o n of the Recovery of Copper, Lead, Z i n c , Gold and S i l v e r from S i l v e r Queen Mine Ore Samples, January 18, 1988, Report to Houstin Metals Inc., by S. B u l a t o v i c . Progress Report #1. L a n t u e j o u l , Ch., 1988, On the Importance of Choosing a Change of Support Model f o r G l o b a l Reserves E s t i m a t i o n , Math, Geol., V o l . 29, No. 8, p. 1001-1019. L e i t c h , C.H., e t a l , 1990, S t r u c t u r a l Character of Epithermal P o l y m e t a l l i c V e i n and Bearing on G e o s t a t i s t i c a l Studies at the S i l v e r Queen Mine, Near Owen Lake, West-Central B.C., U n i v e r s i t y of B r i t i s h Columbia, Vancouver. Matheron, G., 1963, P r i n c i p l e s of G e o s t a t i s t i c s , Economic Geology V o l . 58, p.1246-1266 Myers, D.E., 1989, To Be Or Not To Be . . . S t a t i o n a r y ? That i s the Question., Math, Geol., V o l . 21, No. 3, p.347-362. Parker, H., Oct. 1979, The Volume-Variance r e l a t i o n s h i p : A U s e f u l Tool f o r Mine Planning, Engineering and Mining J o u r n a l , p.106-123 128 Rendu, J . M., et a l , 1982, Geology and The Semivariogram - A C r i t i c a l R e l a t i o n s h i p , 17th APCOM Symposium, p.771-783 Sibson, R.H., McMoore, J . and Rankin, R.H., 1975, Seismic Pumping - A Hydrothermal F l u i d Transport Mechanism, Jo u r n a l of the G e o l o g i c a l S o c i e t y of London, V o l . 131, p.653-659. S i n c l a i r , A.J., 1976, A p p l i c a t i o n s of P r o b a b i l i t y Graphs i n M i n e r a l E x p l o r a t i o n , S p e c i a l Volume No. 4, The A s s o c i a t i o n of E x p l o r a t i o n Geochemists. Isaaks, E., S r i v a s t a v a , R.M., 1988, S p a t i a l C o n t i n u i t y Measures f o r P r o b a b i l i s t i c and D e t e r m i n i s t i c G e o s t a t i s t i c s , Math. Geol., V o l . 20, No. 4, P. 313-341. S r i v a s t a v a , R.M., and Parker, H., 1988, Robust Measures of S p a t i a l C o n t i n u i t y , G e o s t a t i s t i c s : Proceedings of The T h i r d I n t e r n a t i o n a l G e o s t a t i s t i c s Congress, Avignon, France. Thomson, M.L., and S i n c l a i r , A.J., 1991, Syn-Hydrothermal Development of Fractures i n the S i l v e r Queen Mine Area, Owen Lake, C e n t r a l B r i t i s h Columbia, The U n i v e r s i t y of B r i t i s h Columbia, Vancouver. 129 APPENDIX I Examples of Assignment of Some D r i l l Hole M i n e r a l i z e d I n t e r s e c t i o n s t o No. 3 Vei n The assignment of some d r i l l hole m i n e r a l i z e d i n t e r s e c t i o n s to No. 3 v e i n may sometimes cause problems due t o the complexity of the g e o l o g i c a l environment. The choice was based on the drawn g e o l o g i c a l c r o s s e c t i o n s . In some cases two or three v e i n s were found at the d i s t a n c e s not l a r g e enough t o separate them i n t o f o o t w a l l and hangingwall v e i n s . The choice i n such cases had t o be made on the b a s i s of v e i n t h i c k n e s s and s t r e n g t h of m i n e r a l i z a t i o n . Gold, s i l v e r , and z i n c were the minerals of i n t e r e s t . In eleven d r i l l holes the v e i n was not found. In such cases the v e i n thickness assigned was 0.01 and the values were considered unknown. In the mining p a r t of a n a l y s i s the v e i n t h i c k n e s s assigned was 4.0 f t (minimum mining width) and t r a c e values f o r each metal entered (only gold was assumed at zero v a l u e ) . Although i t was p o s s i b l e t o f i n d i n t e r s e c t i o n s i n the d r i l l hole w i t h grades higher than assigned i t was f e l t t h a t because of our i n a b i l i t y t o f i n d the v e i n , the assignment of grades higher than background may be m i s l e a d i n g and o v e r - o p t i m i s t i c . In a couple of cases two w e l l m i n e r a l i z e d v e i n s were found c l o s e t o each other but at the d i s t a n c e which precludes 130 simultaneous mining of the two. Only one of them was chosen. The f o l l o w i n g are d r i l l holes where the choice had t o be made based on s u b j e c t i v e judgement: - D r i l l holes where the v e i n was not found: S73-BS145 - Assumed t h a t i t should be found at 138.0 f t down the hole 573- BS167 - The v e i n should be found at 187 f t . 574- 001 - The v e i n should be found at 220.0 f t . U73-BUI60 - The v e i n should be found at 160.0 f t . U81-009 - The v e i n should be found at 180.0 f t . U87-013 - Only f o o t w a l l v e i n found at 224.0-225.0 f t . According t o c r o s s e c t i o n s the v e i n should be found at 150.0 f t . D r i l l e d at the f a r south end of the v e i n . U87-014 - Crossed o n l y hanging w a l l at 116.0-117.0 f t . and the v e i n should be found a t approx 340.0 f t . D r i l l e d at the f a r south end of the v e i n . U87-021 - The v e i n should be found at 20.0 f t . U88-065,U88-066 - D r i l l e d at lower e l e v a t i o n s on the boundary between C e n t r a l and Southern zone. The v e i n should be found at 228.0 f t . U89-004 - Only f o o t w a l l v e i n found at 284.5- 287.5. The v e i n found at 360.0 f t . - D r i l l holes where more than one v e i n was found: 1 131 S88-037 - Two veins separated by 13.0 f t down the hole. The intersection chosen was 213.67-215.17 because of larger thickness. Drilled above the stoped out area was not included in reserve calculations. S88-044 - Two veins separated by less than a foot of waste, assumed one vein. U88-013 - Two veins separated by 2.0 f t of waste. In geological analysis the intersected waste excluded in calculation of the composite grades. U88-014 - Three veins found at the distance up to 10.0 f t from each other. Interval 262.17-265.67 was chosen as best mineralized. U88-015 - Two weakly mineralized veins separated a distance of 4.5 f t . Interval 333.42-338.58 entered. U88-023 - Two veins separated by a distance of 6.0 f t . Interval 261.75-262.67 chosen based on gold and zinc mineralization. U88-028 - Two veins separated by 11 f t . of microdiorite. Interval 257.0-272.0 entered as a wider section. U88-030 - Two veins separated by 10.5 f t of waste. The intersection 215.0-218.5 was chosen because of higher silver and zinc values. U88-035 - Two veins separated by 13.0 f t distance. Intersection 348.0-354.0 was entered because of higher si l v e r and zinc values. 132 U88-053 - Two veins separated by 9.0 f t . I n t e r v a l 304.0-318.0 was entered because of the width of the v e i n . M i n e r a l i z a t i o n i s comparable. U88-058 - Two veins separated by 4.5 f t of waste were j o i n e d together. Waste not i n c l u d e d i n the g e o l o g i c a l approach t o reserve e s t i m a t i o n . S88-058 - Two veins separated by 2.0 f t of waste. The waste grade i n c l u d e d i n the composite grade. U81-024 - Two veins separated by d i s t a n c e of 48.0 f t . I n t e r v a l 252.4-256.7 was chosen based on wider i n t e r s e c t i o n and s t r o n g g o l d m i n e r a l i z a t i o n . - Other d r i l l holes S73-BS149 - Only 6.0 i n c h of v e i n m a t e r i a l was found. Entered as i n t e r v a l from 152.0-152.3 w i t h no grades assigned. U73-BU191 - The so c a l l e d m i n e r a l i z e d zone i s present from 111.0-111.5, no grades assigned. U88-051 - Although the i n t e r v a l 108.0-111.0 was entered t h i s i s an example where one might suspect en echelon s t r u c t u r e because of the apparent s h i f t of the v e i n . This apparent s h i f t i s probably caused by the s i n u s o i d a l behavior of the v e i n . S72-NGV3 - Vein entered as 2.0 f t i n t e r s e c t i o n although no values were assigned because the sample i n t e r v a l taken was 133 10.0 f t . The assay value was considered i n mining approach towards the e s t i m a t i o n . U81-010 - Judging from the c r o s s e c t i o n the v e i n i n t e r v a l 206.0-213.0 chosen appears t o be s l i g h t l y higher than expected due t o probably s i n u s o i d a l behaviour of the v e i n . 134 APPENDIX I I A n a l y s i s of Bimodal D i s t r i b u t i o n of Thickness of No. 3 Vein As i t i s shown i n F i g . A I I . l and A l l . 2 cumulative d i s t r i b u t i o n of t h i c k n e s s from C e n t r a l and Southern s e c t i o n s p l o t t e d on a p r o b a b i l i t y paper represent forms suggestive of a bimodal d i s t r i b u t i o n . As described by S i n c l a i r (1976) i t i s p o s s i b l e t o e x t r a c t from the bimodal curve i n f o r m a t i o n the two normal populations t h a t comprise i t . P a r t i t i o n i n g of those bimodal p r o b a b i l i t y curves has been done on the PROBPLOT program in c l u d e d i n S p e c i a l Volume # 14 of the A s s o c i a t i o n of E x p l o r a t i o n Geochemists. As i t i s shown i n F i g . A I I . l the two populations f o r the C e n t r a l s e c t i o n are represented approximately i n the same q u a n t i t y i n the data set (proportion of p o p u l a t i o n 1 i s 45%). S i m i l a r a n a l y s i s of Southern s e c t i o n ( F i g . A l l . 2 ) shows tha t mostly the p o p u l a t i o n 1 (75% of t o t a l data set) i s represented i n t h i s area. The f a c t t h a t the two narrow populations from two s e c t i o n s are comparable (the same mean and s i m i l a r variance) suggest that they may represent the same population and t h e r e f o r e the same process of development. Thomson and S i n c l a i r (1991) describe f r a c t u r e development w i t h i n the S i l v e r Queen de p o s i t as a process of conjugate shear f r a c t u r i n g and e x t e n s i o n a l f a u l t i n g . In the s i m p l e s t form t h i s model suggests t h a t e a r l y f r a c t u r e s are conjugate shear and l a t e f r a c t u r e s are e x t e n s i o n a l f a u l t s . F i e l d evidence i n d i c a t e s t h a t the conjugate shear f r a c t u r e w a l l s are 135 o f t e n l i n e d by a s i n g l e matching l a y e r of gangue and sul p h i d e s , r e s u l t i n g from s i n g l e opening; whereas the e x t e n s i o n a l f a u l t w a l l s are l i n e d by m u l t i p l e bands of gangue and s u l p h i d e s , and have complex b r e c c i a i n the f o o t w a l l s , r e s u l t i n g from repeated v e i n i n g and movement. I t i s suggested t h e r e f o r e t h a t the narrow t h i c k n e s s v e i n p o p u l a t i o n may represent an e a r l y conjugate shear f r a c t u r e s . 136 12.00-1 P O P U L A T I O N S POP. M E A N STD.DEV. % 1 1.700 0.800 45.0 2 5.800 2.000 55.0 POP. T H R E S H O L D S 1 0.100 3.300 2 1.800 9.800 Fig. A.II.I Cumulative frequency distribution of thickness from Central section represented by two normal component populations. 137 9 9 9 8 95 8 5 7 0 5 0 3 0 15 5 2 1 P E R C E N T A R I T H M E T I C V A L U E S V A R I A B L E = T H I C K U N I T = F T . N = 4 9 N C I = 17 P O P U L A T I O N S POP. M E A N S T D . D E V . % 1 1.711 1.200 7 0 . 0 2 4 . 8 8 0 1.400 3 0 . 0 P O P . T H R E S H O L D S 1 0 . 0 0 0 4 . 1 1 0 2 2 . 0 8 0 7 . 6 8 0 Fig. A.II.2 Cumulative frequency distribution of thickness from Southern section represented by two normal component populations. 138 APPENDIX I I I S t a t i s t i c a l A n a l y s i s of Metal Grades i n Wallrock and W i t h i n the No. 3 V e i n S t a t i s t i c a l a n a l y s i s of metal grades adjacent t o the No. 3 v e i n i n d i c a t e s t h a t on average the hangingwall and f o o t w a l l values are higher than very low values encountered away from the v e i n . S c a t t e r p l o t s of w a l l r o c k versus v e i n assays f o r Au, Pb, and Cu as shown i n Figure A . I I I . l , 2 i n d i c a t e t h a t o c c a s i o n a l l y the values o u t s i d e the v e i n may a t t a i n ore grade. Note very low c o r r e l a t i o n between the grades f o r some metals. In order t o g a i n an i n s i g h t i n t o v a r i a b i l i t e s of the grades w i t h i n the v e i n f o r small d i s t a n c e s , the adjacent assay values were compared and s c a t t e r p l o t s f o r a l l metals constructed ( F i g . A . I I I . 3 ) . S u r p r i s i n g l y , the c o n t i n u i t y of m i n e r a l i z a t i o n i n d i c a t e d by the c o r r e l a t i o n c o e f f i c i e n t i s v i r t u a l l y n o n e x i s t e n t . 139 AU4/n 0.6 -0.4 -0.2 , 8 0.0* — I — 0.04 AU-Vn AU-Fr Mean 0.169 0.018 Correlation (Speorman) 0.07 a) ao6 o.oe o.i2 0.14 AU-F r P B - V n 6 -5 -4 3 2 -PB-Vn Mean 1.30 Correlation (Spearman) 0.2 0.4 —r~ 0.6 0.6 1.2 '* PB-Fr PB- Fr 0.13 0.50 b) CU-Vn 0 H i as CU-Vn CU-Fr Mean 0.33 0J08 Correlation (Spearman) 0.45 O I.S CU-Fr . Fig.A.III.I Scatterplot of lowermost vein assays versus footwall assays : a) gold (oz/st, (b) lead (%) c ) copper (%) 140 AU- Vn 1.2 -i -0 3 -0.6 0.4 -0.2 -AU-Vn Mean 0.169 Correlation (Spearman) 002 0j04 0O6 ooe AU -Hr AU-Hr 0.018 0 0 7 a) PB-Vn 6 5 H 4 3 2 I —I— 0.2 0.4 —I— 0.6 PB-Vn PB-Hr Mean 1.30 0.18 Correlation (Spearman) 0.33 b) 0.8 PB-Hr CU-Vn 4 -3 -, CU-Vn Mean 0.39 Correlation (Spearman) 0.5 - 1 — 1.5 CU-Hr 0.07 0.49 C) C U - F r Fig. A.III.2 Scatterplot of uppermost vein assays versus hangingwall assays: a) gold (oz/st.), b) lead (%), c) copper (%) 141 AU (I) 0.6-0.4-0.2-AU(I) AU(2 ) Meon 0.106 0.124 Correlation (Spearman) 0.026 a) M _ r S , ^ 0.2 0.4 I 0.6 0.8 I •2 AU(2) A6( l ) 40-30 20 > o o 10- "o . A6(l ) AG(2) Mean 6.86 6.78 Correlation(Spearman) 0.12 . • •. b) o CU ( I) k 10 20 30 40 - 1 — 50 AG (2) 2 i » CU(I) Mean 0.54 Cor relet ion (Spearman) CU(2) 0.59 0.34 C ) -T-CU(2) Fig.A.III.3 Scatterplot of adjacent vein assays: a) gold (oz/st), b) silver (oz/st), c) copper (%) 142 PB(I) 2 H ZN(I ) SO-40-30-20 10 PB (I) Mean 0.93 Correlation (Spearman) PB(2) ZN(I ) Mean 6.45 Correlation (Spearman ) 10 20 - 1 — 23 3 0 ZN (2 ) A.III.3 Scatterplot of adjacent vein assays : d) lead ( % ) , e) zinc ( % ) PB(2) 0.95 0.21 d) ZN(2) 6.75 0.14 e) 143 APPENDIX IV Data F i l e s Used i n the A n a l y s i s Data f i l e s f o r d r i l l hole i n t e r s e c t i o n s of No. 3 v e i n have the mining coordinates used dur i n g Bradina o p e r a t i o n s . The value -1 represents a marker f o r missing v a l u e s . The f i l e s which represent data from 2600 l e v e l d r i f t have the coordinates t h a t are i n no way r e l a t e d t o the mining g r i d . These coordinates were entered i n such a way as t o giv e t r u e d i s t a n c e s between the assays taken i n one dimension. This approach, i t i s f e l t , i s acceptable as long as the d r i f t assays are not i n c l u d e d i n the estimates of resources. 144 Page No. 1 12/20/90 DRILL HOLE DATA FILE FOR CENTRAL SECTION OF THE NO. 3 VEIN DDH ELEV. DEP. TH AU AG CU PB ZN FT OZ/ST OZ/ST % % % S72--NGV3 2219 26230 1.60 -1 .000 -1.00 -1.00 -1.00 -1.00 S72--NGV5 2891 27613 2.07 -1 .000 4.80 0.12 1.98 12.00 S73--BS137 2997 25600 7.98 -1 .000 0.93 0.18 0.23 0.90 S73--BS138 3003 25804 6.41 -1 .000 4.41 0.03 1.54 10.23 S73--BS139 2890 25804 1.52 -1 .000 1.17 0.10 0.23 0.72 S73--BS140 2988 25998 6.41 -1 .000 5.46 0.07 2.50 5.78 S73--BS141 2924 25996 7.07 -1 .000 2.36 0.04 0.92 3.47 S73--BS142 2952 26206 14.60 -1 .000 4.62 0.08 1.76 7.80 S73--BS143 2873 26203 9.84 -1 .000 3.26 0.06 0.63 1.95 S73- BS144 2999 26394 0.91 -1 .000 1.05 0.05 0.41 4.92 S73- BS145 2945 26393 0.01 -1 .000 -1.00 -1.00 -1.00 -1.00 S73--BS146 2917 26525 3.73 -1 .000 1.17 0.06 0.07 2.77 S73--BS151 2843 28185 5.38 -1 .000 17.56 3.64 1.72 1.49 S73--BS152 2819 28291 1.29 -1 .000 12.09 0.30 0.19 7.28 S73- BS153 2725 28310 6.62 -1 .000 10.58 1.04 0.45 6.29 S73- BS154 2904 27996 5.02 -1 .000 21.60 0.20 0.66 3.54 S73 -BS156 2863 28079 2.89 -1 .000 11.19 0.26 0.86 3.81 S73- BS162 2938 27844 1.37 -1 .000 18.60 0.12 5.52 8.22 S73 -BS163 2868 27842 2.95 -1 .000 7.35 0.10 1.37 3.27 S73 -BS166 2937 27686 7.76 -1 .000 1.56 0.04 0.50 3.00 S73 -BS167 2874 27685 0.01 -1 .000 -1.00 -1.00 -1.00 -1.00 S73 -BS168 2970 27509 4.72 -1 .000 9.93 0.21 0.89 7.28 S73 -BS169 2929 27508 1.55 -1 .000 6.18 0.12 2.85 1.89 S73 -BS170 2965 27270 2.83 -1 .000 9.27 0.08 2.45 9.51 S73 -BS171 2808 27230 7.87 -1 .000 1.05 0.04 0.21 1.05 S73 -BS172 2800 26557 2.07 -1 .000 2.58 0.11 1.55 3.85 S74 -002 2117 27979 4.02 0 .068 1.48 0.04 0.26 1.20 S88 -033 2831 28235 2.36 0 .169 13.87 0.28 0.25 1.16 S88 -035 2761 28232 2.20 0 .039 12.39 2.38 1.63 6.82 S88 -036 2838 28088 2.89 0 .028 3.45 0.21 0.20 2.48 S88 -037 2783 28085 1.20 0 .018 1.65 1.01 0.20 0.29 S88 -038 2879 27884 3.14 0 .091 1.46 0.02 0.72 4.16 S88 -039 2804 27881 0.91 0 .038 2.22 0.03 0.07 1.84 S88 -040 2825 27729 1.35 0.385 21.88 0.31 0.51 0.78 S88 -041 2701 27726 1.52 0 .092 3.27 0.03 0.98 0.90 S88 -042 2947 27583 1.34 0 .193 4.78 0.06 1.28 1.76 S88 -043 2798 27580 3.28 0 .424 7.30 0.07 0.68 3.07 S88 -044 2944 27411 4.47 0 .055 2.97 1.05 0.44 1.70 S88 -045 2814 27405 0.51 0 .319 36.17 0.26 4.39 11.50 U73 -BUI 5 7 2927 25607 6.94 -1 .000 1.07 0.44 0.21 0.75 U73 -BUI 5 8 2838 25601 0.91 -1 .000 33.60 3.83 0.19 0.10 U73 -BUI 5 9 2934 25690 2.23 -1 .000 4.71 0.12 1.54 6.00 U73 -BUI 60 2807 25711 0.01 -1 .000 -1.00 -1.00 -1.00 -1.00 U73 -BUI 91 2610 28299 0.33 -1 .000 -1.00 -1.00 -1.00 -1.00 U81 -001 2511 27920 3.64 0 .305 27.59 0.19 1.06 18.56 U81 -002 2389 27922 4.67 0 .105 13.20 0.24 2.69 23.80 145 Page No. 2 12/20/90 DRILL HOLE DATA FILE FOR CENTRAL SECTION OF THE NO. 3 VEIN DDH ELEV. DEP. TH AU AG CU PB ZN FT OZ/ST OZ/ST % % % U81-003 2271 27928 13.15 0 .100 4 .11 0.18 0.70 6.31 U81-004 2518 28026 9.12 0 .291 5 .98 0.24 1.04 8.73 U81-005 2417 28035 6.45 0 .057 1 .95 0.11 0.36 3.04 U81-006 2304 28051 1.68 0 .101 5 .03 0.05 0.89 4.33 U81-007 2247 27782 2.72 0 .086 1 .70 0.20 0.13 0.14 U81-008 2358 27773 2.37 0 .015 5.30 0.06 0.18 0.84 U81-009 2513 27801 0.01 0 .009 0 .12 **. ** 0.05 0.42 U81-010 2399 28261 3.69 0.301 7 .95 0.04 1.44 7.22 V81-011 2454 28255 7.48 0 .180 17 .93 0.55 1.26 11.20 U81-012 2525 28249 1.44 0.202 22 .90 0.43 5.56 13.90 U81-016 2524 28145 6.56 0 .177 7 .15 0.39 1.35 11.10 U88-001 2516 26701 8.88 0 .159 8 .60 0.27 0.87 6.87 U88-002 2368 26686 4.85 0 .090 1 .46 0.04 0.20 3.43 U88-003 2298 26684 0.42 0 .018 0 .95 0.02 0.23 1.72 U88-004 2498 26814 2.30 0 .025 1 .11 0.02 0.31 1.45 U88-005 2395 26810 3.42 0 .060 4 .88 0.51 0.74 10.76 U88-006 2309 26794 6.51 0 .104 4 .07 0.13 0.89 10.42 U88-007 2515 26503 3.98 0 .015 0 .30 0.09 0.12 0.15 U88-008 2442 26501 3.69 0 .059 9.26 0.07 2.68 6.48 U88-009 2224 26511 1.67 0 .139 1 .70 0.20 0.96 1.48 U88-010 2492 26620 14.99 0 .069 6 .78 0.42 0.75 4.53 U88-011 2417 26608 5.33 0 .031 0 .69 0.04 0.31 2.45 1388-013 2508 26422 5.54 0 .050 0 .86 0.04 1.02 4.85 U88-014 2386 26409 3.10 0 .038 1 .53 0.13 0.14 1.50 U88-015 2272 26405 3.89 0 .046 1 .01 0.04 0.56 2.31 U88-016 2489 26293 6.48 0 .051 10 .90 2.07 2.00 13.74 U88-017 2372 26280 2.30 0 .033. 1 .21 0.32 0.37 2.67 U88-019 2488 27104 7.96 0 .181 5 .99 0.13 2.71 9.71 U88-020 2391 27109 7.23 0 .194 5 .08 0.20 1.62 14.38 U88-021 2291 27095 5.89 0 .052 1 .92 0.18 1.23 14.60 U88-022 2497 27207 6.58 0 .130 7 .28 0.20 1.16 12.95 U88-023 2394 27195 0.69 0 .106 14 .38 0.04 1.79 18.90 U88-024 2140 27088 2.01 0 .043 5 .48 0.15 4.29 13.47 U88-025 2284 27208 4.30 0 .089 6 .21 0.11 3.34 12.41 U88-026 2489 27335 0.96 0 .141 6 .59 0.10 3.58 12.15 U88-027 2486 26901 14.90 0 .056 5 .97 0.21 1.90 11.74 1388-028 2408 26934 13.92 0 .061 1 .40 0.05 0.39 5.86 U88-030 2508 26993 3.29 0 .065 2 .99 0.22 0.58 18.10 1388-031 2432 27021 9.48 0 .054 11 .49 0.05 2.35 13.54 U88-032 2323 26995 6.05 0 .044 0 .61 0.09 0.23 1.42 U88-033 2548 27700 2.77 0 .295 14.29 0.06 1.78 3.38 1388-034 2398 27665 1.63 0 .033 1 .65 0.49 0.04 0.16 U88-035 2278 27683 3.49 0 .020 1 .12 0.13 0.16 6.15 U88-036 2511 27789 4.49 0 .099 2 .99 0.03 0.16 1.34 U88-037 2395 27935 4.59 0.397 11 .96 0.27 2.32 12.60 U88-047 2319 28140 3.31 0 .216 13 .97 0.19 2.78 15.10 146 Page No. 3 12/20/90 DRILL HOLE DATA FILE FOR CENTRAL SECTION OF THE NO. 3 VEIN DDH ELEV.. DEP. TH AU AG CU PB ZN FT OZ/ST OZ/ST % % % U88-•048 2220 28209 5.58 0.013 0.24 0.01 0.18 0.97 U88-•049 2241 28126 1 .50 0.276 23.74 0.25 5.21 3.12 U88-•050 2301 28199 2.88 0.190 20.36 0.24 1.36 1.71 U88-•053 2383 27393 12.73 0.110 4.32 0.05 1.01 5.51 U88-•054 2483 27397 2.99 0.016 0.12 0.01 0.03 0.32 U88-•055 2298 27390 1.16 0.321 6.80 0.07 2.05 8.10 U88-•056 2217 27382 3.30 0.022 0.83 0.02 0.31 2.50 U88-•057 2401 27332 9.30 0.073 2.43 0.09 0.36 6.68 U88-•058 2302 27316 2.55 0.041 2.66 0.06 0.66 5.86 U88-•059 2356 27459 3.56 0.123 7.41 0.07 0.93 18.30 U88-•060 2272 27497 1.83 0.110 1.71 0.13 0.84 15.00 U88-•061 2366 27631 5.31 0.055 1.90 0.02 0.11 1.23 U88-•062 2289 27461 2.10 0.101 1.58 0.09 0.90 6.24 U88-•063 2283 27585 7.07 0.004 0.26 0.01 0.02 0.23 U88-•064 2221 27558 1.30 0.050 2.35 0.14 1.58 14.20 U88-•067 2107 28204 2.18 0.221 43.17 0.23 2.53 0.28 U88-•068 2103 28076 6.25 0.146 10.00 0.38 1.37 8.30 U88-•076 2080 27934 1.44 0.123 18.38 0.14 0.26 1.25 1 147 Page No. 1 12/27/90 DRILL HOLE DATA FILE FOR SOUTH. SECTION OF THE NO. 3 VEIN DDH ELEV. DEP. TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % S73-BS149 2786 28348 0.24 -1.000 -1.00 -1.00 -1.00 -1 .00 S73-BS150 2735 28373 6.50 -1.000 2.52 0.25 0.17 1.54 S73-BS164 2778 28597 0 .81 -1.000 8.73 0.75 3.48 9 .15 S74-001 2891 28558 0 .01 -1.000 -1.00 -1.00 -1.00 -1 .00 S74-003 2320 28609 4 .23 0.320 9.68 0.54 0.18 7 .54 S88-030 2783 28622 3 .89 0.020 2.77 1.22 0.38 0 .96 S88-031 2818 28320 1 .01 0.155 22.75 1.39 3.34 13 .80 S88-032 2708 28332 1 .03 0.006 0.59 0.03 0.84 5 .15 S88-057 2475 28776 6 .91 0.251 10.54 1.70 2.94 10 .05 S88-058 2433 28907 5 .03 0.647 29.08 0.75 1.14 22 .48 U72-BU013 2745 28436 3 .60 -1.000 21.26 2.84 0.51 5 .93 U81-013 2550 28394 4 .19 0.241 17.18 0.96 1.46 4 .87 U81-014 2502 28411 6 .05 0.328 16.90 1.48 1.26 2 .05 U81-015 2470 28428 4 .51 0.194 35.20 1.02 0.66 4 .76 U81-019 2540 28558 3 .71 0.372 17.20 0.26 1.88 18.50 U81-020 2484 28555 5 .17 0.355 14.00 0.31 1.40 17 .40 U81-021 2538 28622 1 .93 0.202 12.70 0.39 1.25 15 .85 U81-023 2432 28550 1 .95 0.118 0.49 0.06 0.09 0 .88 U81-024 2375 28611 1 .87 0.221 4.04 0.08 0.27 1 .64 U81-025 2424 28495 8 .85 0.272 11.85 0.66 0.98 12 .83 U81-026 2486 28499 1 .75 0.291 11.20 0.26 1.44 19 .80 U81-027 2540 28493 2 .92 0.125 4.84 0.14 0.76 3 .95 U87-003 2621 29110 0 .86 0.007 1.00 1.34 0.02 0 .19 U87-004 2621 29078 0 .64 0.026 2.28 0.35 0.73 9 .05 U87-005 2619 28955 5 .17 0.047 11.81 0.44 0.13 0 .45 U87-006 2555 28965 1 .94 0.137 14.29 1.03 0.42 0 .89 U87-007 2613 28449 2 .15 0.029 5.54 0.68 0.39 1 .02 U87-008 2672 28432 1 .25 0.018 1.37 0.72 0.04 0 .13 U87-009 2566 28459 1 .11 0.062 4.46 0.28 0.44 3 .15 U87-010 2626 29324 0.35 0.048 3.09 0.26 0.42 4 .23 U87-012 2619 29208 3 .69 0.058 8.63 0.47 0.47 3 .06 U87-013 2547 29188 0 .01 -1.000 -1.00 -1.00 -1.00 -1 .00 U87-014 2451 29378 0 .01 -1.000 -1.00 -1.00 -1.00 -1 .00 U87-018 2618 28893 1 .27 0.050 4.26 2.07 0.47 3 .92 U87-020 2616 28860 0 .86 0.027 3.69 0.97 0.34 0 .67 U87-021 2609 28866 0 .01 -1.000 -1.00 -1.00 -1.00 -1 .00 U87-022 2665 28851 0 .71 0.033 10.85 3.08 0.34 1 .09 U87-024 2616 28830 1.24 0.030 15.75 1.73 0.34 0 .40 U87-025 2616 28798 2 .06 0.096 8.43 1.33 0.24 0 .51 U88-051 2307 28464 2 .45 0.458 14.53 0.33 0.51 1 .42 U88-052 2285 28592 2 .75 0.183 15.14 0.69 3.02 10 .80 U88-065 2193 28521 0 .01 -1.000 -1.00 -1.00 -1.00 -1 .00 U88-066 2223 28514 0 .01 -1.000 -1.00 -1.00 -1.00 -1 .00 U88-069 2212 28587 3 .40 0.521 13.01 0.24 1.34 12 .45 U88-070 2174 28590 5 .16 0.311 10.62 0.42 1.08 8 .68 U8 8-071 2205 28660 2 .78 0.200 11.75 0.19 2.06 19 .80 148 Page No. 2 12/27/90 DRILL HOLE DATA FILE FOR SOUTH. SECTION OF THE NO. 3 VEIN DDH ELEV. DEP. TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % U88-•072 2145 28633 2.26 0.074 5.83 0 .15 0 .10 0.97 U88-•073 2246 28689 1.84 0.329 11.29 1 .14 0 .46 1.77 U88-•074 2145 28716 2.79 0.311 10.65 0 .65 1.32 12.60 U88-•075 2118 28586 1.29 0.095 4.40 0.54 0 .32 8.22 U89-•001 2435 28842 3.74 0.359 15.63 0 .94 5 .14 18.60 U89-•003 2340 28867 3.16 0.308 20.56 1 .83 3 .65 11.20 U89-•004 2267 28885 0.01 -1.000 -1.00 -1 .00 -1 .00 -1 .00 U89-•005 2386 28813 1.48 0.223 8.46 0 .34 1 .94 5.50 U89-•007 2191 28968 2.10 0.569 10.03 0 .43 0 .90 1.90 U89-008 2347 28923 1.02 0.213 26.83 2 .88 2 .87 9.15 149 Page No. 12/27/90 DRILL HOLE DATA FILE FOR ASSAYS DILUTED TO MINIMUM MINING WIDTH 4.0 FT FOR CENTRAL SECTION OF NO. 3 VEIN DDH ELEV. DEP. TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % S72-NGV3 572- NGV5 573- BS137 S73-BS138 S73-BS139 S73-BS140 S73-BS141 S73-BS142 S73-BS143 S73-BS144 S73-BS145 S73-BS146 S73-BS151 S73-BS152 S73-BS153 S73-BS154 S73-BS156 S73-BS162 S73-BS163 S73-BS166 S73-BS167 S73-BS168 S73-BS169 S73-BS170 S73-BS171 573- BS172 574- 002 S88-033 S88-035 S88-036 S88-037 S88-038 S88-039 S88-040 S88-041 S88-042 S88-043 S88-044 S88-045 U7 3-BUI 57 U7 3-BUI 5 8 U73-BU159 U73-BU160 U73-BU191 U81-001 U81-002 2219 26230 2891 27613 2997 25600 3003 25804 2890 25804 2988 25998 2924 25996 2952 26206 2873 26203 2999 26394 2945 26393 2917 26525 2843 28185 2819 28291 2725 28310 2904 27996 2863 28079 2938 27844 2868 27842 2937 27686 2874 27685 2970 27509 2929 27508 2965 27270 2808 27230 2800 26557 2117 27979 2831 28235 2761 28232 2838 28088 2783 28085 2879 27884 2804 27881 2825 27729 2701 27726 2947 27583 2798 27580 2944 27411 2814 27405 2927 25607 2838 25601 2934 25690 2807 25711 2610 28299 2511 27920 2389 27922 4.0 0.040 4.0 -1.000 8.0 -1.000 6.4 -1.000 4.0 -1.000 6.4 -1.000 7.1 -1.000 14.6 -1.000 9.8 -1.000 4.0 -1.000 4.0 0.000 4.0 -1.000 5.4 -1.000 4.0 -1.000 6.6 -1.000 5.0 -1.000 4.0 -1.000 4.0 -1.000 4.0 -1.000 7.8 -1.000 4.0 0.000 4.7 -1.000 4.0 -1.000 4.0 -1.000 7.9 -1.000 4.0 -1.000 4.0 0.067 4.0 0.101 4.3 0.021 4.0 0.020 4.0 0.005 4.2 0.073 4.0 0.010 4.0 0.139 4.0 0.042 4.0 0.065 4.0 0.349 4.5 0.056 4.0 0.052 6.9 -1.000 4.0 -1.000 4.0 -1.000 4.0 o-.ooo 4.0 0.000 4.0 0.278 4.7 0.105 0.30 0.009 2.49 0.062 0.93 0.180 4.41 0.030 0.45 0.037 5.46 0.070 2.36 0.043 4.62 0.080 3.26 0.058 0.24 0.013 0.01 0.010 1.09 0.055 17.56 3.638 3.90 0.098 10.58 1.036 21.59 0.200 8.09 0.188 6.37 0.040 5.42 0.075 1.56 0.040 0.01 0.010 9.93 0.210 2.40 0.048 6.56 0.058 1.05 0.039 1.34 0.055 1.49 0.045 8.15 0.169 6.61 1.264 2.50 0.150 0.50 0.305 1.13 0.015 0.60 0.008 7.73 0.130 1.37 0.009 1.60 0.020 6.01 0.055 2.97 1.047 4.79 0.042 1.07 0.439 7.65 0.873 2.63 0.068 0.01 0.010 0.01 0.010 25.10 0.175 13.20 0.240 0.03 0.40 1.03 6.21 0.23 0.90 1.54 10.23 0.09 0.27 2.50 5.78 0.92 3.47 1.76 7.80 0.63 1.95 0.09 1.12 0.01 0.01 0.07 2.58 1.72 1.49 0.06 2.35 0.45 6.29 0.66 3.54 0.62 2.75 1.89 2.82 1.01 2.41 0.50 3.00 0.01 0.01 0.89 7.28 1.11 0.73 1.73 6.73 0.21 1.05 0.80 1.99 0.26 1.20 0.15 0.70 0.85 3.57 0.14 1.79 0.06 0.09 0.64 3.21 0.04 0.49 0.24 1.08 0.45 0.91 0.43 0.59 0.61 2.60 0.44 1.70 0.56 1.51 0.21 0.75 0.04 0.02 0.86 3.35 0.01 0.01 0.01 0.01 0.96 16.89 2.69 23.80 150 Page No. 12/27/90 DRILL HOLE DATA FILE FOR ASSAYS DILUTED TO MINIMUM MINING WIDTH 4.0 FT FOR CENTRAL SECTION OF NO. 3 VEIN DDH ELEV. DEP. TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % U81-003 2271 27928 13 .2 0.100 4 .11 0.175 0.70 6.31 U81-004 2518 28026 9 .1 0.291 5 .98 0.236 1.04 8.73 U81-005 2417 28035 6 .5 0.057 1 .95 0.113 0.36 3.04 U81-006 2304 28051 4 .0 0.043 2 .11 0.020 0.38 1.82 U81-007 2247 27782 4 .0 0.058 1 .15 0.136 0.09 0.10 U81-008 2358 27773 4 .0 0.009 3 .14 0.033 0.11 0.50 U81-009 2513 27801 4 .0 0.009 0 .12 0.004 0.05 0.42 U81-010 2399 28261 4 .0 0.278 7 .34 0.033 1.33 6.66 U81-011 2454 28255 7 .5 0.180 17 .93 0.553 1.26 11.20 U81-012 2525 28249 4 .0 0.077 8 .74 0.165 2.59 5.94 U81-016 2524 28145 6 .6 0.177 7 .15 0.390 1.35 11.10 U88-001 2516 26701 8 .9 0.159 8 .60 0.273 0.87 6.87 U88-002 2368 26686 8 .4 0.089 1 .46 0.038 0.20 3.43 U88-003 2298 26684 4 .0 0.005 0 .20 0.013 0.05 0.37 U88-004 2498 26814 4 .0 0.015. 0 .64 0.013 0.18 0.83 U88-005 2395 26810 4 .0 0.052 4.22 0.432 0.65 9.29 U88-006 2309 26794 6 .5 0.104 4 .07 0.134 0.89 10.42 U88-007 2515 26503 4 .0 0.015 0 .30 0.090 0.12 0.15 U88-008 2442 26501 4 .0 0.058 8 .69 0.063 2.49 5.99 U88-009 2224 26511 4 .0 0.058 0 .74 0.083 0.40 0.66 U88-010 2492 26620 15 .0 0.069 6 .78 0.415 0.75 4.53 U88-011 2417 26608 5 .3 0.032 0 .69 0.041 0.31 2.45 U88-013 2508 26422 5 .5 0.051 0 .86 0.036 1.02 4.85 U88-014 2386 26409 4 .0 0.030 1 .20 0.100 0.13 1.20 U88-015 2272 26405 4 .0 0.045 0 .98 0.035 0.55 2.25 U88-016 2489 26293 6 .5 0.051 10 .90 2.065 2.00 13.74 U88-017 2372 26280 4 .0 0.020 0 .70 0.182 0.21 1.54 U88-019 2488 27104 8 .0 0.181 5 .99 0.129 2.71 9.71 U88-020 2391 27109 7 .2 0.194 5 .08 0.201 1.62 14.39 U88-021 2291 27095 5 .9 0.053 1 .92 0.183 1.23 14.60 U88-022 2497 27207 6 .6 0.131 7.28 0.198 1.16 12.95 U88-023 2394 27195 4 .0 0.034 2 .65 0.010 0.37 3.97 U88-024 2140 27088 4 .0 0.036 3.54 0.096 2.59 8.26 U88-025 2284 27208 7 .8 0.056 4 .45 0.170 2.00 8.76 U88-026 2489 2 7335 4 .0 0.048 1 .72 0.028 0.93 3.39 U88-027 2486 26901 24 .8 0.056 4 .21 0.149 1.30 9.11 U88-028 2408 26934 27 .8 0.040 1 .72 0.036 0.55 4.77 U88-030 2508 26993 9 .4 0.081 3 .98 0.747 0.78 7.92 U88-031 2432 27021 14 .8 0.077 7 .78 0.051 1.53 9.57 U88-032 2323 26995 6 .1 0.045 0 .61 0.088 0.23 1.42 U88-033 2548 27700 4 .0 0.205 9 .90 0.043 1.23 2.34 U88-034 2398 27665 4 .0 0.013 0 .67 0.200 0.02 0.07 U88-035 2278 27683 4 .0 0.018 1 .01 0.129 0.14 5.52 U88-036 2511 27789 4 .5 0.098 2 .99 0.031 0.16 1.34 U88-037 2395 27935 5 .7 0.318 10.23 0.232 1.87 10.57 U88-047 2319 28140 4 .0 0.179 11 .62 0.172 2.32 12.94 151 Page No. 3 12/27/90 DRILL HOLE DATA FILE FOR ASSAYS DILUTED TO MINIMUM MINING WIDTH 4.0 FT FOR CENTRAL SECTION OF NO. 3 VEIN DDH ELEV. DEP. TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % U88-048 2220 28209 5 .6 0 .013 0.24 0 .007 0.18 0.97 U88-049 2241 28126 4 .7 0 .112 7.72 0 .080 1.77 2.15 U88-050 2301 28199 4 .0 0 .138 14.73 0 .173 0.98 1.59 U88-053 2383 27393 12 .7 0 .111 4.33 0 .049 1.01 5.51 U88-054 2483 27397 4 .0 0 .015 0.13 0 .008 0.03 0.30 U88-055 2298 27390 4 .0 0 .109 2.12 0 .026 0.61 3.11 U88-056 2217 27382 4 .0 0 .018 0.69 0 .015 0.26 2.08 U88-057 2401 27332 9 .3 0 .073 2.43 0 .087 0.36 6.68 U88-058 2302 27316 5 .8 0 .018 1.16 0 .026 0.29 2.56 U88-059 2356 27459 5 .8 0 .088 4.71 0 .055 0.62 12.80 U88-060 2272 27497 4 .0 0 .052 0.91 0 .061 0.55 7.49 U88-061 2366 27631 5 .3 0 .055 1.90 0 .024 0.11 1.23 U88-062 2289 27461 4 .0 0 .059 0.86 0 .047 0.48 3.35 U88-063 2283 27585 7 .1 0 .004 0.26 0 .010 0.02 0.23 U88-064 2221 27558 4 .2 0 .024 0.88 0 .055 0.58 5.61 U88-067 2107 28204 4 .0 0 .134 24.11 0 .132 1.49 0.66 U88-068 2103 28076 7 .5 0 .124 9.13 0 .334 1.18 7.06 U88-076 2080 27934 4 .0 0 .053 6.79 0 .054 0.11 0.63 U74-004 2467 26745 12 .7 0 .070 7.43 0.432 0.72 6.95 U74-005 2304 26908 7 .1 0 .172 6.07 0 .060 2.30 12.97 U74-006 2455 27139 5 .7 0 .048 6.32 0 .110 1.35 15.63 152 Page No. 1 12/27/90 DRILL HOLE DATA FILE FOR ASSAYS DILUTED TO MINIMUM MINING WIDTH 4.0 FT FOR SOUTH. SECTION OF NO. 3 VEIN DDH ELEV. DEP. TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % S73-BS149 2786 28348 4 .0 -1.000 0.69 0.03 0.13 0.75 S73-BS150 2735 28373 6 .5 -1.000 2.52 0.25 0.17 1.54 S73-BS164 2778 28597 4 .0 -1.000 1.77 0.15 0.71 1.85 S74-001 2891 28558 4 .0 0.000 0.01 0.01 0.01 0.01 S74-003 2320 28609 4 .2 0.319 9.68 0.54 0.18 7.54 S88-030 2783 28622 4 .0 0.020 2.69 1.19 0.37 0.93 S88-031 2818 28320 4 .0 0.055 6.04 0.37 0.84 4.08 S88-032 2708 28332 4 .0 0.002 0.15 0.01 0.22 1.33 S88-057 2475 28776 8 .6 0.206 9.29 1.45 2.40 8.20 S88-058 2433 28907 5 .8 0.571 26.24 0.91 1.03 20.00 U72-BU013 2745 28436 4 .0 0.001 19.52 2.56 0.47 5.36 U81-013 2550 28394 9.0 0.125 10.33 0.72 0.77 2.52 U81-014 2502 28411 6 .1 0.327 16.90 1.48 1.26 2.05 U81-015 2470 28428 6 .2 0.150 26.19 0.76 0.50 3.54 U81-019 2540 28558 4 .0 0.345 15.95 0.24 1.74 17.16 U81-020 2484 28555 5 .2 0.356 14.00 0.31 1.40 17.40 U81-021 2538 28622 4 .0 0.109 6.55 0.23 0.66 8.34 U81-023 2432 28550 4 .0 0.058 0.24 0.03 0.05 0.43 U81-024 2375 28611 4 .0 0.104 1.95 0.06 0.14 0.91 U81-025 2424 28495 8 .9 0.272 11.85 0.66 0.98 12.83 U81-026 2486 28499 4 .0 0.135 5.26 0.18 0.64 8.84 U81-027 2540 28493 4 .0 0.090 3.53 0.10 0.55 2.88 U87-003 2621 29110 4 .0 0.004 0.28 0.34 0.02 0.04 U87-004 2621 29078 4 .0 0.005 0.37 0.06 0.12 1.45 U87-005 2619 28955 5 .2 0.046 11.81 0.44 0.13 0.45 U87-006 2555 28965 4 .0 0.069 7.14 0.53 0.21 0.44 U87-007 2613 28449 4 .0 0.017 3.06 0.37 0.22 0.66 U87-008 2672 28432 4 .0 0.001 0.43 0.23 0.01 0.04 U87-009 2566 28459 4 .0 0.018 1.24 0.08 0.12 0.88 U87-010 2626 29324 4 .0 0.005 0.27 0.02 0.04 0.37 U87-012 2619 29208 4 .0 0.052 7.96 0.43 0.43 2.82 U87-013 2547 29188 4 .0 0.000 0.01 0.01 0.01 0.01 U87-014 2451 29378 4 .0 0.000 0.01 0.01 0.01 0.01 U87-018 2618 28893 4 .0 0.015 1.35 0.66 0.15 1.25 U87-020 2616 28860 4 .0 0.005 0.79 0.21 0.07 0.15 U87-021 2609 28866 4 .0 0.000 0.01 0.01 0.01 0.01 U87-022 2665 28851 4 .0 0.005 1.93 0.55 0.06 0.19 U87-024 2616 28830 4 .0 0.010 4.88 0.54 0.11 0.13 U87-025 2616 28798 4 .0 0.050 4.34 0.69 0.12 0.26 U88-051 2307 28464 4 .0 0.280 8.97 0.20 0.31 1.10 U88-052 2285 28592 4 .0 0.129 10.54 0.48 2.12 7.79 U88-065 2193 28521 4 .0 0.000 0.01 0.01 0.01 0.01 U88-066 2223 28514 4 .0 0.000 0.01 0.01 0.01 0.01 U88-069 2212 28587 4 .0 0.443 11.06 0.21 1.14 10.58 U88-070 2174 28590 5 .2 0.310 10.62 0.42 1.08 8.68 153 Page No. 12/27/90 DRILL HOLE DATA FILE FOR ASSAYS DILUTED TO MINIMUM MINING WIDTH 4.0 FT FOR SOUTH. SECTION OF NO. 3 VEIN DDH ELEV. DEP. TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % U88 -071 2205 28660 5 .9 0.128 9 .09 0 .43 1.06 10.21 U88 -072 2145 28633 4 .0 0.043 3.30 0 .08 0.06 0.55 U88 -073 2246 28689 4 .0 0.160 5 .48 0 .61 0.24 1.11 U88-074 2145 28716 4 .0 0.219 7 .53 0 .46 0.95 8.94 U88 -075 2118 28586 4 .0 0.030 1 .42 0 .18 0.10 2.65 U89 -001 2435 28842 4 .0 0.335 14 .62 0 .88 4.81 17.39 U89-003 2340 28867 4 .0 0.242 16 .24 1 .45 2.88 8.85 U89-004 2267 28885 4 .0 0.000 0 .01 0 .01 0.01 0.01 U89-005 2386 28813 4 .0 0.083 3 .13 0 .13 0.72 2.04 U89 -007 2191 28968 4 .0 0.297 5 .27 0 .23 0.47 1.00 U89-008 2347 28923 4 .0 0.055 6 .84 0 .74 0.73 2.33 154 Page No. 1 12/20/90 DRIFT ASSAYS FROM 2600 LEVEL, READ FROM LEVEL PLANS YCOORD XCOORD TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % 1.001 717.80 1.002 713.30 1.003 709.50 1.004 704.50 1.005 700.30 1.006 696.50 1.007 692.50 1.008 686.50 1.009 680.50 1.010 671.50 1.011 665.50 1.012 659.00 1.013 654.80 1.014 650.00 1.015 644.30 1.016 640.10 1.017 633.90 1.018 629.50 1.019 623.50 1.020 618.50 1.021 613.70 1.022 607.90 1.023 601.90 1.024 597.90 1.025 592.70 1.026 587.70 1.027 586.50 1.028 582.70 1.029 579.20 1.030 576.40 1.031 573.40 1.032 569.40 1.033 564.60 1.034 560.60 1.035 556.40 1.036 551.60 1.037 548.40 1.038 544.40 1.039 538.90 1.040 534.10 1.041 528.60 4 .0 0.06 2.70 4 .0 0.06 4.50 6 .0 0.06 4.50 6 .0 0.06 5.70 6 .0 0.09 3.60 6 .0 0.06 4.50 5 .0 0.06 7.50 5 .5 0.02 8.40 5 .0 0.02 6.30 6 .0 0.03 15.60 6 .0 0.02 5.70 2 .0 0.02 5.10 4 .0 0.03 4.50 3 .0 0.02 3.60 3 .0 0.02 3.00 4 .0 0.08 5.40 2 .0 0.03 3.60 6 .0 0.03 3.00 6 .0 0.02 3.90 3 .0 0.06 5.10 6 .0 0.03 5.40 6 .7 0.03 11.40 2 .0 0.06 8.10 5 .0 0.03 10.80 4 .5 0.03 8.70 5 .0 0.03 5.80 5 .5 0.03 8.70 6 .0 0.03 7.50 5 .6 0.03 6.30 7 .0 0.02 4.20 6 .0 0.03 6.30 4 .0 0.02 1.80 4 .0 0.03 6.00 3 .0 0.02 1.90 3 .5 0.02 1.80 4 .0 0.03 6.00 6 .0 0.02 5.40 6 .0 0.03 15.00 6 .8 0.02 3.30 6 .6 0.03 8.70 6 .0 0.06 7.10 0.45 0.76 8.80 0.50 1.45 8.60 1.10 0.40 6.60 0.11 1.80 11.60 0.41 0.96 12.00 0.36 1.34 13.60 0.14 5.60 9.20 0.27 3.60 12.00 0.05 1.60 9.60 0.39 6.40 15.60 0.09 4.00 5.20 0.05 3.20 6.40 0.04 6.00 6.60 0.03 1.80 5.20 0.02 2.80 4.00 0.03 4.00 6.40 0.36 1.24 12.80 0.08 1.10 14.40 0.06 2.80 9.20 0.07 3.20 14.80 0.05 2.40 9.20 0.10 6.00 19.60 0.09 6.00 10.40 0.08 4.00 10.40 0.11 4.80 13.60 0.18 3.20 15.20 0.36 3.60 10.00 0.06 4.80 9.20 0.17 2.40 7.20 0.23 1.36 4.40 0.40 0.64 4.80 0.10 0.34 7.20 0.11 0.34 7.20 0.20 0.21 7.60 0.09 0.21 8.40 0.38 2.80 11.20 0.34 0.56 7.60 0.80 1.10 9.40 0.20 0.18 8.00 0.90 1.34 19.20 0.52 3.20 15.20 155 Page No. 12/20/90 DRIFT ASSAYS FROM 2600 LEVEL, READ FROM LEVEL PLANS YCOORD XCOORD TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % 1.042 1.043 1.044 1.045 1.046 1.047 1.048 1.049 1.050 1.051 1.052 1.053 1.054 1.055 1.056 1.057 1.058 1.059 1.060 1.061 1.062 1.063 1.064 1.065 1.066 1.067 .068 .069 .070 .071 .072 .073 .074 1.075 1 .076 1 .077 1.078 1.079 1.080 1.081 1.082 523.80 518.80 514.60 510.60 507.10 502.60 498.60 494.80 488.80 483.60 477.80 472.10 466.40 460.20 454.70 449.90 439.90 436.70 432.50 427.00 422.20 416.00 410.00 403.80 396.40 390.40 386.20 380.70 375.70 363.70 357.50 352.50 347.00 322.00 316.50 311.50 305.30 299.80 294.60 229.10 221.90 6.0 7.0 6.5 6.0 6.0 6.0 6.0 5.0 6.8 6.0 6.0 6.5 6.0 5.0 5.6 3.6 4.5 6.0 5.0 5.0 4.2 4.0 2. 5, 4. 5. 2. 2. 2. 3. 2. 2. 3. 2, 3, 5.0 4.0 5.0 3.5 0.5 3.0 0.03 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.03 0.03 0.06 0.06 0.06 0.06 0.09 0.06 0.03 0.03 0.02 0.02 0.03 03 03 03 06 02 0.03 0.06 0. 0. 0. 0. 03 02 03 03 0.03 0.02 0.06 0.02 0.02 0.02 0.02 0.03 0.02 5.70 3.00 1.80 2.40 3.30 6.60 5.70 6.90 6.90 5.70 4.50 6.30 00 20 80 25 10 1.95 3.60 6.60 6.90 3.00 1.80 5.40 9.00 3.30 1.56 50 90 30 08 90 60 32 08 84 80 3.00 3.00 1.80 6.60 90 16 20 70 22 00 31 27 0.50 0.65 0.07 0.14 0.31 0.05 0.38 0.07 0.07 0.14 14 16 31 06 30 30 65 19 06 19 06 04 06 10 06 10 22 23 0.28 0.27 0.06 0.11 0.60 1.20 1.80 0.60 0.18 0.16 0.29 0.36 0.38 0.88 0.40 2.60 2.10 2.10 4.80 4.00 1.00 1.68 .60 ,00 13.20 12.00 12.80 80 20 00 70 80 12 30 48 92 80 32 0.27 0.51 0.29 0.70 0.80 0.31 0.16 0.02 0.26 0.90 70 32 14 10 54 0.38 0.44 0.08 0.04 11.20 9.60 6.80 4.40 4.00 4.00 1.48 2.40 5.20 6.50 6.50 1.80 6.80 2.80 6.40 11.80 13.60 3.60 12.20 6.40 00 80 16.60 6.80 8.40 15.60 10.00 4.40 1.04 2.48 156 Page No. 3 12/20/90 DRIFT ASSAYS FROM 2600 LEVEL, READ FROM LEVEL PLANS YCOORD XCOORD TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % 1.083 215.90 1.084 211.40 1.085 204.60 1.086 198.60 1.087 192.60 1.088 182.60 1.089 176.10 1.090 170.90 1.091 165.90 1.092 161.70 1.093 119.70 1.094 114.70 1.095 110.50 1.096 103.80 1.097 98.00 1.098 92.20 1.099 88.20 1.100 82.70 1.101 76.70 1.102 67.20 1.103 63.20 1.104 58.40 1.105 52.90 1.106 47.70 1.107 41.70 1.108 35.70 1.109 29.70 1.110 24.50 1.111 20.00 1.112 15.00 1.113 10.00 1.114 0.00 0.001 1117.00 0.002 1122.40 0.003 1131.40 0.004 1135.40 0.005 1144.00 0.006 1148.00 0.007 1152.80 0.008 1181.80 0.009 1185.00 6 .0 0 .02 10.50 5 .0 0 .06 10.50 7 .0 0 .06 9.00 8 .0 0 .09 8.10 5 .0 0 .06 6.30 4 .0 0 .06 4.80 5 .0 0 .03 4.80 3 .0 0 .06 3.60 5 .0 0 .02 5.70 5 .0 0 .02 5.40 6 .0 0 .02 0.30 6 .0 0 .02 3.90 6 .0 0 .02 3.60 6 .5 0 .02 7.50 6 .5 0 .02 6.60 5 .6 0 .02 12.60 7 .0 0 .02 12.00 8 .0 0 .02 6.90 6 .0 0 .02 14.40 6 .0 0 .02 24.00 6 .0 0 .02 10.80 6 .0 0 .03 10.20 6 .0 0 .02 16.55 5 .0 0 .03 8.70 5 .0 0 .03 18.00 6 .0 0 .02 44.90 6 .5 0 .02 5.70 6 .3 0 .04 7.00 13 .0 0 .03 6.60 13 .0 0 .02 8.90 13 .0 0 .02 8.90 12 .0 0 .05 9.50 3 .5 0 .02 2.01 4 .5 0 .02 1.32 6 .5 0 .02 1.32 6 .0 0 .02 1.88 6 .0 0 .02 3.50 6 .0 0 .02 4.50 6 .0 0 .02 4.20 2 .7 0.32 22.00 4 .0 0 .30 15.00 2.60 0.20 12.00 1.20 0.12 14.40 0.75 0.20 15.20 0.68 0.22 12.80 0.25 0.14 3.20 0.12 0.28 7.60 0.56 0.52 3.50 0.10 0.36 8.80 0.07 0.20 0.04 0.12 0.20 1.60 0.19 0.22 0.80 0.46 0.24 4.40 0.19 0.60 7.60 0.35 0.40 4.20 0.43 0.50 5.20 0.70 0.84 6.40 0.50 1.32 7.20 0.02 1.20 6.80 1.70 1.32 10.00 2.20 1.80 7.20 0.20 3.40 6.80 0.27 1.18 11.20 0.45 3.63 19.05 0.40 1.50 12.40 1.20 1.24 3.60 3.40 1.60 13.23 0.90 0.11 9.20 0.65 0.54 14.60 0.60 0.96 8.80 0.55 2.50 7.50 0.25 1.75 12.60 0.29 1.30 6.80 0.23 0.08 2.40 0.07 0.12 2.80 0.07 0.11 3.00 0.10 0.14 6.00 0.70 0.28 12.00 0.50 0.15 7.20 0.55 0.16 4.00 0.08 1.80 7.00 0.05 0.72 6.80 157 Page No. 12/20/90 DRIFT ASSAYS FROM 2600 LEVEL, READ FROM LEVEL PLANS YCOORD XCOORD TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % 0.011 1189.20 0.012 1191.20 0.013 1195.80 0.014 1197.80 0.015 1199.40 0.017 1215.20 0.018 1219.20 0.020 1224.60 0.021 1229.60 0.022 1231.00 0.023 1233.40 0.024 1244.80 0.025 1248.80 0.027 1254.40 0.028 1257.80 0.029 1260.40 0.030 1262.00 0.031 1268.20 0.034 1279.20 0.036 1286.00 0.037 1295.20 0.038 1301.60 0.040 1315.40 0.043 1325.00 0.044 1331.00 0.045 1335.00 0.047 1343.00 0.048 1347.00 0.049 1351.00 0.050 1357.00 0.051 1363.00 0.052 1367.00 0.054 1373.00 0.055 1381.00 0.057 1385.00 0.058 1391.00 0.060 1397.00 0.061 1401.00 0.063 1407.00 0.064 1411.00 0.066 1417.00 2 .6 0.10 5.10 2 .4 0.03 5.90 2 .4 0.03 3.30 1 .8 0.30 23.70 2 .2 0.20 9.60 2 .3 0.22 9.30 2 .0 0.24 9.90 4 .5 0.29 9.60 3 .0 0.25 15.60 1 .9 0.08 3.90 2 .0 0.32 21.00 2 .0 0.30 15.00 2 .5 0.26 20.30 1 .6 0.26 8.10 2 .2 0.16 12.30 2 .6 0.10 7.20 2 .7 0.12 3.10 1 .0 0.03 3.90 4 .2 0.16 21.00 2 .5 0.12 4.50 1 .5 0.06 3.00 2 .5 0.03 6.00 2 .2 0.18 12.90 5 .0 0.18 13.50 2 .5 0.30 18.00 3 .0 0.35 27.00 1 .2 0.12 3.60 1 .9 0.25 9.90 3 .0 0.25 2.90 2 .0 0.20 5.40 2 .0 0.35 9.90 2 .5 0.20 6.90 4 .5 0.10 4.50 3 .3 0.25 18.00 2 .7 0.38 7.20 4 .5 0.38 10.20 3 .8 0.30 9.60 3 .6 0.29 18.00 2 .2 0.35 18.00 3 .0 0.24 9.90 2 .5 0.20 10.50 0.06 0.44 1.92 0.08 0.01 1.40 0.05 0.32 3.20 0.10 0.62 2.10 0.08 0.22 2.40 0.07 0.12 0.40 0.10 1.40 3.20 0.11 1.00 " 3.20 0.16 0.68 1.20 0.08 0.22 1.80 0.20 1.65 6.00 0.09 1.90 8.00 0.17 0.74 1.64 0.08 1.78 8.60 0.23 1.80 13.60 0.81 1.60 7.80 0.19 0.40 5.20 0.17 0.14 6.80 0.23 2.00 14.40 0.15 0.90 0.40 0.17 0.16 1.20 0.11 1.08 2.40 0.11 5.60 12.00 0.13 2.50 12.00 0.13 4.00 18.20 0.22 2.60 13.20 0.10 0.78 3.20 0.14 1.80 4.00 0.07 1.40 8.00 0.06 1.22 4.40 0.19 2.20 7.60 0.10 0.32 5.20 0.17 0.80 10.00 0.10 1.60 16.00 0.13 1.48 8.80 0.07 1.70 11.00 0.09 1.64 10.40 0.16 4.40 14.20 0.09 3.20 6.80 0.10 1.40 6.20 0.13 1.44 8.00 158 Page No. 12/20/90 DRIFT ASSAYS FROM 2600 LEVEL, READ FROM LEVEL PLANS YCOORD XCOORD TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % 0 .067 1421.00 2 .5 0.24 18.00 0.15 1.20 6 .40 0 .069 1425 .00 2 .0 0.08 6.00 0.15 0.60 6 .40 0 .070 1483 .00 1 .5 0.36 30.00 0.14 0.18 0 .56 0 .071 1489 .00 2 .6 0.36 24.00 0.14 0.80 5 .50 0 .072 1501 .00 2 .5 0.32 12.60 0.09 1.68 18 .80 0 .073 1505 .00 2 .3 0.38 33.00 0.16 3.20 8 .40 0 .074 1511 .00 4 .0 0.24 24.00 0.21 2.25 16 .00 0 .075 1517 .00 2 .8 0.24 21.00 0.21 3.20 8 .00 0 .076 1523 .00 4 .5 0.32 27.00 0.11 0.38 9 .60 0 .077 1529 .00 3 .5 0.24 10.50 0.09 2.00 13 .60 0 .078 1533 .00 2 .0 0.20 9.00 0.06 1.80 7 .80 0 .079 1539 .00 2 .8 0.16 9.60 0.06 2.50 5 .60 0 .080 1587 .00 6 .0 0.02 1.83 0.02 0.36 7 .40 0 .081 1593 .00 4 .6 0.30 8.55 0.05 1.15 16.20 0 .082 1599 .00 5 .0 0.35 21.00 0.10 1.20 10 .80 0 .084 1605 .00 3 .6 0.16 21.00 0.13 0.62 4 .40 0 .085 1611 .00 2 .3 0.40 37.50 0.15 1.60 9 .60 0 .087 1615 .00 2 .2 0.24 16.65 0.12 0.98 3 .60 0 .088 1619 .00 3 .2 0.16 18.00 0.22 1.10 4.00 0 .089 1625.00 2 .2 0.40 24.00 0.16 1.80 8 .80 0 .090 1631 .00 3 .3 0.36 21.00 0.24 1.22 9 .20 0 .091 1633 .00 3 .3 0.20 12.00 0.14 2.10 16 .80 0 .092 1637.00 3 .8 0.20 21.00 0.14 1.76 6 .00 0 .093 1641 .00 5 .0 0.20 21.00 0.19 0.56 4 .40 0 .094 1645 .00 6 .0 0.08 3.30 0.11 0.67 7 .00 0 .095 1647 .00 5 .0 0.24 24.00 0.19 1.36 4 .80 0 .096 1651 .00 3 .7 0.21 15.60 0.16 0.80 4 .90 0 .097 1655 .00 2 .5 0.24 20.50 0.25 1.22 7 .00 0 .098 1657 .00 3 .0 0.30 39.00 0.13 0.76 2 .40 0 .099 1665 .00 5 .5 0.18 18.00 0.11 0.62 4 .00 0 .100 1667 .00 4 .2 0.18 13.70 0.13 0.60 2 .00 0 .101 1669 .00 4 .0 0.21 13.20 0.11 1.60 5 .60 0 .102 1673 .00 4 .0 0.24 21.00 0.49 0.68 4 .00 0 .104 1679 .00 3 .4 0.32 27.00 0.18 9.20 8 .80 0 .105 1685 .00 5 .0 0.20 30.00 0.40 4.80 5 .00 0 .106 1687 .00 6 .2 0.20 9.75 0.23 8.62 3 .00 0 .107 1691 .00 4 .9 0.20 24.00 0.18 4.80 5 .80 0 .108 1697 .00 3 .4 0.38 13.20 0.21 4.20 4 .82 0 .109 1701 .00 3 .0 0.34 30.00 0.73 1.60 5.20 0 .110 1707 .00 3 .4 0.18 10.80 0.17 4.00 8 .90 0 .111 1713 .00 3 .6 0.21 13.20 0.15 5.60 14 .60 159 Page No. 12/20/90 DRIFT ASSAYS FROM 2600 LEVEL, READ FROM LEVEL PLANS YCOORD XCOORD TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % 0.112 1717.00 0.113 1725.00 0.114 1729.00 0.115 1733.00 0.001 1738.08 0.002 1743.15 0.003 1748.23 0.004 1755.31 0.005 1760.38 0.006 1769.46 0.007 1774.54 0.008 1781.61 0.009 1788.69 0.010 1795.77 0.011 1798.84 0.012 1801.92 0.013 1805.00 0.014 1812.08 0.015 1819.15 0.016 1822.23 0.017 1825.31 0.018 1832.38 0.019 1847.46 0.020 1852.54 0.021 1859.61 0.022 1864.69 0.023 1871.77 0.024 1876.84 0.025 1883.92 0.026 1889.00 0.027 1894.07 0.028 1899.15 0.029 1906.23 0.030 1911.30 0.031 1916.38 0.032 1923.46 0.033 1930.53 0.034 1939.61 0.035 1946.69 0.036 1953.76 0.037 1960.84 3 .4 0.36 60.00 3 .6 0.10 6.00 4 .0 0.32 7.35 5 .5 0.12 9.90 4 .2 0.28 12.00 5 .6 0.12 8.90 3 .3 0.12 16.20 4 .0 0.12 10.30 3 .9 0.18 11.10 3 .0 0.18 11.00 1 .9 0.06 4.50 1 .5 0.15 21.00 2 .7 0.12 12.60 3 .3 0.12 24.00 3 .0 0.12 12.60 2 .7 0.12 6.80 4 .5 0.15 4.80 2 .7 0.04 8.55 3 .3 0.04 8.10 2 .7 0.05 8.85 3 .3 0.09 7.80 1 .0 0.06 4.60 5 .0 0.18 10.80 3 .5 0.16 7.80 1 .3 0.36 27.00 1 .5 0.06 8.70 1 .2 0.06 7.50 1 .2 0.06 7.50 2 .0 0.09 6.90 4 .0 0.06 4.30 2 .6 0.12 9.00 6 .0 0.12 6.90 5 .0 0.09 6.00 6 .0 0.09 4.50 2 .2 0.12 15.60 2 .5 0.03 1.58 4 .0 0.16 6.90 3 .0 0.12 6.90 4 .0 0.16 6.60 4 .2 0.12 7.20 6 .0 0.20 16.00 0.21 9.20 16.00 0.12 3.60 10.00 1.40 6.20 9.40 0.22 1.80 14.00 0.23 5.00 11.90 0.25 2.00 13.90 0.94 5.90 14.00 0.80 1.30 19.60 0.48 2.00 17.20 0.20 4.40 10.80 0.40 7.20 9.20 0.19 3.20 7.20 0.80 4.00 4.80 2.30 2.03 6.80 1.90 1.64 8.00 0.78 1.04 4.40 0.22 1.60 6.80 0.75 1.14 19.80 0.42 0.44 5.20 0.80 0.48 2.70 1.00 0.50 10.00 0.40 0.60 6.40 0.14 4.80 8.40 0.09 1.12 2.00 0.25 2.60 6.40 0.29 3.48 9.40 0.80 1.30 6.80 0.83 1.30 6.20 0.34 0.50 4.40 0.50 0.44 3.20 0.42 1.00 4.40 0.12 0.20 6.80 0.50 0.44 4.50 0.50 0.10 0.80 2.50 0.18 4.40 0.17 0.06 1.20 0.17 0.28 0.40 0.60 0.76 2.50 1.10 0.32 1.20 1.30 1.60 4.00 1.90 0.45 2.80 160 Page No. 12/20/90 DRIFT ASSAYS FROM 2600 LEVEL, READ FROM LEVEL PLANS YCOORD XCOORD TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % 0.038 1967.92 0.039 1973.00 0.040 1978.07 0.041 1983.15 0.042 1990.23 0.043 1995.30 0.044 2000.38 0.045 2005.46 0.046 2010.53 0.047 2017.61 0.048 2022.69 0.049 2027.76 0.050 2032.84 0.051 2037.92 0.052 2042.99 0.053 2048.07 0.054 2053.15 0.055 2058.22 0.056 2065.30 0.057 2072.38 0.058 2077.45 0.059 2084.53 0.060 2091.61 0.061 2096.68 0.062 2101.76 0.063 2104.84 0.064 2109.92 0.065 2114.99 0.066 2120.07 0.067 2125.15 0.068 2130.22 0.069 2135.30 0.070 2140.38 0.071 2145.45 0.072 2152.53 0.073 2157.61 0.074 2164.68 0.075 2173.76 0.076 2176.84 0.077 2181.91 0.078 2186.99 3 .6 0.12 12.90 1 .5 0.20 16.00 1 .0 0.12 12.90 2 .0 0.04 16.80 2 .8 0.06 5.10 5 .0 0.06 6.00 5 .5 0.03 10.20 4 .0 0.06 7.50 3 .0 0.75 12.00 6 .5 0.15 18.00 6 .0 0.38 18.36 3 .6 0.24 20.00 3 .0 0.24 21.00 3 .0 0.27 45.00 2 .6 0.63 18.00 4 .0 0.30 21.00 3 .0 0.18 10.80 2 .6 0.09 4.80 4 .5 0.06 1.32 1 .8 0.12 8.40 4 .0 0.12 15.00 5 .0 0.06 10.30 4 .0 0.06 3.00 3 .0 0.15 7.50 5 .5 0.09 5.70 5 .0 0.06 6.90 4 .0 0.06 7.50 3 .5. 0.21 10.80 3 .0 0.09 6.60 5 .0 0.15 8.70 3 .0 0.32 36.00 4 .5 0.18 15.60 3 .0 0.26 21.00 7 .0 0.21 30.00 4 .5 0.24 24.00 6 .0 0.15 30.00 6 .0 0.12 7.20 5 .3 0.04 4.05 7 .0 0.06 5.90 3 .0 0.27 24.00 5 .0 0.29 13.20 0.70 0.14 0.80 1.90 0.45 2.80 0.70 0.14 0.80 5.50 0.40 10.00 0.70 0.20 3.20 0.80 0.20 1.20 2.30 0.14 2.80 1.00 0.84 10.00 0.90 2.00 17.20 1.90 0.78 13.60 1.15 2.12 12.40 2.00 1.68 44.00 0.70 0.04 8.00 2.80 1.30 6.40 0.25 0.90 2.00 3.20 1.40 6.40 0.24 1.25 8.00 0.08 1.00 6.40 0.10 0.20 1.12 0.21 0.86 1.34 0.47 0.88 8.40 0.70 0.06 6.00 0.14 0.06 0.44 0.16 0.16 1.20 0.32 0.08 10.60 1.00 0.20 1.10 1.60 0.32 0.80 0.36 0.10 0.20 0.23 0.16 1.80 0.35 0.14 1.64 0.70 0.20 1.80 0.54 0.20 2.00 0.10 0.40 3.00 1.10 0.12 4.00 1.10 0.72 4.00 1.70 0.52 1.60 0.72 0.32 1.40 0.35 0.16 0.76 0.32 0.20 0.60 0.58 0.32 0.96 0.53 0.18 1.80 161 Page No. 12/20/90 DRIFT ASSAYS FROM 2600 LEVEL, READ FROM LEVEL PLANS YCOORD XCOORD TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % 0.079 2192.07 0.080 2199.14 0.081 2204.22 0.082 2209.30 0.083 2212.37 0.084 2215.45 0.085 2220.53 0.086 2225.61 0.087 2230.68 0.088 2235.76 0.089 2240.84 0.090 2245.91 0.091 2250.99 0.092 2254.07 0.093 2257.14 0.094 2260.22 0.095 2263.30 0.096 2268.37 0.097 2273.45 0.098 2278.53 0.099 2291.60 0.100 2296.68 0.101 2301.76 0.102 2306.83 0.103 2311.91 0.104 2316.99 0.105 2322.06 0.106 2327.14 0.107 2332.22 0.108 2337.30 0.109 2342.37 0.110 2347.45 0.111 2352.53 0.112 2357.60 0.113 2362.68 0.114 2365.76 0.115 2372.83 0.116 2377.91 0.117 2382.99 0.118 2388.06 0.119 2393.14 4.5 0.16 17 .40 6.0 0.24 33 .00 3.5 0.34 21 .00 4.5 0.15 45 .00 3.8 0.16 36 .00 2.6 0.12 12 .60 4.5 0.06 11 .10 4.5 0.15 9 .30 4.0 0.12 18.00 4.5 0.15 15 .60 3.7 0.18 21 .00 3.5 0.12 4.50 3.0 0.16 18 .00 2.0 0.12 12 .00 2.0 0.08 8 .70 3.3 0.12 14 .10 3.0 0.08 6 .90 2.6 0.12 11 .40 2.0 0.08 8 .70 6.5 0.02 0 .30 0.4 0.05 3 .95 2.0 0.12 6 .00 3.0 0.28 33 .00 6.8 0.32 15 .00 7.5 0.20 7 .80 5.9 0.40 11 .40 6.1 0.29 8 .70 4.7 0.32 8 .40 4.3 0.28 8 .40 6.6 0.36 7 .80 6.2 0.24 8 .70 7.0 0.16 8 .10 5.7 0.24 9 .60 6.8 0.16 9 .00 6.5 0.16 18 .00 6.4 0.20 7 .50 6.0 0.16 6 .60 6.6 0.40 10 .30 6.8 0.32 7 .80 3.2 0.60 8 .40 3.2 0.04 6 .00 0.32 0.18 3 .20 0.40 0.24 1 .20 0.40 0.20 1.20 0.18 0.24 0.36 0.18 0.18 0 .28 0.15 0.19 0 .78 0.20 0.12 0 .60 0.17 0.32 0 .56 0.45 0.24 0 .96 0.23 0.92 1 .04 0.22 0.32 0 .24 0.12 0.08 0 .92 0.27 0.56 2 .40 0.20 0.36 0 .48 0.46 0.47 3 .60 0.37 0.82 5 .40 0.15 0.20 0 .40 0.19 0.22 3.20 0.46 0.48 3 .60 0.04 0.06 0 .28 0.18 0.20 1 .64 0.38 2.60 17.20 0.60 0.80 3 .60 0.18 0.36 1 .60 0.23 0.50 4 .40 0.19 1.00 6 .60 0.26 0.86 3 .30 0.19 0.76 4 .00 0.26 0.66 3 .20 0.26 0.70 2 .00 0.25 0.90 2 .80 0.41 0.30 5 .60 0.29 2.00 2 .80 0.37 0.76 2 .00 0.64 0.92 2 .40 0.22 0.90 3 .60 0.21 1.90 2 .40 0.25 2.20 2 .40 0.56 2.00 4 .00 0.30 5.00 3 .20 0.08 2.00 5 .20 162 Page No. 12/20/90 DRIFT ASSAYS FROM 2600 LEVEL, READ FROM LEVEL PLANS YCOORD XCOORD TH AU AG CU PB ZN FT FT FT OZ/ST OZ/ST % % % 0. 120 2398.22 3 .0 0.12 10 .00 0.40 0 .60 1 .68 0. 121 2403.29 3 .0 0.04 5 .40 0.14 0 .20 0 .84 0. 122 2414.37 1 .4 0.32 9 .25 0.31 0 .44 1 .10 0. 123 2423.45 3 .7 0.12 13 .80 0.66 0 .82 7 .40 0. 124 2434.52 5 .8 0.10 10 .80 0.33 0 .44 0 .94 0. 125 2445.60 4 .7 0.20 11 .70 0.42 0 .49 3 .00 0. 126 2452.68 1 .3 0.24 7 .80 0.30 0 .64 2 .00 0. 127 2459.76 1 .8 0.20 12 .00 0.70 0 .68 3.20 0. 128 2464.83 4 .5 0.16 21 .00 0.50 2 .00 10 .00 0. 129 2469.91 5 .0 0.21 18 .00 0.19 2 .10 8 .40 0. 130 2474.99 3 .0 0.25 21 .00 0.39 0 .80 0.56 0. 131 2480.06 3 .0 0.24 11 .70 0.61 0 .90 1 .68 0. 132 2487.14 4 .3 0.14 11 .70 0.32 2 .28 7 .80 0. 133 2490.22 6 .4 0.16 11 .10 0.75 0 .64 2 .00 0. 134 2495.29 5 .5 0.28 13 .00 0.33 1 .12 2 .50 0. 135 2500.37 4 .8 0.24 13 .50 0.30 1 .26 1 .60 0. 136 2505.45 5 .6 0.28 18 .00 0.55 1 .12 2 .60 0. 137 2510.52 5 .0 0.24 30 .00 0.75 1.20 6 .40 0. 138 2517.60 4 .6 0.28 15 .00 0.35 1 .90 9 .20 0. 139 2524.68 4 .3 0.50 15 .30 0.50 2 .80 5 .00 0. 140 2529.75 4 .4 0.80 24 .00 0.70 2 .00 9 .60 0. 141 2534.83 4 .0 0.24 10 .50 0.29 2 .80 7 .80 0. 142 2539.91 3 .0 0.20 12 .90 0.33 2.20 11 .20 0. 143 2544.98 3 .5 0.24 11 .70 0.22 1 .02 4 .60 0. 144 2550.06 2 .5 0.15 7 .50 0.19 1 .40 6 .40 0. 145 2555.14 1 .5 0.15 21 .60 0.65 1 .98 4 .90 0. 146 2560.21 3 .2 0.15 15 .90 0.60 3 .00 3 .60 0. 147 2565.29 2 .9 0.32 15.30 0.30 1 .34 16 .40 0. 148 2570.37 2 .7 0.28 21 .00 0.45 0 .98 2 .90 0. 149 2575.45 1 .1 0.12 8 .70 0.20 1 .10 6 .30 0. 150 2580.52 1 .0 0.04 1 .50 0.08 0 .18 1 .10 0. 151 2587.60 1 .0 0.08 9 .90 0.45 0 .61 2 .60 0. 152 2592.68 2 .5 0.04 5.25 0.81 0 .38 2 .40 0. 153 2597.75 2 .3 0.04 9.30 0.38 0 .68 2 .44 0. 154 2602.83 2 .0 0.04 5 .10 0.22 0 .48 7.20 0. 155 2607.91 2 .7 0.04 2 .70 0.09 0 .40 1 .80 0. 156 2612.98 2 .8 0.08 5 .40 0.25 0 .68 1 .12 163 Page No. 1 12/20/90 READINGS OF VEIN THICKNESS TAKEN BY AUTHOR FROM 2600 LEVEL DRIFT YCOORD XCOORD THICK FT FT 0 85.80 4.41 0 92.40 4.00 0 99.00 4.75 0 105.60 3.83 0 112.20 5.75 0 118.80 6.83 0 125.40 7.08 0 132.00 7.50 0 138.60 6.00 0 198.00 3.00 0 204.60 2.00 0 1650.00 . 1.00 0 1656.60 0.83 0 1663.20 1.08 0 1669.80 1.08 0 1676.40 0.83 0 1689.60 1.00 0 1610.40 2.67 0 1603.80 3.33 0 1597.20 2.25 0 1590.60 3.00 0 1577.40 1 .50 0 1570.80 0.42 0 1564.20 1.00 0 1557.60 1.08 0 1551.00 2.08 0 1544.40 1.75 0 1537.80 1.50 0 1531.20 1.17 0 1524.60 1.58 0 1518.00 1.25 0 1511.40 1.00 0 1504.80 0.75 0 1498.20 1.00 0 1491.60 1.00 0 1485.00 1.42 0 1478.40 0.92 0 1471.80 0.92 0 1465.20 2.50 0 3300.00 1.50 0 3306.60 2.25 0 3313.20 2.92 0 3319.80 2.67 0 3326.40 2.83 0 3333.00 2.92 164 Page No. 2 12/20/90 READINGS OF VEIN THICKNESS TAKEN BY AUTHOR FROM 2600 LEVEL DRIFT YCOORD XCOORD THICK FT FT 0 3339.60 3.00 0 3346.20 3.42 0 3352.80 2.33 0 3359.40 2.00 0 3379.20 5.50 0 3385.80 4.75 0 3392.40 4.25 0 3399.00 3.75 0 3405.60 2.75 0 3412.20 3.67 0 3418.80 2.67 0 3425.40 3.50 0 3432.00 3.00 0 3445.20 2.17 0 3451.80 3.00 0 3458.40 3.08 0 3465.00 1.58 0 3471.60 . 2.33 0 3478.20 0.17 0 3484.80 2.33 0 3491.40 0.50 0 3498.00 1.00 0 3504.60 1.25 0 3531.00 2.42 0 3537.60 2.33 0 3544.20 3.25 0 3550.80 3.75 0 3557.40 5.00 0 3564.00 4.00 0 3570.60 3.50 0 3577.20 3.08 0 3583.80 1.50 0 3590.40 2.00 0 3597.00 1.00 0 3603.60 1.25 0 3610.20 0.67 0 3293.40 1.50 0 3286.80 2.58 0 3280.20 2.42 0 3273.60 2.25 0 3267.00 2.33 0 3260.40 2.00 0 3253.80 2.17 0 3247.20 3.33 0 3240.60 3.33 165 APPENDIX V Comparison of Correlogram Functions f o r D i f f e r e n t Sections of the No. 3 Vein and of the 2600 L e v e l D r i f t Although i t was shown i n s e c t i o n VI.1.2 t h a t when r e l a t i v e variograms are considered they do not d i f f e r i n C e n t r a l and Southern zone and they represent pure nugget e f f e c t more d i r e c t approach t o the l a c k of s t a t i o n a r i t y by u s i n g correlograms could have r e v e a l e d the presence of some s t r u c t u r e . As shown i n F i g . A.V.I both data sets represent once again pure nugget e f f e c t s c a l e d t o one. In the c l a s s i c a l correlogram f u n c t i o n t h i s value would be zero suggesting t o t a l l a c k of c o r r e l a t i o n between the po i n t s considered. D r i f t data comes from sampling probably more promising s e c t i o n s of the v e i n when 2600 l e v e l d r i f t was d r i v e n ( F i g . A.V.2) . I t was thought p o s s i b l e t h a t d i f f e r e n t p o s s i b l e apparent change i n the c o n t i n u i t y as described by correlograms may be caused by d i f f e r e n t sampling approaches i n the two se c t i o n s considered. Both nugget e f f e c t and range should i n d i c a t e i f i n f a c t i t was the case here. As shown i n F i g . A.V.2 the nugget e f f e c t and a small range are comparable suggesting t h a t data from two s e c t i o n s may be used as one sample. 166 Mod.Cor A 1.5-1.2 0.9 0.6 0.3 X X X X X X x X X x-x-x X X-X-X X 1 1 1— 0 160 1 1 1— 320 480 1 1 1 *~ 640 800 h a ) Mod. Cor A 1.02 4 0.85 0.68 -0.51 -0.34-0.17-X X X X X X X „ X X X X X X T 1 1 " 1 1 1 1 1 1 1 • 0 160 320 480 640 800 h b) Fig.A.V.I Correlogram of thickness from drill hole data a ) South b) Central Mod. Cor A 1.08. 0.90 -0.72 -0.54-4 X 0.36-1 X 0.18 X X X X X x x x X X X x x T ' 1 1 1 ' r -0 28 56 84 i ' r 112 140 h a) Mod.Cor A 0.98-J 0.81 x x x x x X X x x X X 0.65-| X X 0.49 0.32 0.16 T 1 1 1 1 1 1 -1 1 1 1 0 20 40 60 80 100 h b) Fig.A.V2 Correlogram of thickness from section of a drift a ) 114 data b) 251 data 167 APPENDIX VI M o d i f i e d Correlogram Models of Copper, Lead, and Zinc Accumulations M o d i f i e d correlogram of copper accumulations as shown i n F i g . A . V I . l a represents pure nugget e f f e c t w i t h q u i t e n o i s y behaviour f o r s m a l l e r d i s t a n c e s . The same f u n c t i o n c a l c u l a t e d from d r i f t data gives an i n d i c a t i o n of a weak hole e f f e c t at around 150.0 f t . One may argue t h a t the same holds t r u e f o r DDH, but i t i s f e l t t h a t the r e p r e s e n t a t i o n i s not strong enough t o g a i n i n e s t i m a t i o n when t h i s f e a t u r e i s included i n the model. The chosen model represents high nugget e f f e c t shown i n f i g . A . V I . l c . Correlograms of l e a d accumulations f o r both se t s of data are given i n F i g . A.VI.2 . The nugget e f f e c t appears to be s m a l l e r than i n case of copper. The apparent hole e f f e c t i s not present. F i n a l model, as shown i n F i g . A.VI.2c, represents a s p h e r i c a l s t r u c t u r e w i t h a range 180.0 f t . The correlogram model f o r z i n c accumulations appears to be a nested s t r u c t u r e of a nugget e f f e c t and two s p h e r i c a l models. Figure A.VI.3 shows the behaviour f o r d i f f e r e n t l a g ranges. 168 Mod. Cor L 1.08 0.97 0.80-0.64-0.48-0.32 0.16-X X X X X X X X x x x x x x X X x x x a) Mod. Cor 1.03-0 3 6 -0.68 0.51 0 3 4 -0.17 1 1 1 1 1 1 1 1 1 1 1 0 200 400 600 800 1000 h X X X X X X X X X X X X ) X X X X X a) T 1 1 1 1 1 1 1 1 1 1 * ~ 0 200 400 600 800 OOO h Mod. Cor I .07 0 .96-0.80 0.64 0.48-0.32 0.16 Mod. Cor >< x X X X X X X X X X X X X b) 1.05-0.87-0.70-0.52- X 0.35-0.17-1 — i 1 1 1 1 1 1 | 1 I • 0 60 120 180 240 300 h X X X X X X X X X x x X X b) 1 — ' 1 ' 1 — ' 1 1 1 1 — I — * ~ 0 60 120 ISO 240 300 h Mod Cor 1.2 1.0-0.8-0 . 6 - * -0.4-02-0.0 Cor( h) = 0.6+0.4 x S p h 2 5 0 ( h) Mod.Cor 1.2 .x-x-t x x - x - x - i.o -I . _ - x - x " x x J£— — x x o.8 0J6 " 0.4 -0.2 OJO C ) —1 1 1 1 1 — 32 104 156 208 260 Cor (h ) = 0.5 + 0.5 x S p h l 8 0 ( h ) C ) 43 86 ~\ 1 1 129 172 215 Fig.A.VI.I Correlograms of copper accum. a) Drill hole assays b) Drift assays c) Correlogram model Fig.A.VI.2 Correlograms of lead accum. a) Drill hole assays b) Drift assays c) Correlogram model 169 Mod.Cor f 1.03-0.86 -0.68 -O.SI 0.34-j A 0.17 -X X X X X X X X X X X X X X X a) T 1 1 1 1 1 1 ' 1 1 1 0 ZOO 400 600 800 1000 Mod.Cor f 0.90 0.75 -0.60-0 .45-0 .30-0.15 • X X X X X X X X X X X X b) —I— 88 —I— 176 264 352 440 Mod.Cor / t 1.0 0.8-1 0.6 0.4-1 0.2 QO Cor(h) = 0 . 2 6 * 0 .45 « S p h 3 0 ( h ) + 0 . 2 9 « S p h 4 0 0 ( h ) xx __ ,-x-x 2L-x- " c) I 80 —I— 160 240 I 320 400 480 Fig.A.VI.3 a) Correlogram of zinc accumulation from drill hole assays b) Correlogram of zinc accumulations from drift assays c) Correlogram model of zinc accumulations. 170 APPENDIX V I I C r o s s v a l i d a t i o n of Gold Accumulations Based on D r i f t Data C r o s s v a l i d a t i o n of a model chosen may sometimes pose c e r t a i n problems i n cases where the average d i s t a n c e s between data values are l a r g e , and a high nugget e f f e c t i s present. In such cases i t i s advantageous t o do the estimations f o r d i f f e r e n t search radius and analyze the r e s i d u a l s . Figure A . V I I . l shows t h a t i f we choose r a d i u s 150x150 f t the variance of r e s i d u a l s i s comparable to the va r i a n c e of estimated data i n d i c a t i n g no improvement i n e s t i m a t i o n i n respect t o , f o r example, simple averaging of data i n the neighbourhood. In th a t respect search r a d i u s 200x200 performs s l i g h t l y b e t t e r . A l l chosen models are f o r s m a l l e r d i s t a n c e s based on the d r i f t data v a l u e s . I t was f e l t t h a t c r o s s v a l i d a t i o n on those data would c l e a r l y i n d i c a t e i f the models chosen improve the e s t i m a t i o n when compared w i t h pure nugget e f f e c t model or compared w i t h the more c l a s s i c a l methods ( i . e . polygons, inverse square d i s t a n c e w e i g h t i n g ) . The f o l l o w i n g i s noted from estimates based on nested s t r u c t u r e model ( F i g . A.VII.2): estimates are unbiased; histograms and s t a t i s t i c s of t r u e values and estimates are s i m i l a r ; v a r i a n c e of r e s i d u a l s i s much lower than of t r u e values; and s u b s t a n t i a l c o r r e l a t i o n between t r u e and estimated data. 171 Pure nugget e f f e c t model returns the f o l l o w i n g ( F i g . A.VII.3): estimates are unbiased; histogram of estimates i s c l e a r l y d i f f e r e n t than histogram of r e a l data; variance of r e s i d u a l s i s higher than the one d e r i v e d from the nested s t r u c t u r e model; c o e f f i c i e n t of c o r r e l a t i o n between tr u e and estimated values i s lower than from the nested s t r u c t u r e model. Comparison of the k r i g i n g r e s u l t s based on nested s t r u c t u r e model w i t h ISD method re t u r n s very s i m i l a r r e s u l t s (see F i g . A.VII.2 and F i g . A.VII.4). The polygonal method of e s t i m a t i o n i s once again i n f e r i o r w i t h respect t o ISD and k r i g i n g (see F i g . A.VII.5). 172 N J, II9 -102-S 5 -6 8 -51 -3 4 - " 17-N = 365 Mean = 0.53 Var iance = 0.25 Coef. var. = 95.7 a) 0.0 r........p.. - , 1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 ACCAU N A 77-66-55 4 4 -3 3 - i 22-Mean = 0.54 Va r i ance : 0.15 Coef. var. = 72.5 liri-rT i f f>n, b) 0.07 042 0.77 1.12 1.47; 1.82 N 4 147 126 105-84 6 3 -— • ACCAU 42 21 -\ 0 Mean = 0.007 Va r i ance = 0.114 - 4 c) -2.3 -1.8 -1.3 -0.8 -0.3 0.2 0.7 ERR(ACCAU) ACCAU A 1.0 0.3 -Correlation ( Pearson) : 0.75 Correlation ( Spearman ) : 0.79 d) 2.0 3.0 TRUE Fig A.VII.2 Crossvalidation of gold accumulations from drift assays, correlogram model used: a) Histogram of true values; b) Histogram of estimates; c) Histogram of residuals; d) Scatterplot of estimates versus true values. 173 N 11 3 5 -3 0 -2 5 - ' 2 0 -15 -1 0 -5 -0X1 2 .0 3.0 N n 14 -12 . 10 -e -6 -4 2 N = 94 Meon = 0.63 Variance = 0.43 Coef. var = 103.2 a) ACCAU Mean = 0.62 Variance : 0.16 Coef. var. : 64.1 b) 0 . 0 0 0 4 0 0 * 0 L 2 0 ISO ACCAU N 2 8 -2 4 2 0 16 1 2 -8 -4 0 -41 -Z* -1 .6 -OJB 0 . 4 1.4 ACCAU* 1.5 -1.0 OS 0 .0 i • i • i OJO as 1.0 Mean = -0.01 Variance = 0.43 C ) ERR. (ACCAU) Correlation (Pearson) : 0.291 Correlation ( Spearmon ): 0.406 d) 1.5 2.0 2.5 3.0 TRUE .A.VII.l Crossvalidation of gold accumulations from drillholes, search radius 150 x 150ft: a) Histogram «f known data; b ) Histogram of estimates; c) Histogram of residuals; d ) Scatterplot of estimates versus true values. 174 N A 91 65-52-39-26-13" N Mean Variance Coef. var 365 0 5 4 0.08 54.2 t 0.12 0.32 0.52 0.72 0.92 a) 1.12 A C C A U N A 147 126" 105-84 63-( 42-21 0 -3.0 -2.0 -1.0 OD 1.0 A C C A U * li 1.2 -1.0-0.6 0.4 0.2 » t • a ••5i Y—v\* Mean - 0.006 Variance - 0.184 b) ERR (ACCAU ) Correlation ( Pearson) : 0.54 Correlation ( Spearman ) : 0.59 C ) i.o 2.0 3 0 TRUE Fig.A.VII.3 Crossvalidation of gold accumulations from drift assays, pure nugget effect model : a) Histogram of estimates, b) Histo-gram of residuals; c) Scatterplot of estimates versus true values. 175 N 84 -7 0 -56-42-2 8 -14 -Efci_ T 0O0 040 0.80 1.20 1.60 2.00 N Meon Va r i ance Coef. vor. 365 0.53 0.15 74.2 a ) INVEST N -147-126-105-84-63-42-21-0 - . M e a n - -0.00 V a r i a n c e = 0.11 b) 1.2 -07 -0.2 0.3 0.8 1.3 1.8 2.3 RESINU INVEST 2.0 1.3 1.0 0.5 -r.» if' .* » oo 1.0 I 2.0 Correlation ( Pearson) : 0.758 Correlation ( Spearman) : 0.809 C ) I 3.0 4.0 TRUE .A.VII.4 Crossvalidation of gold accumulations from drift assays, inverse square distance weighting method: a) Histogram of estimates b) Histogram of residuals; c) Scatterplot of estimates versus true values. 176 114-9 5 -7 6 -5 7 -3 8 -19 -N Mean Varionce Coef. var. 365 0.54 0.28 98.2 a) T ~ — i r — 0 .0 0 .5 1.0 1.5 2 . 0 2 5 3.0 3.3 POLEST Mean = -0.011 Variance = 0.1 78 -. " rh-a_ b) - 2 . 6 -1.6 - 0 . 6 0 .4 1.4 RESPOL POLEST 3.0 -Correlation (Pearson) : 0.674 Correlation (Spearman) :0.755 2.0 -i.o -o.o 1.0 -1 1-2.0 C ) 3JO T R U E .AVII.5 Crossvalidation of gold accumulations from drift assays, polygonal method : a) Histogram of estimates; b) Histogram of residuals c) Scatterplot of estimates versus true values. 177 APPENDIX VIII Contour Maps of Copper and Lead Accumulations Based on Ordinary P o i n t K r i g i n g The contour map of l e a d accumulations as given i n F i g u r e A.VIII.1 p o i n t s t o high values present around s e c t i o n 27000 and 28800. Note t h a t the northern anomaly i s mainly due t o l a r g e t h i c k n e s s whereas the southern one i s due to very high grades. The absence of l a r g e r values i n case of copper accmulations ( F i g . A.VIII.2) up t o s e c t i o n 28100 i s n o t i c a b l e i n d i c a t i n g once again t h a t the best p o r t i o n of deposit w i t h respect to q u a n t i t y of metal values i s found between s e c t i o n s 28000 and 29000. > i i - £ ^ -3 I M P E R I A L ( f t ) 0 150 3 0 0 4 5 0 Sca le : I : 3600 Fig. A. VIII.2 Contour map of Pb accumulations calculated by ordinary point kriging . 180 APPENDIX IX Ordinary Block K r i g i n g of C e n t r a l and Southern S e c t i o n of No. 3 Vein Thickness, Copper, Lead, and Zinc Accumulations Ordinary b l o c k k r i g i n g of v e i n thickness and copper, l e a d , and z i n c accumulations allows f o r e s t i m a t i o n of average grades w i t h i n the b l o c k s . Figures A . I X . l - A.IX.6 show midpoints f o r each bl o c k and the estimates of average grade and t h i c k n e s s . Although the C e n t r a l and the Southern s e c t i o n s are represented here s e p a r a t e l y p r a c t i c a l l y they represent the same continuous v e i n . o o m u> 8 o M SURFACE 3 0 0 0 L E V E L + .487 4.2 .144 3.9 2500 L E V E L .719 "4 .8 " + .499 4.0 + .158 2.7 + .269 7 . 9 " .181 6.1 + .059 3.4 + .240 8 . 2 " + .160 6.9 + .138 ' 8 . 0 " .119 8.2 + .105 6.9 .151 5 . 6 " .125 5 .5 + .134 3.6 .531 2.8 + .278 3.2 .084 5 . 5 " + .208 3.0 H .102 2.1 T - T .061 .090 5.6 3 .4 -r + .062 .081 3.5 3 .5 + .065 2.1 + .102 2.9 -t-.096 2.0 + .067 1.7 .085 2 . 7 " + .153 3.8 + .178 5.0 .202 2.9 .676 2.8 .244 ' 6 . 2 ~ I .624 " 4 . 8 " CO ~T" .185 -r .380 5.7 i 4.3 J -r .183 .158 5.6 2.7 1 + + .212 .283 5.0 2.9 2 0 0 0 L E V E L —< I 7 ~ I M P E R I A L ( f t . 1 5 0 3 0 0 4 5 0 Scale I 3600 pj g A . IX. I Estimates of average thickness and Cu grade of blocks 200*150 ft.2, by ordinary kriging method, Central section of No. 3 vein. 3 0 0 0 L E V E L + 1.01 2.4 - S U R F A C E -t-1.89 1.2 -t-.90 2.0 .46 H-.94 -r 1,46 .85 3.4 3.5 3.0 2.6 H- H- " I - + .48 .82 1.45 1.34 3.7 3.1 3 .3 2.6 ~i' + .50 .51 1.52 2.7 2.8 1.9 + + .36 .45 2.3 ?. ' / 2 5 0 0 L E V E L 2 0 0 0 L E V E L I M P E R I A L ( (t. 150 3 0 0 4 5 0 Sca le I 3600 Fig.A.IX.2 Estimates of average thickness and Cu grade of blocks 200*150 ft2, by ordinary kriging method, Southern section of No.3 vein. S U R F A C E 3 0 0 0 L E V E L + .416 4.2 -r 1.132 3.9 2 5 0 0 L E V E L ~r 1.272 + .813 .938 -H 1.546 T 1.591 4.8 7.9 8.2 8.0 "' 1 . 5.6 + T T .1 T T 1.051 .647 .757 1.335 1.449 4.0 6.1 6.9 8.2 1 5.5 + + +' + .576 .385 1.117 2.121 2.7 3.4 6.9 3.6 + 1.247 2.8 + .752 3.2 .825 5.5 .829 5.6 .845 3.5 + .821 2.1 + 1.017 3.0 + 1.158 2.1 .379 3.4 + .304 3.5 -t-1.416 2.9 -»-1.030 2.0 .822 1.7 .753 2.7 " + .914 3.8 + .771 5.0 .994 2.9 .1 -i" .755 2.8 1.192 "6 .2 " 1.178 2.8 + 1.027 2.8 H-1.309 2.9 1.632 ~ 4 . 8 --r 1.206 1.328 5.7 4.3 1 + 1.145 1.583 5.6 2.7 + + .978 1.888 5 .0 2.9 2 0 0 0 L E V E L IMPERIAL (ft.) 1 5 0 3 0 0 4 5 0 Scale I 3600 Fig A.IX. 3 Estimates of average vein thickness and Pb grade of blocks 200* 150ft2 by ordinary kriging method, Central section of No. 3 vein. 3 0 0 0 L E V E L + .92 2.4 1.19 3.4 SURFACE + 1.78 -3.5 4-.35 1.2 2.65 3.0 + + • f 1.01 1.49 3.30 3.7 3.1 3.3 T - i • + 1.31 1.09 3.44 2.7 2.8 1.9 + + 1.57 1.02 2.3 2.7 H-.27 2.0 + -1.22-2.6 + 2.66 2.6 2 5 0 0 L E V E L 2 0 0 0 L E V E L I M P E R I A L ( ft.) 150 3 0 0 S c a l e : I 4 5 0 3600 Fig. A.IX.4 Estimates of average vein thickness and Pb grade of blocks 200* 150ft2, by ordinary kriging method, Southern section of No. 3 vein. 26 500 SURFACE 27000 | 27500 28000 1 '— 3 0 0 0 LEVEL + T + + -»- H i-1.538 5.954 4.897 4.672 4.686 3.514 3.366 4.2 3.9 2.8 3.0 2.9 2.9 2.8 + + -f- ~i* H-2.183 4.191 3.541 2.843 3.708 3.2 2.1 2.0 -t-1.766 1.7 2.J 2.8 + 7.169 2.9 -r + - i - + T T - i - T 2500 L E V E L 6.599 4.516 8.070 11.150 10.763 7.149 6.907 10.939 9.513 4.8 7.9 8.2 " 8.0 "" b.6 5.5 2.1 6.2 4.8 + T" -T . T -J- - r + . T T 5.439 3.965 7.737 9.675 11.440 6.482 4.477 7.656 10.037 6.911 4.0 6.1 6.9 8.2 5.5 5.6 3.4 3.8 5.7 4.3 + + + + -i- + + + 2.475 2.830 9.299 11.588 7.543 4.573 7.310 7.509 4.633 2.7 3.4 6.9 3.6 3.5 3.5 5.0 'I 2.7 + + + 7.112 5.462 4.779 2.1 5.( ) 2.9 2 0 0 0 L E V E L _ U IMPERIAL ( ft.) 0 150 300 450 Scale : 1 3600 Fig. A. IX.5 Est imates of average vein thickness and Zn grade of blocks 200x 150 ft 2, by ordinary kriging method, Central section of No. 3 vein as Ln 00 Fig. A. IX .6 Estimation of average vein thickness and Zn grade of blocks 200x|50f t 2 , by ordinary kriging method, Southern section of No. 3 vein. 187 APPENDIX X Further Notes on I n d i r e c t Lognormal C o r r e c t i o n Model of Blocks 25x25 f t 2 and of Blocks 30x7 f t 2 I f we assume d a i l y production as 300 st/day a block of 25x25 f t f o r the mean v e i n t h i c k n e s s 4.83 f t i d e a l l y represents a s e l e c t i o n mining u n i t of about one day's production. The assumption would be t h a t one day production can be s t o c k p i l e d f o r a few days. During t h a t p a r t i c u l a r day, grab car samples and c h i p samples from stopes are taken and sent t o the l a b o r a t o r y . Based on assay r e s u l t s and p o s s i b l y a d d i t i o n a l assays from the s t o c k p i l e the ore can be sent e i t h e r t o the m i l l or t o the waste dump. The tonnage and grade recovery c a l c u l a t e d from the i n d i r e c t lognormal method i s given i n Table AX.1. When comparing the r e s u l t s w i t h Table XI.3 i t appears t h a t f o r the median c u t o f f , metal recovery i s greater f o r gold and s i l v e r and does not d i f f e r f o r other metals. The s i t u a t i o n changes d r a m a t i c a l l y when higher c u t o f f s are taken i n t o account. The "improvement" i n the q u a n t i t y of metal might lead t o the erroneous d e c i s i o n of mine management. In r e a l i t y when mining from three d i f f e r e n t stopes t h i s r e l a t i v e l y l a r g e tonnage of h i g h grade w i l l not show up. Table AX.2 shows gross p r o f i t i n c u r r e d when i t i s decided to base production on three working stopes f o r the median c u t o f f . 188 Aver. T(ILN) Aver. t h i c k . 25 x 25 gr.(ILN ) METAL Cutof f ( f t ) ST Sgr (short tons) 25 x 25 0.00 4.84 1.00 1.00 403,679 0.110 0.07 4.9 0.77 1.18 268,474 0.140 Au oz/T 0.10 4.57 0.94 1.10 151.696 0.180 0.13 4.50 0.97 1.12 85,878 0.227 0.00 4.84 1.00 1.00 441,233 6.00 3.5 5.02 0.93 1.10 326,371 7.53 Ag oz/T 5.7 4.52 0.95 1.11 142,285 10.85 8.6 4.00 1.33 1.05 91,241 13.81 0.00 4.84 1.00 1.00 441.233 0.21 0.12 4.88 0.91 1.11 287,986 0.29 Cu % 0.2 5.09 0.90 1.14 137,794 0.42 0.3 4.69 0.86 1.23 53,469 0.69 0.0 4.84 1.00 1.00 441,233 1.05 0.7 4.97 0.97 1.09 366,415 1.23 Pb % 1.1 4.31 0.89 1.15 185,548 1.59 1.6 3.55 1.16 1.06 39,278 1.96 0.0 4.84 1.00 1.00 441,233 7.11 3.7 5.41 0.94 1.07 382,837 8.03 Zn % 6.2 5.08 0.98 1.07 276,055 9.32 9.2 4.60 1.21 1.08 161,368 11.14 Table A X . l Estimated resources f o r the s e l e c t i o n mining u n i t 25x25 f o r d i f f e r e n t c u t o f f s , C e n t r a l s e c t i o n of No. 3 v e i n METAL CUTOFF PROFIT QUANTITY FROM ORD. KRIG QUANTITY FROM LGN 3X30X7 PRICE OF METAL GROSS A B $ (A-B) * $ Au/0.1 Ag/5.7 Cu/0.2 Pb/1.1 Zn/6.2 26,466 oz 1,464,789 oz 1,132,977 l b 5,754,103 l b 49,070,224 l b 26,685 1,543,970 1,131,748 5,889,180 51,420,034 371.1/oz 4.23/oz 1.24/lb 0.35/lb 0.61/lb 81,270 296,865 -1,523 47,276 1,433,384 TOTAL 1,857,272 Table AX.2 C a l c u l a t i o n of p o s s i b l e gains r e s u l t i n g from a s e l e c t i o n mining u n i t of one days's p r o d u c t i o n 189 S u b s t a n t i a l gain i s evident f o r z i n c values whereas f o r other metals p o s s i b l y e x c l u d i n g s i l v e r the gain i s n e g l i g i b l e . N a t u r a l l y there would be some a d d i t i o n a l costs i n v o l v e d i f i t was decided to do the s e l e c t i o n on t h a t b a s i s . 190 APPENDIX XI A n a l y s i s of D i s t r i b u t i o n of Cu Grades and I t s Influence on the variogram I t was dis c u s s e d i n Chapter XI t h a t poor performance of i n d i r e c t lognormal method i n comparison w i t h o r d i n a r y k r i g i n g r e s u l t s when based on the same support i s the r e s u l t of high grade areas w i t h i n the v e i n . The l a r g e s t d i f f e r e n c e s were encountered f o r copper m i n e r a l i z a t i o n . I f we examine average thickness and accumulations as a f u n c t i o n of l o c a t i o n i n the v e i n (Table AXI.l) i t i s apparent t h a t as we progress f a r t h e r south the average grade inc r e a s e s . SECTION AVERAGE ACCUMULATION AVERAGE THICKNESS AVERAGE GRADE 26,600 - 27,000 1.40 7.37 0.19 27,000 - 27,300 0.66 5.48 0.12 27,300 - 27,600 0.61 3.78 0.16 27,600 - 27,900 0.26 2.92 0.09 27,900 - 28.100 1.05 4.79 0.22 28,100 - 18,300 2.55 3.17 0.80 Table A X I . l Comparison of average copper grades f o r d i f f e r e n t areas i n the C e n t r a l s e c t i o n of No. 3 v e i n For a c u t - o f f grade of 0.2% Cu only the blocks south of s e c t i o n 27900 can be considered f o r mining. 191 The ILN method is based on the variogram model chosen (in our case a modified correlogram) and this spatial relationship is by no means recognized by i t when estimating recoverable reserves. Furthermore, the variogram model does not take into account local higher continuities which would allow, when modelled by a variogram, lesser reduction in variance of the "theoretical distribution of blocks" and by those means lower estimations above the median. Table AXi.2 shows the relative variogram value for the two subsets of copper accumulations and f i r s t two lags. The continuity represented by a relative variogram calculated for accumulations higher than one (look Table AXI.1) appears to be better than for lower values. This feature is not revealed by the variogram model chosen which averages a l l pairs within a particular lag. 192 RELATIVE VARIOGRAM VALUE [ACCUMULATION Cu] 1 AVERAGE DISTANCE SUBSET SUBSET NUMBER OF PAIRS 0 - 1.0 1.0 - oo 81 37 0.52 83 10 0.30 124 66 0.67 0.32 122 18 0.32 Table AXI.2 Comparison of r e l a t i v e variogram values of Cu accumulations f o r d i f f e r e n t subsets of data, f i r s t two lags taken, C e n t r a l s e c t i o n of No. 3 v e i n . 193 APPENDIX XII Examples of Increases of Quantity of Metals when M i n e r a l i z a t i o n i s Found Outside the No. 3 Vei n There are a number of d r i l l holes which prove t h a t m i n e r a l i z a t i o n i s not confined t o the v e i n . Most of them are found between the s e c t i o n 26850 and 27100. This i s the area where grade c o n t r o l and d i f f i c u l t y i n assessing the f o o t w a l l and hangingwall of the v e i n may cause some problems when mining i s considered. The t a b l e below shows the most important increases i n accumulations of metals when mining widths are taken i n t o account. V K T N DDH THICK NESS ACCUMULATION Au Ag Cu Pb Zn U88 - 024 • 2.01 11.02 27.08 U88 - 025 4.30 0.38 26.69 0.48 53.36 U88 - 027 14.90 0.83 88.91 174.90 U88 - 028 13.92 0.85 19.47 0.65 5.36 81.61 U88 - 030 3.29 0.21 9.84 0.73 1.91 59.55 U88 - 031 9.48 0.51 108.90 0.47 128.30 U88 - 071 2.78 32.60 0.53 55.04 194 MTNTNft WTDTH DDH THICK NESS ACCUMULATION Au Ag Cu Pb Zn U88 - 024 4.00 14.17 33.04 U88 - 025 7.75 0.43 34.47 1.31 67.88 U88 - 027 24.80 1.38 104.4 225.9 U88 - 028 27.80 1.11 47.68 1.00 15.29 132.60 U88 - 030 9.40 0.76 37.41 7.00 7.32 74.43 U88 - 031 14.80 1.14 115.1 0.75 141.60 U88 - 071 5.90 53.62 2.53 60.23 Table A X I I . l Examples of increases of metal accumulations when minimum mining width 4.0 f t i s assumed and m i n e r a l i z a t i o n of i n t e r e s t i s found outside the v e i n 195 APPENDIX XIII M o d i f i e d Correlograms of Accumulations of Ag, Cu, and Zn based on minimum mining widths 4.0 f t . M o d i f i e d correlograms of accumulations of s i l v e r , copper, and z i n c from d r i l l hole data and d r i f t data are shown i n f i g u r e s A . X I I I . 1 , 2, 3. S t r u c t u r a l c o n t i n u i t y represented i s very s i m i l a r t o the experimental f u n c t i o n s c a l c u l a t e d on v e i n assays i n Chapter VI. Based on t h a t , the same models, as given i n Table VI.1, are used i n mining ore reserve e s t i m a t i o n . 196 Cor 1 1.00 - X X X X X X X X X X X X X x x x X X Cor 1.04 -0.83-X 0.86-0 .66- 0.69-0. 30- 0.52-0.33 -J 0.34-0.16 - a) 0.17 -1 1 1 0 200 1 1 1 1 1 1 1 1 * 400 600 800 1000 h X X X X X XX X X X X X X X X x x x b) —I 1 1 1 1 1 1 1 1 — • 60 120 180 24 0 300 h Fig.A.XIII.I Corre logram of s i l ve r accumulations, minab le w id ths : a ) dr i l l hole a s says , b ) d r i f t assays. Cor 0.93-0.79-0.63-0.47-0.31-0.15-X X X X X X X X X X X X X X X X x x x a) Cor 1.96-1.80-1.64-1.48-1.32-1.16-1 1 1 1 1 1 1 1 1 1 0 200 400 600 800 1000 h X X X X X X X x x x x x x x b) 1 1 r— 0 60 i 1 1 • 1 1 120 I80 240 300 h Fig. A.XIII.2 Cor re logram of copper accumulations, minable widths a ) dri l l hole assays , b) dr i f t assays. Cor I .02-0.85-0.68-0.SI 0.34 0.I7-I X X X X X X X x X XX X X X a) Cor ^ 0.89-0.74-0.59 0.44 0.29 0.15-1 1 1 1 1 1 1 1 1 1 0 200 400 600 800 1000 h X X X X X X x x x x x x x x x x x b) —l— 88 —i 1 1 1 1 1 r— 176 264 332 440 h Fig.A.XIII.3 Corre logram of z inc accumula t ions , minable widths : a ) dr i l l hole assays, b) d r i f t a ssays . 197 APPENDIX XIV Estimates of No. 3 Vein Thickness and Average Grade of Blocks 200x150 f t 2 f o r C e n t r a l and Southern S e c t i o n The f o l l o w i n g f i l e s g ive u n d i l u t e d (vein) and d i l u t e d t o 4.0 f t . estimates of thickness and average grade of metals f o r blocks 200x150 f t 2 . The coordinates given are the mining coordinates used during Bradina operations and represent a midpoint f o r each block. A l l estimates are c a l c u l a t e d by o r d i n a r y k r i g i n g based on m o d i f i e d correlogram model. I t should be noted here t h a t the k r i g i n g variance of t h i c k n e s s ( l a s t column) represents the variance as d e r i v e d from o r d i n a r y k r i g i n g , and i s fdnot adjusted to the v a r i a n c e i n the area. Furthermore, the gross value of each block based on Oct 24, 1990 metal p r i c e s as w e l l as based on the recovery as given i n Chapter X I I i s shown i n separate f i l e s . Zero values given f o r some blocks represent not minable areas. 198 Page No. 1 12/20/90 AVERAGE THICKNESS AND GRADES FOR BLOCK SIZE 200X150 UNDILUTED ESTIMATES, CENTRAL SECTION OF NO. 3 VEIN ELEV. DEP. TH AU AG CU PB ZN KRIG.VAR FT FT FT OZ/ST OZ/ST % % % FOR THICK 2938 25600 4 .23 -1 .100 3.16 2938 25800 3 .91 -1 .000 3.30 2264 26400 2 .65 0 .068 1.66 2399 26400 3 .95 0 .044 4.31 2534 26400 4 .81 0 .045 4.70 2264 26600 3 .40 0 .070 1.29 2399 26600 6 .10 0 .073 4.49 2534 26600 7 .91 0 .079 5.22 2399 26800 6 .90 0 .076 3.86 2534 26800 8 .20 0 .079 5.41 2264 27000 6 .87 0 .072 4.22 2399 27000 8.21 0 .079 4.69 2534 27000 7 .96 0 .090 5.51 2264 27200 3 .62 0 .092 4.12 2399 27200 5 .46 0 .116 5.96 2534 27200 5 .63 0 .143 5.38 2129 27400 2 .05 0 .081 1.95 2264 27400 3 .53 0 .080 3.46 2399 27400 5 .27 0 .099 3.42 2534 27400 5.53 0 .094 4.38 2803 27400 3 .20 -1 .000 4.69 2938 27400 2 .82 -1 .000 7.03 2264 27600 3 .49 0 .040 1.68 2399 27600 3 .44 0 .069 3.28 2803 27600 2 .11 0.303 7.30 2938 27600 3 .03 -1 .000 5.87 2264 27800 5 .01 0 .104 5.40 2399 27800 3 .82 0 .125 7.62 2534 27800 2 .69 0 .192 12.85 2669 27800 1 .73 0 .178 8.69 2803 27800 2 .04 -1 .000 7.24 2938 27800 2 .86 -1 .000 9.10 2129 28000 4 .98 0 .116 7.21 2264 28000 5 .65 0 .125 6.44 2399 28000 5 .73 0 .173 8.11 2534 28000 6.23 0.236 9.21 2803 28000 2 .78 -1 .000 11.87 2938 28000 2 .90 -1 .000 11.17 2129 28200 3 .66 0 .134 14.58 2264 28200 3 .13 0 .173 12.00 0.49 0.42 1.54 0.19 0.14 1.13 5.95 0.19 0.16 0.58 2.48 0.21 0.50 1.05 5.44 0.17 0.72 1.27 6.60 0.22 0.06 0.39 2.83 0.24 0.18 0.65 3.97 0.15 0.27 0.81 4.52 0.19 0.16 0.76 8.07 0.15 0.24 0.94 8.07 0.19 0.11 1.12 9.30 0.23 0.12 1.34 9.68 0.12 0.14 1.55 11.15 0.19 0.13 2.12 11.59 0.17 0.13 1.45 11.44 0.13 0.15 1.59 10.76 0.22 0.07 0.82 7.11 0.36 0.06 0.85 7.54 0.11 0.06 0.84 6.49 0.13 0.08 0.83 7.15 0.26 0.28 0.75 2.18 0.24 0.53 1.25 4.90 0.19 0.08 0.30 4.57 0.12 0.09 0.38 4.48 0.17 0.10 1.16 4.19 0.16 0.21 1.02 4.67 0.11 0.18 0.77 7.31 0.19 0.15 0.91 7.66 0.15 0.09 0.75 6.91 0.20 0.07 0.82 1.77 0.25 0.10 1.03 3.54 0.15 0.10 1.42 4.69 0.16 0.21 0.98 5.46 0.17 0.18 1.15 7.51 0.16 0.19 1.21 10.04 0.14 0.24 1.19 10.94 0.19 0.68 0.76 2.84 0.17 0.20 0.99 3.51 0.20 0.22 1.50 3.79 0.22 0.14 1.36 3.98 0.14 199 Page No. 2 12/20/90 AVERAGE THICKNESS AND GRADES FOR BLOCK SIZE 200X150 UNDILUTED ESTIMATES, CENTRAL SECTION OF NO. 3 VEIN ELEV. DEP. TH AU AG CU PB ZN KRIG.VAR FT FT FT OZ/ST OZ/ST % % % FOR THICK 2399 28200 4.35 0.196 12.47 0.38 1.32 6 .86 0.15 2534 28200 5.39 0.222 13.56 0.55 1.44 8 .41 0.20 2669 28200 3.54 0.107 10.07 0.95 1.08 5 .90 0.24 2803 28200 3.04 0.049 10.54 1 .47 0.93 3 .37 0.12 2938 28200 2.91 -1.000 12.19 1.57 1.12 3 .19 0.31 200 Page No. 12/21/90 AVERAGE THICKNESS AND GRADES FOR BLOCK SIZE 200X150 UNDILUTED ESTIMATES, SOUTH. SECTION OF NO. 3 VEIN ELEV. DEP. TH AU AG CU PB ZN KRIG. VAR FT FT FT OZ/ST OZ/ST % % % FOR THICK. 2399 28391 4 .4 0.252 16 .91 2534 28391 3 .4 0.246 17 .73 2669 28391 2 .6 0.102 12 .77 2803 28391 2 .6 0.048 11 .98 2129 28532 2 .3 0.267 15 .56 2264 28532 2 .7 0.347 12 .32 2399 28532 3 .7 0.288 13 .21 2534 28532 3 .4 0.265 14.59 2669 28532 2 .4 0.140 10 .40 2129 28674 2 .7 0.265 10 .30 2264 28674 2 .8 0.289 10 .97 2399 28674 3 .1 0.258 10 .23 2534 28674 3 .5 0.260 12 .00 2264 28815 1 .9 0.387 19 .42 2399 28815 3 .3 0.376 18 .75 2534 28815 3 .0 0.309 13 .96 2669 28815 1 .2 0.066 9 .46 2399 28956 2 .6 0.500 26 .04 2534 28956 2 .6 0.283 16 .79 2669 28956 2 .0 0.059 10.33 0.57 1.27 7.67 0.14 0.86 1.54 7.63 0.10 1.20 0.82 5.16 0.10 1.40 0.65 5.30 0.16 0.36 1.57 8.71 0.15 0.50 1.31 10.40 0.11 0.48 1.01 9.96 0.12 0.46 1.19 11.30 0.10 1.00 0.91 7.00 0.22 0.45 1.02 9.98 0.17 0.51 1.09 9.20 0.14 0.82 1.49 9.21 0.20 0.94 1.78 12.10 0.24 1.50 3.44 13.60 0.23 1.40 3.30 15.20 0.15 1.50 2.65 10.90 0.17 1.90 0.34 1.23 0.19 1.30 2.66 17.50 0.22 0.85 1.22 10.70 0.18 0.90 0.27 1.34 0.21 201 Page No. 1 12/20/90 DILUTED TO MIN. MINING WIDTH 4.0 FT AVERAGE ESTIMATED THICKNESS AND GRADES OF BLOCKS 200X150 IN THE CENTRAL SECTION OF NO. 3 VEIN ELEV. DEP. TH AU AG CU PB ZN KRIG.VAR FT FT FT OZ/ST OZ/ST % % % THICK. 2938 25600 5 .67 2938 25800 5.29 2399 26400 4 .48 2534 26400 4 .99 2264 26600 4 .91 2399 26600 7 .04 2534 26600 8 .48 2399 26800 9 .98 2534 26800 12 .29 2264 27000 8 .82 2399 27000 12 .44 2534 27000 12.69 2264 27200 5 .70 2399 27200 6 .92 2534 27200 6 .42 2129 27400 4 .05 2264 27400 5 .46 2399 27400 6 .80 2534 27400 6.56 2803 27400 4 .82 2938 27400 4.23 2264 27600 4 .84 2399 27600 4 .74 2803 27600 4 .24 2938 27600 4 .67 2264 27800 5 .85 2399 27800 4 .94 2534 27800 4 .10 2669 27800 4 .05 2803 27800 4 .31 2938 27800 4 .64 2129 28000 6.30 2264 28000 6 .70 2399 28000 6 .26 2534 28000 6 .42 2803 28000 4 .27 2938 28000 4 .28 2129 28200 4 .91 2264 28200 4 .35 2399 28200 5 .14 2534 28200 6 .19 2669 28200 5 .04 2803 28200 4 .46 2938 28200 4 .29 2264 26400 4 .00 0.000 1.93 0.32 0.27 0.99 0.18 0.000 2.09 0.09 0.75 3.95 0.18 0.039 3.82 0.44 0.94 4.80 0.16 0.043 4.56 0.69 1.23 6.37 0.21 0.049 0.90 0.04 0.27 1.98 0.24 0.066 4.74 0.20 0.61 4.12 0.14 0.076 5.67 0.29 0.79 4.92 0.18 0.067 3.85 0.16 0.77 6.94 0.13 0.067 4.79 0.26 0.81 6.72 0.17 0.080 4.03 0.08 1.18 8.65 0.19 0.072 3.77 0.12 1.10 7.71 0.11 0.076 4.26 0.22 1.16 8.30 0.18 0.063 2.96 0.12 1.44 8.09 0.17 0.089 4.86 0.11 1.10 9.64 0.12 0.116 4.86 0.13 1.35 10.08 0.21 0.047 1.08 0.04 0.47 4.14 0.36 0.055 2.39 0.05 0.58 5.39 0.11 0.080 2.69 0.05 0.67 5.32 0.13 0.081 3.71 0.07 0.71 6.10 0.26 0.000 3.16 0.19 0.51 1.47 0.24 0.000 4.72 0.36 0.83 3.27 0.19 0.032 1.26 0.06 0.25 3.67 0.12 0.052 2.42 0.07 0.29 3.53 0.17 0.135 3.30 0.05 0.54 2.00 0.16 0.000 3.42 0.12 0.62 2.80 0.11 0.089 4.71 0.16 0.66 6.33 0.19 0.097 5.95 0.12 0.71 6.00 0.15 0.128 8.46 0.06 0.51 4.61 0.21 0.081 3.82 0.03 0.39 1.08 0.25 0.000 3.13 0.04 0.47 1.67 0.15 0.000 5.09 0.06 0.83 2.66 0.16 0.096 5.96 0.17 0.80 4.53 0.17 0.107 5.58 0.16 0.98 6.51 0.16 0.158 7.51 0.17 1.11 9.27 0.14 0.229 9.01 0.24 1.16 10.67 0.18 0.000 7.75 0.44 0.51 1.87 0.17 0.000 7.59 0.14 0.69 2.40 0.21 0.087 8.78 0.14 0.96 2.59 0.19 0.113 7.46 0.09 0.90 2.84 0.11 0.167 10.62 0.32 1.14 5.98 0.14 0.175 10.92 0.46 1.22 6.75 0.14 0.063 6.63 0.62 0.67 3.77 0.18 0.035 6.89 0.99 0.63 2.21 0.11 0.000 8.34 1.07 0.76 2.25 0.30 0.041 0.80 0.07 0.33 1.25 0.21 202 Page No. 1 12/20/90 AVERAGE THICKNESS AND GRADES FOR BLOCK SIZE 200X150 DILUTED TO MINIMUM MINING WIDTH 4.0 FT FOR SOUTHERN SECTION OF NO. 3 VEIN ELEV. DEP. TH AU AG CU PB ZN KRIG. VAR. FT FT FT OZ/ST OZ/ST % % % FOR THICK. 2399 28391 5 .5 0.204 13.90 0.5 1 .0 6.3 0.14 2534 28391 5 .5 0.142 10.57 0.5 1 .0 4.5 0.10 2669 28391 4 .7 0.034 6.11 0.6 0 .3 2.5 0.10 2803 28391 4 .5 0.019 6.22 0.7 0 .3 2.8 0.16 2129 28532 4 .4 0.113 7.05 0.2 0 .6 3.7 0.15 2264 28532 4 .5 0.164 6.31 0.2 0 .6 5.1 0.11 2399 28532 4 .9 0.205 9.25 0.4 0 .7 7.1 0.12 2534 28532 4 .8 0.192 10.80 0.4 0 .9 8.2 0.10 2669 28532 4 .0 0.074 6.28 0.6 0 .6 4.2 0.22 2129 28674 4 .4 0.168 7.00 0.3 0 .6 6.3 0.17 2264 28674 4 .4 0.195 7.79 0.4 0 .7 6.2 0.14 2399 28674 4 .7 0.172 6.94 0.6 1 .0 6.2 0.20 2534 28674 5 .0 0.185 8.68 0.7 1 .3 8.6 0.24 2264 28815 4 .0 0.144 7.48 0.5 1 .2 5.2 0.23 2399 28815 5 .0 0.229 11.22 0.9 2 .0 9.2 0.15 2534 28815 5 .0 0.179 8.14 0.9 1 .5 6.3 0.17 2669 28815 4 .0 0.018 2.49 0.5 0 .1 0.3 0.19 2399 28956 4 .4 0.266 13.45 0.8 1 .4 9.1 0.22 2534 28956 4 .4 0.164 9.61 0.5 0 .7 6.1 0.18 2669 28956 4 .3 0.027 4.63 0.4 0 .1 0.6 0.21 203 Page No. 1 12/20/90 VALUE OF METALS IN BLOCKS, CENTRAL SECTION OF NO. 3 VEIN LEV. DEP. TH AUVAL AGVAL CUVAL PBVAL ZNVAL TOTAVL FT FT FT xlOOO xlOOO xlOOO xlOOO xlOOO XlOOO $US $US $US $US $US $US 2938 25600 5.7 -1 63 57 14 99 233 2938 25800 5.3 -1 126 30 72 734 963 2399 26400 4.5 123 196 125 77 756 1276 2534 26400 5.0 150 260 218 112 1116 1856 2264 26600 4.9 169 50 12 24 341 597 2399 26600 7.0 326 381 89 78 1019 1894 2534 26600 8.5 422 513 145 114 1368 2562 2399 26800 10.0 469 439 101 140 2434 3583 2534 26800 12.3 289 336 101 91 1451 2268 2264 27000 8.8 495 406 45 190 2682 3818 2399 27000 12.4 628 536 94 250 3369 4877 2534 27000 12.7 225 206 59 90 1233 1813 2264 27200 5.7 252 193 43 150 1620 2258 2399 27200 6.9 432 384 48 139 2345 3348 2534 27200 6.4 173 118 17 52 753 1114 2129 27400 4.1 134 50 10 35 589 818 2264 27400 5.5 211 149 17 58 1033 1468 2399 27400 6.8 381 209 21 83 1271 1965 2534 27400 6.6 162 121 13 37 611 943 2803 27400 4.8 -1 174 58 45 249 525 2938 27400 4.2 -1 121 51 34 257 462 2264 27600 4.8 109 70 18 22 624 843 2399 27600 4.7 173 131 21 25 588 938 2803 27600 4.2 0 0 0 0 0 0 2938 27600 4.7 -1 91 18 26 230 365 2264 27800 5.9 365 315 59 71 1301 2111 2399 27800 4.9 280 280 31 53 869 1515 2534 27800 4.1 368 396 16 38 663 1481 2669 27800 4.1 0 0 0 0 0 0 2803 27800 4.3 0 0 0 0 0 0 2938 27800 4.6 0 0 0 0 0 0 2129 28000 6.3 424 429 68 92 1003 2016 2264 28000 6.7 503 427 68 120 1532 2649 2399 28000 6.3 579 448 56 106 1700 2889 2534 28000 6.4 1031 660 97 136 2406 4331 2803 28000 4.3 0 0 0 0 0 0 2938 28000 4.3 0 0 0 0 0 0 2129 28200 4.9 300 493 43 86 447 1369 2264 28200 4.4 345 371 25 72 434 1247 2399 28200 5.1 501 519 87 89 899 2096 2534 28200 6.2 759 772 180 138 1467 3316 2669 28200 5.0 0 0 0 0 0 0 2803 28200 4.5 0 0 0 0 0 0 2938 28200 4.3 0 0 0 0 0 0 2264 26400 4.0 115 37 18 24 176 369 204 Page No. 1 12/20/90 VALUE OF METALS IN BLOCKS, SOUTHERN SECTION OF NO. 3 VEIN LEV. DEP. TH AUVAL AGVAL CUVAL PBVAL ZNVAL TOTVAL FT FT FT xlOOO xlOOO xlOOO xlOOO xlOOO xlOOO $US $US $US $US $US $US 2399 28391 5.5 149 166 31 20 230 597 2534 28391 5.5 290 352 101 51 456 1250 2669 28391 4.7 0 0 0 0 0 0 2803 28391 4.5 0 0 0 0 0 0 2129 28532 4.4 239 243 31 34 390 937 2264 28532 4.5 479 300 64 45 744 1632 2399 28532 4.9 312 230 48 29 544 1162 2534 28532 4.8 640 587 107 75 1374 2783 2669 28532 4.0 0 0 0 0 0 0 2129 28674 4.4 515 349 95 52 967 1978 2264 28674 4.4 599 390 115 59 956 2118 2399 28674 4.7 541 355 163 82 975 2116 2534 28674 5.0 646 493 219 115 1512 2985 2264 28815 4.0 404 342 136 88 725 1695 2399 28815 5.0 795 634 291 183 1593 3497 2534 28815 5.0 633 469 277 142 1107 2629 2669 28815 4.0 50 114 124 7 44 339 2399 28956 4.4 822 677 214 110 1407 3231 2534 28956 4.4 508 485 148 56 944 2142 2669 28956 4.3 81 226 107 10 90 513 

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