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UBC Theses and Dissertations

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

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A COMPARISON OF VARIOUS ORE RESERVE ESTIMATES AT THE BUCKHORN MINE, EUREKA COUNTY, NEVADA By MIT D. TILKOV B . S c , The U n i v e r s i t y o f W a t e r l o o , 1975 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF GEOLOGICAL SCIENCES We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA March 1989 © M i t D. T i l k o v , 1989 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 Geological Sciences The University of British Columbia Vancouver, Canada Date A p r i l 3, 1989 DE-6 (2/88) A b s t r a c t An abundance o f computer i zed e x p l o r a t i o n d r i l l h o l e and p r o d u c t i o n b l a s t h o l e d a t a from Cominco R e s o u r c e s ' Buckhorn Mine i n Nevada p r o v i d e s the o p p o r t u n i t y f o r a comprehens ive s tudy to. e v a l u a t e v a r i o u s g r a d e ' e s t i m a t i o n t e c h n i q u e s . The Buckhorn o r e - body i s a b u l k m i n e a b l e , v o l c a n i c h o s t e d , e p i t h e r m a l g o l d - s i l v e r d e p o s i t t h a t formed i n a Miocene hot s p r i n g s sys tem. F o r t y s e p a r a t e b l o c k mode l s , e s t i m a t e d from e x p l o r a t i o n d r i l l h o l e d a t a , were compared w i t h 12 b l o c k models d e r i v e d from b l a s t h o l e d a t a . The e f f e c t o f c h o o s i n g a s m a l l e r m i n i n g s i z e b l o c k over the l a r g e r b l o c k s i z e t h a t might be d i c t a t e d by d r i l l h o l e s p a c i n g was examined i n some c a s e s . Some b l o c k models and d a t a s e t s had g e o l o g i c a l c o n s t r a i n t s imposed on them w h i l e o t h e r s d i d n o t . F o r each o f f o u r major b l o c k model c o n f i g u r a t i o n s v a r i o u s p o l y g o n a l b a s e d , i n v e r s e d i s t a n c e and g e o s t a t i s t i c a l e s t i m a t e s were c a l c u l a t e d and compared to each o t h e r and t o known p r o d u c t i o n d a t a . D u r i n g the c o u r s e o f t h i s s t u d y , many o f the common s t a t i s t i c a l and g e o s t a t i s t i c a l t e c h n i q u e s f o r a n a l y s i s o f d a t a were employed and i n some c a s e s , t h e methods themse lves were q u e s t i o n e d . R e s u l t s showed t h a t e s t i m a t i n g s m a l l , m i n i n g s i z e b l o c k s i s i m p o r t a n t r e g a r d l e s s o f the grade i n t e r p o l a t i o n method used because the b e s t o f these b l o c k mode l s , a l t h o u g h l e s s a c c u r a t e p r e d i c t o r s o f a c t u a l grade a t any g i v e n l o c a t i o n , tended to r e f l e c t the o v e r a l l t r u e grade d i s t r i b u t i o n o f the ore b l o c k s which were e v e n t u a l l y mined . Because a l l ore e s t i m a t e s are c a l c u l a t e d from n e a r e s t e x p l o r a t i o n c o m p o s i t e s , some o f the s m a l l b l o c k s i z e models can be seen as f a i r l y a c c u r a t e , g e o m e t r i c a l l y c o r r e c t a p p r o x i m a t i o n s (one p o s s i b l e r e a l i z a t i o n ) o f the t r u e , unknown shape o f the orebody . I t was found t h a t , i n a d d i t i o n t o s e p a r a t i n g o x i d e from s u l f i d e e x p l o r a t i o n c o m p o s i t e s , the i m p o s i t i o n o f a second type o f g e o l o g i c a l boundary , an ore zone o u t l i n e w i t h i n which ore was l i k e l y t o o c c u r and o u t s i d e o f which t h e r e was l i t t l e b a s i s f o r p r e d i c t i n g the e x i s t e n c e o f r e c o v e r a b l e r e s e r v e s , measurably improved the e s t i m a t e s o f tonnage and g r a d e . And f i n a l l y , the method o f c a l c u l a t i n g c o n d i t i o n a l p r o b a b i l i t y proposed by G . F . Raymond (Raymond 1979, 1982, and 1984) , and as f u r t h e r r e f i n e d h e r e , was found t o be the most a c c u r a t e , s t a b l e , and g e n e r a l l y u s e f u l o f the v a r i o u s methods used t o g e n e r a t e b l o c k models and e s t i m a t e s o f o r e r e s e r v e s a t the Buckhorn M i n e . i i i Table of Contents page A b s t r a c t i i T a b l e o f C o n t e n t s i v L i s t o f T a b l e s v i i L i s t o f F i g u r e s v i i i Acknowledgements x C h a p t e r 1. INTRODUCTION 1 2. GEOLOGY OF THE BUCKHORN DEPOSIT 8 3. AVAILABLE DATA AND BLOCK MODELS 13 3.1 EXPLORATION DATA 13 3.2 BLASTHOLE DATA 14 3.3 BLOCK MODELS 15 3 . 3 . 1 I n t r o d u c t i o n > 15 3 . 3 . 2 Four F o o t B l o c k Models 15 3 . 3 . 3 Twenty F o o t B l o c k Models 18 3 .3 .4 S i x t y F o o t B l o c k Models 19 3.4 SUMMARY OF BLOCK MODELS AND DATASETS 19 4. STATISTICS 21 5. ORE RESERVE CALCULATIONS 31 5.1 INTRODUCTION 31 5.2 POLYGONAL ESTIMATES 32 5.3 INVERSE DISTANCE 32 i v 5.4 KRIGING 35 5 . 4 . 1 V a r i o g r a m A n a l y s i s 35 5 . 4 . 2 Some O b s e r v a t i o n s on V a r i o g r a m M o d e l l i n g 38 5 . 4 . 3 K r i g i n g and Back A n a l y s i s 49 6. CONDITIONAL PROBABILITY 52 6.1 THEORY 52 6 . 1 . 1 I n t r o d u c t i o n 52 6 . 1 . 2 The C o n d i t i o n a l D i s t r i b u t i o n 52 6 . 1 . 3 D i s t r i b u t i o n o f Sample Grades and B l o c k Grades . 56 6 .1 .4 C o n s t a n t K r i g i n g V a r i a n c e 59 6 . 1 . 5 Combining 3-Parameter Lognormal Data w i t h R e l a t i v e V a r i o g r a m s 60 6 . 1 . 6 D e t e r m i n i n g the C o n s t a n t R e l a t i v e B l a s t h o l e K r i g i n g V a r i a n c e 61 6.2 CALCULATION OF CONDITIONAL PROBABILITY 62 6 . 2 . 1 Example C a l c u l a t i o n Of C o n d i t i o n a l P r o b a b i l i t y 66 6.3 DISCUSSION 70 7. COMPARISON OF RESULTS 79 7.1 INTRODUCTION 7 9 7.2 METAL GRAPHS 7 9 7.3 ORE RESERVE CHARTS 88 7.4 SUMMARY CHART AND RANKING OF THE RESULTS 94 7.5 EXAMINATION OF SCATTERGRAMS AND BENCH PLANS 97 7.6 SIXTY FOOT V S . TWENTY FOOT ESTIMATES 101 7.7 CONSTRAINED V S . UNCONSTRAINED ESTIMATES 102 7.8 USING CONDITIONAL PROBABILITY ESTIMATES 103 8. CONCLUSIONS 107 v R e f e r e n c e s 109 Append ix A - Bench Maps o f Raw Data and O u t l i n e s 110 Appendix B - Bench Maps o f R e s u l t s 120 Appendix C - Ore Reserve R e p o r t s 233 Append ix D - L i s t i n g o f C a l c u l a t e d V a r i o g r a m V a l u e s 254 Append ix E - L i s t i n g o f Var iograms Generated by Maximum D i f f e r e n c e Method 261 Appendix F - S c a t t e r g r a m s 267 v i L i s t o f T a b l e s page T a b l e I . Summary o f b l o c k models and d a t a s e t s 20 T a b l e I I . S i m p l e s t a t i s t i c s o f the e x p l o r a t i o n and b l a s t h o l e d a t a " 27 T a b l e I I I . Parameters used t o genera te i n v e r s e d i s t a n c e weighted e s t i m a t e s from e x p l o r a t i o n compos i tes 34 T a b l e I V . Ore r e s e r v e s p r e d i c t e d by u s i n g the " r o t a t e d " v a r i o g r a m compared t o k r i g e d e x p l o r a t i o n e s t i m a t e and " a c t u a l " f o r the BUCKG model 41 T a b l e V . Parameters used f o r k r i g i n g 50 T a b l e V I . Parameters used to c a l c u l a t e c o n d i t i o n a l p r o b a b i l i t y 65 T a b l e V I I . Comparison o f b l a s t h o l e i n d i c a t e d r e s e r v e s w i t h r e s e r v e s c a l c u l a t e d by each e x p l o r a t i o n method f o r the BUCK b l o c k model 89 T a b l e V I I I . Comparison o f b l a s t h o l e i n d i c a t e d r e s e r v e s w i t h r e s e r v e s c a l c u l a t e d by each e x p l o r a t i o n method f o r the BUCKG b l o c k model 90 T a b l e I X . Comparison o f b l a s t h o l e i n d i c a t e d r e s e r v e s w i t h r e s e r v e s c a l c u l a t e d by each e x p l o r a t i o n method f o r the BUCK60 b l o c k model 91 T a b l e X . Comparison o f b l a s t h o l e i n d i c a t e d r e s e r v e s w i t h r e s e r v e s c a l c u l a t e d by each e x p l o r a t i o n method f o r the BUCK60G b l o c k model 92 T a b l e X I . Summary compar i son o f ore r e s e r v e methods . . . . 95 v i i L i s t o f F i g u r e s page F i g u r e l . L o c a t i o n map 2 F i g u r e 2. R e g i o n a l geo logy map o f an a r e a encompassing the Buckhorn mine 9 F i g u r e 3. G e o l o g i c a l map o f the Buckhorn mine 11 F i g u r e 4. Two methods o f a c c e p t i n g o r r e j e c t i n g b l o c k s w i t h i n an o u t l i n e 17 F i g u r e 5. P a r t i t i o n e d l o g p r o b a b i l i t y p l o t o f 20' e x p l o r a t i o n compos i tes 2 3 F i g u r e 6. Log p r o b a b i l i t y p l o t o f b l a s t h o l e d a t a compared t o p a r t i t i o n e d e x p l o r a t i o n d a t a 25 F i g u r e 7. Log p r o b a b i l i t y p l o t s showing t h e e f f e c t o f add ing a c o n s t a n t o f 0.005 o p t . t o the o r i g i n a l d a t a to c r e a t e a 3 -parameter l o g n o r m a l d i s t r i b u t i o n 28 F i g u r e 8. G r a p h i c a l e x p l a n a t i o n o f the p o l y g o n weighted method o f c a l c u l a t i n g b l o c k grades 3 3 F i g u r e 9. M o d e l l e d r e l a t i v e v a r i o g r a m o f the BEX d a t a 38 F i g u r e 10. M o d e l l e d r e l a t i v e v a r i o g r a m o f the BEXG d a t a 39 F i g u r e 11. E x p e r i m e n t a l r e l a t i v e v a r i o g r a m from the BBH d a t a 47 F i g u r e 12. E x p e r i m e n t a l r e l a t i v e v a r i o g r a m from the BBHG d a t a 48 F i g u r e 13. The c o n d i t i o n a l d i s t r i b u t i o n 54 F i g u r e 14. E x p e c t a t i o n s o f o r e and waste d e r i v e d from n o r m a l l y d i s t r i b u t e d b l o c k grades 55 F i g u r e 15. P r o b a b i l i t y p l o t s o f p e r f e c t and i m p e r f e c t l o g n o r m a l d i s t r i b u t i o n s 57 v i i i F i g u r e 16. The e f f e c t o f e s t i m a t i n g ore and waste p e r c e n t a g e s from i m p e r f e c t normal d i s t r i b u t i o n s 58 F i g u r e 17. C u m u l a t i v e p r o b a b i l i t y p l o t o f t h e grades o f a c t u a l b l o c k s g i v e n k r i g e d b l o c k grades . . . . 74 F i g u r e 18. Computer p r i n t o u t o f the compar i son between a c t u a l grades and k r i g e d e s t i m a t e s 76 F i g u r e 19. M e t a l graph f o r the BUCK b l o c k model 80 F i g u r e 20. M e t a l graph f o r the BUCKG b l o c k model 81 F i g u r e 21. M e t a l graph f o r the BUCK60 b l o c k model 82 F i g u r e 22. M e t a l graph f o r the BUCK60G b l o c k model 83 i x Acknowledgements The a u t h o r i s i n d e b t e d to Cominco L t d . f o r p r o v i d i n g the f u n d i n g and the o p p o r t u n i t y t o p u b l i s h t h i s r e s e a r c h and f o r a l l o w i n g t ime o f f work t o a t t e n d c l a s s e s when n e c e s s a r y . T h i s d u r i n g a p e r i o d o f unprecedented t u r m o i l i n the m i n e r a l i n d u s t r y when t h e company might j u s t as e a s i l y have d e c i d e d t o "go i t " w i t h o u t a p a r t - t i m e s t u d e n t i n i t s ' employ. In p a r t i c u l a r , Russ S p r o u l e , my b o s s , now r e t i r e d , thanks f o r encouragement and s u p p o r t . R u s s ' s down t o e a r t h approach to o r e r e s e r v e p r o b l e m s , and h i s p h i l o s o p h y o f k e e p i n g t h i n g s s i m p l e and u n d e r s t a n d a b l e i f a t a l l p o s s i b l e , has (I hope) g r e a t l y i n f l u e n c e d my approach to t h i s work and a l s o gu ides me i n the s o l u t i o n o f day t o day problems t h a t a r i s e i n my j o b . And s p e c i a l thanks t o my w i f e , Susan , and my k i d s , Jaime and C h r i s t o p h e r , whose p a t i e n c e w i t h l a t e n i g h t s and absences to c o n v e r s e w i t h the l i k e s o f IBM, VAX, Calcomp, and o t h e r s u b - s e n t i e n t p r e d i c t o r s o f r e a l i t y , a l t h o u g h s t r e t c h e d a t t i m e s , h e l d t o the e n d . S u s a n ' s encouragement t o f i n i s h t h i s t h i n g , when at t imes I d i d n ' t want t o , i s now p a r t i c u l a r l y a p p r e c i a t e d . x 1 1. INTRODUCTION The Buckhorn Mine i s a s m a l l , low grade e p i t h e r m a l go ld d e p o s i t h o s t e d by a l t e r e d T e r t i a r y v o l c a n i c r o c k s . I t i s l o c a t e d i n E u r e k a C o u n t y , Nevada a p p r o x i m a t e l y 60 m i l e s southwest o f the town o f E l k o ( F i g . 1 ) . The mine i s a j o i n t v e n t u r e o f Cominco Resources I n t e r n a t i o n a l L t d . (76%) and Equinox Resources (24%). Bar Resources r e t a i n s a 20% net proceeds i n t e r e s t . Go ld and s i l v e r m i n e r a l i z a t i o n i s d i s s e m i n a t e d a l o n g NNW t r e n d i n g f a u l t s and f r a c t u r e s w i t h ore grades encountered i n a n e a r s u r f a c e o x i d e zone and e x t e n d i n g downward i n t o s u l f i d e ore a t d e p t h . Only the o x i d e ore i s mined i n the open p i t o p e r a t i o n . G o l d and s i l v e r are e x t r a c t e d u s i n g heap l e a c h t e c h n o l o g y . P u b l i s h e d minab le r e s e r v e s a r e 3.1 m i l l i o n tons o f ore c o n t a i n i n g 0.04 o z . / t o n g o l d and 0.6 o z / t o n s i l v e r a t a 0.02 o z . / t o n g o l d c u t o f f grade (Munroe e t a l . , 1988) . A l t h o u g h t h e r e has been s p o r a d i c m i n i n g a c t i v i t y on the p r o p e r t y s i n c e the e a r l y 1900 ' s , the c u r r e n t open p i t o p e r a t i o n was s t a r t e d up i n F e b r u a r y o f 1984. I n i t i a l l y , o r e r e s e r v e s were c a l c u l a t e d by an o u t s i d e c o n s u l t i n g company u s i n g a 20' b l o c k model w i t h k r i g e d b l o c k grades and an open p i t was d e s i g n e d u s i n g t h i s m o d e l . In 1985, r e s e r v e s were r e c a l c u l a t e d by Cominco L t d . u s i n g i n v e r s e d i s t a n c e cubed i n t e r p o l a t i o n , l o g n o r m a l k r i g i n g , and o r d i n a r y k r i g i n g and the open p i t was r e d e s i g n e d u s i n g the i n v e r s e d i s t a n c e model because e s t i m a t e s u s i n g t h i s method most 2 c l o s e l y resembled mined tonnage and grade figures available for the f i r s t year's production. Although blasthole data was avail a b l e a f t e r the f i r s t few months of operation, no attempt was made to compare estimates from exploration d r i l l i n g to blasthole r e s u l t s . The blasthole data i s the only data on which production can be reported from the mine because no other r e l i a b l e measure of head grade i s available. Ore i s dumped from stockpiled material into the crusher and samples are taken sporadically 3 e v e r y 2 o r 3 hours from the c o n v e y o r s . There i s no good way o f document ing where i n the main p i t o r e i s b e i n g sampled from and, i n some c a s e s , whether the ore i s coming from the main p i t , a low grade s t o c k p i l e , an ore s t o c k p i l e o r from o t h e r s m a l l p i t s which have been mined on the p r o p e r t y . The c u r r e n t s tudy was des igned t o answer a number o f q u e s t i o n s , no t the l e a s t o f which was why t h e r e appeared to be b e t t e r e s t i m a t e s o f tonnage and grade by the i n v e r s e d i s t a n c e cubed method than by k r i g i n g . Other t o p i c s t o be i n v e s t i g a t e d i n c l u d e : 1) E f f e c t o f E s t i m a t i o n B l o c k S i z e : I t i s commonly accepted by g e o s t a t i s t i c i a n s t h a t r e g a r d l e s s o f the b l o c k s i z e u s e d , k r i g i n g w i l l genera te r e s e r v e f i g u r e s which a r e c o r r e c t on average and t h a t the b e s t b l o c k s i z e f o r e s t i m a t i o n purposes i s one t h a t i s c l o s e to the o r i g i n a l e x p l o r a t i o n d r i l l h o l e s p a c i n g , and f u r t h e r m o r e , t h a t we are f o o l i n g o u r s e l v e s i f any attempt to e s t i m a t e grades f o r v e r y s m a l l s i z e m i n i n g b l o c k s i s made. T h i s i s t r u e i f one i s i n t e r e s t e d i n p r e d i c t i n g the grade o f an i n d i v i d u a l b l o c k , but i n t u i t i v e l y , i t can be surmised t h a t f o r mine p l a n n i n g purposes and the e s t i m a t i o n o f g l o b a l r e s e r v e s , a d i f f e r e n t p h i l o s o p h y must be a d o p t e d . F o r example , i f o n l y one b l o c k was e s t i m a t e d (the whole d e p o s i t ) , any e s t i m a t e ( i n c l u d i n g k r i g i n g ) s h o u l d g i v e an average b l o c k grade which i s e q u a l to the average o f a l l o f the samples used t o c a l c u l a t e the g r a d e , and t h a t grade w i l l p r o b a b l y be below c u t o f f ( i . e . 0 tons o f o r e ) . I f the d e p o s i t i s d i v i d e d up i n t o 9 e q u a l s i z e b l o c k s , t h e r e may r e s u l t one b l o c k i n the m i d d l e whose grade i s s l i g h t l y above the m i n i n g c u t o f f , and 8 a t below c u t o f f g r a d e . I f t h i s analogy i s 4 c o n t i n u e d down t o a m i n i n g s c a l e , i t i s more i m p o r t a n t to e s t i m a t e t o the mine d e s i g n b l o c k s i z e (20' x 20' x 20* at Buckhorn) than t o a 50' x 50' x 20' b l o c k s i z e (Buckhorn d r i l l h o l e s are spaced on a f a i r l y r e g u l a r 50' e x p l o r a t i o n g r i d ) , because i n m i n i n g no one i s impressed by a " c o r r e c t on average" e s t i m a t e u n l e s s t h a t e s t i m a t e i s c o r r e c t on average above a chosen m i n i n g c u t o f f g r a d e . F o r any 50' b l o c k t h a t i s e s t i m a t e d a t below c u t o f f t h e r e i s some r e a s o n a b l e p r o b a b i l i t y t h a t at l e a s t one 20 1 b l o c k c o n t a i n e d w i t h i n the l a r g e r b l o c k would have been e s t i m a t e d t o have a grade above c u t o f f . A l t h o u g h the grade o f each o f the s m a l l e r m i n i n g b l o c k s may not have been a c c u r a t e l y p r e d i c t e d , a b e t t e r o v e r a l l p i c t u r e o f the t r u e d i s t r i b u t i o n o f the b l o c k grades and ore r e s e r v e s expected a t the m i n i n g s c a l e has been o b t a i n e d . To see what d i f f e r e n c e i n g l o b a l tonnage and grade t h e r e might b e , 2 b l o c k models were g e n e r a t e d , one w i t h 20' x 20' x 20' b l o c k s , and one w i t h 60' x 60' x 20' b l o c k s . I t was expected t h a t ore r e s e r v e s based on the 60' b l o c k would be lower than f o r the 20' b l o c k s i z e . 2) E f f e c t o f Ore Zone O u t l i n e s : The importance o f c o n s t r a i n i n g the i n t e r p o l a t i o n t o w i t h i n g e o l o g i c a l boundar ie s has been amply demonstrated by numerous p r a c t i t i o n e r s o f g e o s t a t i s t i c s over the y e a r s ( e . g . D a v i d , 1988) . In t h i s s t u d y , o n l y e x p l o r a t i o n d r i l l h o l e s w i t h i n the o x i d e zone were used because i t was obv ious t h a t the s u l f i d e ore would not be mined, and t h a t s u l f i d e m i n e r a l i z a t i o n was more e r r a t i c and showed e v i d e n c e o f b e l o n g i n g t o a d i f f e r e n t s t a t i s t i c a l p o p u l a t i o n o f samples . S i m i l a r l y , o n l y o x i d e zone b l a s t h o l e s were used f o r 5 c o m p a r i s o n . However, as w i l l be s e e n , t h e r e i s a second type o f g e o l o g i c a l boundary i n the Buckhorn d a t a and i n many o ther d a t a s e t s t h a t the author has e n c o u n t e r e d . T h i s i s the r o c k t y p e "ore" . I t i s f e l t by the author t h a t i f an i n t u i t i v e l y or q u a n t i t a t i v e l y d e r i v e d boundary can be d e f i n e d which e n c i r c l e s m i n e r a l i z e d a r e a s , t h a t t h i s i n i t s e l f i s an i m p o r t a n t g e o l o g i c a l boundary w h i c h , i f t aken i n t o a c c o u n t , m i n i m i z e s numerous e r r o r s o f p o p u l a t i o n m i x i n g which r e s u l t i n unwarranted e x t r a p o l a t i o n a n d / o r "smoothing" o f o r e g r a d e s . To t e s t t h i s i d e a r i g o r o u s l y , 2 f u r t h e r b l o c k models were generated which took the o r i g i n a l 20 1 and 60" b l o c k models and imposed t h i s new g e o l o g i c a l boundary on them. F o r e s t i m a t e s on these 2 b l o c k mode l s , o n l y e x p l o r a t i o n compos i te s w i t h i n t h i s "ore zone" o u t l i n e were used t o generate o r e r e s e r v e f i g u r e s . These were l a t e r compared t o p r o d u c t i o n e s t i m a t e s based on b l a s t h o l e i n f o r m a t i o n w i t h i n the same o u t l i n e . 3) A c c u r a c y o f V a r i o u s P o l y g o n a l and I n v e r s e D i s t a n c e E s t i m a t e s : We a r e o f t e n t o l d t h a t , i n most c a s e s , p o l y g o n a l e s t i m a t e s a r e dangerous and t h a t i n v e r s e d i s t a n c e methods w i l l range from an e s t i m a t e which resembles k r i g i n g w i t h a v a r i o g r a m showing pure nugget e f f e c t , t h r o u g h t o an e s t i m a t e which most c l o s e l y resembles a p o l y g o n a l e s t i m a t e when the power o f d i s t a n c e i s h i g h enough ( J o u r n e l and H u i j b r e g t s , 1978) . Somewhere i n between (we d o n ' t know where b e f o r e h a n d ) , t h e r e may be a power o f i n v e r s e d i s t a n c e t h a t would resemble the k r i g e d e s t i m a t e — e s p e c i a l l y i f a n i s o t r o p i e s i n the v a r i o g r a m a r e taken i n t o account and sample s p a c i n g i s on a r e g u l a r g r i d . A t Buckhorn , the i n v e r s e d i s t a n c e cubed i n t e r p o l a t i o n method was chosen (no a n i s o t r o p i e s were m o d e l l e d ) , so i t was d e c i d e d t o t r y p o l y g o n a l 6 e s t i m a t e s and v a r i o u s powers o f i n v e r s e d i s t a n c e from power zero ( s t r a i g h t average) t o power t e n i n o r d e r t o see i f any o f these o t h e r e s t i m a t e s would p e r f o r m b e t t e r than the i n v e r s e d i s t a n c e cubed method. In p a r t i c u l a r , the b e h a v i o u r o f the i n v e r s e d i s t a n c e cubed i n t e r p o l a t o r t h a t was used f o r the 20 1 b l o c k model o f t h e o r i g i n a l mine d e s i g n was m o n i t o r e d t o see i f i t would work e q u a l l y w e l l on a l l o f the o t h e r 3 b l o c k mode l s , and to compare t h i s method t o k r i g e d e s t i m a t e s . 4) E f f e c t i v e n e s s o f C o n d i t i o n a l P r o b a b i l i t y E s t i m a t e s : D u r i n g the p e r i o d 1979 t o 1985, most g e o s t a t i s t i c a l s t u d i e s at Cominco were performed by G . F . Raymond. P i v o t a l t o h i s p h i l o s o p h y o f p r a c t i c a l g e o s t a t i s t i c s i s the method o f c a l c u l a t i o n o f c o n d i t i o n a l p r o b a b i l i t i e s u s i n g r e l a t i v e v a r i o g r a m s and o r d i n a r y k r i g i n g which he has deve loped over the p a s t 12 y e a r s (Raymond 1979, 1982, 1984) . E a r l y at tempts i n d i c a t e d t h a t p r o s p e c t s f o r u s i n g k r i g e d e s t i m a t e s as an a c c u r a t e b l o c k e s t i m a t o r a t Buckhorn were g r i m . C o n s e q u e n t l y , i t seemed r e a s o n a b l e to at tempt Raymond's approach o f " c o n d i t i o n a l p r o b a b i l i t y 1 1 . 5) Comparison W i t h B l a s t h o l e D a t a : The l a s t and most i m p o r t a n t q u e s t i o n t o be addressed was no t o n l y how w e l l the v a r i o u s o r e r e s e r v e e s t i m a t e s performed a g a i n s t each o t h e r , but how w e l l they compared w i t h the r e s e r v e s c a l c u l a t e d from a c t u a l p r o d u c t i o n b l a s t h o l e d a t a . F o r each o f the 4 e x p l o r a t i o n b l o c k mode l s , a p a r a l l e l b l o c k model u s i n g 20' o r 60' b l o c k s w i t h and w i t h o u t the p r e v i o u s l y mentioned ore zone o u t l i n e was c o n s t r u c t e d which c o n t a i n e d b l o c k e s t i m a t e s based on b l a s t h o l e d a t a on each bench and w i t h i n the o u t l i n e s . G r e a t c a r e was taken to ensure 7 t h a t p a r t i a l b l o c k p e r c e n t a g e s were c a l c u l a t e d on the edges o f the o u t l i n e s , and t h a t these "block p a r t i a l s " were used when r e p o r t i n g tonnages d e r i v e d e i t h e r from e x p l o r a t i o n d r i l l i n g or b l a s t h o l e e s t i m a t e s so t h a t the t o t a l tonnages e s t i m a t e d from e i t h e r s e t o f samples would be e x a c t l y the same, and would l i e c o m p l e t e l y w i t h i n the v a r i o u s o u t l i n e s imposed on the b l o c k m o d e l s . F o r each mode l , s i m p l e s t a t i s t i c a l parameters were c a l c u l a t e d , d i s t r i b u t i o n s were m o d e l l e d and examined by use o f h i s t o g r a m s and p r o b a b i l i t y g r a p h s , s e p a r a t e v a r i o g r a m s were c a l c u l a t e d , back e s t i m a t i o n t e c h n i q u e s were employed, and each o f 10 s e p a r a t e r e s e r v e c a l c u l a t i o n s were compared t o the best a v a i l a b l e b l o c k e s t i m a t e s t h a t c o u l d be d e r i v e d from the b l a s t h o l e d a t a . I t i s i m p o r t a n t t o note t h a t t h i s work i s devoted m a i n l y to d e t e r m i n i n g the b e s t p o s s i b l e ore r e s e r v e e s t i m a t e . The d i s t i n c t i o n i s made between p r o v i d i n g the b e s t e s t i m a t e o f the grade o f an i n d i v i d u a l b l o c k and the r e l a t e d , but s e p a r a t e problem o f p r e d i c t i n g the d i s t r i b u t i o n and average grade o f a l l b l o c k s w i t h i n and above grade c u t o f f s . The b e s t p o s s i b l e c a l c u l a t i o n o f o r e r e s e r v e s , which w i l l be used by the m i n i n g company t o d e t e r m i n e the economic p o t e n t i a l o f the d e p o s i t p r i o r t o a p r o d u c t i o n d e c i s i o n , i s the g o a l o f t h i s s t u d y . In the case o f t h e Buckhorn M i n e , t h i s c a l c u l a t i o n would r e s u l t i n f o u r c r u c i a l numbers — tons o f o r e , grade o f o r e , tons o f waste , and the c u t o f f grade t h a t i s used i n the c a l c u l a t i o n . 8 2. GEOLOGY OP THE BUCKHORN DEPOSIT The g o l d and s i l v e r a t Buckhorn i s hos t ed by a l t e r e d T e r t i a r y v o l c a n i c f lows w i t h m i n e r a l i z a t i o n l o c a l i z e d a l o n g h i g h a n g l e normal f a u l t sys tems . The d e p o s i t i s s i m i l a r t o the many o t h e r v o l c a n i c hos ted p r e c i o u s m e t a l d e p o s i t s wh ich have been formed i n near s u r f a c e hot s p r i n g env ironments i n t h e B a s i n and Range p r o v i n c e o f the southwes tern U n i t e d S t a t e s . R e g i o n a l l y , the T e r t i a r y v o l c a n i c and sed imentary rocks unconformably o v e r l y P a l e o z o i c sed imentary and v o l c a n i c u n i t s which a r e b r o a d l y r e p r e s e n t e d by two assemblages r e f e r r e d t o as the autochthonous e a s t e r n c a r b o n a t e assemblage and the a l l o c h t h o n o u s wes tern s i l i c e o u s and v o l c a n i c assemblage . L o c a l l y , the two assemblages are j u x t a p o s e d a l o n g the R o b e r t s Mounta ins t h r u s t f a u l t , which s u r f a c e s a few m i l e s t o the west o f t h e Buckhorn and C o r t e z a r e a s . G e n e r a l l y , e a s t e r n assemblage r o c k s o f the lower p l a t e are exposed to the west whereas the wes tern assemblage o f the upper p l a t e shows up t o the e a s t o f the t h r u s t f a u l t s u r f a c e t r a c e and s i l i c e o u s and v o l c a n i c u n i t s o f the wes tern f a c i e s o u t c r o p to the n o r t h , e a s t and west o f the Buckhorn mine a r e a ( F i g . 2 ) . A t h i r d s u i t e , r e f e r r e d t o as the P a l e o z o i c o v e r l a p assemblage , i s r e p r e s e n t e d l o c a l l y by the Brock Canyon f o r m a t i o n and i s made up l a r g e l y o f c o a r s e c l a s t i c rocks which were d e r i v e d from the p o s t - t h r u s t i n g e r o s i o n o f bo th the e a s t e r n c a r b o n a t e and the wes tern s i l i c e o u s r o c k s . To the n o r t h |Qa I 1 ALLUVIUM j J r i | JURASSIC INTRUSIVE I T i |TERTIARY INTRUSIVE 1 Po 1 PALEOZOIC OVERLAP 1 Tv |TERTIARY VOLCANICS 1 Ws | WESTERN S I L I C E O U S | T g |TERTIARY GRAVELS f E c " ] EASTERN CARBONATE F i g . 2. R e g i o n a l Geology Map o f an a r e a encompass ing the Buckhorn mine ( a f t e r Munroe, G o d l e w s k i , and P l a h u t a , 1988) . 10 o f the Buckhorn d e p o s i t , J u r a s s i c q u a r t z monzoni te s t o c k s i n t r u d e the P a l e o z o i c u n i t s . T e r t i a r y r o c k types i n c l u d e a 750 f o o t t h i c k n e s s o f b a s a l a l l u v i a l f a n d e p o s i t s , which are o v e r l a i n by up t o 350 f e e t o f Miocene b a s a l t i c a n d e s i t e t h a t h o s t s the Buckhorn m i n e r a l i z a t i o n . In p l a c e s the b a s a l t s are o v e r l a i n by younger sediments which i n c l u d e r e l a t i v e l y c o a r s e c l a s t i c m a t e r i a l s i m i l a r to the e a r l i e r T e r t i a r y f a n d e p o s i t s , some p e l i t e s , and s i l i c e o u s hot s p r i n g s i n t e r d e p o s i t s c o n t a i n i n g f o s s i l r e e d s . On the mine p r o p e r t y , and more s p e c i f i c a l l y , around the main N o r t h Buckhorn P i t s tudy area ( F i g . 3 ) , the dominant r o c k t y p e i s b a s a l t i c a n d e s i t e , but t h e r e are a l s o some o f the younger Miocene sediments exposed i n the area o f the open p i t , and a b r e c c i a u n i t j u s t t o the n o r t h e a s t . In areas o f m i n e r a l i z a t i o n , the v o l c a n i c s have been e x t e n s i v e l y a r g i l l i c a l l y a l t e r e d . The a l t e r a t i o n zone extends f o r about 3,000 f e e t a l o n g the s t r i k e o f a major N10°W h i g h ang le f a u l t and ranges from 100 f e e t t o 1,000 f e e t i n w i d t h . The c l a y a l t e r a t i o n extends to a depth o f about 200 f e e t . The upper two t h i r d s o f the a l t e r e d volume has been o x i d i z e d whereas the lower one t h i r d i s a reduced s u l f i d e zone . Both the o x i d e and the s u l f i d e zones c o n t a i n g o l d and s i l v e r . L a t e r a l l y , k a o l i n i t e c l o s e t o the f a u l t g i v e s way t o m o n t m o r i l l i n i t e and the t r a n s i t i o n from one c l a y t o t h e o t h e r appears t o d e f i n e the l i m i t s o f the o r e body on e i t h e r s i d e o f the s t r u c t u r e ( P l a h u t a , 1986) . As e v i d e n c e d by s i n t e r s , a r g i l l i c a l t e r a t i o n , and the p r e s e n c e o f e x p l o s i o n b r e c c i a s i n the v i c i n i t y o f the mine , the 1 7 0 0 0 6 0 0 0 •m- 4 0 0 F e e t Tbrl B R E C C I A T_sJ M I O C E N E S E D I M E N T S M I O C E N E B A S A L T I C A N D E S I T E E A R L Y T E R T I A R Y F A N G L O M E R A T E STUDY A R E A P I T O U T L I N E 1 5 0 0 0 Tb LU O O O F i g . 3. G e o l o g i c a l map o f the Buckhorn Mine ( a f t e r Munroe, God lewsk i and P l a h u t a , 1988) . m i n e r a l i z a t i o n has been d e p o s i t e d i n a near s u r f a c e hot s p r i n g e n v i r o n m e n t . The h i g h ang le f a u l t s and f r a c t u r i n g i n the area p r o v i d e d c o n d u i t s f o r hot h y d r o t h e r m a l f l u i d s and p r e p a r e d the b a s a l t i c a n d e s i t e f o r a l t e r a t i o n and s tockwork m i n e r a l i z a t i o n . The o c c u r r e n c e o f e x p l o s i o n b r e c c i a s i n d i c a t e s t h a t s p o r a d i c b r e a c h i n g o f a s e a l e d system r e l i e v e d p r e s s u r e b u i l d u p , i n i t i a t e d h y d r a u l i c f r a c t u r i n g and lowered b o i l i n g h o r i z o n s which would i n t u r n cause g o l d and s i l v e r t o d e p o s i t from the c o o l e d f l u i d s and t o d e p o s i t i n t o the p o r o u s , f r a c t u r e d h o s t r o c k s . 13 3. AVAILABLE DATA AND BLOCK MODELS 3.1 EXPLORATION DATA E x p l o r a t i o n d r i l l h o l e s were d r i l l e d a p p r o x i m a t e l y on a r e g u l a r 50' x 50' g r i d . The m a j o r i t y o f the d a t a comes from r o t a r y d r i l l c u t t i n g s which were sampled e v e r y 10' from the c o l l a r and f i r e assayed f o r b o t h g o l d and s i l v e r . A l t h o u g h s i l v e r grades were a v a i l a b l e from e x p l o r a t i o n d r i l l h o l e s , t h e r e a r e no s i l v e r assays from b l a s t h o l e s , and t h e r e f o r e e s t i m a t e s o f s i l v e r grades c o u l d no t be compared t o b l a s t h o l e d a t a and were i g n o r e d i n t h i s s t u d y . The o n l y g e o l o g i c a l i n f o r m a t i o n a v a i l a b l e was the l o c a t i o n o f the o x i d e / s u l f i d e boundary i n f e e t from the c o l l a r o f the h o l e . The r o t a r y d r i l l h o l e s are v e r t i c a l , but t h e r e are a few i n c l i n e d diamond d r i l l h o l e s t h a t were i n c l u d e d because these and a few o t h e r c l o s e spaced r o t a r y h o l e s p r o v i d e d the on ly i n f o r m a t i o n on l a g d i s t a n c e s o f l e s s than 50' f o r c a l c u l a t i n g h o r i z o n t a l v a r i o g r a m s . There were v a r i o u s campaigns o f r o t a r y d r i l l i n g on the p r o p e r t y , a l l i n c l u s t e r s , which d e f i n e d v a r i o u s areas i n the open p i t , d r i l l e d i n d i f f e r e n t y e a r s and assayed by d i f f e r e n t l a b s . The i n c l i n e d h o l e s , and the d i f f e r e n t s e r i e s o f r o t a r y h o l e s , might t h e r e f o r e c o n s t i t u t e d i f f e r e n t s u p p o r t s . T h e r e was no adequate method o f comparing e i t h e r the r e l i a b i l i t y o f t h e diamond d r i l l h o l e assays a g a i n s t the r o t a r y d r i l l h o l e s , or indeed the v a r i o u s d i f f e r e n t s e r i e s o f r o t a r y d r i l l h o l e s a g a i n s t each o t h e r . A l l samples were accepted i f they were w i t h i n the o x i d e zone and f e l l w i t h i n 100' o f the r e c t a n g u l a r s tudy area shown on F i g u r e 3. Raw 10' d r i l l h o l e samples were compos i ted t o 20' l e n g t h s s u c h t h a t each weighted compos i te f e l l w i t h i n a 20' m i n i n g bench s t a r t i n g a t e l e v a t i o n 6900' w i t h i t ' s c e n t e r v e r t i c a l l y i n the m i d d l e o f the bench . Composi tes o f l e s s than 5' were d i s c a r d e d . Bench p l a n s showing the e x p l o r a t i o n compos i tes can be found i n Appendix A . A l t o g e t h e r t h e r e were 3,670 e x p l o r a t i o n compos i tes g e n e r a t e d , o f which 2,432 f e l l w i t h i n the r e c t a n g u l a r s tudy area where p r o d u c t i o n d a t a from the main N o r t h Buckhorn p i t was a v a i l a b l e f o r c o m p a r i s o n . 3.2 BLASTHOLE DATA The b l a s t h o l e s (shown on the bench p l a n s i n Appendix A) are spaced a p p r o x i m a t e l y 12 - 14' a p a r t . B l a s t h o l e c u t t i n g s f o r the upper 20' a r e sampled from the r i n g o f c u t t i n g s a t the c o l l a r and f i r e assayed f o r g o l d o n l y . A l t h o u g h t h e r e appears to be a f a i r l y c o n s t a n t s i l v e r t o g o l d r a t i o (about 1 5 : 1 ) , the r e c o v e r y o f s i l v e r from the heap l e a c h i n g p r o c e s s i s low (< 40%). T h e r e f o r e any s i l v e r r e c o v e r e d i s c o n s i d e r e d a bonus and s i l v e r v a l u e s are n o t used f o r the open p i t d e s i g n , or t o de termine mine c u t o f f s o r d a i l y p r o d u c t i o n o r e l i m i t s . T h e r e are a t o t a l o f 8,752 b l a s t h o l e as says a v a i l a b l e t h a t r e p r e s e n t p r o d u c t i o n d a t a t o the end o f J u l y , 1986. The o u t l i n e o f the p e r i m e t e r o f the i n d i v i d u a l b l a s t s was used t o determine the mined out a r e a w i t h i n which ore r e s e r v e s would be c a l c u l a t e d . A l l b l a s t h o l e s are i n the o x i d e zone; the s u l f i d e m i n e r a l i z a t i o n was no t encountered u n t i l l a t e r i n 1986,. 3.3 BLOCK MODELS 3 . 3 . 1 I n t r o d u c t i o n To save on computer t ime and c o s t s , o n l y 2 benches (6860 and 6840) were m o d e l l e d . The 2 benches r e p r e s e n t a w e l l sampled area b o t h f o r e x p l o r a t i o n and b l a s t h o l e d a t a i n t h a t t h e r e i s adequate s a m p l i n g w i t h i n the mined a r e a on b o t h benches and on the 2 benches immedia te ly above and below. The volume c o n t a i n e d w i t h i n the m i n i n g o u t l i n e s on the 6840 and 6860 benches , t o g e t h e r r e p r e s e n t a t o t a l o f 1.155 m i l l i o n tons o f ore and waste m a t e r i a l . T h i s was c o n s i d e r e d s u f f i c i e n t t o g e n e r a t e a r e l i a b l e e s t i m a t e o f p r o d u c t i o n a g a i n s t which e x p l o r a t i o n ore r e s e r v e e s t i m a t e s c o u l d be compared. 3 . 3 . 2 F o u r F o o t B l o c k Models One o f the aims o f t h i s s tudy i s t o compare e s t i m a t e s o f a c t u a l p r o d u c t i o n tons and grade w i t h e x p l o r a t i o n ore r e s e r v e e s t i m a t e s genera ted from b o t h 20' and 60' b l o c k models w i t h i n f i x e d b o u n d a r i e s . To do t h i s i n a c o n s i s t e n t manner so t h a t p o l y g o n a l e s t i m a t e s c o u l d be compared t o e s t i m a t e s on b o t h 20' and 60 1 b l o c k s i z e s such t h a t a l l t h r e e c a l c u l a t i o n s r e p o r t e d the same o v e r a l l tonnage , a 4' x 4' x 20' b l o c k model was generated on the 2 benches . T h i s b l o c k s i z e was chosen f o r two p r i n c i p a l r e a s o n s : 1) R e p r e s e n t a t i v e p o l y g o n a l e s t i m a t e s c o u l d be c a l c u l a t e d to v e r y s m a l l b l o c k s which c o u l d be recombined i n groups t h a t would c l o s e l y resemble t r a d i t i o n a l hand drawn p o l y g o n a l b o u n d a r i e s . Because the average sample b l a s t h o l e s p a c i n g i s a t l e a s t 1 2 ' , t h e r e a r e , on a v e r a g e , a t l e a s t 9 c l o s e s t n e i g h b o u r 4' b l o c k s . 2) The 4' b l o c k s i z e d i v i d e s e v e n l y i n t o the 20' and 60' b l o c k s i z e s and the 20' b l o c k s d i v i d e e v e n l y i n t o the 60' b l o c k s . Because the o r i g i n s o f the 3 b l o c k models are e x a c t l y the same, 25 o r i g i n a l 4' b l o c k s e x a c t l y r e p r e s e n t each 20' b l o c k , 225 4' b l o c k s f i t i n t o a 60' b l o c k , and 9 20' b l o c k s a r e c o n t a i n e d i n a 60' b l o c k . Because d i f f e r e n t o u t l i n e s (mined l i m i t s , ore zone b o u n d a r i e s ) a r e imposed on the v a r i o u s b l o c k mode l s , the 4' model was used t o de termine which v e r y s m a l l b l o c k s were w i t h i n a boundary and which were o u t s i d e . T h e n , the number o f v a l i d 4' b l o c k s i n s i d e the l a r g e r b l o c k s were used t o c a l c u l a t e f r a c t i o n a l b l o c k p e r c e n t a g e s ( b l o c k p a r t i a l s ) w i t h i n p a r t i c u l a r b o u n d a r i e s . In t h i s way, e x a c t l y the same tonnage was r e p r e s e n t e d by each o f the l a r g e r b l o c k s i z e models and , f o r example , a l a r g e 60' b l o c k whose grade i s l a t e r e s t i m a t e d , might be weighted by as l i t t l e as 1/225 o f i t s volume when c a l c u l a t i n g t o t a l r e s e r v e s because 224/225 o f the b l o c k i s o u t s i d e the a r e a t o be e s t i m a t e d . Normal methods o f a c c e p t i n g o r r e j e c t i n g b l o c k s t end t o throw out a b l o c k i f i t ' s c e n t e r i s o u t s i d e o f a boundary . F i g u r e 4 shows r + 408 TONS + + + + + ~7T • + A METHOD 1 USUALLY, IF A B L O C K ' S CENTRE IS INSIDE THE 1 , BOUNDARY. IT IS ?| ACCEPTED. RESULT ' 1) THE 6 0 ' BLOCK IS REJECTED - 0 TONS. 2) 2 2 0 ' BLOCKS ARE KEPT - 816 TONS. 3) 54 4 ' BLOCKS ARE KEPT - 881 TONS. ORE ZONE OUTLINE METHOD 2 THE METHOD USED HERE. LARGER BLOCKS ARE WEIGHTED BY THE NUMBER OF 4 ' BLOCKS THAT Q U A L I F I E D . RESULT« 1) THE 6 0 ' BLOCK IS RETAINED. TONNAGE IS WEIGHTED 54/225 - 881 TONS. 2) 3 2 0 ' BLOCKS ARE RETAINED. WEIGHTED 1 2 / 2 5 . 2 5 / 2 5 , AND 17/25 - 881 TONS. 3) 4 ' BLOCKS, AS ABOVE, 881 TONS. 6ir + 408 TONS + + + + | : A + + + + < + + + + + + + + + + + 4 + + + + + + i > + + + + + + + + ,i / • + + + + + + + + + A + + + + + + + + + ORE ZONE OUTLINE / F i g . 4. Two methods o f a c c e p t i n g o r r e j e c t i n g b l o c k s w i t h i n an o u t l i n e . Method 2. i s used i n t h i s work. 1 8 the d i f f e r e n c e i n r e s u l t s between t h i s method and the one employed f o r t h i s s t u d y . 3.3.3 Twenty F o o t B l o c k Models Two 20' b l o c k models were g e n e r a t e d . The f i r s t r e p r e s e n t s t h e a c t u a l b l o c k s i z e and o u t l i n e used i n i n i t i a l p r o d u c t i o n p l a n n i n g . Each b l o c k r e p r e s e n t s 408 tons o f m a t e r i a l i f 100% o f the b l o c k f a l l s i n s i d e the mined l i m i t s . A l l b l o c k s a l o n g the mined l i m i t s were checked to see i f any s e l e c t e d 4' b l o c k s were c o n t a i n e d w i t h i n i t , and , based on the number o f these s m a l l b l o c k s w i t h i n the o u t l i n e , a p e r c e n t a g e f r a c t i o n was generated a l o n g w i t h the b l o c k l o c a t i o n which c o u l d l a t e r be used to c a l c u l a t e a c t u a l tonnage w i t h i n the o u t l i n e . F o r t h i s mode l , p e r c e n t a g e s were m u l t i p l e s o f 4% because t h e r e are a maximum o f 25 4' b l o c k s e x a c t l y c o n t a i n e d i n a 20' b l o c k . The second 20' b l o c k model i s a subse t o f the f i r s t . A c o n s e r v a t i v e o r e zone o u t l i n e (shown on bench p l a n s , Appendix A) which g e n e r a l l y c o n t a i n e d o n l y e x p l o r a t i o n compos i tes t h a t graded b e t t e r t h a n 0.01 o p t . was d i g i t i z e d (see C h a p t e r 4. f o r r a t i o n a l e ) . A g a i n , b l o c k p a r t i a l s were c a l c u l a t e d f o r t h i s s u b s e t o f 20' b l o c k s from the 4' model t o e s t i m a t e tonnages s t r a d d l i n g the boundary . S i m u l t a n e o u s l y , second e x p l o r a t i o n and b l a s t h o l e d a t a f i l e s were c r e a t e d which c o n t a i n e d o n l y d r i l l h o l e compos i t e s o r b l a s t h o l e s which were c o m p l e t e l y i n s i d e the ore zone o u t l i n e (even i f o u t s i d e the mined l i m i t s ) . These f i l e s are used l a t e r t o s tudy s t a t i s t i c s and g e n e r a t e v a r i o g r a m s , and to g e n e r a t e v a r i o u s p o l y g o n a l , e s t i m a t e s f o r t h i s b l o c k mode l . 3 . 3 . 4 S i x t y F o o t B l o c k Models i n v e r s e d i s t a n c e , and k r i g e d The 60' b l o c k models were generated i n e x a c t l y the same way as the 20' b l o c k mode l s . The f i r s t 60' model c o n t a i n e d b l o c k s which were c o m p l e t e l y or p a r t l y i n s i d e the mine l i m i t s on the 6840 and 6860 benches and b l o c k p a r t i a l p e r c e n t a g e s were s t o r e d . The second was a subse t which c o n t a i n e d 60' b l o c k s which r e p r e s e n t e d t h o s e l a r g e b l o c k s or p a r t i a l b l o c k s which were c o n t a i n e d i n s i d e the s e l e c t e d ore zone boundary . A l t h o u g h the 60' b l o c k s are s l i g h t l y l a r g e r than the 50' e x p l o r a t i o n d r i l l h o l e s p a c i n g , t h i s b l o c k s i z e was chosen because i t approx imates the s p a c i n g o f the d r i l l h o l e s and a l s o f i t s the 4' and 20' b l o c k mode l s . A l l t h r e e models s h a r e the same o r i g i n and t h e r e f o r e the s m a l l e r b l o c k s f i t i n s i d e the 60' b l o c k s . 3.4 SUMMARY OF BLOCK MODELS AND DATASETS The n e t r e s u l t i s 6 b l o c k models and 4 s e p a r a t e d a t a s e t s . These are summarized i n T a b l e I . In o r d e r t o r e f e r t o the v a r i o u s d a t a s e t s and b l o c k mode l s , s h o r t names have been as s igned w h i c h may be used e l sewhere i n the t e x t and f i g u r e s . 20 T a b l e I Summary o f B l o c k Models and D a t a s e t s S h o r t Name #Blocks or Composi tes W i t h i n Mine L i m i t s ? W i t h i n Ore Zone O u t l i n e ? Bench B l o c k Models 4x4 1 4 FOOT 70,775 yes no 6840-6860 4FOOTG 46,331 yes yes 6840-6860 20x20 1 BUCK 2,999 yes no 6840-6860 BUCKG 2,089 yes yes 6840-6860 60x60• BUCK60 386 yes no 6840-6860 BUCK60G 305 yes yes 6840-6860 E x p l o r a t i o n Compos i tes BEX 2,432 no no 6600-6900 BEXG 1,036 no yes 6780-6880 B l a s t h o l e Samples BBH 8,752 yes no 6780-6880 BBHG 6,315 yes yes 6780-6880 21 4 . S T A T I S T I C S In any o r e r e s e r v e s t u d y , a s t a t i s t i c a l e v a l u a t i o n o f the d a t a i s c o n s i d e r e d i m p o r t a n t . One o f the most i m p o r t a n t r e s u l t s t h a t can be o b t a i n e d i s the c o n f i r m a t i o n o f the normal or l o g n o r m a l n a t u r e o f the sample d a t a . V e r y few p e o p l e r i g o r o u s l y t e s t t h e i r r e s u l t s i n any way — u s u a l l y a h i s t o g r a m or p r o b a b i l i t y graph i s drawn, and a b e s t f i t c u r v e o r s t r a i g h t l i n e i s used (depending on which t y p e o f graph was chosen) t o p o i n t out t h a t " i t ' s c l o s e enough" and t h a t ' s the l a s t we hear about i t . A l t e r n a t i v e l y , v a r i o u s newer and much more complex k r i g i n g methods a r e employed t o o f f s e t the d e l e t e r i o u s e f f e c t o f h a v i n g n o n - p e r f e c t d a t a d i s t r i b u t i o n s (examples are m u l t i g a u s s i a n , i n d i c a t o r and p r o b a b i l i t y k r i g i n g ) . Because o f t h e i r c o m p l e x i t y , the se methods are o f t e n d i f f i c u l t t o " s e l l " t o management i n a m i n i n g company. One f u r t h e r o b j e c t i v e o f t h i s s tudy w i l l be t o show t h a t much s i m p l e r e s t i m a t i o n methods can be used ( p r o b a b l y over 90% o f the t ime) i f a de termined e f f o r t i s made to u n d e r s t a n d the n a t u r e o f the r e s u l t s from a c l a s s i c a l s t a t i s t i c a l s t u d y . The a u t h o r has s t u d i e d numerous g e o c h e m i c a l , g e o p h y s i c a l , d r i l l h o l e , and remote s e n s i n g d a t a s e t s over the p a s t 5 o r 6 years and has f o u n d , a lmost w i t h o u t e x c e p t i o n , t h a t n o n - l o g n o r m a l a p p e a r i n g d a t a s e t s can be e x p l a i n e d by i n a p p r o p r i a t e m i x i n g o f d a t a from s e p a r a t e p o p u l a t i o n s . Where c l a s s i c a l s t a t i s t i c a l parameters such as mean and v a r i a n c e a r e r e p o r t e d f o r these mixed d a t a s e t s , they a r e n e a r l y m e a n i n g l e s s . What i s needed i s a way o f s p l i t t i n g up these s e p a r a t e , ( u s u a l l y ) l o g n o r m a l p o p u l a t i o n s ( D a v i d , 1988) , and a way o f t e s t i n g whether the r e s u l t i n g p a r t i t i o n e d p o p u l a t i o n s have any b a s i s i n f a c t . One such method has been documented and demonstrated ( S i n c l a i r , 1976) , and w i l l be used h e r e . In the case o f t h i s s t u d y , use o f the c o n d i t i o n a l p r o b a b i l i t y e s t i m a t e (which w i l l be d e s c r i b e d l a t e r ) i s c r i t i c a l l y dependent on the assumpt ion t h a t the d a t a i s l o g n o r m a l l y d i s t r i b u t e d . The 2,388 n o n - z e r o e x p l o r a t i o n 20' compos i t e s from the o r i g i n a l (BEX) d a t a s e t were used t o c o n s t r u c t a p r o b a b i l i t y graph ( F i g . 5 ) . A t f i r s t g l a n c e , a bes t f i t s t r a i g h t l i n e can be drawn t h r o u g h the p o i n t s on the c u r v e which would seem t o adequate ly i n d i c a t e a l o g n o r m a l d i s t r i b u t i o n . However, i f a r u l e r i s p l a c e d between the f i r s t and the l a s t o r second l a s t p o i n t , i t can be seen t h a t e v e r y s i n g l e p o i n t on the p l o t i s above the s t r a i g h t l i n e , and t h a t they seem t o d e f i n e a g e n t l y c u r v i n g l i n e o f p o i n t s . E x a m i n a t i o n o f the h i s t o g r a m below shows t h a t the d i s t r i b u t i o n o f the samples does no t d e f i n e a " b e l l " shaped c u r v e . The q u e s t i o n i s , can 2 o r more p o p u l a t i o n s be d e f i n e d w h i c h , when added i n the p r o p e r p r o p o r t i o n s , add up t o c r e a t e a c u m u l a t i v e p r o b a b i l i t y which resembles the one shown f o r a l l o f t h e 20' e x p l o r a t i o n compos i te s? U s i n g S i n c l a i r ' s method, two s t r a i g h t l i n e p o p u l a t i o n s were m o d e l l e d which show t h a t i f 2 l o g n o r m a l p o p u l a t i o n s (A and B , F i g . 5) a r e added t o g e t h e r i n the p r o p o r t i o n A=60% and B=40%, the o r i g i n a l d a t a p o i n t s can be approximated (check p o i n t s , F i g . 5 ) . 23 N= 2 3 8 8 - PROBAB IL ITY ( CUM % ) LOWER % LOWER % LIMIT LIMIT 0.000 6.2 ****** 0.000 0.0 0.001 0.0 0.001 2.9 *** 0 .001 3.0 *** 0 .002 3.1 *** 0.002 4.5 ***** 0 .003 2.6 *** 0.003 3.7 **** 0.004 2.4 ** 0.004 4.5 **** 0 .005 3.8 **** 0.005 9.0 ********* 0.007 6.4 ****** 0.008 8.3 ******** 0 .010 8.4 ******** 0 .011 7.5 ******* 0 .014 9.5 ********* 0.015 8.9 ********* 0.019 12.1 ************ 0.020 10.7 *********** 0.026 12.4 ************ 0.028 10.5 ********** 0.036 10.7 *********** 0.039 8.1 ******** 0.049 8.1 ******** 0 .054 6.0 ****** 0.066 5.4 ***** 0 .075 4.3 **** 0 .091 3 . 3 *** 0.104 1.8 ** 0.124 1.9 ** 0.143 1.4 * 0.169 1.2 * 0.198 0.8 * BEX DATA 0.230 0.6 * BBH DATA F i g . 5. P a r t i t i o n e d l o g p r o b a b i l i t y p l o t o f 20' e x p l o r a t i o n c o m p o s i t e s . The h i s t o g r a m below shows a l a r g e number o f low grade samples which cause the o r i g i n a l c u r v e t o d e p a r t from a p e r f e c t l o g n o r m a l d i s t r i b u t i o n . By s t u d y i n g the r e s u l t i n g l o g n o r m a l p o p u l a t i o n s , as s t r a i g h t l i n e s on a p r o b a b i l i t y g r a p h , one can d e f i n e a range o f grades from a p p r o x i m a t e l y 0.005 o p t . t o 0.0 35 o p t . f o r which t h e r e i s some p r o b a b i l i t y t h a t a sample i s drawn from one or the o t h e r p o p u l a t i o n . A l s o , i t can be seen t h a t 90% o f the members o f p o p u l a t i o n A ( a p p r o x i m a t e l y 1,300 samples) s h o u l d be above 0.010 o p t . , whereas o n l y 28% o f p o p u l a t i o n B s h o u l d be above 0.010 o p t . ( a p p r o x i m a t e l y 265) samples . I t was t h i s 0.01 grade c u t o f f t h a t was s e l e c t e d t o d e f i n e the o r e o u t l i n e s t h a t were used to c o n s t r u c t the second s e t o f 3 "ore zone" b l o c k models examined i n t h i s s t u d y . A c o n s e r v a t i v e boundary was drawn on e v e r y bench f o r which t h e r e was a m i n i n g o u t l i n e ( b l a s t h o l e d a t a ) . The ore zone boundary i s c o n s i d e r e d c o n s e r v a t i v e because i t l i e s c l o s e r to the " g r e a t e r t h a n 0.01 o p t . e x p l o r a t i o n compos i tes" than t o the n e a r e s t compos i t e which grades l e s s than 0.01 o p t . The l i n e e s s e n t i a l l y e n c l o s e s zones which a r e bounded by 0.01 o p t . g o l d e x p l o r a t i o n c o m p o s i t e s . A c c o r d i n g t o the p r o b a b i l i t y g r a p h , i f the o u t l i n e d zone t r u l y r e p r e s e n t s t h e m o d e l l e d p o p u l a t i o n "A" i n F i g u r e 5, t h e n i t s h o u l d a l s o i n c l u d e a number o f v a l u e s (10%) which a r e l e s s t h a n 0.01 o p t . Two s e p a r a t e d a t a s e t s were c r e a t e d , one which r e p r e s e n t s e x p l o r a t i o n d a t a w i t h i n the o u t l i n e (BEXG d a t a s e t ) , and one which r e p r e s e n t s the b l a s t h o l e d a t a w i t h i n the same zone (BBHG d a t a s e t ) . The r e s u l t i n g d a t a were then p l o t t e d on a l o g p r o b a b i l i t y graph ( F i g . 6) a l o n g w i t h the h i g h e r model led p o p u l a t i o n " A " . W i t h i n each o f the new d a t a s e t s t h e r e are va lues below 0.01 (8% f o r the e x p l o r a t i o n compos i tes and 9% f o r the 25 1 .000 - i i I I i i i i i i i \ A BEXG DATA (N = 1032) i i i i _ _ \ ° a BBHG DATA (N = 6308) z D. 100 o — h— \ — NJ — o * ô . UJ Q < cr o Q O 0.010 O — •\ — * ^ \ A " c .001 i i I I i i i i i i i i i 1 I 0 . i 2 10 30 50 70 90 98 99.9 P R O B A B I L I T Y ( CUM % ) LOWER % LOWER % LIMIT T T M T T j j i n i j. 0.003 c .5 * 0.003 0.8 * 0 .004 1 .4 * 0.004 2.1 ** 0 .005 1 .8 ** 0.006 1.1 * 0.007 0.5 * 0.007 3.0 *** 0 .008 c . 3 ***** 0.009 5 . 7 ****** 0.011 7 .3 ******* 0.012 6 . 3 ****** 0 .014 1 .2 ******* 0.015 7.8 ******** 0 .017 12.5 ************* 0.019 10.2 ********** 0 .022 11 .8 * * * * * * * * * * * * o ! o 2 4 10 . 2 ********** 0.028 10 . 3 * * * * * * * * * * o!o3o 11.2 *********** 0.035 10.9 * * * * * * * * * * * o!038 11.0 *********** 0 .045 7 .9 ******** o!048 9.0 ********* 0 .056 6 .1 ****** 0*.061 6.0 ****** 0.071 c .9 ****** 0.077 4.6 ***** 0.090 2 .4 ** 0.097 3.2 *** 0.113 1 .7 ** 0.122 2.1 ** 0.143 1 .5 * 0.154 1.6 ** 0.180 0 .9 * 0.195 0.9 * 0.228 0 .5 * BEXG DATA 0.245 0.6 * BBHG DATA F i g . 6 Log p r o b a b i l i t y p l o t o f b l a s t h o l e d a t a compared t o p a r t i t i o n e d e x p l o r a t i o n d a t a . The s t r a i g h t l i n e i s the mode l l ed p o p u l a t i o n A from F i g u r e 5. Bo th s e t s o f d a t a r e p r e s e n t e d above are drawn from w i t h i n the o r e o u t l i n e i n t e r p r e t e d from the graph i n F i g . 5 • b l a s t h o l e s ) which compare f a v o u r a b l y w i t h the expected 10% from t h e model p o p u l a t i o n " A " . The b l a s t h o l e d a t a w i t h 6,308 samples i s a c c u r a t e l y r e p r e s e n t e d by the s t r a i g h t l i n e mode l . The e x p l o r a t i o n d a t a shows smoothing t h a t was apparent o n l y s u b t l y i n t h e raw d a t a — namely a s l i g h t u n d e r e s t i m a t i o n o f t h e percentage o f compos i t e s expected a t h i g h e r grades and a s l i g h t o v e r e s t i m a t i o n o f the p e r c e n t a g e o f compos i tes a t lower g r a d e s . T h i s i s c o n s i s t e n t w i t h the expec ted r e s u l t when u s i n g the we ighted a v e r a g i n g p r o c e s s which o r i g i n a l l y c r e a t e d the c o m p o s i t e s , and i t i s a c c e n t u a t e d by the f a c t t h a t t h e r e are fewer samples i n the e x p l o r a t i o n d a t a s e t ( on ly 1,032 c o m p o s i t e s ) . B o t h the e x p l o r a t i o n and the b l a s t h o l e p l o t t e d p o i n t s show a s l i g h t tendency t o " r i s e " t o h i g h e r grades between the 2nd and 5 t h p e r c e n t i l e s i n the g r a p h . F o r the b l a s t h o l e s t h i s p r o b a b l y i n d i c a t e s t h a t t h e r e are a few areas o f u n e x p e c t e d l y h i g h g r a d e s , but f o r the e x p l o r a t i o n d a t a i t i s a lmost c e r t a i n l y due t o a s m a l l e r number o f i r r e g u l a r d r i l l h o l e s which were c l o s e r t h a n 50 1 a p a r t (not on the g r i d p a t t e r n ) and which were a lmost e x c l u s i v e l y c o l l a r e d i n h i g h e r grade o r e a r e a s . T h i s g i v e s a s l i g h t l y h i g h e r than expec ted number o f samples i n the h i g h grade c a t e g o r i e s . G e n e r a l l y however, the m o d e l l i n g seems t o have a c c u r a t e l y p r e d i c t e d the e x i s t e n c e o f t h e s e d i s c r e e t zones o f h i g h e r g r a d e s . N o t i c e a l s o t h a t whether the model i s t o be b e l i e v e d o r n o t , the e x p l o r a t i o n and b l a s t h o l e grade d i s t r i b u t i o n s i n t h i s o u t l i n e are n e a r l y i d e n t i c a l which i n d i c a t e s t h a t t h e r e i s l i t t l e o r no b i a s between the 2 types o f samples . The reason f o r o n l y g e n e r a t i n g the BEXG and BBHG d a t a s e t s on benches where t h e r e was b l a s t h o l e d a t a was so t h a t the e x i s t e n c e o f any s a m p l i n g b i a s c o u l d be 27 T a b l e I I S i m p l e S t a t i s t i c s o f the E x p l o r a t i o n and B l a s t h o l e Data A r i t h . A r i t h . R e l a t i v e L o g 1 0 L o g 1 0 Data n Mean V a r i a n c e V a r i a n c e Mean V a r i a n c e BEX 2432 0.031 0.00224 2.3 - 1 . 8 2 0.311 BEXG 1036 0.043 0.00276 1.5 - 1 . 5 5 0.162 BBH 8752 0.037 0.00310 2.2 - 1 . 7 1 0.288 BBHG 6315 0.047 0.00380 1.7 - 1 . 5 1 0.162 checked i n t h i s way. A c h a r t summarizes the s i m p l e s t a t i s t i c s o f the f o u r d a t a s e t s (Tab le I I ) . R e l a t i v e v a r i a n c e s were c a l c u l a t e d because , i n o r d e r t o use Raymond's c o n d i t i o n a l p r o b a b i l i t y method, r e l a t i v e v a r i o g r a m s a r e u s e d . The p o p u l a t i o n r e l a t i v e v a r i a n c e s h o u l d be a g u i d e i n c h o o s i n g the s i l l v a l u e i n a r e l a t i v e v a r i o g r a m i n the same way t h a t the v a r i a n c e s h o u l d be an i n d i c a t o r f o r a c t u a l v a r i o g r a m s . These s i m p l e s t a t i s t i c s w i l l be a n a l y z e d f u r t h e r i n the s e c t i o n on v a r i o g r a p h y ( S e c t i o n 5 . 4 . 1 ) . T h e r e i s ano ther method o f m o d e l l i n g l o g n o r m a l p o p u l a t i o n s ( e . g . Raymond, 1982) which i s i n t e g r a l t o the c o n d i t i o n a l p r o b a b i l i t y approach to ore r e s e r v e e s t i m a t i o n ; t h i s i s , t o add a c o n s t a n t t o i n d i v i d u a l grades t o c r e a t e a 3 -parameter l o g n o r m a l m o d e l . F i g u r e 7 shows t h a t a c o n s t a n t o f 0.005 o p t . added t o the o r i g i n a l s e t o f a r i t h m e t i c g o l d grades produces a s e r i e s o f p o i n t s which approach a s t r a i g h t l i n e l o g n o r m a l m o d e l . T h i s v a l u e s h o u l d be used l a t e r t o compute c o n d i t i o n a l p r o b a b i l i t y f o r t h e 2 "non-ore o u t l i n e " b l o c k models (BUCK and BUCK60) because , 28 I.000. F r o i — \ M 0.100 o ID O O O < o Q 0.010 _j o o 0.001 0. 1 i—i—i—i—r j i i_ i i i i—r i zn 10 30 50 70 90 PROBABILITY ( CUM % ) j i_ 98 99.9 F i g . 7. Log p r o b a b i l i t y p l o t shows the e f f e c t o f a d d - i n g a c o n s t a n t o f 0.005 o p t . t o the o r i g i n a l d a t a t o c r e a t e a 3 -parameter l o g n o r m a l d i s t r i b u t i o n . a c c o r d i n g t o Raymond (1982, 1984) , i t i s the o n l y way t o ensure t h a t k r i g i n g v a r i a n c e s are r e l a t e d t o a l o g t r a n s f o r m e d k r i g e d g r a d e . However i t s h o u l d be mentioned h e r e , and i t w i l l be a m p l i f i e d on f u r t h e r i n l a t e r s e c t i o n s , t h a t the 3-parameter l o g n o r m a l concept i s one which the a u t h o r has d i f f i c u l t y w i t h . C o n c e p t u a l l y , a d i s t r i b u t i o n can be m o d e l l e d by a s s i g n i n g a f r e q u e n c y t o e v e r y s i n g l e v a l u e i n t h a t d a t a s e t a n d , r e g a r d l e s s o f what c o n s t a n t one adds t o each d i s c r e e t v a l u e , i t d o e s n ' t change the f r e q u e n c y w i t h which t h a t v a l u e o c c u r s . The f a c t t h a t i t appears t o g e n e r a t e a s t r a i g h t e r l i n e when p l o t t e d on a l o g p r o b a b i l i t y graph d o e s n ' t change the f a c t t h a t one r e a l l y h a s n ' t a l t e r e d the d i s t r i b u t i o n o f the raw a r i t h m e t i c d a t a . M o d e l l i n g the 3-parameter l o g n o r m a l d i s t r i b u t i o n w i t h a p o s i t i v e c o n s t a n t does have an e f f e c t however. What happens i s t h a t the r e l a t i v e and l o g n o r m a l p o p u l a t i o n v a r i a n c e s are d e c r e a s e d . The l o g n o r m a l mean i s s h i f t e d up and the bes t f i t l i n e t h r o u g h the d i s t r i b u t i o n f l a t t e n s out and becomes l e s s s teep (the s t e e p e r the l i n e , the g r e a t e r the v a r i a n c e ) . E f f e c t i v e l y , t h i s p r o c e d u r e c r u d e l y models the l i n e a r p o r t i o n o f the l i n e on the l o g p r o b a b i l i t y p l o t which r e p r e s e n t s the upper p o p u l a t i o n . The c l o s e r the o r i g i n a l d i s t r i b u t i o n i s t o l o g n o r m a l , the b e t t e r the chance t h a t the 3-parameter a p p r o x i m a t i o n w i l l come c l o s e to the t r u t h . The at tempt however can never t o t a l l y succeed i n m o d e l l i n g the h i g h e r mean and lower v a r i a n c e o f the u p p e r , h i g h grade p o r t i o n o f the d a t a because , a l t h o u g h the e f f e c t o f the lower grade p o p u l a t i o n i s m i n i m i z e d (mainly by b r i n g i n g the v a l u e s i n t o the same o r d e r o f magnitude as the h i g h g r a d e s ) , t h i s p o p u l a t i o n i s s t i l l r e p r e s e n t e d i n the c a l c u l a t i o n o f l ognormal mean and v a r i a n c e . The e f f e c t w i l l be t h a t t h e p r e d i c t e d mean i s low and the p r e d i c t e d v a r i a n c e i s h i g h f o r the upper p o p u l a t i o n o f g r a d e s . The advantage o f u s i n g S i n c l a i r ' s method t o a c c u r a t e l y p a r t i t i o n t h e d a t a i s t h a t b o t h the upper and lower p o p u l a t i o n s a r e m o d e l l e d c o r r e c t l y , and more i m p o r t a n t l y , f u r t h e r s t u d i e s o f t h e p a r t i t i o n e d l o g p r o b a b i l i t y p l o t p r o v i d e p e r c e n t a g e s which r e p r e s e n t the a c t u a l numbers o f samples which can be expected from e i t h e r mode l l ed p o p u l a t i o n w i t h i n a grade r a n g e , as was shown e a r l i e r . These v a l u e s can be used t o s e p a r a t e the d i f f e r e n t p o p u l a t i o n s i f i t can be shown t h a t they are l o c a t e d i n d i s c r e e t zones as they a r e f o r the Buckhorn s t u d y . However, use o f the 3-parameter l o g n o r m a l d i s t r i b u t i o n i s b e t t e r t h a n not d o i n g a n y t h i n g a t a l l . The e f f e c t o f t h i s m o d e l l e d d i s t r i b u t i o n on k r i g i n g v a r i a n c e s w i l l be d i s c u s s e d i n l a t e r c h a p t e r s . 31 5. ORE RESERVE CALCULATIONS 5.1 INTRODUCTION F o r each o f the 20' and 60' b l o c k mode l s , g o l d r e s e r v e s were c a l c u l a t e d u s i n g 10 d i f f e r e n t methods — 2 p o l y g o n a l , 6 i n v e r s e d i s t a n c e based c a l c u l a t i o n s , o r d i n a r y k r i g i n g and c o n d i t i o n a l p r o b a b i l i t y . T h i s r e s u l t e d i n 40 s e p a r a t e e x p l o r a t i o n ore r e s e r v e c a l c u l a t i o n s which c o u l d t h e n be compared t o the k r i g e d b l a s t h o l e r e s u l t s f o r each o f the 4 b l o c k mode l s . U n d i l u t e d r e s e r v e s were c a l c u l a t e d s e p a r a t e l y on each o f the 2 benches s t u d i e d (6840 and 6860) and a t o t a l r e s e r v e f o r the 2 benches combined was a l s o c a l c u l a t e d . The b l o c k p a r t i a l p e r c e n t a g e s which were s t o r e d f o r each b l o c k f o r every model were used t o produce volume weighted grade e s t i m a t e s and t o t a l tonnages . T h i s meant t h a t each o f the r e s e r v e c a l c u l a t i o n s on any b l o c k model produced i d e n t i c a l t o t a l tonnages a t a 0.0 c u t o f f g r a d e . T h i s g r e a t l y f a c i l i t a t e d the compar i son o f d i f f e r e n t methods o f r e s e r v e c a l c u l a t i o n w i t h i n each mode l . A l s o , any 4 ' , 2 0 ' , o r 60' model f o r which r e s e r v e s were c a l c u l a t e d ( r e g a r d l e s s o f whether e x p l o r a t i o n or b l a s t h o l e d a t a was used) and which shared the same o u t l i n e c o n s t r a i n t s , a l l produced the same t o t a l tonnage . T h i s meant t h a t the 20' b l o c k v s . 60' b l o c k r e s e r v e c a l c u l a t i o n s y i e l d i d e n t i c a l t o t a l tonnages w i t h i n the o u t l i n e and t h e r e f o r e the d i f f e r e n t b l o c k s i z e models can be compared d i r e c t l y w i t h each o t h e r . 32 5.2 POLYGONAL ESTIMATES In p l a c e o f t r a d i t i o n a l hand drawn p o l y g o n a l o u t l i n e s , a computer g e n e r a t e d 4 1 b l o c k model was employed. The grade a s s i g n e d t o any 4' b l o c k i s the grade o f the compos i te or b l a s t h o l e on the same bench n e a r e s t t o the c e n t e r o f the s m a l l b l o c k . Four such e s t i m a t e s were made — two f o r e x p l o r a t i o n da ta (one w i t h i n the mined l i m i t s and one which r e p r e s e n t e d a subset i n s i d e the o r e zone o u t l i n e ) , and two comparable e s t i m a t e s u s i n g b l a s t h o l e d a t a . Reserve r e p o r t s were generated f o r each o f the models (Appendix C ) . The b l a s t h o l e p o l y g o n a l e s t i m a t e s i n f a c t r e p r e s e n t the tonnage and grade t h a t would have been r e p o r t e d a t the mine i n t h e i r p r o d u c t i o n s t a t i s t i c s . Because the e x p l o r a t i o n d a t a was no t i n t e r p o l a t e d u s i n g the v a r i o u s o t h e r methods down t o the 4' b l o c k mode l s , the p o l y g o n a l e s t i m a t e was not used f o r d i r e c t compar isons w i t h o t h e r methods. I n s t e a d , the 4' b l o c k s were recombined i n t o the 20' and 60' b l o c k models and grades were volume weighted t o produce what w i l l be r e f e r r e d t o as the p o l y g o n weighted grade e s t i m a t e (see F i g . 8 f o r a g r a p h i c a l e x p l a n a t i o n o f the p o l y g o n weighted method) . 5 .3 INVERSE DISTANCE S i x i n v e r s e d i s t a n c e r e s e r v e e s t i m a t e s were c a l c u l a t e d f o r a l l 20' and 60' b l o c k mode l s . These were i n v e r s e d i s t a n c e to the 33 i i i i i i i i • • • • F i g . 8. G r a p h i c a l e x p l a n a t i o n o f the p o l y g o n weighted method o f c a l c u l a t i n g b l o c k g r a d e s . The s m a l l s o l i d boxes show the l o c a t i o n o f d r i l l h o l e s , whereas shaded areas r e p r e s e n t the sub-volumes w i t h i n a l a r g e b l o c k which w i l l assume the grade o f the n e a r e s t d r i l l h o l e . z e r o ( IDO) , i n v e r s e d i s t a n c e ( ID1) , i n v e r s e d i s t a n c e squared ( ID2) , i n v e r s e d i s t a n c e cubed ( ID3) , i n v e r s e d i s t a n c e to the f i f t h power ( ID5) , and i n v e r s e d i s t a n c e t o the t e n t h (ID10) . A l l o f these e m p i r i c a l models have been used i n p r a c t i c e and are i n c l u d e d h e r e because o f the u n c e r t a i n t y o f knowing which i n v e r s e d i s t a n c e approach t o use i n a p r a c t i c a l s t u d y . IDO r e p r e s e n t s the s t r a i g h t average o f a l l o f the q u a l i f y i n g d r i l l h o l e compos i te s whereas each o f the o t h e r e s t i m a t e s i s d i s t a n c e weighted t o some power. I t was expected t h a t ID10 would be a h i g h enough power t o be comparable t o a p o l y g o n a l e s t i m a t e , the d i f f e r e n c e b e i n g t h a t d r i l l h o l e s on the bench above and below 34 T a b l e I I I Parameters Used t o Generate I n v e r s e D i s t a n c e Weighted B l o c k Model E s t i m a t e s from E x p l o r a t i o n C o m p o s i t e s . Compos i te l e n g t h 20' A n i s o t r o p y none Minimum number o f samples accepted 5 Maximum number o f samples accepted 12 Maximum s e a r c h r a d i u s 150' R e c t a n g u l a r s e a r c h r a d i u s 150' x 150' x 30' Power o f d i s t a n c e 0, 1, 2, 3, 5 & 10 would have some s m a l l weight a s s i g n e d t o them (the composi tes v e r t i c a l l y above and below the n e a r e s t compos i te to the b l o c k c e n t e r would p r o b a b l y be ranked second and t h i r d i n the w e i g h t i n g ) . The s e a r c h parameters used are shown i n T a b l e I I I . These were chosen because they a r e e x a c t l y the same v a l u e s t h a t were i n i t i a l l y used t o genera te the 20' i n v e r s e d i s t a n c e cubed b l o c k model t h a t was used f o r open p i t d e s i g n and mine p l a n n i n g at B u c k h o r n . T h e r e f o r e , the ID3 e s t i m a t e c a l c u l a t e d f o r the 20' b l o c k model which wasn ' t c o n s t r a i n e d by the o r e zone o u t l i n e (BUCK b l o c k m o d e l ) , i s i d e n t i c a l t o the one used a t the mine and can be s c r u t i n i z e d c a r e f u l l y r e l a t i v e t o a l l o t h e r e s t i m a t e s t h a t c o u l d have been g e n e r a t e d . No at tempt was made t o weight i n v e r s e d i s t a n c e e s t i m a t e s d i f f e r e n t l y r e l a t i v e t o any p r e f e r r e d d i r e c t i o n . The ID3 e s t i m a t e t h a t was used f o r mine p l a n n i n g can be thought o f as the g e o l o g i s t ' s "gut f e e l " b e s t e s t i m a t e b e f o r e the mine went i n t o p r o d u c t i o n . As w i l l be s e e n , t h i s may be because t h i s p a r t i c u l a r c a l c u l a t i o n performed w e l l when e s t i m a t i n g b l o c k grades i n e v e r y c u t o f f c a t e g o r y . T h i s f a c t seemed t o be apparent b e f o r e t h i s s tudy was i n i t i a t e d and i t s e r v e s t o remind us t h a t t h e g e o l o g i s t s f e e l i n g s about the a c c u r a c y o r u s e f u l n e s s o f a grade e s t i m a t e s h o u l d not be i g n o r e d — any c a l c u l a t i o n should l o o k r e a s o n a b l e r e g a r d l e s s o f the advanced methods which may be used t o g e n e r a t e an o r e r e s e r v e e s t i m a t e . However, w i thout a t t e m p t i n g t o a n a l y z e the r e s u l t s a t t h i s p o i n t , i t s h o u l d be p o i n t e d out t h a t the ID3 e s t i m a t e d o e s n ' t produce the bes t p r e d i c t i o n o f tonnage — the performance o f the grade e s t i m a t e i s e a s i e r t o get a f e e l i n g f o r than the e s t i m a t e o f tonnage . In f a c t , o f the i n v e r s e d i s t a n c e methods, i t t u r n s out t h a t i n v e r s e d i s t a n c e t o the f i f t h comes c l o s e r t o p r e d i c t i n g the b l a s t h o l e k r i g e d tonnage a t each grade c u t o f f f o r the BUCK b l o c k model . 5 .4 KRIGING 5 . 4 . 1 V a r i o g r a m A n a l y s i s The approach t a k e n i n t h i s s tudy was t o s tudy e x p l o r a t i o n d a t a as i f i t was the o n l y d a t a a v a i l a b l e because the g e n e r a l aim was t o make t h e b e s t r e s e r v e c a l c u l a t i o n p o s s i b l e b e f o r e p r o d u c t i o n s t a r t e d , and then compare the e s t i m a t e s w i t h the known b l a s t h o l e r e s u l t s . T h e r e f o r e , a l l v a r i o g r a m s were c a l c u l a t e d and m o d e l l e d from e x p l o r a t i o n compos i tes and the parameters d e r i v e d were used t o k r i g e the e x p l o r a t i o n d a t a b e f o r e any attempt was made t o de termine a b e t t e r v a r i o g r a m d e r i v e d from the b l a s t h o l e d a t a . T h r e e b a s i c t ypes o f v a r i o g r a m were c a l c u l a t e d f o r each o f t h e two e x p l o r a t i o n d a t a s e t s (BEX and BEXG) i n the f o u r p r i n c i p a l compass d i r e c t i o n s s t a r t i n g a t 0 ° (north) and i n c r e m e n t i n g by 4 5 ° . The s e a r c h window was 3 0 ° on each s i d e o f the d i r e c t i o n b e i n g c a l c u l a t e d , and f o r l a g s g r e a t e r than 2 0 ' , the compos i tes on the bench above and below were used i n the c a l c u l a t i o n . F o r the v e r t i c a l v a r i o g r a m , the l a g d i s t a n c e was 20' w i t h a 5 ° window - - e s s e n t i a l l y a down h o l e v a r i o g r a m on the v e r t i c a l d r i l l h o l e s . A c t u a l , l o g n o r m a l and r e l a t i v e v a r i o g r a m s were c a l c u l a t e d w i t h 40' l a g increments i n the h o r i z o n t a l d i r e c t i o n s which i n c l u d e d weighted d i s t a n c e c a l c u l a t i o n s to de termine the average l a g f o r p l o t t i n g and m o d e l l i n g the r e s u l t s . A l l t h r e e types o f v a r i o g r a m show c o n s i s t e n t r e s u l t s (Appendix D c o n t a i n s a l i s t i n g o f a l l o f the c a l c u l a t e d v a r i o g r a m v a l u e s ) , but because c o n d i t i o n a l p r o b a b i l i t y e s t i m a t e s as d e f i n e d l a t e r r e l y on the r e l a t i v e v a r i o g r a m , the r e l a t i v e v a r i o g r a m was m o d e l l e d . The t h r e e types o f v a r i o g r a m f o r both d a t a s e t s a l l i n d i c a t e d s i m i l a r a n i s o t r o p y p a t t e r n s . The N-S d i r e c t i o n has a lower v a r i o g r a m v a l u e a t the f i r s t l a g than does the E-W d i r e c t i o n and y ( r ) i n the NW-SE d i r e c t i o n i s lower t h a n f o r NE-SW. W i t h one e x c e p t i o n ( the l o g n o r m a l v a r i o g r a m on the BEX e x p l o r a t i o n d a t a s e t ) , the NW-SE d i r e c t i o n showed the l owes t v a r i o g r a m v a l u e a t the f i r s t s i g n i f i c a n t l a g . The major s t r u c t u r a l t r e n d determined from g e o l o g i c a l mapping on the p r o p e r t y i s thought to be N10°W ( P l a h u t a 1986); t h e r e f o r e the m o d e l l e d a n i s o t r o p i e s are c o n s i s t e n t w i t h e x p e c t a t i o n s . The v e r t i c a l v a r i o g r a m was used to d e f i n e the nugget e f f e c t . The models t h a t were used f o r each o f the e x p l o r a t i o n d a t a s e t s are shown i n F i g u r e s 9 and 10. N o t i c e t h a t , a l t h o u g h the v a r i o g r a m s are shown o n l y t o l a g d i s t a n c e s o f 1 5 0 ' , a l l v a r i o g r a m s ( a c t u a l , l o g n o r m a l and r e l a t i v e ) reached c o n s t a n t s i l l v a l u e s i n a l l h o r i z o n t a l d i r e c t i o n s . The f i n a l v a r i o g r a m s were c a l c u l a t e d o n l y t o 150' because , a f t e r assuming t h a t the c o n s t a n t s i l l v a l u e s demonstrated s t a t i o n a r i t y ( D a v i d , 1977) , a l l subsequent v a r i o g r a m s were s i m u l t a n e o u s l y c a l c u l a t e d i n a l l d i r e c t i o n s as v a r i o g r a m c l o u d s w i t h 4' l a g s . T h i s r e s u l t e d i n f i v e , l a r g e a r r a y s (38 l a g s X 1024 gamma v a l u e s x 5 d i r e c t i o n s ) h e l d i n c o r e on Cominco ' s IBM mainframe computer . A l l f i n a l v a r i o g r a m s were o n l y c a l c u l a t e d to 150' t o c u t down on c o s t s o f comput ing . B l a s t h o l e v a r i o g r a m s ( F i g s . 11 and 12) w i t h s m a l l e r l a g d i s t a n c e s and more d a t a c o n f i r m e d t h a t l a g s beyond t h i s d i s t a n c e need not be c a l c u l a t e d . I t s h o u l d a l s o be noted t h a t , a l t h o u g h c l o s e spaced samples which i n c l u d e d ang led diamond d r i l l h o l e s i n i t i a l l y were r e t a i n e d i n the hope t h a t they would be u s e f u l i n showing s t r u c t u r e a t l a g s o f l e s s than 5 0 ' , the r e s u l t i n g v a r i o g r a m v a l u e s were thought t o be u n r e l i a b l e . In g e n e r a l the average grade o f these sample p a i r s was about 0.015 o p t . g r e a t e r t h a n the average grade o f p a i r s a t l o n g e r l a g d i s t a n c e s . As might be e x p e c t e d , o n l y the r e l a t i v e v a r i o g r a m s c o n s i s t e n t l y showed gamma v a l u e s at the f i r s t l a g which were lower than a t the second l a g . These 38 RELAT IVE VARIANCE = 2 . 3 2 9 _© ' 1 — i — 50 LAG (FEET) F i g . 9. M o d e l l e d r e l a t i v e v a r i o g r a m o f the BEX d a t a . o o NE-SW X X e—w • • NW-SE v a l u e s were i n i t i a l l y noted and p l o t t e d on e a r l y v e r s i o n s o f the v a r i o g r a m s , but were no t used i n m o d e l l i n g because they were c o n s i d e r e d too u n r e l i a b l e and i n c o n s i s t e n t between the v a r i o u s t y p e s o f v a r i o g r a m s . 5 . 4 . 2 Some O b s e r v a t i o n s on V a r i o g r a m M o d e l l i n g H a v i n g d e f i n e d the v a r i o g r a m s which w i l l be used l a t e r i n t h i s s t u d y , a s l i g h t d i g r e s s i o n i n t o the n a t u r e o f v a r i o g r a m s i s 39 S 5 • 2 . 0 - a •J <« > 2 i .s- R E L A T I V E VARIANCE = 1 . 4 9 7 " ' „ 'JT - „ R E L A T I V E  V A R I O G R A  b „ _ - - „ i - " - " ^ - - •* LEGEND 0 0 V E R T I C A L + * N-S 0 - - o 0 . 5 - N E - S W X K E - W O D N W - S E 0 . 0 - 1 1 1 1 I I 1 1 IO 3 0 SO 7 0 9 0 1 1 0 I S O 1 9 0 L A G ( F E E T ) F i g . 10. M o d e l l e d r e l a t i v e v a r i o g r a m o f the BEXG d a t a . u n d e r t a k e n . A l t h o u g h t h i s p a r t i c u l a r s e c t i o n o f t h e t h e s i s might have been one o f the s h o r t e s t were i t no t f o r the f o l l o w i n g d i s c u s s i o n , t h e s tudy o f v a r i o g r a m s a c t u a l l y consumed over 50% o f t h e t ime spent on the e n t i r e p r o j e c t because o f the b e l i e f on the p a r t o f t h e a u t h o r t h a t r e p e a t e d , s o p h i s t i c a t e d at tempts at v a r i o g r a m m o d e l l i n g would a) p r o v i d e b e t t e r v a r i o g r a m s which would b) p r o v i d e b e t t e r k r i g e d e s t i m a t e s . Complex c o l o u r coded v a r i o g r a m c l o u d s were drawn on a h i g h r e s o l u t i o n g r a p h i c s m o n i t o r , and at tempts were made t o d e v e l o p b e t t e r var iograms based on median squared p a i r d i f f e r e n c e s and o t h e r p e r c e n t i l e s , 40 o r a " d i f f e r e n t " r e l a t i v e v a r i o g r a m which was c a l c u l a t e d as one h a l f the mean squared p a i r d i f f e r e n c e s d i v i d e d by t h e i r mean p a i r v a l u e , e t c . These v a r i o g r a m s d i d n ' t p r o v i d e any new, or more u s e f u l i n f o r m a t i o n than was a l r e a d y apparent from the a c t u a l , l o g n o r m a l and r e l a t i v e v a r i o g r a m s . A f t e r r e t u r n i n g t o b a s i c s and m o d e l l i n g the b e s t r e l a t i v e v a r i o g r a m s a v a i l a b l e , and p r o c e e d i n g t o k r i g e the d a t a i n the most r e a s o n a b l e f a s h i o n ( i n c l u d i n g p r e r e q u i s i t e back a n a l y s e s ) , and then c o n t i n u i n g on to c o n d i t i o n a l p r o b a b i l i t y and f i n a l compar i son o f the r e s u l t s , i n a f i n a l a c t o f d e s p e r a t i o n a s i m p l e exper iment was p e r f o r m e d . The f i n a l r e l a t i v e v a r i o g r a m was r o t a t e d such t h a t the major a x i s o f a n i s o t r o p y was 9 0 ° away, and one o f the 20' b l o c k models (BUCKG) was r e - k r i g e d . Then the two k r i g e d e s t i m a t e s were compared. Both models c a l c u l a t e s i m i l a r k r i g e d e s t i m a t e s and k r i g i n g v a r i a n c e s and produce n e a r l y i d e n t i c a l o r e r e s e r v e e s t i m a t e s i n e v e r y grade range c a t e g o r y . The exper iment tends t o su p p or t D a v i d ' s s ta tement t h a t the v a r i o g r a m i s r o b u s t and t h a t "the e f f e c t s o f m i s i n t e r p r e t i n g C and a , are no t v e r y important" ( D a v i d , 1977) . However, t h e r e a r e s l i g h t d i f f e r e n c e s i n the r e s u l t s from the two d i f f e r e n t v a r i o g r a m s ( T a b l e I V ) . The e s t i m a t e s u s i n g the r o t a t e d v a r i o g r a m p r e d i c t a t o t a l o f 6,500 more tons above the 0.020 c u t o f f a t a s l i g h t l y lower grade t h a n the o r i g i n a l v a r i o g r a m (0.041 o p t . v s . 0.042 o p t . ) , and i t p r e d i c t s about 4,600 tons l e s s above the 0.050 c u t o f f a t t h e same grade as the o t h e r e s t i m a t e . Even more i n t e r e s t i n g was the f a c t t h a t when the d i f f e r e n c e between the 2 e s t i m a t e s i s g r e a t e r t h a n 0.010 o p t . ( a r b i t r a r i l y chosen t o d i f f e r e n t i a t e between s i m i l a r and 41 Table IV Ore Reserves Predicted by Using the "Rotated" Variogram Compared to Kriged Exploration Estimate and "Actual" f o r the BUCKG Model. BLOCK MODEL: BUCKG 20' BLOCKS - WITHIN ORE ZONE OUTLINE METHOD: BHKRIGE BLASTHOLE KRIGED - "ACTUAL n RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES TOTAL 0.000 756122.25 0.040 30336.14 28070.44 0.007 184.60 TOTAL 0.010 728051.81 0.041 30151.54 124929.62 0.016 2012.15 TOTAL 0.020 603122.19 0.047 28139.39 276722.06 0.027 7487.60 TOTAL 0.035 326400.12 0.063 20651.79 143338.62 0.042 5952.25 TOTAL 0.050 183061.50 0.080 14699.55 183061.50 0.080 14699.55 BLOCK MODEL: BUCKG 20* BLOCKS - WITHIN ORE ZONE OUTLINE METHOE "GOOD" EXPLORATION •GOOD" KRIGED ESTIMATE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES TOTAL 0.000 756122.25 0.039 29523.88 408.00 0.009 3.73 TOTAL 0.010 755714.25 0.039 29520.15 86186.00 0.017 1500.25 TOTAL 0.020 669528.25 0.042 28019.90 350814.87 0.028 9654.29 TOTAL 0.035 318713.37 0.058 18365.61 182996.25 0.041 7531.16 TOTAL 0.050 135717.12 0.080 10834.45 135717.12 0.080 10834.45 BLOCK MODEL: BUCKG 20' BLOCKS - WITHIN ORE ZONE OUTLINE METHOD: "ROTATED • EXPLORATION "ROTATED" KRIGED ESTIMATE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES TOTAL 0.000 756122.25 0.039 29212.79 0.00 0.000 0.00 TOTAL 0.010 756122.25 0.039 29212.79 80163.87 0.017 1390.62 TOTAL 0.020 675958.37 0.041 27822.17 358860.69 0.027 9746.67 TOTAL 0.035 317097.69 0.057 18075.50 185966.44 0.041 7628.64 TOTAL 0.050 131131.25 0.080 10446.85 131131.25 0.080 10446.85 d i s s i m i l a r e s t i m a t e s ) , the e s t i m a t e from the r o t a t e d v a r i o g r a m tends t o be c l o s e r t o the a c t u a l b l o c k grade de termined from b l a s t h o l e k r i g i n g s i g n i f i c a n t l y more o f t e n (204 e s t i m a t e s v s . 137) , and the average e r r o r o f the e s t i m a t e i s 7% lower than f o r t h e v a r i o g r a m t h a t i s a c t u a l l y used i n t h i s s t u d y . B l o c k grades u s i n g the r o t a t e d v a r i o g r a m are a l s o more l i k e l y t o be c l o s e to t h e t r u e grade i n the h i g h e s t c a t e g o r y above 0.050 o p t . by almost a two t o one m a r g i n . But s t i l l , the f a c t remains t h a t the o r i g i n a l l y m o d e l l e d v a r i o g r a m d i d a s l i g h t l y b e t t e r j o b o f p r e d i c t i n g h i g h e r t o t a l r e s e r v e s i n t h e h i g h e s t and most p r o f i t a b l e grade ranges and t h e r e was no good reason t o model the a n i s o t r o p y i n any o t h e r d i r e c t i o n than t h a t i n d i c a t e d by geo logy . P e r h a p s , even though the a n i s o t r o p y i s s l i g h t , the 4 5 ° d i r e c t i o n i s a c t u a l l y the t r u e a n i s o t r o p y t h a t s h o u l d have showed up on the v a r i o g r a m s . As was mentioned above , many var iograms were examined, and i n the c o u r s e o f s t u d y i n g the r e s u l t s , the f o l l o w i n g c o n c l u s i o n was r e a c h e d : when d a t a i s l o g n o r m a l l y d i s t r i b u t e d the v a r i o g r a m c a l c u l a t e d from a l l sample p a i r s i s more l i k e l y t o be a measure o f the c o n t i n u i t y o f grades between s t r u c t u r e s t h a n a measure o f the magnitude and d i r e c t i o n o f d i s c o n t i n u i t i e s w i t h i n s t r u c t u r e s . The v a r i o g r a m s used here are b i a s e d toward showing a n i s o t r o p i e s which r e l a t e t o areas o f h i g h e s t grade d i f f e r e n t i a l s . T h i s i n c l u d e s the r e l a t i v e v a r i o g r a m which has been c a l c u l a t e d as y{h) / m(h)2 ( D a v i d , 1977) where m(h) i s f a i r l y c o n s t a n t a t B u c k h o r n . These areas o f h i g h e s t grade d i f f e r e n t i a l o c c u r a t b o u n d a r i e s where g o l d grades i n c r e a s e r a p i d l y from low background v a l u e s . W i t h i n the s m a l l e r h i g h grade s t r u c t u r e s , a l t h o u g h t h e r e i s some p o t e n t i a l f o r a c h i e v i n g h i g h grade d i f f e r e n c e s amongst samples s e p a r a t e d by a g i v e n d i s t a n c e , t h e r e a r e fewer p a i r s . T h e r e f o r e , the s u b t l e d i r e c t i o n a l t r e n d s t h a t might show up w i t h i n the h i g h grade areas where sampled v a l u e s are s i m i l a r , w i l l be "drowned out" by the numerous p a i r s which are d e t e c t i n g h i g h g r a d e / l o w grade b o u n d a r i e s . In o t h e r words , u s i n g Buckhorn as an example , the model led v a r i o g r a m does no t i n d i c a t e i n any way t h a t where a b l o c k i s e v a l u a t e d i n a h i g h grade a r e a where a l l samples a r e s i m i l a r i n g r a d e , t h a t the e r r o r e s t i m a t e s h o u l d be l o w e r . I n s t e a d what i t shows i s t h a t where t h e r e i s a t r a n s i t i o n from v e r y h i g h t o very low v a l u e s , on a v e r a g e , i t i s b e t t e r t o weight the e s t i m a t e r e l a t i v e t o a 1 3 5 ° a n i s o t r o p y and to assume a h i g h k r i g i n g v a r i a n c e . U n f o r t u n a t e l y , the same assumptions a r e a p p l i e d i n d i s c r i m i n a t e l y t o the c a l c u l a t i o n o f e v e r y k r i g e d grade i n the d e p o s i t . The v a r i o g r a m tends t o p i c k up the edges o f s t r u c t u r e s and does no t show the lower v a r i a n c e amongst samples w i t h i n e i t h e r the low grade areas or the h i g h grade a r e a s . More complex forms o f k r i g i n g , l i k e i n d i c a t o r and p r o b a b i l i t y k r i g i n g , t ake account o f t h i s o b s e r v a t i o n by assuming t h a t d i f f e r e n t grade ranges might b e s t be kept s e p a r a t e and be m o d e l l e d by d i f f e r e n t v a r i o g r a m s but these methods have the i n h e r e n t drawback o f no t h a v i n g an a s s o c i a t e d k r i g i n g v a r i a n c e and c r e a t i n g numerous s e p a r a t e e s t i m a t e s f o r a b l o c k u s i n g i n d i c a t o r s o n l y i n s t e a d o f a c t u a l g r a d e s . To propose a d i f f e r e n t s o l u t i o n t o t h i s p r o b l e m , what i f 3 o r 4 a c t u a l o r r e l a t i v e v a r i o g r a m s were mode l l ed? By examining a v a r i o g r a m c l o u d , de termine 3 i n t e r v a l s o f a b s o l u t e d i f f e r e n c e s between samples t h a t would (say) r e p r e s e n t squared d i f f e r e n c e s f o r about 50% o f a l l p a i r s i n l a g windows p a s t the assumed range , t h e n 70% o f the squared d i f f e r e n c e s , then 90%, and f i n a l l y 100%. Thus r e g a r d l e s s o f the l a g b e i n g c a l c u l a t e d , i f the squared d i f f e r e n c e exceeds the 50th p e r c e n t i l e squared d i f f e r e n c e s , but no t the 70th p e r c e n t i l e t h r e s h o l d , then t h a t p a i r would be used i n the c a l c u l a t i o n o f each o f the t h r e e h i g h e s t v a r i o g r a m s . When k r i g i n g , the maximum squared d i f f e r e n c e between any two o f the samples s e l e c t e d t o e s t i m a t e a b l o c k would d e t e r m i n e which one o f the 3 o r 4 v a r i o g r a m s t o u s e . T h i s method might have the advantage o f c a l c u l a t i n g an a c c u r a t e k r i g e d e r r o r e s t i m a t e which takes i n t o account the f a c t t h a t the samples used i n k r i g i n g ( r e g a r d l e s s o f t h e i r a c t u a l grade) e i t h e r were r e l a t i v e l y the same g r a d e s , or c o n v e r s e l y , v a r i e d t r e m e n d o u s l y . A l s o s e p a r a t e s t r u c t u r e s ( a n i s o t r o p i c s ) might a c t u a l l y show up f o r each o f the v a r i o g r a m s . T h i s seems t o be the case a t B u c k h o r n . Appendix E c o n t a i n s a l i s t i n g o f v a r i o g r a m v a l u e s t h a t were genera ted i n a p p r o x i m a t e l y the same way as d i s c u s s e d above and the v a r i o u s v a r i o g r a m s show t h a t the major axes o f a n i s o t r o p y v a r y between 0 ° and 4 5 ° except f o r the one v a r i o g r a m which has been computed from a l l o f the v a l u e s i n the compos i ted d a t a . A l t h o u g h k r i g i n g u s i n g the r o t a t e d v a r i o g r a m at Buckhorn showed a r e s u l t t h a t might no t o c c u r o f t e n e l s ewhere , and a l t h o u g h t h e r e i s always the p o s s i b i l i t y t h a t b o t h var iograms are wrong, t h e r e may be some m e r i t i n the i d e a t h a t v a r i o g r a m s , e s p e c i a l l y those d e r i v e d from l o g n o r m a l l y d i s t r i b u t e d d a t a , r e p r e s e n t s t r u c t u r e s r e l a t i n g t o the areas where the h i g h e s t grade d i f f e r e n t i a l s e x i s t . E s s e n t i a l l y , i n s t e a d o f g r o u p i n g the d a t a on the b a s i s o f grade r a n g e s , the i d e a p r e s e n t e d above would make the d i v i s i o n s on the b a s i s o f the v a r i a b i l i t y ranges o f the d a t a used t o c a l c u l a t e the k r i g e d e s t i m a t e . I f the 10 or 12 v a l u e s used t o k r i g e the b l o c k grade were a l l s i m i l a r , one can be s u r e t h a t the grade e s t i m a t e w i l l be b e t t e r t h a n i f the grades v a r i e d over a wide range o f v a l u e s . I t s h o u l d n ' t mat ter i f a c t u a l or r e l a t i v e v a r i o g r a m s are used t o r e p r e s e n t these s t r u c t u r e s . In a d d i t i o n t o those d i s c u s s e d above, the v a r i o g r a m s tudy produced some f u r t h e r o b s e r v a t i o n s : 1) V a r i o g r a m c l o u d s , a l t h o u g h p r o v i n g n o t t o be too u s e f u l f o r a c t u a l m o d e l l i n g , were most u s e f u l i n d e t e r m i n i n g the l a g windows which were u s e d . These graphs showed the d e n s i t y o f p a i r s a t d i f f e r e n t d i s t a n c e s , and r e s u l t e d i n the f i n a l s e l e c t i o n o f o n l y 3 l a g windows i n every h o r i z o n t a l d i r e c t i o n . In p a r t i c u l a r , the c l u s t e r i n g o f numerous p a i r s a t a p p r o x i m a t e l y 110' i n the 4 5 ° and 1 3 5 ° d i r e c t i o n s showed up n i c e l y . Because o f the 3 0 ° s e a r c h window, the p a i r s a t t h i s d i s t a n c e r e p r e s e n t e d samples t h a t were s e p a r a t e d by 50' i n one d i r e c t i o n and 100' i n the o t h e r . A l s o shown c l e a r l y on the v a r i o g r a m c l o u d s were the mis takes t h a t c o u l d be made by c h o o s i n g i n c o r r e c t or s m a l l e r l a g windows f o r the sake o f c r e a t i n g more p o i n t s on the v a r i o g r a m c u r v e . In some c a s e s , because t h e r e were fewer samples i n a s m a l l l a g window, the v a r i o g r a m would become a lmost r h y t h m i c a l l y s p i k y and i n o t h e r c a s e s , where a s i g n i f i c a n t d i s t a n c e was d i s s e c t e d by s h o r t l a g windows, an a p p a r e n t l y n e s t e d v a r i o g r a m s t r u c t u r e might show u p . 2) The premise t h a t the v a r i o g r a m s i l l s h o u l d e q u a l the v a r i a n c e (or r e l a t i v e v a r i a n c e ) o f the compos i ted d a t a was examined ( i . e . D a v i d , 1988) . where o n l y one p o p u l a t i o n o f assays ( i n s i d e t h e o r e o u t l i n e ) was m o d e l l e d , the v a r i o g r a m s i l l and the p o p u l a t i o n r e l a t i v e v a r i a n c e c o i n c i d e d ( F i g . 1 0 ) . Where t h e r e was a mix o f samples i n the o r i g i n a l d a t a s e t , the s i l l was s i g n i f i c a n t l y lower than might be p r e d i c t e d by the r e l a t i v e v a r i a n c e ( F i g . 9 ) . T h i s phenomenon was noted i n a c t u a l , l o g n o r m a l and r e l a t i v e v a r i o g r a m s . In f a c t i t may make sense to use t h i s o b s e r v a t i o n as a t e s t f o r i n a p p r o p r i a t e m i x i n g o f sample p o p u l a t i o n s . The d i s c r e p a n c y between the v a r i o g r a m s i l l and the p o p u l a t i o n v a r i a n c e i n the l a t t e r case might be e x p l a i n e d by the f a c t t h a t samples c l o s e s t t o each o t h e r tend t o be from the same p o p u l a t i o n g e n e r a l l y (not a l w a y s , but g e n e r a l l y ) and t h e r e f o r e , even though t h e r e i s some m i x i n g which w i l l i n c r e a s e the v a r i o g r a m v a l u e s c a l c u l a t e d , the average v a r i a n c e amongst sample p a i r s i s n o t as h i g h as the sample s e t ' s o v e r a l l v a r i a n c e . On the o t h e r hand , i f a s i n g l e p o p u l a t i o n can be d e f i n e d , the t h e o r e t i c a l e x p e c t a t i o n t h a t the v a r i o g r a m s i l l s h o u l d e q u a l the p o p u l a t i o n v a r i a n c e i s f u l f i l l e d . A l t h o u g h a l l o f the above o b s e r v a t i o n s may be on shaky ground because they are based o n l y on the r e s u l t s from one d e p o s i t , and a l t h o u g h t h e r e i s no t enough t ime t o t e s t a l l o f t h e s e i d e a s out e x h a u s t i v e l y i n the p r e s e n t s t u d y , the r e s u l t s 47 u < > < K 0 O OS > > w os R E L A T I V E VARIANCE = 2.2 * " j " <*// 4" -1— 10 —I— 30 1 1 70 90 L A G ( F E E T ) —I— 130 LEGEND o o VERTICAL © O Nf-SW • Q NW-SE F i g . 11 . E x p e r i m e n t a l r e l a t i v e v a r i o g r a m from the BBH d a t a . seemed t o be c o n s i s t e n t i n the c o n t e x t o f the Buckhorn s t u d y , and i t was f e l t t h a t t h e s e p o i n t s s h o u l d be ment ioned . I t i s a l s o worth n o t i n g t h a t the b l a s t h o l e d a t a was e v e n t u a l l y m o d e l l e d and showed a v e r y s l i g h t a n i s o t r o p y i n the 1 3 5 ° and N-S d i r e c t i o n s w i t h the N-S d i r e c t i o n showing lower v a r i o g r a m v a l u e s a t l o n g e r l a g d i s t a n c e s , w h i l e the 1 3 5 ° d i r e c t i o n showed the l owes t v a l u e s o f y ( h ) a t d i s t a n c e s up to 5 0 ' . T h e r e may be n e s t e d s t r u c t u r e s , but no t a t any d i s t a n c e t h a t c o u l d have been i n f e r r e d from the e x p l o r a t i o n v a r i o g r a m s . 48 w > S < K O O 5 > w > s td RELATIVE VARIANCE = 1.7 — B — a © ? ' H ^ 70 90 LAO (FEET) F i g . 12. E x p e r i m e n t a l r e l a t i v e v a r i o g r a m from the BBHG d a t a . 0- -o VERTICAL o — -o NE-SW X X E-W Q • NW—SE G e n e r a l l y however, the b l a s t h o l e c a l c u l a t i o n s i n d i c a t e e s s e n t i a l l y i s o t r o p i c v a r i o g r a m s ( F i g s . 11 and 1 2 ) . F i n a l l y , b e f o r e l e a v i n g the s u b j e c t o f v a r i o g r a m s , the e f f e c t o f t h e 3-parameter l o g n o r m a l d i s t r i b u t i o n c a l c u l a t i o n s h o u l d be m e n t i o n e d . In o r d e r to c r e a t e a r e l a t i v e k r i g i n g v a r i a n c e which would be c o n s i s t e n t w i t h the c a l c u l a t i o n o f c o n d i t i o n a l p r o b a b i l i t i e s c a l c u l a t e d from a 3 -parameter l o g n o r m a l d i s t r i b u t i o n , the v a l u e a t each l a g i s c a l c u l a t e d as y / (mean grade + constant)2. To make s u r e t h a t k r i g e d grades would not be a f f e c t e d by d i f f e r e n t c o n s t a n t s a p p l i e d t o the r e l a t i v e v a r i o g r a m mode l s , f o u r s e p a r a t e k r i g e d e s t i m a t e s f o r the BUCK 20' model u s i n g the BEX d a t a s e t were g e n e r a t e d , one w i t h no c o n s t a n t , and t h r e e w i t h c o n s t a n t s o f 0 .002 , 0.005 and 0 .050 . The r e s u l t i n g k r i g e d e s t i m a t e s were compared and a l l f o u r were v i r t u a l l y i d e n t i c a l . The r e l a t i v e shapes o f the d i f f e r e n t v a r i o g r a m s i s a l l t h a t i s i m p o r t a n t — the o n l y d i f f e r e n c e i s t h a t each e s t i m a t e now produces d i f f e r e n t r e l a t i v e k r i g i n g v a r i a n c e s . In o r d e r t o make the r e l a t i v e shapes the same, o n l y C 0 and C were r e c a l c u l a t e d f o r the BEX d a t a v a r i o g r a m u s i n g the d i f f e r e n t c o n s t a n t s . Ranges and a n i s o t r o p i c s were m o d e l l e d i d e n t i c a l l y . The f a c t t h a t the k r i g e d grades would be the same was not an unexpected r e s u l t . K r i g i n g w i t h e i t h e r an a c t u a l o r r e l a t i v e v a r i o g r a m produces an averaged v a l u e which i s d e r i v e d from the raw a r i t h m e t i c d a t a . When a r i t h m e t i c d a t a has a c o n s t a n t added to every v a l u e , the new mean minus the c o n s t a n t w i l l e q u a l the o r i g i n a l mean and the a r i t h m e t i c v a r i a n c e w i l l be i d e n t i c a l . On ly the r e l a t i v e v a r i a n c e changes and t h i s change i s a l s o r e f l e c t e d i n the k r i g i n g v a r i a n c e s which a r e c a l c u l a t e d d u r i n g k r i g i n g w i t h a r e l a t i v e v a r i o g r a m t h a t has the c o n s t a n t added i n t o the d e n o m i n a t o r . 5 . 4 . 3 K r i g i n g and Back A n a l y s i s There i s l i t t l e t o say about the method t h a t was used to k r i g e the d a t a . Once the parameters were d e f i n e d ( T a b l e V ) , the d a t a was used t o c a l c u l a t e k r i g e d p o i n t samples a t l o c a t i o n s where compos i te s were removed and the a c t u a l v e r s u s p r e d i c t e d grades were compared both i n grade ranges and a c r o s s v a r i o u s 50 T a b l e V Parameters Used f o r K r i g i n g E x p l o r a t i o n Data Composi te l e n g t h 20 ' Minimum number o f samples accepted 5 Maximum number o f samples accepted 12 Maximum s e a r c h r a d i u s 150 ' R e c t a n g u l a r s e a r c h r a d i u s 150' x 150' x 30' R e l a t i v e v a r i o g r a m BEX C „ , C 0.26 1.15 ( y / ( m + 0.005 ) 2 ) a (135°) 120 ' a (45°) 90' a (vert) 72 1 R e l a t i v e v a r i o g r a m BEXG C „ , C 0.45 1.05 ( y / m 2 ) a (135°) 120 ' a (45°) 70 ' a (vert) 70 ' Maximum k r i g i n g v a r i a n c e n/a k r i g i n g v a r i a n c e r a n g e s . Because r e l a t i v e v a r i o g r a m s produce r e l a t i v e k r i g i n g v a r i a n c e s which are i n f l u e n c e d o n l y by the geometry o f the samples used ( d i s c u s s e d l a t e r i n the s e c t i o n on c o n d i t i o n a l p r o b a b i l i t y ) , and because h i g h e r grade samples tended t o be i n the m i d d l e o f the v a r i o u s imposed o u t l i n e s , k r i g e d e s t i m a t e s i n the back a n a l y s i s d i d no t s u f f e r s i g n i f i c a n t l y when k r i g i n g v a r i a n c e s were h i g h e r n e a r the edges o f the o u t l i n e s . A l s o t o ensure t h a t the p r o p o r t i o n a l e f f e c t was indeed accounted f o r by u s i n g the r e l a t i v e v a r i o g r a m , r e l a t i v e k r i g i n g v a r i a n c e s were p l o t t e d a g a i n s t k r i g e d grades and showed comparable r e l a t i v e k r i g i n g v a r i a n c e s a c r o s s a l l grade r a n g e s . The v a r i o g r a m models were deemed a c c e p t a b l e and the 20' compos i t e s were t h e n used t o c a l c u l a t e k r i g e d b l o c k g r a d e s . 52 6. CONDITIONAL PROBABILITY 6.1 THEORY 6 . 1 . 1 I n t r o d u c t i o n The f o l l o w i n g d e s c r i p t i o n i s the method proposed and used by G . F . Raymond (Raymond 1979, 1982, 1984) . T h e r e i s some d i sagreement as t o whether the method s h o u l d be c a l l e d by the name c o n d i t i o n a l p r o b a b i l i t y or changed to a v o i d c o n f l i c t w i t h o t h e r meanings o f the term but t r a d i t i o n a l usage i n the l i t e r a t u r e by Raymond i s used h e r e . That i s , i t s use i s c o n t i n u e d here w i t h the u n d e r s t a n d i n g t h a t i t r e f e r s s t r i c t l y to the method r e f e r r e d t o by Raymond and a l l r e f e r e n c e s to c o n d i t i o n a l p r o b a b i l i t y are used i n t h i s c o n t e x t . 6 . 1 . 2 The C o n d i t i o n a l D i s t r i b u t i o n K r i g e d b l o c k grades have an advantage over o t h e r e s t i m a t e s i n t h a t t h e r e i s a s i m u l t a n e o u s l y c a l c u l a t e d measure o f the e r r o r ( k r i g i n g v a r i a n c e ) . A l t h o u g h grades e s t i m a t e d by k r i g i n g have the f u r t h e r t h e o r e t i c a l p r o p e r t y o f b e i n g c o r r e c t on average (a p r o p e r t y known as c o n d i t i o n a l u n b i a s ) , the e s t i m a t e s tend to smooth t h e t r u e p i c t u r e ( D a v i d , 1977) . I f an o p e r a t i o n were to mine t o c u t o f f b o u n d a r i e s e s t a b l i s h e d from k r i g e d e s t i m a t e s from e x p l o r a t i o n g r a d e s , the p r e d i c t e d grade and tonnage sh ou ld be r e c o v e r e d , but i n p r a c t i c e , t h e r e i s u s u a l l y b e t t e r i n f o r m a t i o n a v a i l a b l e ( g e o l o g i c a l i n f o r m a t i o n , v i s u a l e s t i m a t e s , b l a s t h o l e d a t a , e t c . ) upon which p r o d u c t i o n d e c i s i o n s can be made. In g e n e r a l , t h i s b e t t e r s e l e c t i v i t y can l e a d t o m i n i n g a h i g h e r grade o f o r e t h a n p r e d i c t e d by o r d i n a r y k r i g i n g from e x p l o r a t i o n samples . The method o f c a l c u l a t i n g c o n d i t i o n a l p r o b a b i l i t i e s a t tempts t o p r e d i c t the e f f e c t t h a t the more abundant i n f o r m a t i o n w i l l have on the f i n a l grade e s t i m a t e , and on the d i s t r i b u t i o n o f o r e b l o c k s w i t h i n the orebody . The method depends on an assumpt ion o f normal d a t a d i s t r i b u t i o n . When one t a l k s about k r i g e d g r a d e , the p r e d i c t e d , or expec ted average grade (x) o f a b l o c k i s b e i n g r e f e r r e d t o . K r i g i n g v a r i a n c e ( o 2 ) i s the magnitude o f an expected squared d e v i a t i o n from the p r e d i c t e d mean grade f o r the b l o c k (a p r e d i c t i o n o f the e r r o r a s s o c i a t e d w i t h the e s t i m a t e ) . In o t h e r words , a l t h o u g h i t i s n e a r l y c e r t a i n t h a t the grade won' t be e x a c t l y as p r e d i c t e d , t h e r e i s an e x p e c t a t i o n (based on the knowledge o f the p r o p e r t i e s o f the normal d i s t r i b u t i o n ) t h a t i f the d a t a i s n o r m a l l y d i s t r i b u t e d , 67% o f a l l t r u e grades w i l l be between x ± o (where o i s the square r o o t o f the k r i g i n g v a r i a n c e and can be thought o f as a s t a n d a r d e r r o r ) . T h i s means t h a t some p e r c e n t a g e o f the b l o c k s w i t h k r i g e d grades above c u t o f f w i l l , i n f a c t , be waste and o t h e r s w i t h p r e d i c t e d grades below c u t o f f w i l l a c t u a l l y be ore ( F i g . 13 ) . I f the d i s t r i b u t i o n o f a c t u a l grades f o r a p a r t i c u l a r expected k r i g e d grade i s normal as shown i n F i g u r e 13, b o t h a tonnage above c u t o f f and the average grade o f the o r e f r a c t i o n o f the b l o c k s can be c a l c u l a t e d , based on the knowledge o f the p r o p e r t i e s o f the normal c u r v e . T h i s 54 K r i g e d Grade C u t o f f Grade i i i i x-2o x -o x x+o x+2o Grade F i g . 13. The c o n d i t i o n a l d i s t r i b u t i o n . G i v e n a k r i g e d b l o c k grade (x) and k r i g i n g v a r i a n c e ( a 2 ) , the a c t u a l b l o c k grades w i l l be n o r m a l l y d i s t r i b u t e d about the mean. A c e r t a i n p e r c e n t a g e o f b l o c k s whose k r i g e d grade i s above c u t o f f w i l l e v e n t u a l l y t u r n out to be waste (shaded area under the c u r v e ) . average grade w i l l be h i g h e r than the k r i g e d grade because waste tons have now been e l i m i n a t e d . N o t i c e t h a t a l t h o u g h i t i s p o s s i b l e to p r e d i c t how many b l o c k s a r e expec ted to be ore or waste , i t i s not p o s s i b l e t o p r e d i c t which ones w i l l be o r e . The p r e d i c t e d d i s t r i b u t i o n o f sample o r b l o c k grades g i v e n e s t imated b l o c k g r a d e s , i s c a l l e d the c o n d i t i o n a l d i s t r i b u t i o n . The mean v a l u e o f the d i s t r i b u t i o n ( the e x p l o r a t i o n k r i g e d e s t i m a t e ) i s the c o n d i t i o n a l e x p e c t a t i o n , and the c o n d i t i o n a l v a r i a n c e i s a measure o f expec ted d i s p e r s i o n o f a c t u a l grades about t h i s mean. As an example o f the use o f the c o n d i t i o n a l d i s t r i b u t i o n , suppose t h e r e a r e 3 s t o c k p i l e s r e p r e s e n t i n g waste , low g r a d e , and 55 Low Grade S t o c k p i l e 67% T 0.015 0.020 0.025 0.030 0.035 Grade F i g . 14. E x p e c t a t i o n s o f ore and waste d e r i v e d from n o r m a l l y d i s t r i b u t e d b l o c k g r a d e s . I f the k r i g e d b l o c k grade i s 0.025 and k r i g i n g v a r i a n c e i s 0 .000025, (o = 0 . 0 0 5 ) , 16.5% o f the t r u e b l o c k grades w i l l be waste and 16.5% w i l l a c t u a l l y be ore g r a d e . m i l l g r a d e , w i t h c u t o f f s a t 0.020 and 0.030 o p t . g o l d . I f a l l b l o c k s w i t h a k r i g e d grade o f 0.025 o p t . have a c o n s t a n t k r i g i n g v a r i a n c e o f 0.000025 o z / t o n 2 (o = 0.005 o p t . ) , t h e n based on the normal d i s t r i b u t i o n , t h e r e i s an e x p e c t a t i o n t h a t 16.5% o f a l l b l o c k s w i t h k r i g e d grade o f 0.025 o p t . s h o u l d a c t u a l l y go to the waste s t o c k p i l e and 16.5% s h o u l d go to the o r e s t o c k p i l e ( F i g . 1 4 ) , a l t h o u g h even w i t h these e r r o r s , the average grade o f the low grade s t o c k p i l e would remain 0.025 o p t . C o n d i t i o n a l p r o b a b i l i t y uses e x p l o r a t i o n d a t a and b l o c k e s t i m a t e s based on t h a t d a t a t o e s t i m a t e tonnages and grades which e v e n t u a l l y w i l l be mined . The c a l c u l a t i o n i s r e f i n e d by s u b t r a c t i n g the k r i g i n g v a r i a n c e o f p r o d u c t i o n b l o c k e s t imates from e x p l o r a t i o n b l o c k k r i g i n g v a r i a n c e s a c c o r d i n g to the "smoothing r e l a t i o n s h i p " ( D a v i d , 1977) . The remain ing c o n d i t i o n a l v a r i a n c e w i l l approximate the u n c e r t a i n t y i n the k r i g e d b l o c k e s t i m a t e s u s i n g e x p l o r a t i o n d a t a (an amount o f e r r o r which c a n ' t be e l i m i n a t e d even when the d e p o s i t i s m i n e d ) . The r e s u l t i n g c o n d i t i o n a l d i s t r i b u t i o n can be used t o p r e d i c t new p r o b a b l e tonnage and grade f i g u r e s f o r the mine . In the p r e c e d i n g d i s c u s s i o n t h e r e were a t l e a s t two assumpt ions made. F i r s t , the 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 known and assumed t o be n o r m a l l y d i s t r i b u t e d — t h i s can be v e r i f i e d s t a t i s t i c a l l y w i t h r e a l d a t a . The second assumpt ion i s t h a t k r i g i n g v a r i a n c e s o f bo th the e x p l o r a t i o n and b l a s t h o l e k r i g e d grades a r e known ( i . e . b l a s t h o l e k r i g i n g v a r i a n c e c o u l d be c a l c u l a t e d i n advance o f h a v i n g the p r o d u c t i o n d a t a a v a i l a b l e ) . In p r a c t i c e , the problem i s more complex. 6.1.3 D i s t r i b u t i o n o f Sample Grades and B l o c k Grades In many grade e s t i m a t i o n p r o b l e m s , the sample grades f o l l o w a l o g n o r m a l d i s t r i b u t i o n and , f o r p r a c t i c a l p u r p o s e s , t h i s r e s u l t s i n a c o r r e s p o n d i n g l o g n o r m a l d i s t r i b u t i o n o f a c t u a l b l o c k grades about the e s t i m a t e d grades ( J o u r n e l and H u i j b r e g t s , 1978) . L i k e t h e normal d i s t r i b u t i o n , the c h a r a c t e r i s t i c s o f the l o g n o r m a l d i s t r i b u t i o n are a l s o w e l l known. U n f o r t u n a t e l y grade d i s t r i b u t i o n s a r e r a r e l y p e r f e c t l y l o g n o r m a l . I f a l o g n o r m a l d i s t r i b u t i o n i s p l o t t e d on l o g p r o b a b i l i t y p a p e r , a s t r a i g h t l i n e 57 A . B . 2% 50% 98% 2% 50% 98% P r o b a b i l i t y P r o b a b i l i t y F i g . 15. P r o b a b i l i t y p l o t s o f p e r f e c t (A) and i m p e r f e c t l o g n o r m a l d i s t r i b u t i o n s ( B ) . The c u r v e d p o r t i o n o f c u r v e B i s due t o a l a r g e r than expected number o f low grade samples . can be expected ( F i g . 15a) . However i n r e a l i t y , the l o g t r a n s f o r m e d grades o f r e a l e x p l o r a t i o n d a t a r a r e l y p l o t as a s t r a i g h t l i n e , but due i n p a r t t o an abundance o f low grade m a t e r i a l around the orebody , the p l o t t e d d i s t r i b u t i o n i s n o n - l i n e a r as i n F i g u r e 15b. F o r s i m p l i c i t y , the example shown i n F i g u r e 16 i l l u s t r a t e s t h e prob lem f o r the case o f a normal d i s t r i b u t i o n o f m i n e r a l i z e d compos i t e s which have numerous low grade samples i n c l u d e d i n the s t u d y o f the h i s t o g r a m s . I f these compos i te s are used to e s t i m a t e the b l o c k s , c o n d i t i o n a l p r o b a b i l i t y w i l l no t p r e d i c t the c o r r e c t d i s t r i b u t i o n o f a c t u a l b l o c k g r a d e s . I f the erroneous 58 Low Grade S t o c k p i l e ? % 0.015 0.020 0.025 . 0.030 0.035 Grade F i g . 16. The e f f e c t o f e s t i m a t i n g ore and waste p e r - centages from i m p e r f e c t normal d i s t r i b u t i o n s . The number o f m i s c a l c u l a t e d b l o c k s w i l l no l o n g e r be p r e d i c t a b l e . a s sumpt ion i s made t h a t the d i s t r i b u t i o n o f a c t u a l b l o c k s i s n o r m a l , t h e r e w i l l be a s e r i o u s e r r o r i n p r e d i c t i n g the p e r c e n t a g e o f m a t e r i a l above c u t o f f as w e l l as i n the d e t e r m i n a t i o n o f average grade o f t h i s m a t e r i a l . Based on the same f i g u r e s as i n the p r e v i o u s example , ( k r i g e d grade = 0.025 o p t . and o 2 = 0.000025 o z / t o n 2 ) , 16.5% o f the b l o c k s are s t i l l p r e d i c t e d t o be waste when i n f a c t maybe 20% o r more w i l l be l e s s t h a n 0.02 o p t . and s i m i l a r l y , l e s s than 16.5% w i l l r e a l l y be ore g r a d e . The l o g t r a n s f o r m e d grades i n the BEX d a t a s e t a t Buckhorn show a s i m i l a r i m p e r f e c t p a t t e r n ( F i g . 5 ) . 59 In o r d e r t o c a l c u l a t e c o n d i t i o n a l p r o b a b i l i t i e s , a way must be found t o work w i t h p o p u l a t i o n s o f a known d i s t r i b u t i o n w i t h p r e d i c t a b l e a t t r i b u t e s ( i . e . normal or l o g n o r m a l ) . T h i s d o e s n ' t p r e s e n t a problem w i t h the BEXG d a t a s e t which i s a l o g n o r m a l s u b s e t o f the complete d a t a , but i n o r d e r t o c a l c u l a t e c o n d i t i o n a l p r o b a b i l i t y f o r b l o c k models whose grades were i n t e r p o l a t e d from the BEX o r BBH d a t a s e t s , something w i l l have to be done to c o r r e c t f o r t h e i r i m p e r f e c t d i s t r i b u t i o n . Raymond (1982) shows t h a t many grade d i s t r i b u t i o n s can be made n e a r l y l o g n o r m a l by the a d d i t i o n o f an e x p e r i m e n t a l l y d e r i v e d c o n s t a n t t o the raw grades b e f o r e l o g t r a n s f o r m i n g . The o r i g i n a l d i s t r i b u t i o n o f samples i s n e i t h e r normal nor l o g n o r m a l . However, the d i s t r i b u t i o n o f In(grade + constant) approximates an a c c e p t a b l e l o g n o r m a l d i s t r i b u t i o n t h a t can be used f o r m o d e l l i n g ore r e s e r v e s . As d i s c u s s e d e a r l i e r , a c o n s t a n t o f 0.005 appears to s t r a i g h t e n out the l o g p r o b a b i l i t y p l o t s o f g o l d d i s t r i b u t i o n s f o r the BEX d a t a s e t . In c a l c u l a t i n g c o n d i t i o n a l p r o b a b i l i t y , 0.005 o p t . was added t o the grades b e f o r e l o g t r a n s f o r m i n g . F o r the BEXG d a t a s e t , no c o n s t a n t was n e c e s s a r y . 6.1.4 C o n s t a n t K r i g i n g V a r i a n c e Because o f the n a t u r e o f the k r i g i n g e q u a t i o n s , k r i g i n g v a r i a n c e i s a f u n c t i o n o f bo th the geometry o f the samples around the b l o c k t o be e s t i m a t e d , and t h e i r g r a d e s . W i t h l ognormal d a t a , one o f the major problems t h a t has t o be f a c e d i s what 's known as the p r o p o r t i o n a l e f f e c t — as grade i n c r e a s e s , k r i g i n g 60 v a r i a n c e (or the e r r o r o f the e s t i m a t e ) i n c r e a s e s . A l t h o u g h an at tempt c o u l d be made t o model t h i s i n c r e a s e f o r v a r i o u s sample geometr i e s and grade r a n g e s , i t would be s i m p l e r i f a way c o u l d be found t o o b t a i n k r i g i n g v a r i a n c e s t h a t changed o n l y due to changes i n the p a t t e r n o f the samples around the b l o c k to be e s t i m a t e d . Thus i f t h e r e was, f o r i n s t a n c e , a square d r i l l i n g p a t t e r n , a r e a s o n a b l y c o n s t a n t k r i g i n g v a r i a n c e c o u l d be e x p e c t e d . T h i s can be done by use o f r e l a t i v e v a r i o g r a m s . Because i t has been observed t h a t k r i g i n g v a r i a n c e tends to i n c r e a s e p r o p o r t i o n a l l y w i t h grade s q u a r e d , the v a r i o g r a m v a l u e s a t every l a g d i s t a n c e can be d i v i d e d by the square o f the mean grade o f a l l o f the samples used to c a l c u l a t e the v a l u e . When the r e l a t i v e v a r i o g r a m i s used t o e s t i m a t e b l o c k s which are k r i g e d from d r i l l h o l e s on a square or r e c t a n g u l a r g r i d around the b l o c k , k r i g i n g v a r i a n c e s w i l l be f a i r l y c o n s t a n t . In e f f e c t r e l a t i v e k r i g i n g v a r i a n c e s w i l l change o n l y i f the geometry or s p a c i n g o f the samples around the b l o c k t o be e s t i m a t e d i s changed. 6.1.5 Combin ing 3-Parameter Lognormal D i s t r i b u t i o n s w i t h R e l a t i v e Var iograms I f the grades can be assumed t o be 3 -parameter l o g n o r m a l , t h e n k r i g i n g v a r i a n c e w i l l have t o be c a l c u l a t e d i n such a way as t o p r e d i c t the v a r i a n c e o f the 3 -parameter l o g n o r m a l d i s t r i b u t i o n . To do t h i s , the r e l a t i v e v a r i o g r a m i s c a l c u l a t e d as y{h) / (m(h) + constant) 2. The c o n s t a n t i s the same one t h a t i s added t o grades t o produce the 3 -parameter l ognormal d i s t r i b u t i o n , whereas m i s the average o f a l l samples used to 61 c a l c u l a t e y(A>) a t h. The r e l a t i v e k r i g i n g v a r i a n c e w i l l now c o r r e s p o n d t o the same a l t e r e d d i s t r i b u t i o n as the g r a d e s . A t B u c k h o r n , i t i s p o s s i b l e to assume c o n s t a n t r e l a t i v e k r i g i n g v a r i a n c e s where e x p l o r a t i o n g r i d d r i l l i n g i s r e g u l a r l y a r r a n g e d r e l a t i v e t o b l o c k s b e i n g e s t i m a t e d , and these r e l a t i v e v a r i o g r a m s can be used i n c o n j u n c t i o n w i t h a 3-parameter l o g n o r m a l model o f the sample d a t a . 6.1.6 D e t e r m i n i n g t h e C o n s t a n t R e l a t i v e B l a s t h o l e K r i g i n g V a r i a n c e Use o f the r e l a t i v e v a r i o g r a m w i l l t h e o r e t i c a l l y p r o v i d e the c o n s t a n t k r i g i n g v a r i a n c e w i t h o u t r e g a r d t o grade o f the samples , dependent o n l y on the c o m b i n a t i o n o f b l o c k s i z e to be e s t i m a t e d from b l a s t h o l e k r i g i n g , and the b l a s t h o l e p a t t e r n or s p a c i n g . I f t h e r e i s no b l a s t h o l e d a t a a v a i l a b l e , r e a s o n a b l e grades c o u l d be s u b s t i t u t e d a t the a n t i c i p a t e d b l a s t h o l e l o c a t i o n s , and a s m a l l subse t o f the t h e o r e t i c a l p a t t e r n c o u l d be k r i g e d . The r e s u l t i n g r e l a t i v e k r i g i n g v a r i a n c e c o u l d be used i n the c o n d i t i o n a l p r o b a b i l i t y c a l c u l a t i o n . The assumpt ion w i l l have t o be made t h a t the e x p l o r a t i o n and b l a s t h o l e v a r i o g r a m s are the same and the same c o n s t a n t (and t h e r e f o r e the same var iogram) i s used t o model i d e n t i c a l 3 -parameter l o g n o r m a l d i s t r i b u t i o n s . A l t e r n a t i v e l y , i f a c t u a l b l a s t h o l e d a t a i s a v a i l a b l e f o r a few o f the benches (as a t B u c k h o r n ) , the r e a l b l a s t h o l e d a t a can be k r i g e d . Because a l l e s t i m a t e s i n t h i s s tudy are based on e x p l o r a t i o n r e s u l t s o n l y , k r i g e d e s t i m a t e s from the e x p l o r a t i o n d e r i v e d v a r i o g r a m s were c a l c u l a t e d from the a v a i l a b l e b l a s t h o l e d a t a at B u c k h o r n . These b l o c k grades were p l o t t e d and r e l a t i v e k r i g i n g v a r i a n c e s were c o n t o u r e d . By v i s u a l e x a m i n a t i o n o f the bes t sampled a r e a s , and comparisons w i t h h i s t o g r a m s o f k r i g i n g v a r i a n c e s , o n l y two c o n s t a n t r e l a t i v e k r i g i n g v a r i a n c e s were n e c e s s a r y , one f o r each o f the 20' b l o c k models and the o t h e r f o r t h e 60' b l o c k mode l s . These are shown l a t e r i n T a b l e VI a long w i t h o t h e r parameters used i n c a l c u l a t i n g c o n d i t i o n a l p r o b a b i l i t y . Once the c o n s t a n t b l a s t h o l e k r i g i n g v a r i a n c e i s c a l c u l a t e d , e x p l o r a t i o n b l o c k models a r e examined t o see i f t h e r e i s a maximum r e l a t i v e k r i g i n g v a r i a n c e . U s u a l l y any b l o c k w i t h a h i g h e r r e l a t i v e k r i g i n g v a r i a n c e than the maximum w i l l be i g n o r e d i n subsequent c a l c u l a t i o n s because the k r i g e d grade would be c o n s i d e r e d too u n r e l i a b l e . T h i s parameter was c o n s i d e r e d u n n e c e s s a r y a t Buckhorn because the sample d e n s i t y was adequate i n a l l l o c a t i o n s and back e s t i m a t i o n showed t h a t k r i g e d grades d i d no t s u f f e r s i g n i f i c a n t l y i n any k r i g i n g v a r i a n c e r a n g e . 6.2 CALCULATION OF CONDITIONAL PROBABILITY F o r each b l o c k i n the mine mode l , the f o l l o w i n g i n f o r m a t i o n i s now a v a i l a b l e : 1) The e x p l o r a t i o n k r i g e d e s t i m a t e . 2) The a s s o c i a t e d e x p l o r a t i o n k r i g i n g v a r i a n c e . 3) A maximum a l l o w a b l e e x p l o r a t i o n k r i g i n g v a r i a n c e . 4) The c o n s t a n t r e l a t i v e k r i g i n g v a r i a n c e from p r o - d u c t i o n k r i g i n g o f b l a s t h o l e s . 5) A knowledge o f the expected shape o f the e r r o r d i s t r i b u t i o n and , i f n e c e s s a r y , the c o n s t a n t r e q u i r e d f o r t h e 3-parameter l o g n o r m a l d i s t r i b u t i o n . Other parameters t h a t are r e q u i r e d f o r t h e c a l c u l a t i o n i n c l u d e the s p e c i f i c g r a v i t y so t h a t ore f r a c t i o n s ( p r o b a b i l i t i e s ) can be c o n v e r t e d to tonnage , an a r b i t r a r y minimum v a l u e t o c o n s i d e r f o r ore ( to p r e v e n t mean ing le s s c a l c u l a t i o n s i n areas o f w a s t e ) , and f i n a l l y the s i g n i f i c a n t c u t o f f grades must be s p e c i f i e d . T h e r e f o r e , assuming a b l o c k model has been p r e p a r e d which c o n t a i n s k r i g e d grade and r e l a t i v e k r i g i n g v a r i a n c e , o n l y the f o l l o w i n g i n p u t parameters are needed to run the computer program which w i l l c a l c u l a t e the c o n d i t i o n a l p r o b a b i l i t i e s : 1) C u t o f f g r a d e . 2) C o n s t a n t t o add t o grades f o r the 3 -parameter l o g - normal d i s t r i b u t i o n . 3) Minimum e x p l o r a t i o n k r i g e d v a l u e f o r i n c l u s i o n i n the c a l c u l a t i o n . 4) Maximum a c c e p t a b l e e x p l o r a t i o n k r i g i n g v a r i a n c e . 5) C o n s t a n t r e l a t i v e k r i g i n g v a r i a n c e o f p r o d u c t i o n e s t i m a t e s . 6) S p e c i f i c g r a v i t y o f o r e . Then f o r each b l o c k : 1) Check i f the b l o c k i s below minimum e x p l o r a t i o n k r i g e d g r a d e , or i f k r i g i n g v a r i a n c e i s above the maximum a l l o w a b l e — i g n o r e the b l o c k c a l c u l a t i o n i f e i t h e r c o n d i t i o n i s t r u e . 2) Assume c o n d i t i o n a l e x p e c t a t i o n i s k r i g e d grade p l u s the c o n s t a n t . 3) Assume c o n d i t i o n a l v a r i a n c e i s the e x p l o r a t i o n r e l a t i v e k r i g i n g v a r i a n c e minus the c o n s t a n t b l a s t h o l e k r i g i n g v a r i a n c e . M u l t i p l y by (kriged grade + constant)2 t o o b t a i n a r i t h m e t i c v a r i a n c e . 4) T r a n s f o r m the c o n d i t i o n a l d i s t r i b u t i o n t o a l o g - normal model and c a l c u l a t e the p e r c e n t a g e o f m a t e r i a l t h a t i s l i k e l y to be above the l o g t r a n s f o r m e d c u t o f f and t h e n c a l c u l a t e the expected l o g a r i t h m i c grade o f the ore f r a c t i o n o f the b l o c k . 5) T r a n s f o r m the p r e d i c t e d grade back t o an a r i t h m e t i c v a l u e and s u b t r a c t the c o n s t a n t . 6) M u l t i p l y o r e f r a c t i o n t imes t h e b l o c k tonnage t o o b t a i n tonnage above c u t o f f f o r the b l o c k . A f t e r c a l c u l a t i n g c o n d i t i o n a l p r o b a b i l i t y f o r each b l o c k , the l a s t s t e p i s t o t a l l y up the tonnages and de termine the new grade t o o b t a i n f i n a l g l o b a l e s t i m a t e s f o r the d e p o s i t . The parameters used f o r the Buckhorn c o n d i t i o n a l p r o b a b i l i t y runs are summarized i n T a b l e V I . The c a l c u l a t i o n was performed on each o f the 20' and 60' b l o c k models a t 4 c u t o f f grades ( 0 . 0 1 , 0 .02 , 0.0 35 and 0.05 o p t . g o l d ) , a t o t a l o f 16 r u n s . Ore r e s e r v e s to 65 T a b l e VI Parameters Used t o C a l c u l a t e C o n d i t i o n a l P r o b a b i l i t y B l o c k s i z e 20' x 20' x 20' or 60' x 60' x 20' BUCK BUCK60 B l a s t h o l e k r i g i n g v a r i a n c e 0.080 0.040 C o n s t a n t added t o grades 0.005 0.005 BUCKG BUCK60G B l a s t h o l e k r i g i n g v a r i a n c e 0.080 0.040 C o n s t a n t added to grades n/a n/a C u t o f f grades 0.010 0.020 0.035 0.050 Minimum v a l u e t o c o n s i d e r f o r ore 0 .005 S p e c i f i c G r a v i t y 1.634 compare w i t h the o t h e r types o f e s t i m a t e s were c a l c u l a t e d by assuming t h a t t o t a l ounces on a bench were the same as t o t a l ounces p r e d i c t e d by k r i g i n g . F o r each o f the o t h e r r e s e r v e r e p o r t s , r e s e r v e s were c a l c u l a t e d w i t h i n c u t o f f ranges and then c u m u l a t i v e l y above c u t o f f g r a d e s . F o r c o n d i t i o n a l p r o b a b i l i t y , t o t a l r e s e r v e above a c u t o f f grade i s the r e s u l t o f the c a l c u l a t i o n . To c a l c u l a t e grades w i t h i n c u t o f f r a n g e s , i t was n e c e s s a r y t o work backwards — tons and grade above 0.05 o p t . were s u b t r a c t e d from tons and grade above 0.035 o p t . by c o n v e r t i n g t o m e t a l (ounces o f g o l d ) . T h i s p r o c e d u r e was r e p e a t e d u n t i l the c a l c u l a t i o n o f m e t a l i n the 0.0 t o 0.01 range was r e a c h e d . F o r t h i s grade range , t o t a l ounces (and tons) above 0.01 o p t . were s u b t r a c t e d from t o t a l ounces above 0.0 p r e d i c t e d by the c o r r e s p o n d i n g k r i g e d b l o c k mode l . In t h i s way i t was p o s s i b l e t o g e n e r a t e r e s e r v e r e p o r t s t h a t were i d e n t i c a l i n form t o the o t h e r r e p o r t s and which c o u l d t h e r e f o r e be compared w i t h them. 6.2.1 Example C a l c u l a t i o n o f C o n d i t i o n a l P r o b a b i l i t y To i l l u s t r a t e the c a l c u l a t i o n o f c o n d i t i o n a l p r o b a b i l i t y , the f o l l o w i n g example i s c a l c u l a t e d u s i n g a k r i g e d b l o c k grade o f 0.030 o p t . w i t h a r e l a t i v e b l o c k k r i g i n g v a r i a n c e o f 0 .28 . Assume t h e c o n s t a n t b l a s t h o l e k r i g i n g v a r i a n c e has been c a l c u l a t e d as 0 .080 , a c o n s t a n t o f 0.005 i s added t o c r e a t e a 3- parameter l o g n o r m a l d i s t r i b u t i o n and s p e c i f i c g r a v i t y i s 1.6 34. The c o n d i t i o n a l p r o b a b i l i t y c a l c u l a t i o n w i l l be c a l c u l a t e d f o r a 0.035 c u t o f f g r a d e . The c o n d i t i o n a l e x p e c t a t i o n (x) w i l l be t h e k r i g e d grade + the 0.005 c o n s t a n t . B e f o r e work ing w i t h the l o g n o r m a l d i s t r i b u t i o n , the 0.005 c o n s t a n t must a l s o be added t o the c u t o f f grade ( x c ) : x = 0.030 + 0.005 = 0.035 x c = 0.035 + 0.005 = 0.040 The c o n d i t i o n a l v a r i a n c e ( o 2 ) i s the e x p l o r a t i o n r e l a t i v e b l o c k k r i g i n g v a r i a n c e minus the b l a s t h o l e c o n s t a n t r e l a t i v e 67 b l o c k k r i g i n g v a r i a n c e . A r i t h m e t i c (as opposed t o r e l a t i v e ) k r i g i n g v a r i a n c e i s c a l c u l a t e d as f o l l o w s : a2 = ( 0.28 - 0.08 ) x ( 0.030 + 0.005 ) 2 = 0.000245 The l o g a r i t h m i c mean ( x / n ) and l o g a r i t h m i c v a r i a n c e (ojn) can now be c a l c u l a t e d u s i n g s t a n d a r d e q u a t i o n s : In [1] 0.000245 - /n ( 1 + ) (0.035) = In (1 .2) = 0.18232 In = In (x) - In [2] 0.18232 = In (0.035) - = -3 .44357 68 Above a g i v e n c u t o f f grade ( x c ) , the ore f r a c t i o n , or p r o b a b i l i t y (T) and the grade above c u t o f f (G) are c a l c u l a t e d as f o l l o w s : x c °ln T = 1 - F [ In — + j [3] In G = — [ 1 F [ — In — - — ) ] T o l n x 2 [4] where F(z) can be read from s t a n d a r d t a b l e s showing the c u m u l a t i v e normal d i s t r i b u t i o n ( i . e . D a v i d , 1977, page 9 ) . The program used f o r the a c t u a l c a l c u l a t i o n s uses an a p p r o x i m a t i o n f o r m u l a . U s i n g v a l u e s c a l c u l a t e d p r e v i o u s l y , and s u b s t i t u t i n g i n t o e q u a t i o n s [3] and [4] above: 1 0.040 /0 .18232 T = 1 - F [ • In + ) / 0 .18232 0.035 2 = 1 - F (0.526) I n t e r p o l a t i n g F(0.526) from the t a b l e , g i v e s ore f r a c t i o n (T) e q u a l t o 0 .299 . 0.035 1 0.040 /0 .18232 G = [ 1 - F [ In )] 0.299 /0 .18232 0.035 2 = 0.1169 [ 1 - F (0.099) ] 69 A g a i n u s i n g a s t a n d a r d t a b l e F ( 0.099) can be i n t e r p o l a t e d . The r e s u l t i n g grade above c u t o f f (G) i s 0 .0538. The cons tant which was o r i g i n a l l y added t o the k r i g e d grade must now be s u b t r a c t e d t o y i e l d a grade o f 0.049 o p t . Assuming b l o c k s i z e f o r t h i s example i s 20' x 20' x 2 0 ' , and knowing t h a t s p e c i f i c g r a v i t y i s 1.6 34, the tonnage o f the whole b l o c k can be c a l c u l a t e d : 62.42796 T o t a l B l o c k Tons = 20 x 20 x 20 x 1.634 x 2000 = 408.03 Tons Ore Tons = T o t a l B l o c k Tons x T = 408.03 x .299 = 122.16 Tons T h e r e f o r e , when t a l l y i n g up r e s e r v e s above a 0.0 35 o p t . c u t o f f , the 20' b l o c k w i l l c o n t r i b u t e 122 Tons a t a grade o f 0.049 o p t . g o l d . A l t h o u g h i t i s u n l i k e l y t h a t t h i s s p e c i f i c b l o c k w i l l y i e l d e x a c t l y 122 tons o f o r e , the r e s u l t can be r e - s t a t e d . S i n c e we are d e a l i n g w i t h c o n s t a n t r e l a t i v e v a r i a n c e s , i n g e n e r a l i t can be s a i d t h a t a p p r o x i m a t e l y 30% o f a l l b l o c k s which had an i n i t i a l k r i g e d grade o f 0.030 o p t . , w i l l i n f a c t be found t o be above the 0.035 c u t o f f and the grade o f these ore b l o c k s w i l l average 0.049 o p t . g o l d . 70 6.3 DISCUSSION In Raymond's method o f d e a l i n g w i t h c o n d i t i o n a l p r o b a b i l i t y , he uses p o i n t k r i g i n g on the c e n t e r s o f a g r i d f o r k r i g i n g e x p l o r a t i o n grades and f o r d e t e r m i n i n g c o n s t a n t r e l a t i v e k r i g i n g v a r i a n c e s o f b l a s t h o l e s . He says t h a t s i z e o f the chosen g r i d w i l l no t a f f e c t any e s t i m a t e except to improve l o c a l p r e c i s i o n , and the assumpt ion i s t h a t m i n i n g w i l l be t o c o n t o u r s around k r i g e d b l a s t h o l e p o i n t e s t i m a t e s (Raymond, p e r s . comm.). T h i s i s a p r a c t i c a l approach which he has t e s t e d over the y e a r s , but i t draws c r i t i c i s m from those who would argue t h a t the p o i n t e s t i m a t e s d o n ' t r e p r e s e n t b l o c k g r a d e s . In the approach used h e r e , b l o c k grades are k r i g e d , and f u r t h e r m o r e , comparisons are made t o b l a s t h o l e k r i g e d b l o c k grades where the b l o c k s i z e i s e x a c t l y the same as e s t i m a t e d from e x p l o r a t i o n d a t a . In o t h e r words , when 60' b l o c k s are k r i g e d from e x p l o r a t i o n d a t a , the m i n i n g method i s assumed t o be s e l e c t i v e t o 6 0 ' . The c o n s t a n t r e l a t i v e k r i g i n g v a r i a n c e i s computed f o r the 60' b l o c k s , and c o n d i t i o n a l p r o b a b i l i t y i s c a l c u l a t e d f o r the l a r g e b l o c k s i z e u s i n g a 12' t o 14' t h e o r e t i c a l b l a s t h o l e s p a c i n g . T h i s a l l e v i a t e s any problem o f d e c i d i n g which i s the b e s t b l o c k d i s p e r s i o n t o super impose on a k r i g e d mean. T h e r e i s no need t o a p p l y the a f f i n e c o r r e c t i o n methods d e s c r i b e d by some a u t h o r s ( i . e . D a v i d , 1977, 1988; G i r o u x and S i n c l a i r , 1986) . The k r i g i n g v a r i a n c e o f the b l o c k i s t h e o r e t i c a l l y t h e r e q u i r e d d i s p e r s i o n minus the k r i g i n g v a r i a n c e o f a s i m i l a r s i z e b l o c k which w i l l be k r i g e d u s i n g b l a s t h o l e da ta a c c o r d i n g t o the "smoothing r e l a t i o n s h i p " ( D a v i d , 1988) . A n o t h e r assumpt ion s t a t e d by Raymond, and suppor ted by S i n c l a i r ( p e r s . comm.) i s t h a t the d i s t r i b u t i o n o f e r r o r s i s assumed t o be l o g n o r m a l , and t h a t t h i s i s the weakest o f the assumpt ions made when d e a l i n g w i t h t h i s method o f c o n d i t i o n a l p r o b a b i l i t y . I t i s the a u t h o r ' s c o n v i c t i o n t h a t t h i s assumption i s n e i t h e r n e c e s s a r y , nor i s i t used i n any way when c a l c u l a t i n g c o n d i t i o n a l p r o b a b i l i t y as d e s c r i b e d e a r l i e r . The o n l y assumpt ions made i n t h i s r e g a r d are t h a t the d i s t r i b u t i o n o f k r i g e d b l a s t h o l e grades i s l o g n o r m a l , t h a t the e x p l o r a t i o n k r i g e d e s t i m a t e i s c o n d i t i o n a l l y u n b i a s e d ( i . e . k r i g e d grade c o n d i t i o n a l e x p e c t a t i o n ) , and t h a t e x p l o r a t i o n k r i g i n g v a r i a n c e s minus b l a s t h o l e k r i g i n g v a r i a n c e s r e f l e c t s the expected b l o c k d i s p e r s i o n ( c o n d i t i o n a l v a r i a n c e ) . The o n l y q u e s t i o n a b l e assumpt ion t h a t Raymond makes, i s t h a t the n o r m a l i z e d shape o f the 3-parameter l o g n o r m a l d i s t r i b u t i o n w i l l be r e p l i c a t e d i n every grade range ( i . e . t h a t the 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 3 -parameter l o g n o r m a l r e g a r d l e s s o f k r i g e d g r a d e ) . In the case o f the BEX d a t a s e t a t B u c k h o r n , a 3- parameter d i s t r i b u t i o n was mode l l ed e x a c t l y as l a i d out by Raymond i n h i s v a r i o u s p a p e r s . In the case o f the BEXG d a t a s e t t h e r e was no need t o add a c o n s t a n t and t h e r e f o r e , t h e o r e t i c a l l y , the l a t t e r c a l c u l a t i o n would l e a d to r e s u l t s which render any doubts about the 3-parameter d i s t r i b u t i o n i r r e l e v a n t . What about t h e two models (BUCK and BUCK60) which used the assumption? I t i s obv ious t h a t i n the case o f t h i s s t u d y , the s u b s e l e c t e d BEXG and BBHG d a t a s e t s r e p r e s e n t the upper p o r t i o n s 72 o f the BEX and BBH d a t a s e t s r e s p e c t i v e l y . They i n d i c a t e near p e r f e c t l o g n o r m a l d i s t r i b u t i o n s . T h i s means t h a t the d i s t r i b u t i o n o f a c t u a l b l o c k grades g i v e n p r e d i c t e d g r a d e s , i n a l l 4 b l o c k mode l s , i n any a r e a t h a t c o u l d p o t e n t i a l l y be ore (> 0.020 o p t . g o l d ) , i s l o g n o r m a l . The shape o f a h i s t o g r a m o f the p r e d i c t e d grades w i l l a l s o be l o g n o r m a l and w i l l not l ook l i k e the h i s t o g r a m o f the raw BEX d a t a s e t compos i tes ( tha t was m o d e l l e d as 3 -parameter l ognormal ) i n any o f the 4 b l o c k models . T h e r e f o r e , i n r e a l i t y , the problem i s no t the d i s t r i b u t i o n o f the 20' e x p l o r a t i o n compos i tes i n the BEX d a t a , or the c o r r e s p o n d i n g k r i g e d b l o c k grades — i n h i g h e r grade areas they are b o t h a c t u a l l y l o g n o r m a l , i n s t e a d the problem w i l l be k r i g i n g v a r i a n c e s . By u s i n g a v a r i o g r a m which i s c a l c u l a t e d from a l l o f the a v a i l a b l e d a t a w i t h o u t r e g a r d t o m i x i n g o f d i f f e r e n t p o p u l a t i o n s , the a n i s o t r o p i e s were about the same and the ranges were s i m i l a r , but p r e d i c t e d k r i g i n g v a r i a n c e s w i l l be h i g h e r than they s h o u l d be . The c o n d i t i o n a l d i s t r i b u t i o n o f low grade areas i s l o g n o r m a l but an i n c o r r e c t v a r i o g r a m model i s b e i n g a p p l i e d and t h e r e f o r e k r i g i n g v a r i a n c e s i n these areas a r e c a l c u l a t e d i n c o r r e c t l y . S i n c e , i n the case o f the Buckhorn d e p o s i t , n e a r l y 100% o f the lower grade p o p u l a t i o n i s below the l owes t grade o f o r e t h a t i s o f i n t e r e s t (0.02 o p t . g o l d ) , t h e r e i s no r e a l p r o b l e m . In the h i g h grade a r e a s , the 3-parameter a p p r o x i m a t i o n , a l t h o u g h never p e r f e c t , i s a much b e t t e r p r e d i c t o r o f r e l a t i v e k r i g i n g v a r i a n c e than i f the c o n s t a n t h a d n ' t been u s e d . But when c o n d i t i o n a l p r o b a b i l i t y i s m o d e l l e d from t h i s v a r i o g r a m , the c o n d i t i o n a l d i s t r i b u t i o n s w i l l s t i l l be w ider (and t h e r e f o r e l e s s p r e c i s e ) t h a n they s h o u l d be . When grade e s t i m a t i o n i s performed 73 f o r a b l o c k where k r i g i n g used samples from b o t h p o p u l a t i o n s , t h e r e ' s g o i n g t o be t r o u b l e , r e g a r d l e s s o f the m o d e l l e d frequency d i s t r i b u t i o n o r v a r i o g r a m u s e d . A g r e a t e r amount o f e f f o r t s h o u l d go i n t o c h o o s i n g a v a r i o g r a m which w i l l m i n i m i z e k r i g i n g v a r i a n c e i n the obvious a r e a s o f i n t e r e s t — i . e . i n areas o f h i g h e r grade o r e . As w i l l be shown i n the next c h a p t e r the e f f o r t w i l l be r e p a i d w i t h a b e t t e r g l o b a l o r e r e s e r v e e s t i m a t e . In o r d e r t o s u p p o r t the b a s i c methodology and assumptions used i n Raymond's approach t o c o n d i t i o n a l p r o b a b i l i t y , the f o l l o w i n g summary i s o f f e r e d w i t h c o r r e s p o n d i n g quotes or r e f e r e n c e s , m a i n l y from M i c h e l D a v i d ' s most r e c e n t t e x t - b o o k on g e o s t a t i s t i c a l o r e r e s e r v e e s t i m a t i o n ( D a v i d , 1988): 1) O r d i n a r y k r i g i n g i s used t o d e f i n e the c o n d i t i o n a l d i s t r i b u t i o n . " O r d i n a r y k r i g i n g . . . i s s t i l l the t o o l t o use i n most c i r c u m s t a n c e s " ( D a v i d , 1988, page 112) . 2) The r e l a t i v e v a r i o g r a m can be c a l c u l a t e d as y(h)/m{h) 2 ( i b i d . , page 4 3 ) . The r e l a t i v e v a r i o g r a m i s the "favoured a l t e r n a t i v e " t o the l o g a r i t h m i c v a r i o g r a m when d e a l i n g w i t h p r o p o r t i o n a l e f f e c t ( i b i d . , page 4 2 ) . I t i s the bes t v a r i o g r a m t o use w i t h o r d i n a r y k r i g i n g ( i b i d . , page 127) . The r e l a t i v e v a r i a n c e t imes the k r i g e d grade squared w i l l y i e l d the a r i t h m e t i c v a r i a n c e ( i b i d . , page 99 ) . The r e l a t i v e v a r i o g r a m s h o u l d r e a c h a s i l l v a l u e which i s e q u a l t o the p o p u l a t i o n r e l a t i v e v a r i a n c e ( i b i d . , page 4 7 ) . The t h e o r e t i c a l e x p e c t a t i o n t h a t the use o f the r e l a t i v e v a r i o g r a m w i l l y i e l d c o n s t a n t r e l a t i v e k r i g i n g v a r i a n c e s can be checked e x p e r i m e n t a l l y 74 1 .000 )E  (O Z. /T O N ) a o o Ii i i i i i i i <  in  I i i i i i i i i i i i i i i i i i N i i _ < o - Q O 0.010 o 0 . 0 0 1 - i i I I i i i i i i i I I i i 0.1 2 10 30 50 70 90 PROBABILITY ( CUM % ) 98 99.9 F i g . 17. C u m u l a t i v e p r o b a b i l i t y p l o t o f the grades o f a c t u a l ( b l a s t h o l e k r i g e d ) b l o c k s g i v e n e x p l o r a t i o n k r i g e d b l o c k grades w i t h i n 2 grade ranges where t h e r e were a s i g n i f i c a n t number o f b l o c k s . The p l o t shows t h a t a c t u a l b l o c k grades are l o g n o r m a l l y d i s t r i b u t e d about the mean ( k r i g e d g r a d e ) . u s i n g back e s t i m a t i o n t e c h n i q u e s . T h i s e x p e c t a t i o n was checked a t Buckhorn u s i n g b o t h back e s t i m a t i o n and c o n t o u r maps o f e x p l o r a t i o n and b l a s t h o l e r e l a t i v e k r i g i n g v a r i a n c e s and proves t o be t r u e . 3) The l o g n o r m a l case i s most common i n m i n i n g a p p l i c a t i o n s ( D a v i d , 1988, page 123) . "On the b a s i s o f e x p e r i e n c e " , e s t i m a t e d b l o c k s w i l l f o l l o w a l o g n o r m a l d i s t r i b u t i o n w i t h a s m a l l e r v a r i a n c e ( i b i d . , page 74 ) . F i g u r e 17 shows t h a t w i t h i n the two grade ranges where t h e r e a r e t h e most samples e s t i m a t e d (0 .020- 0.035 o p t . and 0.035 - 0.050 o p t . ) , the d i s t r i b u t i o n o f a c t u a l k r i g e d b l a s t h o l e b l o c k grades i s a l s o a p p r o x i m a t e l y l o g n o r m a l at Buckhorn (as p r e d i c t e d by J o u r n e l and H u i j b r e g t s , 1978) . 4) In the non-normal c a s e , k r i g i n g i s the best a p p r o x i m a t i o n t o the c o n d i t i o n a l e x p e c t a t i o n ( D a v i d , 1977, page 255 and page 309) . In the a u t h o r ' s o p i n i o n , the weak as sumpt ion , the one which may have the g r e a t e s t e f f e c t on the c o n d i t i o n a l p r o b a b i l i t y e s t i m a t e i s t h i s assumpt ion t h a t the o r d i n a r y k r i g e d e s t i m a t e , u s i n g l o g a r i t h m i c d a t a , w i l l be c o n d i t i o n a l l y u n b i a s e d . F i g u r e 18 shows a compar i son o f k r i g e d b l a s t h o l e b l o c k grades ( v a r i a b l e 1) w i t h i n ranges o f e x p l o r a t i o n k r i g e d e s t i m a t e s ( v a r i a b l e 2 ) . The r e s u l t s show a c c e p t a b l e comparisons w i t h i n the i m p o r t a n t grade ranges (0.020 - 0.065 o p t . ) where 90% o f the e s t i m a t e d o r e b l o c k s are c o n t a i n e d , but o v e r a l l , t h e r e i s not a p e r f e c t c o r r e s p o n d e n c e between expected and a c t u a l average g r a d e s . However, the assumpt ion t h a t the k r i g e d e s t i m a t e a c t u a l l y i s c o n d i t i o n a l l y u n b i a s e d i s the same one t h a t i s made by the many g e o s t a t i s t i c i a n s who work w i t h o r d i n a r y k r i g i n g and r e l a t i v e v a r i o g r a m s . 5) The l a s t assumpt ion i s a l s o t r a d i t i o n a l l y w e l l accepted by g e o s t a t i s t i c i a n s . That i s the "smoothing r e l a t i o n s h i p " d e s c r i b e d by D a v i d (1988, page 74) : VAR(Z*) = VAR(Z) - o £ " T h i s r e l a t i o n s h i p has been checked e x p e r i m e n t a l l y v e r y w e l l " . 7 COMPARE ACTUAL VS. EXPLORATION KRIGED BLOCK GRADES NORTH EAST ELEV I REG. VARIANCE I RANGES MIN. 1ST INC NO.INC1 2ND INC MIN. 0.0 0.0 0.0 I CONST 0.000 I VARIABLE 1 0.000 1.000 2 1.500 MAX. 99999.0 99999.0 99999.0 I POWER 2.000 I VARIABLE 2 0.000 1.000 2 1.500 VARIABLE ELEMENT MULTIPLIER DESCRIPTOR FILENAME FILETYPE 1 DEPENDENT AU 100.0000 BBHG KRIGED BLOCK GRACES - •ACTUAL" ACTUAL2G KRIGE 2 INDEPENDENT AU 100.0000 BEXG EXPLORATION KRIGED BLOCK GRADES BEXGKRIG KRIGE LOCATION 20' BLOCK MODEL WITIN OUTLINE BUCKG GRID VAR 1 < < VAR 2 MIDPOINTS > > ROW MIDPT 0.92 1.74 2.75 4.11 5.59 7.06 8.71 10.34 11.61 13.27 14.83 16.47 17 .81 18.92 0.00 TOTAL 0.62 0 21 60 16 3 0 1 0 2 1 0 0 0 0 0 104 1.60 0 76 217 60 11 4 3 3 2 3 1 0 0 0 0 380 2.70 0 122 409 148 32 14 12 7 6 3 1 0 0 0 0 754 4.16 0 21 174 129 28 12 12 2 0 0 0 0 0 0 0 378 5.71 0 4 81 68 35 5 6 0 1 0 0 0 0 0 0 200 7.16 0 1 25 34 16 12 8 0 1 1 0 0 0 0 0 98 B.69 0 2 7 18 11 6 3 6 2 2 1 0 0 0 0 58 10.10 1 0 11 12 18 1 2 5 1 1 0 1 1 0 0 54 11.62 0 1 3 8 4 1 2 1 1 4 2 0 1 2 0 30 13.02 0 0 1 3 3 1 0 0 0 0 0 2 1 1 0 13 H.66 0 0 0 2 1 2 1 1 0 0 0 0 0 0 0 7 16.65 0 0 0 1 0 0 0 0 0 1 0 2 0 0 0 4 17.84 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 3 19.18 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 4 0.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 24.19 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 27.88 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 TOTAL 1 248 989 500 164 58 50 26 16 17 6 5 4 3 0 2089 VARIABLE 2 MEAN 0.92 1.74 |2.75 4.11 5.59 VARIABLE 1 MEAN 10.06 2.41 SO. 0.00 1.36 VARIA 0.00 1.84 13.12 4.32 5.84 1.89 3.57 2.64 3.51 6.97 12.29 7.06 8.71 10.34 11.61 13.27 14.83 16.47 1 7.81 18.92 5.66 3.12 9.71 5.37 7.30 2.99 5.58 8.91 31.11 4.50 7.53 9.01 3.55 5.31 5.51 12.59 28.23 30.40 2.60 3.51 6.75 12.29 18.92 0.00 3.826 12.32 0.00 3.848 0.59 0.00 2.290 0.34 0.00 5.865 0.002 0.000 0.363 ABSOLUTE DIFFERENCE VARIABLES(1-2) MEAN 9.14 0.99 1.29 1.90 2.65 2.91 3.94 4.88 7.11 6.67 7.00 3.05 5.00 6.60 0.00 1.791 RT MS 9.14 1.52 1.B9 2.62 3.52 3.51 4.48 6.33 7.98 7.87 8.19 3.80 5.61 6.62 0.00 2.451 MN SQ 83.63 2.30 3.56 6.86 12.42 12.29 20.10 40.04 63.61 61.91 67.08 14.43 31.44 43.80 0.00 7.352 REGMS99.891 0.819 0.473 0.404 0.403 0.247 0.263 0.376 0.469 0.350 0.298 0.052 0.098 0.122 0.000 0.523 CUMULAT1VES ABOVE LOWER LIMIT VARIABLE 1 LOLIM 0.00 1.00 2.00 3.50 5.00 6.50 8.00 9.50 11.00 12.50 14.00 15.50 17.00 18.50 20.00 NO. 2089 1985 1605 851 473 273 1 75 117 63 33 20 13 9 6 2 MEAN 3.848 4.017 4.589 6.268 7.955 9.59910.96412.09113.79715.78017.57419.14620.25621.46326.033 VARIABLE 2 LOLIM 0.00 1.00 2.00 3.50 5.00 6.50 8.00 9.50 11.00 12.50 14.00 15.50 17.00 18.50 20.00 NO. 2089 2088 1840 851 351 187 129 79 53 37 20 14 9 5 2 MEAN 3.826 3.827 4.108 5.691 7.94810.01411.34213.00714.31315.48117.36218.44719.54620.93623.963 1GIV2 3.848 3.845 4.038 5.109 6.241 6.592 7.012 8.054 8.42110.11712.32013.73713.63013.77515.958 TOTAL VARIABLE 1 I MEAN 3.848 I SD 2.810 I VAR IA 7.898 ! V/(M»C**P) 0.533 TOTAL VARIABLE 2 I MEAN 3.826 t SO 2.428 I VARIA 5.893 I V/(M*C**P) 0.403 F i g . 18. Computer p r i n t o u t o f the compar i son between a c t u a l grades ( v a r i a b l e 1) and k r i g e d e s t i m a t e s ( v a r i - a b l e 2) w i t h i n e s t i m a t e d grade r a n g e s . 90% o f a l l ore grade k r i g e d e s t i m a t e s f a l l i n columns 3,4 and 5. The compar i son shows t h a t k r i g e d e s t i m a t e s a r e c o n d i t i o n - a l l y u n b i a s e d i n these 3 ranges (maximum d i f f e r e n c e i s a p p r o x i m a t e l y 0.004 o p t . ) . However, i n o t h e r co lumns , t h e c o r r e s p o n d e n c e i s no t as good. A l l d a t a has been m u l t i p l i e d by 100. The same program was used i n back e s t i m a t i o n and t o a n a l y z e some o f the o t h e r " a c t u a l v s . p r e d i c t e d " c o m p a r i s o n s . 77 In a d d i t i o n t o the above, D a v i d a l s o p r o v i d e s s u p p o r t f o r t h e assumpt ion t h a t a p r e - d e f i n e d c o n t o u r based on a c u t o f f grade can be u s e f u l f o r d e f i n i n g p o t e n t i a l o r e ( D a v i d , 1988, page 200) , t h a t samples i n a d a t a s e t s h o u l d no t i n c l u d e o b v i o u s l y b a r r e n samples ( i b i d . , page 37) , and t h a t v a r i o g r a m s which a r e computed a c r o s s b o u n d a r i e s w i t h h i g h grade v a r i a t i o n s (as d i s c u s s e d e a r l i e r i n the s e c t i o n on v a r i o g r a m s ) "gives no i n d i c a t i o n about t h e c o n t i n u i t y i n s i d e the m i n e r a l i z e d zone" ( i b i d . , page 37) . F i n a l l y , a l o n g the l i n e s o f computing a v a r i o g r a m w i t h i n a p r e - d e f i n e d boundary ( i b i d . , page 105): " . . . . the e x t e n s i o n v a r i a n c e s h o u l d be d e r i v e d from the v a r i o g r a m o f the grade o f samples i n s e l e c t i o n u n i t s above the c u t - o f f . When the s e l e c t i o n u n i t s a r e p o i n t s , we can s i m p l y compute the v a r i o g r a m o f the grade o f samples above the c u t - o f f . A c t u a l l y , we do no t expect t h a t the s t r u c t u r a l c h a r a c t e r i s t i c s o f the v a r i o g r a m (magnitude o f nugget e f f e c t , r a n g e s , a n i s o t r o p y ) w i l l change d r a m a t i c a l l y w i t h the c u t - o f f . The main changes w i l l most p r o b a b l y a f f e c t the s i l l o f the v a r i o g r a m " . The o n l y p o i n t made i n t h i s t h e s i s t h a t d i f f e r s from t h i s a n a l y s i s , i s t h a t the a n i s o t r o p i e s might a l s o change , depending on the geometry o f the d e p o s i t , and the d i s t r i b u t i o n o f ore grades w i t h i n the orebody . The i t e m i z a t i o n o f a l l o f these p o i n t s has been performed m a i n l y t o i l l u s t r a t e t h a t c o n d i t i o n a l p r o b a b i l i t y , as implemented i n t h i s s t u d y , uses assumptions which a r e commonly made by most g e o s t a t i s t i c i a n s when they employ a r e l a t i v e v a r i o g r a m and 78 o r d i n a r y k r i g i n g t o e s t i m a t e o r e r e s e r v e s . The method deve loped by Raymond i s an e l e g a n t d e r i v a t i o n o f m i n a b l e r e s e r v e s u s i n g common, everyday a s s u m p t i o n s . A l t h o u g h not used h e r e , even the u s e o f p o i n t k r i g i n g from e x p l o r a t i o n e s t i m a t e s s h o u l d be a c c e p t a b l e i f the assumpt ion i s made t h a t m i n i n g w i l l be to c o n t o u r e d p o i n t e s t i m a t e s d e r i v e d from b l a s t h o l e d a t a on the same g r i d — t h e r e i s no change o f s u p p o r t . 79 7. COMPARISON OF CALCULATED ORE RESERVES 7.1 INTRODUCTION V a r i o u s methods were used t o compare the b l o c k models and o r e r e s e r v e s . S c a t t e r g r a m s o f p r e d i c t e d v e r s u s a c t u a l b l o c k grades were produced (Appendix F ) . I n d i v i d u a l r e s e r v e r e p o r t s (Appendix C) were examined t o compare p r e d i c t e d grades and tonnages w i t h i n ranges and t o t a l tonnage and grade above c u t o f f s , and bench maps o f the r e s u l t i n g p r e d i c t e d b l o c k grades (Appendix B) were compared w i t h each o t h e r . The v a s t amount o f d a t a gave a good i d e a o f what the r e s u l t s were, but methods o f d i s t i l l i n g the d a t a i n t o a s m a l l e r amount o f space were r e q u i r e d i n o r d e r t o e x p l a i n the p a t t e r n s . These methods and the broad c o n c l u s i o n s t h a t can be drawn from them a r e d e t a i l e d below. L a t e r , each o f t h e i n d i v i d u a l q u e s t i o n s r a i s e d i n C h a p t e r 1 are re -examined s e p a r a t e l y . 7.2 METAL GRAPHS F o u r graphs were c o n s t r u c t e d ( F i g s . 19, 20, 21 and 22 ) , one f o r each b l o c k m ode l , t o show the t o t a l amount o f m e t a l (ounces o f g o l d ) , f o r b o t h benches , t h a t was above each o f the s i g n i f i c a n t mine c u t o f f s . The g r e a t e r than 0.050 o p t . c u t o f f i s B U C K *oooo F i g . 19. M e t a l graph f o r the BUCK b l o c k mode l . B U C K G 3SOOO F i g . 20. M e t a l graph f o r the BUCKG b l o c k m o d e l . B U C K 6 0 40O0O 35000 F i g . 21. M e t a l graph f o r the BUCK60 b l o c k m o d e l . B U C K 6 0 G L E G E N D T O T A L O U N C E S > C U T O F F 0 . 0 1 0 > C U T O F F 0 . 0 2 0 o © > C U T O F F 0 . 0 3 S Q • > C U T O F F 0 . 0 5 0 1 1 r IDO K R I G E C P R O B INTERPOLATION METHOD U S E D F i g . 22. M e t a l graph f o r the BUCK60G b l o c k m o d e l . 84 n o t a c t u a l l y m o n i t o r e d a t the mine but the o t h e r c a t e g o r i e s are s i g n i f i c a n t . They r e p r e s e n t waste (< 0.010 o p t . ) , l e a n ore (0.010 t o 0.020 o p t . ) , low grade (0.020 to 0.035 o p t . ) and ore (> 0.035 o p t . g o l d ) . E a c h o f the e x p l o r a t i o n e s t i m a t e s i s shown w i t h 3 b l a s t h o l e e s t i m a t e s , where BH4 i s the 4' p o l y g o n a l e s t i m a t e , e i t h e r BH20 or BH60 i s the p o l y g o n weighted 20' or 60' b l o c k e s t i m a t e depending on t h e m o d e l ' s b l o c k s i z e , w h i l e r e s u l t s from b l a s t h o l e k r i g i n g are r e f e r r e d t o as " a c t u a l " . S i m i l a r l y , EX4 and EX20 or EX60, a r e the p o l y g o n a l and p o l y g o n weighted e s t i m a t e s from e x p l o r a t i o n d a t a . The meanings o f the r e s t o f the a b b r e v i a t i o n s on the graphs s h o u l d be s e l f - e v i d e n t . Comparing between 20' and 60' models shows, as would be e x p e c t e d , t h a t the 4' p o l y g o n a l e s t i m a t e based on e i t h e r the e x p l o r a t i o n or the b l a s t h o l e d a t a i s i d e n t i c a l f o r b o t h mode l s . S t r a i g h t p o l y g o n a l e s t i m a t e s are o b v i o u s l y i n s e n s i t i v e to b l o c k s i z e . The 60' b l o c k models are v e r y s e n s i t i v e t o the chosen method o f p r e d i c t i n g o r e r e s e r v e s above lower grade c u t o f f s , and l e s s s e n s i t i v e t o method a t h i g h e r c u t o f f s compared t o the 20' b l o c k mode l s . F o r example , i n b o t h 60' mode l s , t o t a l amount o f m e t a l above 0.050 o p t . i s s i m i l a r a c r o s s a l l a v e r a g i n g methods (po lygon w e i g h t e d , i n v e r s e d i s t a n c e and o r d i n a r y k r i g i n g ) . N o t i c e a l s o , t h a t o r d i n a r y k r i g i n g i n v a r i a b l y produces one o f the l owes t (and l e a s t a c c u r a t e ) e s t i m a t e s above 0.05 o p t . , and a l s o tends t o be lowes t i n the over 0.0 35 o p t . c a t e g o r y f o r 20' b l o c k mode l s . On the o t h e r hand , c o n d i t i o n a l p r o b a b i l i t y , which d i r e c t l y uses b o t h k r i g e d grade and k r i g i n g v a r i a n c e , and which cannot be c a l c u l a t e d from any o f the o t h e r methods, i s 85 c o n s i s t e n t l y e i t h e r the b e s t e s t i m a t e o r i s one o f the 2 or 3 c l o s e s t a p p r o x i m a t i o n s o f the a c t u a l m e t a l above any o f the c u t o f f s shown. T h i s i s e s p e c i a l l y t r u e f o r the BUCKG and BUCK60G b l o c k models where i n t e r p o l a t i o n was c o n f i n e d t o the ore zone o u t l i n e . More i m p o r t a n t , whichever o f the o t h e r e s t i m a t e s i s c l o s e v a r i e s w i t h the s p e c i f i e d c u t o f f . F o r i n s t a n c e , r e f e r r i n g t o the BUCKG graph ( F i g . 20 ) , c o n d i t i o n a l p r o b a b i l i t y shows e x c e l l e n t agreement w i t h a c t u a l e s t i m a t e s on every c u r v e . G e n e r a l l y above 0 . 0 , 0.01 and 0 .02 , k r i g i n g , ID0 , ID1 , ID2 and ID3 a r e a l s o good e s t i m a t o r s . Above 0 .035 , the t h r e e c l o s e s t e s t i m a t e s a r e the s t r a i g h t average ( ID0) , f o l l o w e d by c o n d i t i o n a l p r o b a b i l i t y and ID1, and over 0.05 o p t . , the o n l y e s t i m a t e t h a t even comes c l o s e i s ID10. S t i l l r e f e r r i n g t o the g r a p h s , any e s t i m a t e f o r the g e o l o g i c a l l y c o n s t r a i n e d b l o c k models ( F i g s . 20 and 2 2 ) , has a chance o f p r e d i c t i n g the c o r r e c t ore r e s e r v e s above a g i v e n c u t o f f , w h i l e f o r the o t h e r two u n c o n s t r a i n e d mode l s , no method p r e d i c t s the c o r r e c t ore r e s e r v e s above any c u t o f f range . T h i s i s because a l l o f the e x t r a ounces r e p o r t e d from b l a s t h o l e s i n t h e s e b l o c k models come from areas o f low r e s u l t s from e x p l o r a t i o n d r i l l i n g . No ore r e s e r v e method, no mat ter how s m a r t , can p r e d i c t m e t a l where t h e r e was a b s o l u t e l y no i n d i c a t i o n o f o r e from e x p l o r a t i o n d r i l l i n g . These e x t r a ounces r e p r e s e n t "new" o r e t h a t was found when the d e p o s i t was mined . C o n d i t i o n a l p r o b a b i l i t y comes c l o s e t o p r o v i d i n g not o n l y the b e s t e s t i m a t e o f the grade d i s t r i b u t i o n o f the o r e , i t a l s o produces v e r y s i m i l a r e s t i m a t e s between the d i f f e r e n t mode l s . I t appears t o be the s a f e s t , and most s t a b l e a l l - r o u n d e s t i m a t e o f 86 o r e r e s e r v e s r e g a r d l e s s o f what d a t a i s u s e d , o r f o r which b l o c k model i t i s c a l c u l a t e d . No o t h e r method comes c l o s e t o p r o v i d i n g s i m i l a r (or c o r r e c t ) answers f o r a l l f o u r b l o c k mode l s . Assuming t h a t the most v a l i d comparisons w i l l be p r o v i d e d from the BUCKG and BUCK60G models (which show e x c e l l e n t agreement between c o n d i t i o n a l p r o b a b i l i t y and the k r i g e d b l a s t h o l e d a t a ) , t h e s e two models a l s o show t h a t k r i g i n g does g e n e r a t e "a c o r r e c t on average" e s t i m a t e . K r i g i n g p r o v i d e s a f a i r l y a c c u r a t e e s t i m a t e o f t o t a l ounces i n the d e p o s i t . However, i t does not show a c o r r e c t on average e s t i m a t e o f c o n t a i n e d ounces above any s i g n i f i c a n t c u t o f f g r a d e . What i t does p r o v i d e i s a good, u n b i a s e d d i s t r i b u t i o n o f b l o c k grades and good e s t i m a t e s o f k r i g i n g v a r i a n c e , which i n t u r n a l l o w f o r e x c e l l e n t r e s u l t s from c o n d i t i o n a l p r o b a b i l i t y . N o t i c e a l s o t h a t i n each o f the f o u r g r a p h s , i f the t r e n d o f the i n v e r s e d i s t a n c e c a l c u l a t i o n s i s examined, t h e r e i s some grade a t which the t r e n d o f the l i n e tends t o f l a t t e n , and f o r the 20' models the t r e n d o f the c u r v e then r e v e r s e s i t s e l f . The IDO c a l c u l a t i o n always p r e d i c t s the most t o t a l ounces i n the d e p o s i t and u s u a l l y the lowes t number o f ounces above 0.05 o p t . , w h i l e i n v e r s e d i s t a n c e to the t e n t h (ID10) behaves i n e x a c t l y the o p p o s i t e manner. F o r the 60' mode l s , the l i n e s become f l a t a t e i t h e r 0.035 o r 0.05 o p t . c u t o f f s . F i n a l l y , a l t h o u g h t h e r e are o t h e r p a t t e r n s t h a t might be f o u n d , t h e r e i s one i m p o r t a n t o b s e r v a t i o n t h a t can be made h e r e . The BUCKG b l o c k model i s a p p a r e n t l y a good a p p r o x i m a t i o n o f the o r e r e s e r v e p i c t u r e w i t h i n the imposed o u t l i n e . The a c t u a l p r o d u c t i o n f i g u r e s ( tons and grade) a t the mine are based on 87 s t r a i g h t p o l y g o n a l e s t i m a t e s d e r i v e d from the d a i l y b l a s t h o l e d a t a . The mine was d e s i g n e d on 20' b l o c k s and monthly grade r e c o n c i l i a t i o n ( p r e d i c t e d v s . a c t u a l ) i s a compar i son o f the p o l y g o n a l p r o d u c t i o n e s t i m a t e from b l a s t h o l e s w i t h o r i g i n a l 20' bench p l o t s o f the grade p r e d i c t e d from the e x p l o r a t i o n d r i l l i n g ( u s i n g an i n v e r s e d i s t a n c e cubed c a l c u l a t i o n ) . An e x a m i n a t i o n o f t h e BUCKG m e t a l g r a p h ( F i g . 20 ) , shows t h a t on a v e r a g e , the p o l y g o n a l (BH4) and p o l y g o n weighted (BH20) e s t i m a t e s are s i m i l a r , and t h a t these e s t i m a t e s agree w e l l w i t h the c o n d i t i o n a l p r o b a b i l i t y e s t i m a t e (no e x p l o r a t i o n method p r e d i c t s the h i g h e r amount o f low grade tons shown by b l a s t h o l e k r i g i n g ) . These e s t i m a t e s would not have been c l o s e to the p r e d i c t e d r e s e r v e s i f the p i t was d e s i g n e d u s i n g 60' b l o c k s (compare BH4 and BH60 on F i g . 2 2 ) . T h i s seems t o show t h a t e i t h e r by l u c k , a c c i d e n t , or d e s i g n , the p r o d u c t i o n s t a t i s t i c s a t the mine u s i n g s t r a i g h t p o l y g o n a l b o u n d a r i e s , w i l l r e c o n c i l e t o the p r e d i c t e d ore r e s e r v e s about as w e l l as i f they had t r i e d t o combine the raw d a t a i n t o ' 20' b l o c k s b e f o r e compar ing . On a monthly b a s i s , e i t h e r method w i l l a d e q u a t e l y r e f l e c t p r e d i c t e d p r o d u c t i o n i n e v e r y grade r a n g e , and f o r grade r e c o n c i l i a t i o n ( s u b t r a c t i n g p r o d u c t i o n from r e s e r v e s ) e i t h e r method w i l l a l s o work. K r i g e d b l a s t h o l e g r a d e s , which s h o u l d r e f l e c t the "best e s t i m a t e " , were n o t used a t the mine . A l l i n d i c a t i o n s are t h a t more g o l d would have been r e c o v e r e d i f m i n i n g was done t o k r i g e d b l a s t h o l e o u t l i n e s . In summary, the graphs show the s t r e n g t h s and weaknesses o f the v a r i o u s methods q u i t e w e l l . O v e r a l l , c o n d i t i o n a l p r o b a b i l i t y seems t o be the bes t e s t i m a t o r r e g a r d l e s s o f b l o c k model or what 88 raw d a t a was used — a t l e a s t compared t o each o f the o ther methods shown. However, i n most c a s e s , i t i s no t s u f f i c i e n t to make compar i sons on "metal above c u t o f f " . I f more tons have to be mined t o r e c o v e r the g o l d , the economics o f the p lanned o p e r a t i o n can be d r a s t i c a l l y a f f e c t e d . A compar i son o f tons and grade w i t h i n grade ranges i s a l s o n e c e s s a r y . 7.3 ORE RESERVE CHARTS Many o f the same c o n c l u s i o n s can be drawn from the ore r e s e r v e c h a r t s ( T a b l e s V I I , V I I I , IX and X ) . T h e s e , however, show a number o f t h i n g s i n a d d i t i o n . The c h a r t s e s s e n t i a l l y d i s t i l l a l l o f the r e s e r v e r e p o r t s (Appendix C) i n t o f o u r pages . I n s t e a d o f showing c u m u l a t i v e r e s e r v e s above a grade c u t o f f however, these t a b l e s show the p r e d i c t e d amount o f ore ( tons , g r a d e , and ounces o f go ld ) w i t h i n the grade r a n g e s . In a d d i t i o n , a p e r c e n t a g e e r r o r has been c a l c u l a t e d (compared t o a c t u a l ) , and a rank from b e s t t o worst e s t i m a t e has been a s s i g n e d . The v a r i o u s e s t i m a t e s a r e then p r i n t e d , i n o r d e r o f rank a s s i g n e d , but on e i t h e r s i d e o f the a c t u a l r e s e r v e f i g u r e depending on whether the g i v e n method u n d e r e s t i m a t e d o r o v e r e s t i m a t e d the tonnage , g r a d e , o r ounces , as the case may be . Because the c o n d i t i o n a l p r o b a b i l i t y method at tempts t o p r e d i c t the r e s e r v e s from p r o d u c t i o n b l a s t h o l e k r i g i n g based on an e r r o r e s t i m a t e d e r i v e d from e x p l o r a t i o n k r i g i n g , and because b l a s t h o l e k r i g i n g i n g e n e r a l s h o u l d p r o v i d e the b e s t e s t i m a t e o f mined tons and T A B L E V I I COMPARISON OF BLASTHOLE INDICATED RESERVES WITHIN GRADE CATEGORIES VS. RESERVES CALCULATED BY EACH EXPLORATION METHOD FOR BUCK BLOCK MODEL (20 FOOT BLOCKS. NO ORE OUTLINE). CUT-OFF 0.000 - IDO ID1 102 KRIGE BHK ID3 105 CPROB IDIO EX20 EX4 METHOD 161.9 179.6 228.2 228.7 25Z5 262.7 31&8 325.7 375. 3 407.3 450.3 — TONS ( X 10001 0.359 0.289 0.096 0.094 0.000 0.041 0.251 0. 290 0.487 0.613 0. 784 _ X ERROR T 7 5 3 2 0 1 4 6 8 9 10 _ RANK a oio - E X 4 EX20 1010 BHK 105 CPROB ID3 ID2 KRIGE ID1 IDO 0 21&6 23S 1 243.3 251. 1 275.9 287.0 294.6 304.7 316 0 322. 9 326.9 a 141 0.048 0.007 0.000 0.099 0. 143 0. 173 0.214 0.258 0.286 0.302 N 4 2 1 0 3 5 6 7 8 9 10 0.020 - EX4 EX20 CPROB IDIO 105 BHK ID3 102 KRIGE ID1 IDO N 232. i 254.4 267.8 270.6 302.5 321.5 33a 1 34a 8 350.5 376. 6 395. 2 0.278 0.209 0. 167 0. 158 a 059 0.000 0.042 0.088 0.090 0. 172 0.229 A 10 8 6 5 2 0 1 3 4 7 9 0.035 - EX4 EX20 CPROB 1010 IDS 103 KRIGE ID2 IDO BHK 101 G 110.6 119.6 126.5 126.8 129.4 13Z4 13a 2 147.9 14a 4 150.3 151.7 0.264 a 203 a 158 0. 156 0. 139 a 119 tt 073 0.016 0.012 0.000 0.010 E 10 9 8 7 6 5 4 3 2 0 1 0.050 - KRIBE IDO ID1 ID2 103 ID5 1010 EX20 EX4 CPROB BHK 12a 7 122.7 124.2 124.4 130.3 131.5 133.2 134.5 146.5 148.0 17a7 0.329 a 317 0.309 0.308 0. 275 0.268 0.259 0.252 0. 185 0. 176 0.000 10 9 8 7 6 5 • 4 3 2 1 0 CUT-OFF LMTEPrriMATFTL . . o n . . . n v m S F S T l M A T F I l 0.000 _ EX4 BHK EX20 IDIO CPROB IDS 103 ID2 101 KRIGE IDO _ METHOD 0.004 0.005 0.005 0.005 0.005 0.006 0.006 0.006 0.006 0.006 0.007 GRADE (OPT. ) 0.200 0.000 0.000 0.000 0.000 0. 200 0. 200 0.200 0.200 0.200 0.400 _ % ERROR 1 0 0 0 0 1 1 1 1 1 2 _ RANK a oio _ EX4 IDIO BHK EX20 105 103 ID2 101 IDO KRIGE CPROB G 0.014 0.014 0.015 0.015 0.015 a 015 0.015 a 0 1 5 0.015 0.015 0.015 0.067 0.067 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0. 000 0.000 R 1 1 0 0 0 0 0 0 0 0 0 0.020 - EX4 BHK EX20 IDIO IDS 103 102 101 IDO KRIGE CPROB A 0.026 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.037 0.000 0.000 0.000 0. 000 0.000 0.000 a ooo 0.000 0.000 0. OOO D 1 0 0 0 0 0 0 0 0 0 0 0. 035 - 105 103 ID2 101 KRIGE BHK EX4 EX20 IDIO 100 CPROB E a 041 0.041 0.041 0.04) 0.041 0.042 0.042 0.042 0.042 0.042 0.042 0.024 0.024 0.024 0.024 0.024 0.000 0.000 0.000 0.000 0.000 0.000 1 1 1 1 1 0 0 0 0 0 0 0.050 - IDO 101 BHK 102 KRIGE 103 CPROB IDS IDIO EX20 EX4 0.076 078 0.080 0.082 0.082 0.084 0.086 0.090 0. 095 0.036 0.037 0.050 0.025 0.000 0.025 0.025 0. 050 0.075 0. 125 0. 188 0. 200 0.213 2 1 0 1 1 2 3 4 5 6 7 CUT-OFF UNTFRFSTIMATFTL . . A m i f l t . . . rWFRFSTTMATFTl 0.000 - IDO ID1 BHK KRIGE 102 103 CPROB 105 EX20 EX4 IDIO _ METHOD 1066 1154 1245 1396 1445 1576 1654 1803 1934 2023 2032 OUNCES 0. 143 0.073 0.000 0. 121 0. 161 0.266 0. 329 0. 449 0.554 0.626 0.633 _ % ERROR 3 1 0 2 4 5 6 7 8 3 10 _ RANK a oio - E X 4 EX20 IDIO BHK 105 CPROB 103 ID2 KRIGE 101 100 0 3088 3468 3583 3826 4002 4234 4302 4494 4713 4757 4312 0. 193 0.094 0.062 0.000 0.046 0. 107 0. 124 0. 175 0.232 0. 243 0. 284 U 7 3 2 0 1 4 5 6 8 9 10 a 020 - EX4 EX20 CPROB IDIO ID5 BHK 103 102 KRIGE ID1 IDO N E132 6785 7141 7193 8067 8685 8973 9 3 5 3 9354 10046 10620 0.294 a 219 0. 178 0. 172 0.071 0.000 0. 033 0.077 0. 077 0. 157 0.223 C 9 7 6 5 2 0 1 3 3 4 8 0.035 _ EX4 EX20 CPROB 1010 ID5 ID3 KRIGE ID2 IDO ID1 BHK E 4595 4997 5266 5284 5332 5477 5704 6097 6165 6274 6306 0.771 0.208 0. 165 0. 162 0. 154 0. 132 0.096 0.033 0.022 0.005 0.000 S 10 9 8 7 6 5 4 3 2 1 0 0. 050 _ IDO ID1 KRIGE ID2 ID3 IDS IDIO CPROB EX20 EX4 BHK 9334 3658 3830 10207 11004 11738 12710 12751 12886 14236 14446 0.354 0.331 0. 316 0.293 0.238 0. 183 0. 120 0. 117 0. 108 0.015 0. ooo to 9 8 7 6 5 4 3 2 1 0 CO T A B L E V I I I COMPARISON OF BLASTHOLE INDICATED RESERVES WITHIN GRADE CATEGORIES VS. RESERVES CALCULATED BY EACH EXPLORATION METHOD FOR BUCKG BLOCK MODEL (20 FOOT BLOCKS. WITHIN ORE OUTLINE). CUT-OFF 0.000 _ ID1 100 KRIGE ID2 103 CPROB IDS BHK IDIO EX20 EX4 METHOD 0.0 0.0 0.4 2.9 7.B 14.8 iag 2a i 314 73.6 101.9 TONS <X 1000) 1.000 1.000 0.9B5 a 898 0.720 0.474 0.290 0.000 0.403 1.623 ̂ 631 X ERROR T 7 7 S 5 4 3 I 0 2 8 9 RANK 0. 010 _ IDO ID1 KRIGE ID2 ID3 BHK ID5 CPROB IDIO EX4 EX20 0 60.4 692 86.2 95.9 118 7 124.9 150.4 152 8 163.8 186.4 193. 1 0.516 0.446 0.310 0.233 0.050 0.000 0.204 0.223 0.359 0.492 0.546 N 9 7 5 4 1 0 2 3 6 8 10 0.020 - EX4 EX20 BHK CPROB IDIO IDS 103 ID2 IDO IDI KRIGE N 221.8 243.9 276.7 279.2 280.6 301.7 324.7 32a 9 335.7 338. 2 35tt 8 0. 199 0. 118 0.000 0.009 0.014 0.090 0. 173 0. 189 0.213 0.222 0.269 A 7 4 0 1 2 3 5 6 8 9 10 0.035 _ EX4 EX20 1010 BHK 105 CPROB ID3 KRIGE ID2 IDI IDO G 105.5 114. 1 129 7 143.3 143.9 147.9 159 9 183.0 188. G 210. 1 224. 1 0.264 0.204 0.095 0.000 0.004 0.032 0. 116 0. 277 0.302 0.465 0.553 E 6 5 3 0 1 2 4 7 8 9 10 a 050 _ EX20 KRIGE IDO 1010 ID1 105 EX4 102 103 CPROB BHX 131.3 135.7 135.9 136.6 138.7 14a 2 140.5 141.9 145.0 161.5 183. 1 0.283 0.259 0.258 0.254 0.243 0.234 0.232 0.225 0. 208 0. 118 0.000 10 9 8 7 6 5 4 3 2 1 0 CUT-OFF IMmjFSTIMATFn. . . urrnin .. n w - M - M TMOTFn. 0.000 _ 101 100 EX4 BHK EX20 IDIO ID5 ID3 ID2 CPROB KRIGE METHOD 0.000 0.000 0. 006 0.007 0.007 0.007 0.007 0.007 0. 008 0.008 0.009 GRADE (OPT. ) 1.000 1.000 0. 143 0.000 0.000 0. 000 0.000 0.000 a 143 0. 143 0.286 X ERROR 3 3 1 0 0 0 0 0 1 1 2 RANK a oio _ EX4 EX20 ID10 BHK ID5 103 CPROB 102 KRIGE 101 IDO G 0.014 0.015 0.015 0.016 0.016 0.016 0.016 0.017 0.017 a 018 0.018 0. 125 0.082 0.062 0.000 0.000 0.000 0.000 0.063 0.063 0. 125 0. 125 R 2 1 1 0 0 0 0 1 1 2 2 0.020 - EX4 BHK EX20 IDIO ID5 ID3 CPROB ID2 IDI IDO KRIGE A 0.026 0.027 0.027 0.027 0.027 0.027 0.027 0.028 0.028 0.028 0. 028 0.037 0.000 0.000 0.000 0.000 0.000 0.000 0.037 0.037 0.037 0.037 0 1 0 0 0 0 0 0 1 1 1 1 0.035 _ ID5 ID3 ID2 IDI KRIGE BHK EX4 EX20 IDIO IDO CPROB E 0.041 a 04i 0.041 a 041 0.041 0.042 0.042 0.042 a 042 0.042 0.042 0.024 0.024 0.024 0.024 0.024 0.000 0.000 0.000 0.000 0.000 0.000 1 1 1 1 1 0 0 0 0 0 0 0.050 _ IDO IDI BHX KRIGE ID2 CPROB ID3 105 EX20 IDIO EX4 0.077 0.078 0.080 0.080 0.081 0.082 0.083 0.089 0.096 a 096 0.098 0.037 0.025 0. 000 0.000 0.012 0.025 0.038 a 113 0.200 0. 200 0.225 3 2 0 0 1 2 3 4 5 5 6 CUT-OFF IMFRFCTIMATFn . . e m n ... rM-M-m IM0TFT1. 0.000 _ ID1 IDO KRIGE ID2 ID3 CPROB ID5 BHK IDIO EX20 EX4 METHOD 0 0 4 23 59 125 146 IBS 262 480 561 OUNCES 1.000 1.000 0.980 0.875 0. 682 0.323 0.207 0.000 0.420 1.602 2.041 X ERROR 7 7 6 5 4 2 1 0 3 8 9 RANK 0. 010 _ 100 IDI KRIGE 102 ID3 BHX 105 CPROB 1010 EX4 EX20 0 1072 1219 1500 1632 1949 2012 2386 2406 2580 2672 2837 0.467 0.394 0.254 a 189 0.032 0.000 0. 186 0. 196 0.282 0.328 0. 410 U 10 8 5 3 1 0 2 4 6 7 9 0.020 - EX4 EX20 ID10 BHK CPROB ID5 103 102 IDO IDI KRIGE N 5B48 6500 7472 7488 7535 8174 8882 9050 9371 9386 9654 0.219 0. 132 0.002 0.000 0.006 0.092 a 186 0.209 0.251 0.254 0.289 C 7 4 1 0 2 3 5 6 8 9 10 0.035 _ EX4 EX20 ID10 105 BHX CPROB ID3 KRIGE ID2 IDI IDO E 4394 4771 5414 5931 5952 6146 6572 7531 7634 8630 9309 0.262 0. 198 0.090 0. 004 0.000 0. 033 0. 104 0. 265 0.283 0.450 0.564 S 6 5 3 1 0 2 4 7 8 9 10 0.050 _ IDO KRIGE ID1 ID2 1D3 ID5 EX20 1D10 CPROB EX4 BHX 10486 10834 10853 11473 12069 12494 12615 13063 13312 13732 14700 0.287 0. 2G3 0.282 0. 219 0. 179 0. 150 0. 142 0. Ill 0.094 0. 066 0.000 10 9 8 7 S 5 4 3 2 1 0 VD o T A B L E IX COMPARISON OF BLASTHOLE INDICATED RESERVES WITHIN GRADE CATEGORIES VS. RESERVES CALCULATED BY EACH EXPLORATION METHOD FOR BUCK60 BLOCK MODEL (GO FOOT BLOCKS. NO ORE OUTLINE). CUT-OFF UNDERESTIMATED... ACTUAL ... OVERESTIMATED. 0.000 - IDO IDI KRIGE BHX ID2 CPROB ID3 EXGO 105 IDIO EX4 METHOD 156. 1 169 7 202. 0 222. 7 243.3 275. 1 294.5 309.5 343. 1 395.8 450. 3 _ TONS (X 1000) 0.299 0.238 0.093 0.000 0.092 0.235 0.322 0.390 0.540 0.777 1.022 X ERROR T 5 4 2 0 1 3 6 7 8 9 10 RANK a oio - EX4 BHK IDIO 105 103 ID2 EXGO CPROB KRIGE IDO IDI 0 215 6 232.5 234.3 245.7 272. 4 294.4 302.3 307.2 321.5 332.2 338.6 a 072 0.000 0.008 0.057 0. 172 0.267 0. 300 0.322 0.383 a 429 a 456 N 3 0 1 2 4 5 6 7 8 9 10 0.020 - EX4 EXGO IDIO CPROB ID5 ID3 BHK KRIGE 102 IDI 100 N 232. 1 285.2 292.6 295.8 315.7 345.9 355.4 357.5 368. 1 372. 8 399.3 a 347 0. 198 0. 177 0. 168 a 112 0.027 0.000 0.006 0.036 0.049 0. 123 A 10 9 8 7 5 2 0 1 3 4 6 a 035 - EX4 102 ID3 IDIO EXGO CPROB 105 100 IDI KRIGE BHX G 110.6 113.5 114.9 122.7 136.0 138.6 140.9 142.9 151.8 173.8 178.9 a 382 a 365 a 357 a 314 0.240 0.225 0.212 0.201 0. 152 a 028 0.000 E 10 9 8 7 6 5 4 3 2 1 0 a 050 _ KRIGE IDIO IDS EX60 IDI 100 ID3 ID2 CPROB EX4 BHK 100.3 109.7 109. 7 122. 1 122.2 124.6 127.4 135.7 138 3 146.5 165.6 0.384 0.337 0.337 0. 263 0.262 0.248 0.231 0. 181 0. 165 0. 115 0.000 9 8 8 7 6 5 4 3 2 1 0 CUT-OFF ItOUFSTIMATFTL . . flrnm . . . (^RFCTIMATFTI. 0.000 - EX4 BHK EXGO IDIO IDS ID3 102 101 KRIGE CPROB IDO METHOD 0.004 0.005 0.005 0.005 0.006 0. 006 0.006 0.006 0.006 0.006 a 007 _ GRADE (OPT. ) 0.200 0.000 0.000 0.000 0.200 0.200 0. 200 0.200 0.200 0.200 o. 400 X ERROR 1 0 0 0 1 1 1 1 1 1 2 RANK a oio - EX4 105 ID3 102 IDI BHK EX60 IDIO IDO KRIGE CPROB G 0.014 a 014 a 014 0.014 0.014 0.015 0.015 0.015 a 015 a 015 0.015 0.067 0.067 0.067 0.067 0.067 0.000 0.000 0.000 0.000 0.000 0.000 R 1 1 1 1 1 0 0 0 0 0 0 0.020 _ EX4 IDIO 105 KRIGE BHK EX60 ID3 102 101 100 CPROB A a 026 0.026 0.026 0.026 0.027 0.027 0.027 0.027 0.027 0.027 0.027 0.037 0.037 0.037 0.037 0.000 0.000 0.000 0.000 0.000 0.000 0.000 D 1 1 1 1 0 0 0 0 0 0 0 0.035 - IDS 102 BHX EX4 EX60 IDIO ID3 IDI IDO KRIGE CPROB E 0.041 0.041 0.042 0.042 0.042 0.042 0.042 0.042 0.042 0.042 0.042 0. 024 0.024 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1 1 0 0 0 0 0 0 0 0 0 0. 050 _ ID2 BHK IDI IDO 103 CPROB KRIGE EXGO IDS IDIO EX4 0.076 0.077 0.077 a 078 0.080 0.081 0.083 0.088 0.088 0.092 0.097 0.013 0.000 0.000 0.013 0.039 0.052 0.078 0. 143 0. 143 0. 195 0. 260 1 0 0 1 2 3 4 5 5 6 7 CUT-OFF IM5HESTIMATFJ1.. ACTUAL ... nVFKESTIMATFTl 0. 000 _ 100 IDI BHK KRIGE CPROB EX60 ID2 ID3 105 EX4 IDIO METHOD 1066 1076 1156 1269 1518 1545 1571 1795 1923 2023 2091 OUNCES 0.078 0.069 0.000 0.098 0. 313 0.336 0. 359 0.553 0.664 0.750 0.809 X ERROR 2 1 0 3 4 5 6 7 8 9 10 RANK a oio _ EX4 IDIO 105 BH( ID3 ID2 EX60 CPROB KRIGE IDI IDO 0 3088 3403 3487 3501 3937 4191 4442 4546 4749 4906 4944 0. 118 0. 028 0.004 0.000 0. 125 0. 197 0.269 0. 299 0.356 0.401 0.412 U 3 2 1 0 4 5 6 7 8 9 10 0.020 _ EX4 EX60 IDIO CPROB IDS 103 KRIGE BHK ID2 IDI IDO N 6132 7642 7677 7883 8182 9169 9273 9607 9902 9973 10789 0.362 0.204 0.201 0. 179 0.148 0.046 0.035 0.000 0.031 0. 038 0. 123 C 10 9 8 7 6 4 2 0 1 3 0.035 _ EX4 102 103 IDIO EX60 CPROB IDS IDO 101 KRIGE BHK E 4595 4626 4776 5172 5728 5768 5793 6053 6355 7286 7513 0.388 0.384 0.364 0.312 0.238 0.232 0.229 0. 194 0: 154 0.030 0.000 S 10 9 8 7 6 5 4 3 2 1 0 0.050 - KRIGE IDI IDO IDS IDIO 103 ID2 EX60 CPROB BHK EX4 8327 9372 9664 9680 10106 10243 10363 10717 11188 12683 14236 0. 343 0.261 0. 238 0.237 0.203 0. 192 0. 183 0. 155 0. 118 0. ono 0. 122 10 9 8 7 6 5 4 3 1 0 2 VO T A B L E X COMPARISON OF BLASTHOLE INDICATED RESERVES WITHIN GRADE CATEGORIES VS. RESERVES CALCULATED BY EACH EXPLORATION METHOD FOR BUCKGOG BLOCK MODEL (60 FOOT BLOCKS. WITHIN ORE OUTLINE). CUT-OFF UNDERESTIMATED... ACTUAL ... OVERESTIMATED. 0.000 - 101 IDO KRIGE 102 CPROB BHK 103 EX60 IDS IDIO EX4 METHOD 0.0 0.0 0.0 as 10. 1 21.2 21.8 25.0 31.2 38.3 101.9 TONS (X 10001 1. 000 1.000 1.000 0.601 0.522 0.000 0.028 0. 178 0.467 ft 805 3.600 X ERROR T 7 7 7 5 4 0 1 2 3 6 8 RANK 0.010 - IDO IDI KRIGE BHK 102 103 IDS CPROB IDIO EX4 EXEO 0 54.9 58.5 87.2 sa 6 92 1 101.8 12a 9 145. 3 167.3 isa 4 191.4 0.381 0.340 0.016 0.000 0.040 0. 149 0.466 0.640 0.889 1. 104 1. 160 N 5 4 1 0 2 3 6 7 8 9 10 0.020 - EX4 EXEO CPROB BHK 1010 ID5 IDO 102 KRIGE 103 IDI N 221.8 276 5 293.6 soas 311.8 323.6 34a 2 350.0 357.0 357. 1 365. 1 0.282 0. 104 0.049 0.000 0.010 0.048 0. 121 0. 133 0. 156 0. 156 0. 182 A 10 4 3 0 1 2 5 6 7 8 9 a 035 - EX4 IDIO ID3 EXEO 105 ID2 CPROB BHK 101 KRIGE IDO G 105.5 na9 138.9 142 4 150.2 15a 0 isa 8 162 2 192 5 193.0 2225 0.350 0.261 0. 143 a 122 a 074 0.026 0.015 0.000 0. 187 0. 189 0.372 E 9 8 5 4 3 2 1 0 6 7 10 0.050 - IDIO KRIGE EXEC 105 IDO ID3 101 EX4 CPROB 102 BHK 11&7 119.0 120.7 121.3 132 5 136.4 140. 1 140.5 147.2 147.6 175.3 a 323 a 321 0.312 0.308 0.244 0.222 a 201 0. 198 0. 160 a 158 0.000 10 9 8 7 6 5 4 3 2 1 0 CUT-OFF 1 M T P F S T I M B T F I 1 . . i o n . . . rrm!F<rriMOTFn 0.000 - 101 IDO KRIGE EX4 IDIO BHK ID5 EXEO ID3 ID2 CPROB METHOD 0.000 0.000 0.000 0.006 0.006 ft 007 0.007 0.008 0.008 0.009 0. 009 GRADE (OPT. ) 1.000 1.000 1.000 0. 143 0. 143 0.000 0.000 0. 143 0. 143 0.286 0.286 X ERROR 3 3 3 1 1 0 0 1 1 2 2 RANK a oio - EX4 EX60 BHK IDIO ID5 CPROB ID3 102 IDI IDO KRIGE 6 a 014 0.015 0.016 0.016 ft 016 0.016 ft 017 a 017 ft 017 0 017 0 017 0. 125 0.062 0.000 0.000 0.000 0.000 0.063 0.063 0.063 0.063 0.063 R 2 1 0 0 0 0 I 1 1 1 1 a 020 - EX4 IDIO ID5 BHK EXEO 103 CPROB ID2 IDI IDO KRIGE A 0.026 0.026 0.026 0.027 0.027 0.027 0.027 ft 028 0. 028 0.028 0.028 0.037 a 037 0.037 0.000 0.000 0.000 0.000 0.037 0.037 0.037 0.037 D 1 1 1 0 0 0 0 1 1 1 1 0.035 - 102 ID5 103 ID1 KRIGE CPROB BHK EX4 EXEO IDIO IDO E 0.040 a 041 a 041 0.041 0.041 0.041 0.042 0.042 0.042 0.042 0.042 0.048 0.024 0.024 0.024 0.024 0.024 0.000 0.000 0.000 0. 000 0.000 2 1 1 1 1 1 0 0 0 0 0 a 050 - BHK 102 IDI IDO KRIGE 103 CPROB IDS EX60 IDIO EX4 ft 076 0.077 0.077 0.079 0.080 ft 081 0.081 a 086 0.089 0. 090 0.09B 0.000 0.013 0.013 0. 039 0.053 0.066 0.066 0. 132 0. 171 0. 184 0. 289 0 1 1 2 3 4 4 5 6 7 8 CUT-OFF I t m S F T T T M A T F T L . . n r n m . . . n v F R p r r i M O T F n 0.000 - ID1 100 KRIGE 102 CPROB BHK ID3 EX60 IDS IDIO EX4 _ METHOD 0 0 0 78 89 142 166 197 219 232 561 OUNCES 1.000 1.000 1.000 0.451 0.373 0.000 0. 175 0.389 0.547 0.642 2964 X ERROR 7 7 7 4 2 0 1 3 5 6 8 RANK a oio - IDO 101 BHK KRIGE ID2 103 IDS CPROB 1010 EX4 EXEO 0 959 988 1434 1483 1532 1683 2124 2307 2601 2672 2918 0. 331 0.311 0.000 0.034 0.068 0. 174 0.481 0.609 0.814 0. 863 1.035 U 5 4 0 1 2 3 6 7 8 9 10 0.020 - EX4 EX60 CPROB IDIO BHK 105 102 IDO ID3 KRIGE IDI N 5848 7434 7959 8256 839G 8574 9680 9758 9772 9858 10190 0.304 0. 115 0.052 0.017 0.000 0.021 0. 153 0. 162 0. 164 0. 174 0.214 C 10 4 3 1 0 2 5 E 7 8 9 0.035 - EX4 IDIO ID3 EXEO IDS ID2 CPROB BHK IDI KRIGE IDO E 4394 5028 5761 5955 6163 6354 6624 6859 7929 7955 9353 0.359 0.267 0. 160 0. 132 0. 101 0.074 0. 034 0.000 0. 156 0. 160 0. 364 S 9 8 7 4 3 2 I 0 5 6 10 0.050 - KRIGE 105 IDO IDIO EX60 101 103 102 CPROB BHK EX4 9541 10434 10466 10636 10702 10752 11000 11375 11857 13352 13732 0.285 0.219 0.216 0. 203 0. 198 0. 195 0. 176 0. 148 0. 112 0.000 0.028 10 9 8 7 6 5 4 3 2 0 1 LO to g r a d e , b l a s t h o l e k r i g e d e s t i m a t e s are what i s r e f e r r e d to as " a c t u a l " i n the c h a r t s . The b e s t way o f e v a l u a t i n g how w e l l a method works i s to s e l e c t one t h a t does a good j o b o f p r e d i c t i n g i n a p a r t i c u l a r grade r a n g e , and then t o f o l l o w j u s t t h a t one method t h r o u g h the o t h e r grade r a n g e s . U s u a l l y i t i s bes t t o s t a r t w i t h the t o t a l ounces p o r t i o n o f the c h a r t ( s i n c e t h a t ' s the most i m p o r t a n t i tem t h a t s h o u l d be p r e d i c t e d c o r r e c t l y ) , and then a f t e r c h e c k i n g how w e l l t h e method behaves i n o t h e r grade r a n g e s , l o o k t o tonnage and grade p o r t i o n s o f the t a b l e t o see i f the p a t t e r n i s c o n s i s t e n t t h e r e . As an example , r e f e r t o T a b l e V I I I where the e x p l o r a t i o n p o l y g o n a l e s t i m a t e (EX4) i s the b e s t e s t i m a t e o f t o t a l ounces over a c u t o f f o f 0.050 w i t h o n l y a 6.6% e r r o r i n the e s t i m a t e . C o n d i t i o n a l p r o b a b i l i t y i s second w i t h a 9.4% e r r o r . L o o k i n g back up the ounces p o r t i o n o f the c h a r t , EX4 as an e s t i m a t e l o s e s i t s a p p e a l a b r u p t l y . I t s rank drops t o 6 t h , 7 t h , 7 t h , and 9 t h , and t h e average p e r c e n t e r r o r goes from 26.2%, t o 21.9%, 32.8% and then f i n a l l y t o 204%. Why does EX4 do so w e l l i n p r e d i c t i n g t o t a l ounces over 0.05 o p t . ? L o o k i n g back t o grades and tonnages , the answer i s o b v i o u s . EX4 makes the wors t e s t i m a t e o f g r a d e , o v e r e s t i m a t i n g by 22.5% and i t a l s o makes a bad e s t i m a t e on tonnage . T o g e t h e r , t h i s c o m b i n a t i o n o f tonnage and o v e r e s t i m a t e d grade manage t o come out r e a s o n a b l y c l o s e i n the p r e d i c t i o n o f a c t u a l ounces above the 0.050 o p t . c u t o f f . The c h a r t sugges t s t h a t the e x p l o r a t i o n p o l y g o n a l e s t i m a t e s h o u l d not become t h e method o f c h o i c e . C o n d i t i o n a l p r o b a b i l i t y on the o t h e r h a n d , ranked second i n the i n i t i a l c o m p a r i s o n , then 2nd i n most o t h e r ranges w i t h e r r o r s o f 9.4%, 10.4%, 0.6%, 19.6% and t h e n 32.3% (the h i g h e r r o r s i n the lowes t c a t e g o r y a r e due t o the f a c t t h a t t h e r e a r e a c t u a l l y v e r y few ounces o f g o l d — p r e d i c t i n g even 50 ounces more or l e s s i n the l owes t grade range g i v e s a 27% e r r o r ) . C a r e f u l e x a m i n a t i o n o f the c h a r t shows t h a t no o t h e r method c o n s i s t e n t l y ou tper forms c o n d i t i o n a l p r o b a b i l i t y i n any o f the comparisons ( t o n s , g r a d e , o r o u n c e s ) , and" t h a t t h e r e i s no way o f p r e d i c t i n g which method(s) w i l l do b e t t e r i n any g i v e n grade r a n g e . O v e r a l l , the se c h a r t s show the f u l l d e t a i l o f a l l ore r e s e r v e s c a l c u l a t e d f o r t h i s s tudy and they can be r e f e r r e d to q u i c k l y f o r t h a t d e t a i l as f u r t h e r comparisons are made. 7.4 SUMMARY CHART AND RANKING OF RESULTS The l a s t c h a r t ( T a b l e XI) summarizes the i n f o r m a t i o n i n such a way t h a t c o n c l u s i o n s can be drawn about which methods are bes t and how they rank r e l a t i v e t o each o t h e r w i t h i n a mode l , as w e l l as a c r o s s mode l s . F o r each method, and f o r e v e r y mode l , the t a b u l a t i o n s c o n t a i n the average e r r o r made i n a l l o f the grade c a t e g o r i e s f o r t o n s , grade and ounces , and then the average o f the ranks t h a t were a s s i g n e d from the o r e r e s e r v e c h a r t s . The l o w e s t grade range wasn ' t used because , as was seen e a r l i e r , l a r g e p e r c e n t a g e e r r o r s o c c u r r e d here i n some o f the models which were due o n l y t o the s m a l l amount o f m e t a l a c t u a l l y c o n t a i n e d i n the waste c a t e g o r y . The f i n a l s c o r e i s d e r i v e d by a d d i n g the 3 average r a n k s . T h i s may not be a p e r f e c t way t o rank the methods 95 TABLE XI SUMMARY COMPARISON OF ORE RESERVE METHODS BUCK BLOCK MODEL AVERAGE % ERROR TONS - GRADE - OUNCES - AVERAGE RANK TONS - GRADE - OUNCES - EX4 EX20 21.7 17.8 7.9 5.0 19.3 15.7 EX4 EX20 6.50 5.50 2.25 1.50 6.75 5.25 IDIO 14.5 6.4 12.9 IDIO 4.25 1.50 4.50 ID5 ID3 ID2 IDI IDO KRIG CPROB 14.1 15.2 15.6 19.4 21.5 18.8 16.1 3.7 1.8 1.2 1.2 1.3 1.2 1.9 11.4 13.2 14.5 18.4 22.1 18.0 14.2 ID5 ID3 ID2 IDI IDO KRIG CPROB 4.00 4.50 5.00 6.25 7.50 6.50 5.00 1.25 0.75 0.50 0.50 0.50 0.50 0.75 3.50 4.25 4.75 5.75 7.50 5.75 5.25 TOTAL RANK 15.50 12.25 10.25 8.75 9.50 10.25 12.50 15.50 12.75 11.00 FINAL RANK 9 6 3 1 2 3 7 9 8 5 BUCKG BLOCK MODEL AVERAGE % ERROR TONS - GRADE - OUNCES - EX4 29.7 9.7 21.9 EX20 28.8 6.6 22.1 IDIO 18.1 6.6 12.2 ID5 13.3 3.4 10.8 ID3 13.7 1.5 12.5 ID2 23.7 3.4 22.5 IDI 34.4 5.3 34.0 IDO 38.8 5.0 39.2 KRIG 27.8 3.1 26.8 CPROB 9.5 0.6 8.2 AVERAGE RANK TONS -GRADE -OUNCES - EX4 6.25 2.25 5.25 EX20 7.25 1.50 5.50 IDIO 4.50 1.50 3.25 ID5 2.75 1.25 2.75 ID3 3.00 1.00 4.00 ID2 5.25 1.00 6.00 IDI 7.75 1.50 8.50 IDO 8.75 1.50 9.50 KRIG 7.75 0.75 7.75 CPROB 1.75 0.50 2.50 TOTAL RANK 13.75 14.25 9.25 6.75 8.00 12.25 17.75 19.75 16.25 4.75 FINAL RANK 6 7 4 2 3 5 9 10 8 1 AVERAGE % ERROR TONS GRADE OUNCES AVERAGE RANK TONS GRADE OUNCES BUCK60 BLOCK MODEL EX4 22.9 9.1 24.8 EX60 25.0 3.6 21.6 EX4 EX60 6.00 7.00 2.25 1.25 6.25 6.00 IDIO 10.9 5.8 18.6 IDIO 6.00 1.75 5.75 ID5 18.0 6.8 15.4 ID5 4.75 2.00 4.50 ID3 19.7 2.6 18.2 ID3 4.50 0.75 5.25 ID2 21.2 2.6 19.9 ID2 5.00 0.75 4.75 IDI 23.0 1.7 21.4 IDI 5.50 0.25 5.75 IDO 25.0 0.3 24.2 IDO 5. 75 0.25 6.50 KRIG 20.3 2.9 19.1 CPROB 22.0 1.3 20.7 KRIG CPROB 4.75 5.25 1.25 0.75 5.25 5.00 TOTAL RANK 14.50 14.25 13.50 11.25 10.50 10.50 11.50 12.50 11.25 11.00 FINAL RANK 10 9 8 4 1 1 6 7 4 3 AVERAGE % ERROR TONS GRADE OUNCES AVERAGE RANK TONS GRADE OUNCES TOTAL RANK FINAL RANK BUCK60G BLOCK MODEL EX4 48.3 11.3 38.9 EX60 42.5 5.8 37.0 EX4 EX60 7.75 6.50 2.75 1.75 7.25 6.00 IDIO 37.0 5.5 32.5 IDIO 6.75 2.00 6.00 ID5 22.4 4.8 20.6 ID5 4.50 1.75 5.00 ID3 16.8 3.8 16.8 ID3 5.25 1.50 5.25 ID2 8.9 4.0 11.1 ID2 2.75 1.25 3.00 IDI 22.7 3.4 21.9 IDI 5.75 1.00 5.75 IDO 28.0 3.5 26.8 IDO 6.50 1.00 7.25 KRIG 17.1 4.4 16.3 KRIG 6.00 1.50 6.25 CPROB 21.6 2.2 20.2 CPROB 3.25 1.25 3.25 17.75 14.25 14.75 11.25 12.00 7.00 12.50 14.75 13.75 7.75 10 7 8 3 4 1 5 8 6 2 because much o f the d e t a i l i s o b l i t e r a t e d , but i t adequate ly s i m p l i f i e s the p r o c e s s o f d e c i d i n g which a r e the b e s t 2 or 3 methods , and t h e n the f u l l d e t a i l c h a r t s ( T a b l e s V I I , v i i i , i x and X) and the m e t a l graphs ( F i g s . 19, 20, 21 and 22) can be r e f e r r e d t o when a s s e s s i n g the r e l i a b i l i t y o f the r a n k i n g shown. T a b l e XI shows t h a t the b e s t b l o c k models t o use are the BUCKG and BUCK60G, u s i n g o n l y 20' compos i tes t h a t f a l l i n s i d e o f the o r e zone o u t l i n e , and t h a t the b e s t method f o r c a l c u l a t i n g r e s e r v e s i s c o n d i t i o n a l p r o b a b i l i t y . T h i s c a l c u l a t i o n ranks f i r s t o r second i n these two mode l s , w i t h o n l y ID2 showing s i m i l a r r e s u l t s i n the case o f the BUCK60G m o d e l . C l o s e r e x a m i n a t i o n r e v e a l s t h a t b o t h ID2 and c o n d i t i o n a l p r o b a b i l i t y p e r f o r m w e l l i n the l a t t e r model ; w h i l e t h e i r f i n a l t o t a l ranks a r e s i m i l a r and l e s s than 8 . 0 , no o t h e r method's f i n a l rank i s l e s s than 1 1 . 0 . On a v e r a g e , f o r the 20' b l o c k model (BUCKG), c o n d i t i o n a l p r o b a b i l i t y makes e r r o r s o f 9.5%, 0.6%, and 8.2% on t o n s , grade and ounces r e s p e c t i v e l y , and f o r the 60' model (BUCK60G), 21.69%, 2.2%, and 20.2%. F u r t h e r m o r e , c o n d i t i o n a l p r o b a b i l i t y ranks c o n s i s t e n t l y w e l l i n a l l f o u r b l o c k mode l s , and a s e a r c h f o r n e a r e s t c o m p e t i t o r s shows t h a t t h e r e can be no way o f p r e d i c t i n g beforehand which one w i l l be b e s t . L o o k i n g at the f o u r b l o c k m o d e l s , the methods t h a t come c l o s e , o r even t h a t seem t o o u t p e r f o r m c o n d i t i o n a l p r o b a b i l i t y can be any o f the i n v e r s e d i s t a n c e methods — ID2 does w e l l f o r the 60" mode l s , and ID5 seems t o p e r f o r m w e l l f o r the 20' mode l s . N o t i c e a l s o t h a t f o r the 20' b l o c k mode l s , one o f the lowest o v e r a l l p e r c e n t e r r o r s i n grade e s t i m a t e a t t a i n e d by any method was ID3 on the BUCK b l o c k mode l . T h i s i s the o r i g i n a l i n v e r s e d i s t a n c e c u b e d , 20' b l o c k model w i t h no ore zone o u t l i n e t h a t i s used a t the mine . The o r i g i n a l "gut f e e l " t h a t t h i s method p r o v i d e d the b e s t r e s e r v e e s t i m a t e ( g i v e n the BUCK b l o c k model) was an e x c e l l e n t guess a t the t i m e . L a s t l y , n o t i c e a g a i n t h a t k r i g i n g , by i t s e l f , n e a r l y always p r o v i d e d one o f the worst ore r e s e r v e e s t i m a t e s a t Buckhorn . K r i g i n g a l o n e , w i t h o u t t a k i n g k r i g i n g v a r i a n c e i n t o account ( i . e . i g n o r i n g t h a t measure o f e r r o r t h a t i s supposed t o be k r i g i n g ' s g r e a t e s t s t r e n g t h ) i s j u s t another d i s t a n c e weighted a v e r a g i n g t e c h n i q u e whose performance r e l a t i v e t o any o t h e r e s t i m a t o r cannot be e v a l u a t e d i n advance o f h a v i n g the p r o d u c t i o n d a t a a v a i l a b l e . 7.5 EXAMINATION OF SCATTERGRAMS AND BENCH PLANS A l t h o u g h b o t h bench maps and s c a t t e r g r a m s showing the r e s u l t s have been d u t i f u l l y reproduced h e r e i n (Appendix B and F , r e s p e c t i v e l y ) , they r e a l l y o f f e r v e r y l i t t l e i n f o r m a t i o n from which u s e f u l c o n c l u s i o n s can be drawn. When one i s i n t e r e s t e d i n compar ing ore r e s e r v e e s t i m a t e s , s c a t t e r p l o t s i n p a r t i c u l a r , are n o t the b e s t method o f comparing the d a t a ( a c t u a l v s . p r e d i c t e d ) . In f a c t they can be c o m p l e t e l y d e c e i v i n g , o f t e n l u l l i n g one i n t o a f a l s e sense o f s e c u r i t y . Many p e o p l e p o i n t to the s c a t t e r g r a m which shows the l e a s t amount o f s c a t t e r and , s o l e l y on t h a t b a s i s , use t h i s p l o t t o j u s t i f y t h e i r c h o i c e o f one method over a n o t h e r . T h i s r e a s o n i n g however, i s f lawed i n t h a t t h e r e are two t h i n g s t h a t a r e v i s u a l l y d i s c e r n a b l e on a s c a t t e r g r a m which are 98 independent o f each o t h e r . One i s the amount o f s c a t t e r i n g (a c r u d e v i s u a l a p p r a i s a l o f e r r o r s a s s o c i a t e d w i t h an e s t i m a t e ) , and the o t h e r i s the average "goodness o f f i t " which i s an e v a l u a t i o n o f how c l o s e the s c a t t e r can be m o d e l l e d by the 4 5 ° l i n e which passes from the o r i g i n (0 ,0) t h r o u g h i n t e r s e c t i o n s o f e q u a l grade on the g r a p h . The o n l y p l o t s t h a t can be compared m e a n i n g f u l l y t o each o t h e r a r e those which show i d e n t i c a l s c a t t e r i n g (hard to measure ) , i n which case the graph t h a t shows t h e l e a s t amount o f d e v i a t i o n from the 4 5 ° s l o p e i s b e s t , or e l s e two s c a t t e r s drawn from the same b l o c k model t h a t show i d e n t i c a l s l o p e s can be compared t o see which p r o v i d e s the l e a s t amount o f e r r o r a s s o c i a t e d w i t h the e s t i m a t i o n o f the b l o c k g r a d e s , i n which case the method p r o v i d i n g the l e a s t s c a t t e r i s the one to choose . In f a c t , t aken t o the extreme, i f the o n l y measurement o f impor tance was the v i s u a l amount o f s c a t t e r , the b e s t e s t i m a t e would be one where the p r e d i c t e d grade was c o n s t a n t (any c o n s t a n t ) s i n c e then a p l o t o f a c t u a l v e r s u s p r e d i c t e d grades would appear t o show z e r o " s c a t t e r i n g " . What s c a t t e r g r a m s do show i s the d i f f e r e n c e s i n the c o n d i t i o n a l d i s t r i b u t i o n s f o r every method. Any h o r i z o n t a l l i n e on the s c a t t e r g r a m s shown i n Appendix F i s r e p r e s e n t a t i v e o f the c o n d i t i o n a l d i s t r i b u t i o n a t t h a t expected g r a d e , f o r t h a t p a r t i c u l a r e s t i m a t o r — f o r any g i v e n p r e d i c t e d grade t h e r e i s a s c a t t e r o f a c t u a l grades around i t . F o r any grade e s t i m a t e t h a t i n d i c a t e s t h a t the b l o c k i s waste , t h e r e i s some p e r c e n t a g e o f b l o c k s t h a t a r e a c t u a l l y o r e . I f one c o u l d see e v e r y i n d i v i d u a l p o i n t on the s c a t t e r , i t would be p o s s i b l e t o de termine the p e r c e n t a g e o f b l o c k s t h a t a r e u n d e r e s t i m a t e d a t t h a t g r a d e . Were 99 any o f t h e s e d i s t r i b u t i o n s t o be n u m e r i c a l l y m o d e l l e d , they might do as good a j o b as k r i g i n g d i d i n the c a l c u l a t i o n o f c o n d i t i o n a l p r o b a b i l i t i e s a t B u c k h o r n . But t h i s i s o n l y because t h e r e i s a s q u a r e d r i l l i n g p a t t e r n . A l s o , none o f the o t h e r methods p r o v i d e any way o f c a l c u l a t i n g a c o n d i t i o n a l d i s t r i b u t i o n w i t h o u t the p r e s e n c e o f a v a s t amount o f p r o d u c t i o n d a t a . K r i g i n g , o f c o u r s e , can p r o v i d e t h i s e s t i m a t e o f c o n d i t i o n a l e x p e c t a t i o n s b e f o r e p r o d u c t i o n s t a r t s and , e s p e c i a l l y when d r i l l i n g i s e i t h e r on an i r r e g u l a r g r i d , or when d r i l l h o l e s a r e c l u s t e r e d , k r i g i n g has numerous o t h e r advantages t h a t do i n f a c t make i t "the bes t l i n e a r u n b i a s e d " e s t i m a t e . The s c a t t e r g r a m s i n Appendix F , t h e r e f o r e d o n ' t show a n y t h i n g s u r p r i s i n g . S i x t y f o o t b l o c k models show l e s s s c a t t e r than 20' b l o c k models because the p r e d i c t e d grades are more smoothed than f o r 20 1 b l o c k s and t h e r e f o r e e s t i m a t e d grades f o r 60' b l o c k s c a n ' t r e a c h the same extremes as the e s t i m a t e s t o 20' b l o c k s . F o r the same r e a s o n , p o l y g o n a l and IDIO e s t i m a t e s show more s c a t t e r t h a n IDI and IDO. The k r i g e d e s t i m a t e s a t Buckhorn tend t o be s i m i l a r to the ID2 or IDI e s t i m a t e s and t h e r e f o r e a l s o show l e s s s c a t t e r i n g than o t h e r methods. The IDO e s t i m a t e appears t o show the l e a s t s c a t t e r . On the o t h e r hand , the s l o p e s o f the v a r i o u s b e s t f i t l i n e s v a r y . IDIO and p o l y g o n a l e s t i m a t e s come c l o s e r t o 4 5 ° s l o p e s but show more s c a t t e r than k r i g e d and IDI e s t i m a t e s , w h i l e the k r i g e d and IDI e s t i m a t e s s e r i o u s l y d e p a r t from the 4 5 ° l i n e i n the h i g h e r grade r a n g e s . The bench p l a n s are a l i t t l e b e t t e r , but a g a i n they p r o v i d e o n l y a c r u d e v i s u a l e s t i m a t e o f which method i s the b e s t one to u s e . A l l methods show t h e i r h i g h e s t grades i n the same p l a c e s 100 s i n c e every e s t i m a t e was d e r i v e d from the same 10 o r 12 n e a r e s t e x p l o r a t i o n c o m p o s i t e s . A l l methods missed some areas o f h i g h e r grade and a l l methods f a i l e d t o p r e d i c t some low grade areas f o r the same reasons — the n e a r e s t compos i tes f a i l e d t o show lows or h i g h s i n t h o s e areas because o f the l a r g e d r i l l h o l e s p a c i n g . T h e r e f o r e the o n l y t h i n g t h a t can be compared i n a v e r y i m p r e c i s e way i s the g e n e r a l shape ( w i d t h , l e n g t h and o r i e n t a t i o n ) o f those l a r g e r areas where b l a s t h o l e d a t a c o n f i r m e d the p r e s e n c e o f o r e . T h i s i s no t t o say t h a t maps and s c a t t e r g r a m s a r e u s e l e s s , but v i s u a l methods are not p r e c i s e and t h e r e f o r e are i n a p p r o p r i a t e f o r making the types o f d e t a i l e d compar isons o f ore r e s e r v e e s t i m a t e s based on e x p l o r a t i o n d r i l l i n g which are made h e r e . S c a t t e r g r a m s , i n p a r t i c u l a r , s h o u l d no t be used t o j u s t i f y c h o i c e o f a method on the b a s i s o f a l e s s e r amount o f s c a t t e r a l o n e . B o t h maps and s c a t t e r p l o t s s h o u l d be produced t o g i v e the a n a l y s t p i c t u r e s which he can keep i n mind throughout the s tudy t o h e l p v i s u a l i z e p o s s i b l e outcomes and as se s s r e s u l t s f o r i n d i c a t i o n s o f g r o s s e r r o r . F i g u r e 18 ( c h a p t e r 6) shows a more comprehens ive type o f compar i son t h a t can be used f o r e i t h e r back a n a l y s i s , or f o r e v a l u a t i n g the d i f f e r e n t e s t i m a t e s v e r s u s " a c t u a l " . The ore r e s e r v e c h a r t s shown e a r l i e r ( T a b l e s V I I , V I I I , IX and X) a l s o p r o v i d e a b e t t e r compar i son o f r e s e r v e e s t i m a t e s because they show t h e o v e r a l l d i s t r i b u t i o n o f b l o c k g r a d e s , which i n t u r n p r o v i d e s a d i f f e r e n t p e r s p e c t i v e t h a n the s i m p l e b l o c k - b y - b l o c k v i s u a l compar i son a f f o r d e d by the s c a t t e r p l o t s . These c h a r t s a l s o show v i s u a l l y , and q u a n t i t a t i v e l y , which methods are under o r o v e r e s t i m a t i n g i n the i m p o r t a n t o r e grade r a n g e s . F o r g l o b a l o r e r e s e r v e e s t i m a t e s , the most i m p o r t a n t t h i n g i s t o p r e d i c t the r i g h t d i s t r i b u t i o n o f b l o c k grades above any c u t o f f grade w i t h i n t h e d e s i g n e d open p i t . These numbers p r o v i d e the b a s i s o f economic c a l c u l a t i o n s which are used t o e v a l u a t e the d e p o s i t . T h i s g e n e r a l i d e a i s suppor ted by D a v i d ( 1 9 7 7 ) when he s a y s : "which s m a l l b l o c k s i n the l a r g e one are r e a l l y ore and which are r e a l l y waste i s t o t a l l y i r r e l e v a n t f o r monthly p l a n n i n g , l e s s t o say f o r q u a r t e r l y o r y e a r l y p l a n n i n g as l o n g as t h e i r percentages o f o c c u r r e n c e can be p r e d i c t e d . " 7.6 SIXTY FOOT V S . TWENTY FOOT ESTIMATES As s u s p e c t e d , the r e s e r v e s t a b u l a t e d from the 60' b l o c k models were lower t h a n from the 20' b l o c k mode l s . T h i s would be a c c e p t a b l e i f the m i n i n g method was o n l y c a p a b l e o f a 60' b l o c k s e l e c t i v i t y , but t h i s i s not the case a t B u c k h o r n . A l t h o u g h any i n d i v i d u a l 20' b l o c k cannot be expected t o be e x a c t l y c o r r e c t , the d i s t r i b u t i o n o f b l o c k grades f o r a m i n i n g method t h a t has a 20' s e l e c t i v i t y i s c o r r e c t and t h i s r e s u l t s i n h i g h e r ore r e s e r v e s b e i n g p r e d i c t e d . Not o n l y i s the grade d i s t r i b u t i o n c o r r e c t , but the l o c a t i o n o f t h e b l o c k s i s c o r r e c t on a v e r a g e . I n o t h e r words , i f one 60' b l o c k i s c a l c u l a t e d as waste , but one o f the n i n e c o n t a i n e d 20' b l o c k s i s p r e d i c t e d as o r e , g e n e r a l l y , the e x a c t p r e d i c t i o n t h a t the s m a l l b l o c k i s a c t u a l l y ore may be i n c o r r e c t , but t h e r e i s 102 p r o b a b l y a v a l i d e x p e c t a t i o n t h a t another c l o s e by b l o c k t h a t was p r e d i c t e d t o be waste may be o r e . In e f f e c t , the 20' b l o c k model becomes one r e a l i z a t i o n o f the p o s s i b l e a c t u a l geometry o f the orebody t h a t w i l l be mined , w i t h the f u r t h e r b e n e f i t o f h a v i n g the o r e b l o c k s i n g e n e r a l l y the r i g h t l o c a t i o n around e x p l o r a t i o n o r e i n t e r c e p t s . T h i s w i l l r e s u l t i n an open p i t d e s i g n t h a t i s more a c c u r a t e t h a n one d e s i g n e d on a 60' b l o c k model which i s r e p r e s e n t a t i v e o f the e x p l o r a t i o n d r i l l s p a c i n g . An e x a m i n a t i o n o f the s c a t t e r p l o t s (Appendix F) does show t h a t on a b l o c k by b l o c k b a s i s , 60' e s t i m a t e s have l e s s s c a t t e r when compar ing a c t u a l v e r s u s p r e d i c t e d g r a d e s , but t h i s a l s o i s e x p e c t e d . However, i t s h o u l d not be t a k e n t o mean t h a t the 60' b l o c k models s h o u l d be u s e d . 7.7 CONSTRAINED V S . UNCONSTRAINED ESTIMATES The compar isons and r a n k i n g shown e a r l i e r i n s e c t i o n s 7 . 2 , 7 . 3 , and 7.4 demonstrated t h a t those e s t i m a t e s t h a t were c o n s t r a i n e d by the ore zone o u t l i n e p r e d i c t e d b e t t e r (and h i g h e r ) ore r e s e r v e s t h a n d i d the o t h e r two e s t i m a t e s . A l t h o u g h the u n c o n s t r a i n e d e s t i m a t e s p r e d i c t e d a c o u p l e o f thousand more ounces o f g o l d above a zero c u t o f f , i n a l l cases they were unab le t o p r e d i c t any more ounces above the v e r y low 0.01 o p t . c u t o f f and i n the h i g h e r grade o r e c a t e g o r i e s , e v e r y u n c o n s t r a i n e d method o f o r e r e s e r v e c a l c u l a t i o n produced s i g n i f i c a n t l y l e s s ounces o f g o l d than the c o r r e s p o n d i n g c o n s t r a i n e d e s t i m a t e . T h i s 103 i s s i m p l y one m a n i f e s t a t i o n o f "smearing" o f grades t h a t has been no ted by a lmost anyone who has ever c a l c u l a t e d o r e r e s e r v e s . T h e r e was no rock type change o r change i n a l t e r a t i o n p a t t e r n t h a t c o u l d be imposed on the b l o c k model t o c o n s t r a i n the o r e r e s e r v e e s t i m a t e , but as was s t a t e d i n the i n t r o d u c t i o n , t h e r e i s a measurable and i d e n t i f i a b l e g e o l o g i c a l c o n t a c t t h a t can be drawn. As w i t h a l l changes i n rock t y p e , i t i s based on d i f f e r e n c e s i n the c h e m i c a l make-up o f the h o s t r o c k s i n t h a t t h e r e i s a g r e a t e r amount o f g o l d than n o r m a l l y would be expected i n the c o m p o s i t i o n o f the a l t e r e d v o l c a n i c s . T h i s i s a n u m e r i c a l l y d e f i n e d c o n t a c t between o r e zone and waste r o c k . Not a l l o f the m a t e r i a l i n s i d e the ore zone i s o r e as d e f i n e d by an e c o n o m i c a l l y d e r i v e d c u t o f f g r a d e , but a l l p o t e n t i a l ore o c c u r s w i t h i n t h i s o u t l i n e and a l l grades w i t h i n the o u t l i n e are r e l a t e d i n t h a t they b e l o n g to a d e f i n i t e p o p u l a t i o n o f grades which range from n e a r z e r o to v e r y h i g h , but which form a s i n g l e , v i a b l e l o g n o r m a l d i s t r i b u t i o n . A l l o f the t h e o r y which goes i n t o p r o d u c i n g a c o n d i t i o n a l d i s t r i b u t i o n o f grades r e l i e s upon assumpt ions o f g a u s s i a n d i s t r i b u t i o n o f the d a t a , and i m p o s i t i o n o f the o r e zone o u t l i n e p r o v i d e d a s e t o f v a l u e s which f u l f i l l e d t h i s r e q u i r e m e n t . 7 .8 USING CONDITIONAL PROBABILITY ESTIMATES H a v i n g come t o the c o n c l u s i o n t h a t the c o n d i t i o n a l p r o b a b i l i t y e s t i m a t e o f g l o b a l r e s e r v e s i s b e s t , the q u e s t i o n i s how t o use the e s t i m a t e s t h a t a r e produced? O f the f o u r b l o c k 104 mode l s , the b e s t one t o use a t Buckhorn i s the BUCKG 20' b l o c k model which was c o n s t r a i n e d by the o r e zone o u t l i n e . The f o l l o w i n g are the s t eps t h a t the author would use now, w i t h near p e r f e c t h i n d s i g h t , t o r e d e s i g n the open p i t , c a l c u l a t e g l o b a l ore r e s e r v e s , and then t o do d a i l y and monthly r e c o n c i l i a t i o n a t the mine: 1) K r i g e the e x p l o r a t i o n 20' compos i tes u s i n g the s u b s e t BEXG d a t a and the BUCKG b l o c k model ( t r y out the i d e a o f u s i n g 3 or 4 v a r i o g r a m s which r e f l e c t v a r i o u s maximum p a i r d i f f e r e n c e s ) . 2) C a l c u l a t e g l o b a l g e o l o g i c r e s e r v e s u s i n g c o n d i t i o n - a l p r o b a b i l i t y . 3) Produce i n v e r s e d i s t a n c e weighted e s t i m a t e s w i t h i n c r e a s i n g powers and choose the one which comes c l o s e s t i n g r a d e , tonnage and m e t a l above the mine d e s i g n c u t o f f grades t o the c o n d i t i o n a l p r o b a b i l i t y e s t i m a t e . In t h i s c a s e , i t would be e i t h e r the ID5 or ID3 e s t i m a t e . Both p r e d i c t v e r y c l o s e t o the same tonnage and grade as c o n d i t i o n a l p r o b a b i l i t y a t both the 0.020 o p t . , and the 0.035 o p t . c u t o f f s . The open p i t d e s i g n used 0.035 as the mine d e s i g n c u t o f f , but v a l u e d any b l o c k over 0.020 i n t o the economic c a l c u l a t i o n s which d e c i d e whether o r not a b l o c k would be m i n e d . J u s t l i k e c o n d i t i o n a l s i m u l a t i o n , these i n v e r s e d i s t a n c e b l o c k models w i l l come c l o s e t o b e i n g one p o s s i b l e g e o m e t r i c a l l y c o r r e c t r e a l i z a t i o n o f the p o s s i b l e shape o f the orebody g i v e n the e x p l o r a t i o n d a t a . J o u r n e l and H u i j b r e g t s (1978) s u p p o r t the i d e a t h a t one o f the t r a d i t i o n a l e s t i m a t o r s ( p o l y g o n a l , IDI o r ID2) w i l l be s i m i l a r to a "best" e s t i m a t e . "Depending on the nugget e f f e c t ( i . e . , the degree o f s p a t i a l c o r r e l a t i o n ) , one o r the o t h e r o f the t h r e e s t a n d a r d e s t i m a t o r s i s c l o s e enough t o the k r i g i n g optimum, but o n l y a s t r u c t u r a l a n a l y s i s , i . e . , a g e o s t a t i s t i c a l a p p r o a c h , can t e l l which i s the c l o s e s t " . 4) Assuming t h a t t h i s i s t r u e , d e s i g n the open p i t u s i n g b o t h the ID5 and ID3 b l o c k models (perhaps the ID4 model s h o u l d a l s o be c a l c u l a t e d i n t h i s case) w i t h a p p r o p r i a t e economic i n p u t d a t a ( p r i c e o f g o l d , c o s t t o mine o r e , c o s t t o mine waste , e t c . ) . 5) C a l c u l a t e r e s e r v e s u s i n g each method w i t h i n the r e s p e c t i v e open p i t o u t l i n e s . 6) C a l c u l a t e r e s e r v e s w i t h i n each p i t u s i n g the c o n d i t i o n a l p r o b a b i l i t y b l o c k v a l u e s f o r o r e f r a c t i o n s and grade above c u t o f f , and choose the p i t d e s i g n g e n e r a t e d by the i n v e r s e d i s t a n c e method whose c a l c u l a t e d r e s e r v e s most c l o s e l y matches the r e s e r v e s p r e d i c t e d by c o n d i t i o n a l p r o b a b i l i t y . R e p o r t t h e s e as m i n a b l e o r e r e s e r v e s . A f t e r t h i s compar i son has been made, a l l o f the i n v e r s e d i s t a n c e models s h o u l d be d i s c a r d e d because i t i s u n l i k e l y t h a t any b l o c k model w i l l g i v e p e r f e c t p r e d i c t i o n s o f i n d i v i d u a l b l o c k grades a t any exac t l o c a t i o n . T h e r e i s no need to a d j u s t f o r m i n i n g d i l u t i o n i n the r e s e r v e e s t i m a t e because , a l t h o u g h t h e r e w i l l be d i l u t i o n , t h e r e w i l l no t be any r e l i a b l e measure o f t h i s parameter l a t e r , and the t r u e e f f e c t o f m i n i n g d i l u t i o n w i l l p r o b a b l y be t o "lower" the p e r c e n t a g e o f g o l d r e c o v e r y r e p o r t e d from the l e a c h p a d s . 7) On a d a y - t o - d a y b a s i s , r e c o n c i l e the d a i l y p r o d u c t i o n e s t i m a t e w i t h i n the t o t a l b l a s t o u t l i n e (not i n d i v i d u a l b l o c k s ) to the c o n d i t i o n a l p r o b a b i l i t y e s t i m a t e . The b l a s t o u t l i n e s a t Buckhorn g e n e r a l l y c o n t a i n about 10-15,000 tons o f m a t e r i a l . T h i s s h o u l d p r o v i d e l a r g e enough volumes to p r o v i d e e x c e l l e n t r e c o n c i l i a t i o n . Any ore t h a t i s found o u t s i d e o f the o r i g i n a l e x p l o r a t i o n o r e zone o u t l i n e s h o u l d be t r e a t e d as "new" ore and s h o u l d no t be s u b t r a c t e d from e x p l o r a t i o n r e s e r v e s ( i n s t e a d i t s h o u l d be c u m u l a t i v e l y added t o i n i t i a l ore r e s e r v e s f o r the mine , and then s u b t r a c t e d t o r e p o r t r e m a i n i n g r e s e r v e s ) . 8) Produce monthly p r o d u c t i o n r e p o r t s . These would show f o u r major groups o f headings i n s t e a d o f j u s t two. They would be: 1) p r e d i c t e d tons and g r a d e ; 2) a c t u a l tons and g r a d e ; 3) c u m u l a t i v e e r r o r ( the d i f f e r e n c e t o d a t e between p r e d i c t e d and a c t u a l ) ; and 4) new o r e , no t p r e d i c t e d from e x p l o r a t i o n d r i l l i n g . Had these s t e p s been f o l l o w e d b e f o r e p r o d u c t i o n s t a r t e d i n 1984, the a u t h o r b e l i e v e s t h a t the r e s u l t s would have been e x c e l l e n t , and t h a t the economic c a l c u l a t i o n s performed f o r the f e a s i b i l i t y s t u d y would a l s o have been more a c c u r a t e . 107 8. CONCLUSIONS A l l o f the i n i t i a l q u e s t i o n s asked b e f o r e t h i s s tudy s t a r t e d have been a d e q u a t e l y answered. I t i s i m p o r t a n t t o choose a b l o c k s i z e which r e l a t e s t o m i n i n g s e l e c t i v i t y and not t o e x p l o r a t i o n d r i l l s p a c i n g . Ore zone o u t l i n e s , as c o n s t r u c t e d h e r e , shou ld be imposed on the d a t a and on the b l o c k models i f a t a l l p o s s i b l e , and t h i s a l o n e w i l l a l l e v i a t e the need f o r m o d e l l i n g o t h e r d i s t r i b u t i o n s l i k e the l e s s a c c u r a t e 3 -parameter l o g n o r m a l a p p r o x i m a t i o n o r u s i n g more complex e s t i m a t i o n methods l i k e m u l t i g a u s s i a n k r i g i n g . Some o f the v a r i o u s p o l y g o n a l or i n v e r s e d i s t a n c e ore b l o c k c a l c u l a t i o n s w i l l be f a i r l y a c c u r a t e - - the b e s t one may p r o v i d e a workable " r e a l i z a t i o n " o f the unknown t r u e shape and grade d i s t r i b u t i o n o f the o r e b o d y . However, w i t h o u t c a l c u l a t i n g a c o n d i t i o n a l p r o b a b i l i t y e s t i m a t e , t h e r e i s no way o f knowing beforehand which o f these e s t i m a t e s w i l l be n e a r e s t t o " a c t u a l " . The i n v e r s e d i s t a n c e cubed model (ID3) used a t the mine was d e f i n i t e l y b e t t e r than the k r i g e d grade e s t i m a t e when compared to what was a c t u a l l y mined , but o t h e r methods i n c l u d i n g i n v e r s e d i s t a n c e t o the f i f t h power (ID5) outper formed ID3 f o r the o r i g i n a l b l o c k mode l , w h i l e c o n d i t i o n a l p r o b a b i l i t y and ID5 both gave b e t t e r , o r much b e t t e r , e s t i m a t e s when an o r e zone o u t l i n e was a p p l i e d t o the same s i z e b l o c k mode l . C a r e f u l a p p l i c a t i o n o f c o n d i t i o n a l p r o b a b i l i t y as p r a c t i c e d by G . F . Raymond and m o d i f i e d i n t h i s s t u d y , i s an extremely 108 r o b u s t , a c c u r a t e , and u s e f u l way o f c a l c u l a t i n g ore r e s e r v e s , and indeed t h e s e c a l c u l a t i o n s s h o u l d be used a t a l l s tages o f c a l c u l a t i n g g l o b a l ore r e s e r v e s , i n mine d e s i g n , and f o r r e p o r t i n g d a i l y and monthly p r o d u c t i o n f i g u r e s a t B u c k h o r n . By a p p l y i n g a l l o f the re f inements d i s c u s s e d , e x c e l l e n t agreement w i t h b l a s t h o l e s was a t t a i n e d w i t h c o n d i t i o n a l p r o b a b i l i t y . And f i n a l l y , a l t h o u g h k r i g e d b l o c k v a l u e s were no t the bes t i n t h e m s e l v e s , a p p l i c a t i o n o f the f u l l power o f g e o s t a t i s t i c a l t e c h n i q u e s , which p r o v i d e s b o t h a v e r y n e c e s s a r y u n b i a s e d l i n e a r e s t i m a t e and an e q u a l l y i m p o r t a n t measure o f the e r r o r a s s o c i a t e d w i t h t h e e s t i m a t e , p r o v i d e s the b e s t c o m b i n a t i o n o f t o o l s to e s t i m a t e m i n i n g b l o c k grades and tonnages , as w e l l as g l o b a l ore r e s e r v e s . 109 R e f e r e n c e s D a v i d , M. (1977): G e o s t a t i s t i c a l Ore R e s e r v e E s t i m a t i o n . E l s e v i e r , 364 p . D a v i d , M. (1988): Handbook o f A p p l i e d Advanced G e o s t a t i s t i c a l Ore Reserve E s t i m a t i o n . E l s e v i e r , 216 p . G i r o u x G . H . and S i n c l a i r , A . J . (1986): G e o s t a t i s t i c s a t E q u i t y S i l v e r Mines L t d . : G l o b a l Reserves o f the South T a i l Zone by Volume V a r i a n c e R e l a t i o n s . i n Ore Reserve E s t i m a t i o n , Methods , Models and R e a l i t y ; Symposium P r o c e e d i n g s . D a v i d e t a l . , e d s . , C a n a d i a n I n s t i t u t e o f M i n i n g and M e t a l l u r g y , p p . 218-237. J o u r n e l , A . G . , and H u i j b r e g t s , C h . J (1978): M i n i n g G e o s t a t i s t i c s . Academic P r e s s , 600 p . Munroe, S . C . , G o d l e w s k i , D . W . , and P l a h u t a , J . T . (1988): Geology and M i n e r a l i z a t i o n a t the Buckhorn M i n e , E u r e k a C o u n t y , Nevada, i n B u l k M i n a b l e P r e c i o u s M e t a l D e p o s i t s o f the Western U n i t e d S t a t e s ; Symposium P r o c e e d i n g s . S c h a f e r e t a l . , e d s . , G e o l o g i c a l S o c i e t y o f Nevada, p p . 273-291. P l a h u t a , J . T . (1986): Geology o f the Buckhorn M i n e , Eureka C o u n t y , Nevada. i n P r e c i o u s M e t a l M i n e r a l i z a t i o n i n Hot S p r i n g Systems, N e v a d a - C a l i f o r n i a . T i n g l e y , J . V . , and Bonham, H . F . , e d s . , Nevada Bureau o f Mines and Geology R e p o r t 41 , p p . 103-107. Raymond, G . (1979): Ore Reserve Problems i n an E r r a t i c a l l y M i n e r a l i z e d Orebody . CIM B u l l e t i n , V o l . 72, No. 806, p p . 90-98. Raymond, G . (1982): G e o s t a t i s t i c a l P r o d u c t i o n Grade E s t i m a t i o n U s i n g K r i g i n g i n Mount I s a ' s Copper O r e b o d i e s . P r o c . A u s t . IMM, No. 28, p p . 17-39 . Raymond, G . (1984): 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 i n T a b u l a r S t y l e L e a d - Z i n c Ore a t P i n e P o i n t Canada , i n G e o s t a t i s t i c s f o r N a t u r a l Resource C h a r a c t e r i z a t i o n ; NATO ASI s e r i e s , P a r t I . G . , V e r l y e t a l e d s . , D. R e i d e l P u b l i s h i n g C o . p p . 468-483. S i n c l a i r , A . J . , (1976): A p p l i c a t i o n o f P r o b a b i l i t y Graphs i n M i n e r a l E x p l o r a t i o n . A s s o c i a t i o n o f E x p l o r a t i o n Geochemis t s , S p e c i a l Volume No. 4, 95 p . APPENDIX A BENCH MAPS OF RAW DATA AND OUTLINES LEGEND: Grade ( o p t . ) + 0.000 - 0.010 • 0.010 - 0.020 EB 0.020 - 0.035 m 0.035 - 0.050 • > 0,050 O u t l i n e s Mined L i m i t s "Ore Zone" O u t l i n e ( d e r i v e d from s t a t i s t i c a l s tudy)  B E N C H 6 8 8 0 BEX DATA 2 0 ' C O M P O S I T E S  + • ffl • + ^ ~ \ — — — . + + + + + + / • \ • • + + Q - + BENCH 6 8 8 0 BBH DATA B L A S T H O L E S B L A S T H O L E S 118  120 APPENDIX B BENCH MAPS OF RESULTS (6840* and 6860' ) The f o l l o w i n g bench p l a n s are s o r t e d f i r s t by b l o c k model , t h e n by bench and f i n a l l y by method. F o r any b l o c k mode l , 2 . s e t s o f 13 p l a t e s , s t a r t i n g w i t h the b l a s t h o l e p o l y g o n weighted e s t i m a t e and e n d i n g a t e x p l o r a t i o n c o n d i t i o n a l p r o b a b i l i t y , a l l show r e s u l t s on the same bench so t h a t the d i f f e r e n t methods e a s i l y be compared w i t h each o t h e r and t o " a c t u a l " b l a s t h o l e r e s u l t s . 4' p o l y g o n a l e s t i m a t e s are not shown. In t h e case o f the c o n d i t i o n a l p r o b a b i l i t y p l o t s , the c u t o f f grade i s i n d i c a t e d and c o n t o u r s r e f e r t o the p r o b a b i l i t y o f ore b l o c k s above the c u t o f f w i t h i n the c o n t o u r . C o n t o u r s a r e a t 40, 60, and 80% p r o b a b i l i t i e s and are p l o t t e d on top o f " a c t u a l " b l a s t h o l e k r i g e d r e s u l t s f o r a g i v e n b l o c k mode l . LEGEND; Grade ( o p t . ) + 0.000 - 0.010 • 0.010 - 0.020 E 0.020 - 0.035 0.035 - 0.050 • > 0,050 Method BHK B l a s t h o l e K r i g i n g . BH20 B l a s t h o l e Po lygon o r BH60 Weighted (20' & 60') EX20 E x p l o r a t i o n Po lygon o r EX60 Weighted (20' & 60') B l o c k Models BUCK 20' B l o c k s , no o u t l i n e . BUCKG 20' B l o c k s , with' "ore zone" o u t l i n e . BUCK60 60' B l o c k s , no o u t l i n e . ID10 ID5 ID3 ID2 IDI IDO I n v e r s e D i s t a n c e to the i n d i c a t e d power, KRIG E x p l o r a t i o n K r i g i n g . CPROB C o n d i t i o n a l P r o b a b i l i t y . 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H I I B E E E B B ^ E E E E E E E E E E E E E E • ••••EB • • • E B B • B E E B ^ B B B • • •EBSl^Eai • E B B B B f l + + + • • • • • • • • • • • • • • B E E D D D B E E E D E E • E l l Q D + D + +^mD ffluuuuu ••••••+ + + + + t l ^ B E B E B E E E ^ H B B ^ E E H B f i l + + E B B ^ t l B Q ^••••••••••••++•••••+ •+BBBED+ BBBBt-BBBBBEi BBBBBS • • • B B f l i l ^ f l B B f l ^ ^ E + BEBBB+ +DEBSE3ffliEBEBii E E B B B + + n B E B B B B B H E E B B B ^ H B E n + +BBBE • B B + + n B B ^ B B E + +EEE + • •+ + + B B B B B B E B B B B B + B+ ID ID ID • E E B E B B B B E • • • + EE+ + +EE BE+ +EEE • •EBEBEB^EB^B E + E B B ^ ^ E E E B + O B B ^ B E f l ^••••••+ +EB !&••• + • IBEEE • • • • • • + + + + + • + + [ O CD O O CD 00 CD X O LU CQ O o X CQ BBB^EBEBDEBEHEBEBEB EBEB^EB B B B E B ^ E B D D E B E B f f l f f l E B n i Z O E S E B B B E EBfflfflfflEBDDEBEBEBEBEBDnnEBEBflEB EHEBEBEBnnnnnnDEHDDDnEBEB •fflEHEHDnnEBnn^^DnEBfflfflfflEe + DEBEBEBEBnnnnnEeESDDEBEBEBfflEB EBEBEHDDEBfflffl • • • E B D n n n E S f f l f f l D n n n n n ^EHEBEBCDEHEB • EEEBEBUUUUU SfflUUUUEEEB • • • • • • • • • • • • • • • EBDDDDfflEB • ••EBDESEB • • • • • • EBDnDDEB • • • • • • • • • • • • • • EBEBEBEBEHD • • • • • • EBEB • • • • • • • • • • E B n n n n n n n n D n • • ffl^nnDD + DEB^EBD fflffltJLJDEB EBDDBBB + +•+ + fl^EBEJ EBEBfflEBDEBBB^B^ESBB^+ + DEBEBEB^EB[J EBEBEBEBEBBBBBBBBBBBBBBDnDnEBEJEO EESEaEBEBEBBBBBBBBBBBBBBnDEBEBtBEBDn EBESDESEBESESESBBBBBBBBBBBBBEBEBESEB^BB^ E 3 D L J E B ^ i E B E 3 l l B B B ^ E B B ^ B B B B ^ E B ^ ^ E B + E B D E B E H E H f l B B B B ^ i l B B B B B B ^ f l ^ f l ^ E B E J • ^BBB^EBfflEBfflD + EBEBEBEBEBtlEB^BB • BBBff l D f f l E f f l n + rjEBEBEBEBf^EB^B • ••••EBEafflEBEaDDnnnEBEBEBEB • • • • + D E B E^flESnn+ + EJDEB + • • + + •EHEBEBEHEBnDEBEHfflEBEBD • + + EBBEH! ESEJEBEB^fll 3EBfflG[ZlEBEBEBEBESEBEBJl̂ n • • f f l E 3 3 f f l ^ ^ ^ n n n n E E • • E B E B E B ^ ^ f f l n D + DEBLJl • • • E B ^ ^ E B E B L J + + • • • & ^BBBBfl^DDEBEBEBEHEBEBilBEBtEi^ IDDfflfflEBfl^EBDfflLJEJES I D + LJEHEB^EBEBBEBEBEB IfflDBBf^fflDLJEJEBfl^EJ I B B ^ B B ^ B B ^ B B E I L J E J E J + B E I ^ E J I ^ ^ E B L J L J E B^BB^ E B EHEBEHEBLZ! + EBEQBBB ESEBEBEJLJEJ EB^ • • • I O O CD & 00 — (D C D ^ CO CD \ ^ o ZD CD 154 ^•^B^BOBBBBBBDaBB^ B E B B B D D E B B B B D D B B B B B E E D D D D D D B E D D B B B E B D D D B D D B B D D B •BfflfflfflEBnnnnnfflEHnnffl •••BBBnDDBEDDDDDD • • • • • • • • B B B D D D D D • • • • • • • • • • • • • • • • •DEEDED DDDDDD BDDDDDD DDDD BBEBBD B B E ^ E B BBBBDDBB DBB D BBBDBE 3D BDDBElEBi BDDDBBB EDDDDB DDD • DDDD • • • • • • • • DDDDDDDDD ^BDDDDDBBBB ID + D + Dfl̂ BD l + DDEBBEBD IBDDDBEDD IBDEBBBDD IBBBEEDEBEB^^HI ^•••^•BEBD + DBEEBE^H • ••EBDDfflfflEaEBDDDDDEBfflii BDBD+DBBBBBDDD+BBBD DD+ + DBEBBBBBBBBBBB • ••B^B^BBMBBBBB^ EDDESI DBBBB1 DDBBBi BBDBBBBBBBBi BBDDDBBBB1 EBEBDD + D E B E H I i i l i l fflfflDD + D E B G i i l l i i ^•••EaEBEafflEBiiEBK •••••••^BDBBBg • ••BEE ^•••EE ^••EDDBDI • 1 1 1 • • • • • • • • • EBDD CD CD CD o CD CO CD CD ^1 ro DZ CD CD CD ZD 1—1 CQ LD CD 155 ^ ^ B ^ B E B B B B B B B D B B ^ H B B B ^ B B B E B B B E n D B B E B B E B E B ^ B B B ^ B E E B E BBBBDnnnDDBBnBBBBB B B B B B B E B B B fflEBfflEBnnnnnDfflfflnnfflfflfflfflE B E B B B B B B E B •fflfflfflEBsnnnnofflfflnnfflfflfflfflE B E B B B B B E •••BBBEnEBEnnnnnD B B E B C O B B • • • • • E C O •EBEBDDDDD B B B E E B E B • • • • • • • • • • • • • • • EBDDBEB •••BDBD • • • • • • EDDEEB • • • • • • • • • • • • • • BBBBEE BBBB • • • • • • B E ' B B B B n n n n n • •BDBDDDDEBB B B • ^ ^ B B B D D B B B B B B B B D B ^ ••BHB^nnn+nB^En E B E E^HHHHHHHHHHHHHBDBDBE ]E0EBEBSIIIIIIIIIIIIIiDESE8E0E8E0EB ^ ^ • • • • • • • • • • • • • ^ B B E B B H B E B E B D E B E E ! E B m i l l [ i i l E i l l l l l E i ^ m [ i [ l ! i D (••••BEBEDnBEBEB^^B ( • • iDDEBEBEEBDnnnEBEBMi ^ E B D + D B B B B B D n n D B B B B B B + + D B B B B B B B B B B B B B • • • • ^ B E B E B E B B B B ^ • • • B E B B B B ^ E E B E ^ B E E E E ^ B E n n D B B E B S • B B B ^ f l ^ B B B E B B B B ^ I 3 B B ^ ^ ^ ^ ^ B B D D B B B E ^ I ^ • • • H B E B E E B i E l f f l i i l^fflDfflfflEBWEBDElfflfflE ^ • • • • • • • ^ B D B B E E E E ^ H ^ ^ ^ • ^B B B B B E E E B BBDD BDE [ CD CD O CD 00 CD CD ^ C\J X O Q O O LD OD OD 15 H f l ^ i l B B B f f l B B B B B B B B B i l ^ B B B B B B L J B B B B B B B B B f f l B fflfflEBEB EBDnDDEB B3 EBEBEB EBEBEB EBfflEBfflsnnannEBEBnB3 E B B B B B B B L J B B E B L J B E E • • • f f l f f l f f l f f l n n n n f f i n D D D E B •••••BED • • • B B B L J B • • • • • • • • • • • • • f f l U U • • • • • • • • • • • • • • • • • • • • • • • • • • B B B B • B E D • • • • • EBBS B B B B B E • BED EDDBB E B B B B D B BEBffiBLJfflBE ^ B B B B B B B B B B f l B B B B B B B B B • B B B B E B B B B • ^ • • • B B B B Mf, • ••BBBBE ^ • • B B E B B B E B ^ B L J B B B B B B B B B B f f l B i B B B B B B B B E B B B E • • • • B E B B B B B E E • • E B B B B E B B B E 3 B E B B B 3 B B B D B IfflfflDDD liEBDEBffl mmm BBBS1B N E B B E D B B B B L J B E B B r o o CO 00 CO o L l J CQ o ZD CQ mm mm IE H B H H BI IE H E B E B E n ^ B B B B B B B ^ B ^ E EBEBEBEBDnDDDI EBEBEBnnnnnffli B B n B B B B B B n n B n B ^ B B B B B B I B B B B B B B • • • • • • • • • • • • • • mmi • • • • • • • • a E B ^ E • • • • • • • E E E E E E I ^ • • • • • • E E E B E ^ B I • • • • E E H B B B E B I • • B B E E B B B E B E • • E B B B B E ^ • • • • • B • • • • • • • • E B 1 • • • • • • • • • B E 3 • • • • • • B E E B B • • B B B a D B B B B • B B B B n n E B B • • • B D D B B B • • • • B B B B • • B E E B B B E B B B B B B B B B B B B B n n i IBBBBBB! 0 6 0 ' B E N C H 6 8 6 0 :UCKG iiEBEEBDnEGEanffl B B B B B E l B B B B n n n n n D D • E E E B B B B B B B I I B B B n B B B B B B E E E E E E E E E E ^ B E B B B B B B E B B B B B B B E B B B I t l B B B B n n B E B lEBEBEBEBnaffl ^ B E B B D B E E •• IDO •BBBB 0 60 B E N C H 6 8 6 0 BUCKG • • • • • I B B B B B B B I D E I mmmmmmnum\ ^••EiEHfflEBfflEBfflBannnnnfflffl ^ ^ E E E B E E B E B B B E B B ^ ^ E I E E E E E B E B B E B B E E B B ^ E B E E E D B B E B E B B E E B B B B B B B B ^ B B B B D n D B B B B B B E E D B B B B B B B B B B B B B B B B B B E B B B B D B ^ B B B B B B B B B B B B B B E B B B ^ B B n E B t l B B B B B E B B B B B ^ B B D E B B 3 B B B B B H O B B B B D E E • • B B B E E D D B E l ^ E E E E E E E D E mwnm BBBnEnnnEBB^^Ei^ B E D D n n n B E B B ^ ^ E l •••••EEBBBBBB ••••BEBBBBBB • ••BEBIZOB BDDEEBE •••BEnDDDBB ••BBDEDDBBE ••BnnnnnBBB • • • • • • B B B B • • • • B E E B B • • • • • • • E B • • • • • • E B • • • B B B H H ^ E E B B B B I B ^ B E Q E B E I B E M wmmmmmi I I I B E D B E l E l B B B n n ^ B D B B E E E E BBEBfflnnnnn E E E B E E D E E • B B B B B B B BEBEBEBEBEBEBDD • • B B E E B B E l B B B B B B n n ED BED BEE • • BBQEBB • • • K R I G E 0 6 0 ' B E N C H 6 8 6 0 BUCKG • • • • • • • • • • • + • DEB EBEBEB • ••EBEBEB • ••EBEBEB ••EBEBEB mummm EBEBUU mmu + + H E B D + + E+ + B + + + •••r jp + + • • • • • • • + • • • • • • • • •EBDnnnnnEBEB^^ • • • • • • B B B B B E • ••••EBEBEBOEBE • ••EBEBD+ +• ESEBnnnn + • B B B E E E B B i l son mmuu !•• • • B E l B B B E n E t i • • B E I B B E E D B E mmm ummmmi IDE ! B D I + E]BBBfflDBBBBBBBBB!: + ++mmmmnmmmmmmmmm + + + + + +> + + 3+ + 3 + 2D £ • • • • • • • • • B D D M M B B B D ESQ + • • • • • • • E l B B E D B B B B B M B D D •••••••BDD ED 3 B D D D D E B E D D D E I B B D D B E B D D D + D B ^ E I B D B E I B B D D D D B I ^ B D B E I B B D D + Effl 3 H B B B B B E E D D B B • E 1 B B D D D B B B D D D D B S 1 D E B B B D B B B B B t l E l E l B B B D B B E S E B B B E B D B B B B E B BEBJZI EBEBEB EBEBEB D B B I am D B E D D D D D • + • • • • D D D E E D D D D D E E D D D B B D D D D B E B ESDDDnOOEBEBEBEEl • • • • • • E B EBEBEB • • • • • • B E E • • • • • B B •••EBEBEB • • C P R O B C 0 1 0 ••••• •• ++••••••• w&nu ••• +•••••••• wmmmua B U C K G CPROB 0 = 0 2 0 16 • • Q Dffl IfflEB + DEB iHD + Dffl 3EHEBESDDEB EHfflfflfflEBDffl • ••EEEBEBEBEBEBEH • • • • • • • E H • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • ••EHfflD • • ! ! • • + EBO, • •EH • • • • • • • • • • • • C_ • • • • [ • OSfflEHEHEHEHn • • • • • • • • E B E E O EBEHEBEHEHEHEBann • • • • • • • E E fflEBBEonnno • • • • • EBEHEBnnann •EHEHEHO E B n n n n n n • • • • • • •EH ••EHfflnnnfflEH • + QE • • • E B B • •EH EB EH EH EBEHsnnn EBfflEBnn • • ESErJfBffiSn I o CO o o CO CO co DZ CO LJJ CQ o o ZD CQ LO ro o o CQ o or CL_ CO 16 • • • • • E B • EBI IBB + DEB HI • •tlBLJ + CJfflB ^BBBDLJfflfflBBB EBBBBDBBfflfflBBB • • • • ••••••EBEBEHEBEHEBEBEBEBES • • • • • • • • EBEBBannnnn B B L J B B B D • B B B B B • • • • • • • • • • • • • • • • • • • • • • • ••BBLJ • •[!• + + + ++++++ • + + + + EBDDD • •EBEH • • • • B B • •••B • • • a ••fflffl ••BdmBaffl • • • B B B B • • • B B B B B f f l + nnfflEB3fflB3ffln B B B B D • • • • • • • f f l f f l D mnna • • • • • • • a a a a n n n n n EOEBEBDDDDD a u u u u u u ffluuuuu • • a • • a a n n n a a • • f f l f f l a n + D + n a • • • • • • B S a n n n a a a a EBDESEBEBDDD B f f l a B B D D • a f i f i a n n • • a a a a n • • • •BEB • B E B + + [ o CD o o O CD LO CO o CD CD - ^1 o zc CD o ZD CQ CQ CD LU en CO C P C/  r  •BDBBBuL EBDEBEBSfflES • • • • E ^ T O B D • + • B B B B i ^ B n n E H E E T • + + I H H I 1 D D E B E B + + B B B B B B E 1 Q E S B D D + • BBBBaaBBBBBB •BBBnnBBBBBB^BB B B B B B B B B B B B mmmmmmmmmmmm BBBBnBBBElBElB fflEBDDEBEBBI B D E D D E I B B B B B B B EBDEQEQESBBBBBBBESD + fflDfflfflfflUBBBBBBEBD EEDEBSEH El • • • • • • S-13] f I I I I I • B B B E B B B B B BENCH + +nnnDBBBBBB • • • • • E B B B B D E B ^ B ^ • • ^ B B B E B B B t l • B E B B B B E B B B B l l H l l • • • E ^ B B B E B B B B B B t l + + E B ^ B B B B E B B B B B B + + • E B E B B B B H E 8 B B B B B B + + • • B B B B B B B B B B B B + + E E E ^ B + + ••EBB + • • • • + +•• + 4- + + 3 B E B E 1 B I I B B B B B B B B B OJ LD QJ vZ& XAJ QJ QJ 62J QJ XL :!••••••• 3 E E 1 B B B B + + B E RB s¥l mmmurm • B B E E E n + nm UCKG BJ1BBB B D B B B ^^EBLIIEHEB + D L I B [IJIlllBBE • • + E E H E 1 B B E • • + DB B E E E uumm • • E B B •EBEBEBEBEBEBEBEBEB B B B B B B B E E B , •EBEŜ EBESEBD + D B ^QnEB^EBEBEBn + • B O B B E D •EBB + • 8 3 + EBB ummm +EBBBBBB +BBBBEEE •BBBBEEB BEHBEBBll BBBBEEBE! BBBEEEBB EBDDEBDDEBEa ••••••EBB •••••EBBffl •••EBEBEHEBEB • • • • BEB BD !BB3EBEHEHEBEBEBEB& fHEBEBEJEBEBEBDEBE fBfflEBEHEBfflEBDEBffli EBDEDEBEBEBEJEBEBl + |+ + + + V t i d ifflDDfflfflfflnnffli IB^BBBEBLTJEBEBEBE I^EBEB^EEHEBfflan lEB + ̂HMEBEBETJEBEB 1̂  + M^EBEBEBEBED ]H + DEBB3fflEBEBDnn i + fflnnnnnnE EBnEBEBnDB3EBEBEBEBEBfflEBfflffinn DEB ffl • fflfflfflfflfflfflfflfflEBEfflffl^fflffl^fflfflnfflDDEB [•••fflEBEBEBEBEBEHnnfflB^fflffifflEB^EBDnDEB [••EHEHEHE33EBEB • + • ••EBEBEBSEBEBDDD [DfflfflEBEBOffl + + + + +nnEBnnnnn IEBEBEBSD ++Dffl^B^n • • DDI mmmi + • ••EBB 3 B B B B B B B E 5 B B - - H H B i B H j B | B E • EBLTJEBBI + + DEB • + +• • + +• EBD EBD EBD • EB + + + + EBDD EBnffiEHDDDEnn • + l ••••••• EB EH EH • EH EH E fflfflDEBEB^BBEBD mi •EBE EBE33I EBEBE EHDE ] • + • • • • • • • • • • • •^••H^mHEHH^HBBHBBBB + BBB^B^EB^DEBEBSi^BBBBBB Snffl^BBBB^fflEBDDEBBBBBBBB^ffl 3DEHBBBBB^n^EB^EB^BBBBBEHD+ +1 ]DnEB^BBBEBDBEBE^BBBBBBB^n + + innnn^B^BfflEHH^E^B^BBB^nEBnEBn ]EBnDEB^HBBBEinEHEBEBnEBfflB^EBnE3 BEBDEBnn + n n n + n n ^ IBBBBBB^EB + nnnDEHEHD^BBBBnDEH 3BBBBB^DEBEBESEEEB + EBBBBBBB^D + ID^BBBB^DEBD + ̂ B B B B B B B B D + + DEBnBEBBB^EB+ + + + + •EBEB^DD + • + + • • • • ^ • • • E B D + DfflnnEBnnn + EBD + + + + + +• ++++++ o 00 CD X CD OD CD CD X CQ O CM X CQ • • • • + I EBDDDEfiEB EBEBEB + + + • • B B B B E D E J B M • • B B B B E n D B f l f l H B L J B B B f i • • • + DDDfflnnnn^EBEBDEBi • ••+ +nEB3nnfflfflH^EBEM ••••••ff lff lnnEBaffif it it^fi i • ••EBEBnnnnannff lEBE • • B B B L J D [ J + + D D E B E • • • B B B B L J + + + + • • • E B B B E + + • • • • • • + • • • • + • f f l n n n n B E B B B D + SflilBBBElEJ IfUBBBB + I B B B B B B + • • • • + + + + • • ••1 + UUEBI + EJBBI E D D B B • + +UEB + + D B B B B B B B E E J E J B E J L J E J B + D B B + + + • E D D + B + + iDEBffl + + I B D D B B B B B B B B B B B D B I B B B B D + B B B D E B I Egn+ + l i i E B E B D D D + + + + + • + BBHBBEBEJLJ+ + + + + + [ ! • • • • • • • • • • • • • • • • • + D B B n n B B B B • • • + + + D D B ^ + + + + + + D E B + + + + + DEBEB + + g3iDDDE0E9 + • BB + + + + + BBEJ + +••••• • • • • • • • • f l ^ B • + i + DBBI + + + E U H H H H H E B B E D D n BELIED MEBDD B B B B B E1E1EBBB I + + + !+ + + + n n n B f ^ n B E B n n ^ ^ B B + + + +nnnnBB + + nnnBBnnn • • • B f l B B B B S i+ + iB + n n n n n + B ^ • • • • • • + + • • • • • • • • B B B + + • • + + + + i • • • • • • • • • + ++ • • • • • • • • • + • • + + • • + + + + + + • + + • • • • + + + +••• + + + + • • • ^ E ! + + • • ^•f^+ + + + + fflfflUUUU B E D C O D I O CD O o 00 CD o o IE o C\J CD ID X m LU LU m • • • • • • ••EBEBEBEBS fflffl^HEBEHESEHDHfl^ EBDEBEBEBEBEBnQEflEl̂ fflEBffinnnnfflDDEBffl EBEBD + DDEBEBDDEBEB EBDEBDDDEBEBDDfflEB^^ • DEBEBEBDDDDDDDEBEBEB DDBBB3EBDDDDDDDEBEBEB • DDEBEBEBEBf̂ DEB • DDEB EBEBEB!̂ • DDEBEBJ^ + • • • • • + • • • • 3BHHHHEBDDD ^ • • • • E B D D D E B EBDEBEBEBS f^DDEBdi EBEBEBDDEBEBEBEBEBEBEBEBS DDEBEBEBEBEBEBEBEBG • • •EB 18 • DEB DUf^EBfflEBI I D • EBEBDfflEfflfl^flEB EBEHLTJEH E B B B D D • • • • H H H i DfM i DEIS • •EB fli ^ E B + E B D B EHEBEHEHnn EBEHEHEBrj ID+ + • • • B B B D B + + D D D B + H H H B E B D D + + + • • • • • • • • E B E B E B EBEBEB EBEBEB • • • • + • • • • + + + ^EB+ + • + DBiUfUHH f l B D D + D B B E ^ H B • • • • • • • D B D D B • • • • E B • B t l E l B • • • ••EBEBEQDD B B B D D D E E I ^ D D D H ^ S I D D I E D D B B E D D B B E D D B B B D D B D B B B ^ S I I J j | B B B B B B B D B B B B B B ^ f l B D D B D D D + • • • D f f l B B B B ^ B D f f l ^ P l i l B D B D E D D B D D D D B • B B B D D D D D B B B D D D B B D D a n D D D D D B D E B B ^ D B I ^ B B B D B + + D D D D E B + + + D D D B B D D D + + + • • E B E B D + • • • • + B D D B + D D B D D D + H B B + + + • • • • + • B B B B D f f l F l B B D D D D B B D D D D + • • • + +•• + +•• + + + • + o CD O co CD X CD LU CQ CD CD ZD CQ O Q • • • • • I B O B B B B f i • • • • • ^ B O B ^ • • • B ^ B n B E EBBff lEBBnDBI l^BHBBE^ EEBEBEBfflEBESnDfflEB^FEfflDEEBEa EEBSnnnnESDEHEBEHEHEHnnES^ fflEBfflnnnafflnfflfflffl • • f f l f f l E D D n n n n n • • B B B f f l n f f l n n n n • • B B B H E l ^ B B f l f l • • • B B d f f l H • • • •BBHB + • • • • E B + • • • • • • I B B Q Q B B B B B B B B • • B B B f ^ B I • EBB • EBEBEB'fflEBEBH^ffl BBDB B B B B B O B B B B B B O • HB n f l^B • B B M B f l B D ^ ^ B f f l n a EEBn + E S D M • EBD + •••EB ^ B ^ B D EBfflEDDEE BQBEBBB BOfl H f f l BO • EBHHH • • • • • • • • + n B B B B B B B B B SDD+ + +B B B n + Q + B B ^ ^ H M EEaDDEBEBEBfflEBi • EBDfflfflDDDDEB •EfflfflfflDDDD B B B B n n B B B D B B B E B n B ^ d H H ^ n ^ H H H ^ B D n I B B B B B B B f l f l^ H B B B B n n iEBBfflnDB 1+ + • • • • • f f l B B B B ^ D B I • • • • • f f l E n + O D D f f l B B D D f f l • + + D B f f l f f i D B I i i f f l D f f l B B E B + D B ^ f f i Q E E i i ^ D + + B B B D B D B + • s u s n + +•••• B B f l H H H ^ E l B ^ n + n n ^BtlEBBBHBH+ +•• BBBBBBHBQ+n B f f l f f l B B i i B D E 8 E E D D D B E D D D D O ^ 00 CD o UJ m CD O ZD CQ LO Q • • ••ES B i l B B B B B B f ^ f l • • • • • B B E l ^ B ^ B ^ d t l ^ f l ^ B B B B B B E BBEBBBBBDB^El^BBEEE: E B B B B B B D D B E ^ B D B B F l ^ B B B B f f l E B E B B D D D B B D B B B B B B E B ^ i l E l B B B B B B B B D D D B B D B B B B J I B B B B E I ^ B B B B B B B B B D D B B B E B B B B ^ ^ E I B B B B B B B B BDBBBDDDDBDDBBf^ElBBfflBfflBfflB B D B B B B B E B B B B f l f l ^ H l l B f f i f f l E • DEEBEBr" • •EES ESI DDDBBI + ••••1 • • • • • • • 5 B BBfflffl B B B B B D DBd t l f l E l B B fflffiiffl EBBE ^ B D f ^ B B B B ^ B B B BS1J1B BBE I ^ B f l ^ B B B B B B D B B B i l B E B B B B S i i l H I I l l l l l l l l i l ^ G BEE it^BBEB f!Q[; I^UEB BB I B B ^ B E E t l ^ B B B B H B B B B B B B E E I H B B B B B E B B B B E E B^ B B B B B H H E fflBBBD + D D D B ^ B ^ B B B B BDBD + DBBBBBBBBiUBBBBBffiDDB BDDD + D B B ^ f l ^ B B B ^ B B ^ I l f f l f f l f f l B B B D D D D B ^ d f l ^ f l ^ B B ^ ^ D D B B 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I ^ B E B D E B E E f f l E B f f l ^ E B I EBD EBEBnEBfflEBfflEBEBnDEBEBEBDEBEBEBEBl EBnnnEBEBEfflEBnnEBEBfflfflfflEBEBEB ••••B3H3B3EBEBE0EB • • • E B fflffl^ffl^fflfflEBfflEBfflEEBEBEBEBffl CM mmmmmmmsisiaaiiimmmmmm mmmuuummmmm l^fflffluuuuuEB Î EBfflfflDDEBEBffl m EB EB EB • EB EE EB EB El EB EB EB EB EB EB EB 3EBEBB3fflnDEBEBEBE 0 6 0 ' • • • • • • I •EBffl! • I I l l l I l I I I I i E I l i l l l l l l l l l E B E N C H 6 8 4 0 B U C K G ID I • • • • • • E B E B E 1 E 1 I • ••••SfflEBaESEBEBEBUE ••••B3fflfflfflB3B3EBEBEM •••EBfflEBEBEBDEBEBEBEBE \mnmmmzmmmmi 3EBL7JEBB3EBEBEBEBEBE1EB • I l f f B3EBEBEBEBHdEBEBB3EBEBEBEBEBE o • B B B U B B B L?[a • • • • • • • • • i p i i i f i n i mmmmuuummmmmmmmm wwmmmmmmuuuwmmmmwm uuuuuummmmwmmmmmm, • ••••fflfflBaEBESESEB^^^^^ • •••EflSEBfflfflEBfflElEill^El^ •••^fflEDfflfflfflffl^ mmmmwmnummmmmwmmm fflfflfflfflfflDDHfflEfil 3 B B B B B B E 0 6 0 ^ IE flf RE RE RE RE E ^ BB BB !BB BE BB BE E a VmB BE BE t/v̂  k • I I I I I • • • 3BBE 3 1 I I H I 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ZD CD CD O O LU or CQ Q_ CD 0 6 0 B E N C H 6 8 4 0 + + v BUCKG CPROB 0 . 0 2 0 0 60 ESEBDEBEB + LJESD + • ma + n • + + + + + • B E N C H 6 8 4 0 BUCKG CPROB 0 = 0 3 5 • l l l l i l l l l l l EBES EBEBD EBD 3EBDEB 3B3DDBBDDDDB3B3 3B3B3B3DDDDDDEB IfflEBEBEBEBEBEBDDEBD IfflEBfflEBEBEBDDDDD •DEBDDB3B3EBEBEBDDDDDD + • + + +DfflEEBEBnnnn ••EB • • • s i • + + • + • • • • • EBEBEJnn EBEBD + + DEBEBDDD • EBEB EBEBD • ••EBEB EBEBDDDHHD EBDD + + + + + + DBBD+ + DDEBE DEBDDDt D D + + + + + + + D+ + + + + + + + + + + O CD O o O LO 00 O CD CD • o X CD CD X CQ CQ CD LU en CQ C P o  1  0 A C T U A L B E N C H 6 8 6 0 + B U C K 6 0 BHK BENCH 6 8 6 0 + B U C K 6 0 B H 6 0 • EB + + + • • + + • ffl EH EH EB • E ffl • BB EB • • • ffl • • • • + • • + + + • • • • + + + + + + + + + + • • • ffl • EB EB + • + + • + + + + • + + EB • + + ̂  • ffl ffl • + + ffl ̂  ffl ffl + • ffl ^ • • ffl • ffl M • • • • + + + + + + + • • • • EB • + + , o I + CD O C D + + co • ^ CD ° CD X ^ CD ^ LD m CD 180 + + • EB • EB LB • + + EB • • E • ffl • • + • • + EB • • + + + • + + + + + + + • • • • EB + M EB + + • + LB + • ffl ^ • • • + • + + • • + + • LB EB LB • • + + • LB + • + • + + • + a • + • • • + + 4- + + + + + LB EB + • + + o + CO EB + + + + + C O 00 CO o CO L U m + + + + o CO o ZD CD 1 8 2 + EE + • • ffl • ffl EH • + + ffl • • ffl • ffl • • + • • • + • • • + + + + + + •+ + + + • • • + ffl • ffl + + • + • • • + • ffl ^ ^ ffl ffl • • • ffl • • + + + • • • • + + + + + • + • • + • • • + • • • ffl ffl ^ m EH • EH + EH EH EH EH H ^ i i • ffl ffl + ffl m + E H • + • + EB • • • + -f- + + + + + + + + + -t- + + b + + +° + 'CD ' + [ CD O 00 _ CD ° CD X ^ U J CD OD r o 183 E • • E E f f l E E H n f f l f f i f f i B + E B B B B B B • • • + + • + + + + + + • B • • • + • • B B E • • + + • • + + • • E E • + E ffl + + E + B E E E B + E B ^ E B E B M M E ffl E ffl E ^ • E B E + E E B E B B + + + + + + + + + + + + + + b + + + g E + CO o -Si CO o CO X ^ O <J LU m m CM Q 184 EB • • ffl ffl ffl ffl EB • • + ffl • • • • • • • + • • + • • • • + + • + + + + + + + • EB + + ^ • ffl ffl ffl ffl • • • ffl • • • • + • • • • • • + + + • • • • • • • • + • • • • • + • • • + • ffl ffl ffl ffl • ffl [1 ^ • EB 1 j • [1 n • EB • + • ffl ffl • • • + + + + + + • • + + + + + b + + +SEB + + CD CO CD O CD JZ ^ C D O LU CQ CD ZD CQ 185 m m m rn m rn rn m 1̂  1̂  mc±jc±j •fflfflfflnfflfflfflfflfflfflnn • • ^ • • • • • • • E n n n • • • • • • • + + • • • • • • • •••+ + +.+ +•••• • + + + + + • + • • • • • • • E ffl + + + + • • • • • • ffl ffl • + • ffl • + • + + + + + + + + 0 + + • • • + +5 [ CD 00 CD O CD LU m • o CD CD ZD CD O Q CD cz o o CD m z: o zc CT> 00 O . + + • + • EH • EH cn + 0 + + + + + + • • ffl + + • ffl • ffl ffl ffl • • EH ffl • • ffl + • • + • EH • + • + • • + + + + • • • + + + + + • • + • • • • + + • • + +fflfflfflnnfflfflnn • fflffl^fflffl • EH • + • • • • + + + • • • • • EH + • EH EH + ^ ffl • • • 381 4- ( K + B E N C H 6 8 6 1 ^ . ^ B U C K 6 0 CPROB 0 = 0 1 0 + + B E N C H 6 8 6 0 + + B U C K 6 0 CPROB 0 . 0 2 0 00 03 0 + + + + + + + + + + + 6 0 ' + + + + + 4- B E N C H 6 8 6 0 B U C K 6 0 + + CPROB 0 = 0 3 5 • • • • • • • • + + • • • ffl a • + + ffl • ffl ^fi l • + + ffl • ffl • + BB EB EB a' + + • 0 B U C K 6 0 C P R O B 0 . 0 5 0 + 4- 4- 4- + ffl + + • + 4- 4- + 4- 60' 4- 4- 4- + + • 4- 4- 4- 3 6 0 + 4- 4- 4- 4- • • • • • • ffl ffl • ffl • ffl m w • • EH • O 0 B E N C H 6 8 4 0 B U C K 6 0 A C T U A L - 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4 4- 4-o4- CD [ CD o 00 CD X CD OD CD CD CD X DD r o CD 1 9 7 + • + + + + • • • • • • ffl • ffl • ffl ^ • • • • • • + + + + ffl ffl ffl + + ffl + ffl • • • ffl • ffl • ffl ffl B • B 3 - 3 + + - + • a 3 ffl ^ ffl • ffl ffl • + ffl • + + + ffl ffl + + • ffl -- ffl • • ffl + ffl • • • • ffl + ffl ffl • + • ffl • ffl ffl • • • + • ffl • • • • • + + + + + • • • + + + + + b + o [ CO O 00 CO ZZ CD LU CO o CD \£ CD ZD CO C\J o CO c z o cn o CO m o z c cn 00 -r̂ o o cn fe 4- • + • • ffl + 0 + 4 - 4 - 4 - 4 - • + + + + • • • ffl • • ffl • • ffl ffl • ffl • ffl ffl + • • • • • • ffl • ffl • • ffl ffl ffl ffl + • + • ffl ffl • 4~ ffl ffl ffl • • ffl ^ ffl • • • • • ffl 4- ffl ffl • • 4 4- 4- • • ffl ffl • ffl • ffl ffl ffl ffl ffl ffl • 4- • • • ffl • • • • • ffl + 4- + 4- 4- 861 + + + • + ffl • EB • • EB EB • • • EB ffl ffl ffl ffl ffl ffl E B • • + • • ffl.ffl ffl • ffl ffl ffl E B ffl ffl + • • • ffl + + • • E B ffl ffl • • • • • + • • ffl ffl • E B • • • • + • • + + • ffl • • • • • • • ffl D ffl ffl EB • ^ • • ffl ffl • • ffl ffl ffl • ffl • • ffl ffl ^ ffl • ffl ffl ffl + • • • + + + + + + + + • ffl + + 0 + CD O o 00 CD X CD LU CD O CD CD ZD CD CD Q 200 + • • + • ffl ffl • ••EB • • • • • + + • ffl ^ • • • ffl ffl ffl • • • + + + ffl • + + • + ^ ffl ffl ffl • EB ffl + + +• • EB • • ffl • ffl • • ffl ffl • + ffl • + + + ffl ffl • + • ffl ffl ffl • • ffl • ffl • • • • ffl ffl • ffl ^ • + ^ • + • + ffl ffl • ffl • • • + + + + + b + CD ffl ffl + + [ L - 1 -0 o 00 CD X CD LD OD O CO o X on LD CD OD 0.8 B E N C H 6 8 4 0 B U C K 6 0 CPROB 0 = 0 1 0 • ffl D ' E E B E N C H 6 8 4 0 B U C K 6 0 CPROB 0 . 0 2 0 o to B E N C H 6 8 4 0 + + • ffl • B U C K 6 0 + + + CPROB 0 . 0 3 5 to o 204 • • + ffl ffl i ffl • I • + • ffl • • ffl • + • + + + • + + + + + + + + o + C D CD O oo CD ZZ CD OD O CD CD ZD OD O LO CD O CQ CD OD Q_ CD 0 60 • ffl + B E N C H 6 8 6 - H B U C K 6 0 G + A C T U A L HK ffl ffl ffl • ffl • • • • • • • to o (SI B E N C H 6 8 6 0 B U C K 6 0 G B H 6 0 m x CO o CO CL" o CO o o CO m 2: o zc CO 00 CO o o fe CO o + • ffl • • • • • • + + • • • + • • ffl ffl ffl ffl ffl • • ffl ffl • ffl • ffl • • ^ ^ ffl • • H f f l f f l f f l r ^ f f l f f l • ffl ffl ffl ̂ ffl + + ffl • ffl ffl • • + • ffl • • • ffl • • • ffl ffl ffl • • • • • ffl • ffl • • • + ffl • ffl ffl • ffl • ffl ffl ffl ffl ffl r \ V j a sggB LOZ 208 • ffl EB • 1 + fflfflfflfflffl • • • • • • • ffl • ffl ffl fflffl + fflffl • ffl ffl • ffl • • • • • f f l + ffl ̂  • ffl F + • • ffl • • + ffl ffl + • • ffl • ffl • ffl + • + • + • 1 o CO o o CO 00 CO ZZ o CO o o CO o ZD CO o • B B • + B E • B • B B + • • B • B B E • B B • B B • • + • B • • • • B B B + • • B • B B • ^ • + B + • r o CD O CD 00 CD ZC O LU CQ CD O CO CD ZD CQ 210 ^ P ffl ffl • ffl • • ffl ffl • ffl ffl • ffl • • ffl ffl • • • ^ P • • • • ffl ffl ffl • • • • ffl + ffl ffl • ffl • + ffl ffl • ffl ffl ^ 1 • ffl + ffl ffl • ffl ffl • • • + i j p • • [ o CD O O CD 00 CD JZ CD co CD o CD o ID CD ffl ffl • m • + • • o 6 0 ' • EB B E N C H 6 8 6 0 B U C K 6 0 G + EB • • • • ffl • • • • • ffl W • • ffl m EB • • • • • EB • • • EB • • • EB ffl ffl ID2 {f 0 m m m 6 0 ' B E N C H 6 8 6 0 B U C K 6 0 G ffl ffl • ffl ffl ffl • m EH • EE EB • ffl • • • • • • • • ffl • • ffl • • • • ffl LB • EH • • ID I 0 6 0 ' B E N C H 6 8 6 0 B U C K 6 0 G ffl m a ffl • • ffl ffl ffl • • • ES EB m w • • • EB ffl m m • • ffl ffl w ffl • • • • EB • ffl • • ffl ffl ffl • EB ffl ffl ffl IDO 0 1 6 0 ' B E N C H 6 8 6 0 B U C K 6 0 G • EH • 'A YZA ffl • • EH EH H I 11 m m m E?3 L±j t t l L J J uj w2 H • ffl EB • ffl • • ffl ffl • • ^ ffl • ffl • ffl ffl • • ffl ffl ffl • ffl • • • • • • • • • • ffl ffl EB EB ffl • ffl K R I G E LrjO • ffl 0 6 0 ' BENCH 6 8 6 0 B U C K 6 0 G + ffl/ffl + ffl • ffl • • • • ffl • ffl • ffl • + • ffl • ffl ffl ffl + • ffl • • ffl + • • • • • • • • • CPROB 0 . 0 1 0 B U C K 6 0 G CPROB 0 . 0 2 0 0 6 0 ' B E N C H 6 8 6 0 B U C K 6 0 G CPROB 0 . 0 3 5 V7A V?. ffl • + • • • • • • • ffl • ffl • • 0 6 0 ' B E N C H 6 8 6 0 B U C K 6 0 G A \ZZA EB EB 0 - 4 • ffl + - f + + ffl • + • • • m • • • • f f l f f l f f l ^ + • • ffl • ffl a EB u r n m m + • • • • •, • • a • • ffl CPROB 0 = 0 5 0 B E N C H 6 8 4 0 B U C K 6 0 G A C T U A L - BHK 220 -m- • • ffl • nam + ffl • EB 0 6 0 ' B E N C H 6 8 4 0 B U C K 6 0 G E X 6 0 + • + • • ffl • + • ffl ffl w • • ffl + • • • • • ffl • ffl • • • • ffl ffl' + • ffl + • ffl • + • • • • • + • + • • • • W • ffl w ffl • + ffl ffl ffl • ffl • + • • ffl • ffl ffl ffl ' ffl • ffl • • ffl ffl + • H - - . f f l • ffl ffl • • ffl ffl ffl • • • ffl • ffl ^ • + • ffl • • • • . • ffl + ffl • • • • ffl • • ffl • [ o CD O • ffl • ffl + ffl ffl • • o 00 CD X CD LD DD • • CD O CD \C CD X DD • ffl • • ffl • • + • 0 6 0 ' ffl ffl ffl ffl m • • + ffl ffl B U C K 6 0 G rj rj ID5 B E N C H 6 8 4 0 • ffl + ffl • • • ffl ffl ffl • m m • + • • a • • • • ffl • ffl m u m • ffl EB EB • ffl ffl ffl • ffl • • + • ffl ffl • ffl • ffl • • 0 6 0 ' B E N C H 6 8 4 0 B U C K 6 0 G I D 3 ffl + ffl • ffl • ffl ffl ffl • • ffl ffl ffl ffl • ffl m • A VZA EB BE EE • - R O - BE • + BB • ffl o 6 0 B E N C H 6 8 4 0 B U C K 6 0 G I D 2 ffl • • ffl ffl • ffl EE ffl ffl ffl ffl m u u u • BE • • ffl BB ffl ffl ro to to to IDO • ffl ffl EH • ffl • ffl w m • ffl ffl ffl ffl 0 6 0 ' B E N C H 6 8 4 0 B U C K 6 0 G ffl • EH K R I G E 0 + • EB • EB • • 6 0 ' • EB B E N C H 6 8 4 0 B U C K 6 0 G CPROB 0 . 0 1 0 • + EB + • + + • + 4- • A \AAA EB • ffl • ffl • ffl + + 4- 4- EB • ffl • ffl • ffl • • ffl • ffl • to to to o o 6 0 ' B E N C H 6 8 4 0 B U C K 6 0 G CPROB 0 . 0 3 5 0 6 c r B E N C H 6 8 4 0 + + • ffl • B U C K 6 0 G + + C P R O B 0 . 0 5 0 • ffl ffl ffl ffl ffl • ffl • ffl • ffl ffl ffl • • APPENDIX C ORE RESERVE REPORTS 234 BLOCK MODEL: BUCK 2 0 ' BLOCKS - NO ORE OUTLINE METHOD: BH4 BLASTHOLE POLYGONS RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 3 2 19300 . 41 163657 .00 0 . 004 688 .05 6 8 4 0 . 0 . 010 4 4 7 3 1 5 . 06 0 . 0 4 2 18612 . 36 1 3 1 2 4 5 . 5 0 0 . 015 1934 .85 6 8 4 0 . 0 . 020 3 1 6 0 6 9 . 56 0 . 0 5 3 16677 . 51 144481 .06 0 . 027 3848 .28 6 8 4 0 . 0 . 035 171588 . 50 0 . 0 7 5 12829 . 23 70828 .81 0 . 042 2952 . 16 6 8 4 0 . 0 . 050 100759 . 69 0 . 0 9 8 9 8 7 7 . 07 100759 .69 0 . 098 9877 .07 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 6 14184 . 09 187010 .94 0 . 004 679 .27 6 8 6 0 . 0 . 010 3 5 7 0 6 5 . 44 0 . 0 3 8 13504 . 82 119690 .94 0 . 015 1789 .39 6 8 6 0 . 0 . 020 237374 . 50 0 . 0 4 9 11715 . 43 109507 .25 0 . 027 2905 .93 6 8 6 0 . 0 . 035 127867 . 25 0 . 0 6 9 8 8 0 9 . 50 5 6 8 4 2 . 6 2 0 . 041 2351 .80 6 8 6 0 . 0 . 050 71024 . 62 0 . 0 9 1 6 4 5 7 . 70 7 1 0 2 4 . 6 2 0 . .091 6457 .70 TOTAL 0 . 000 1155048 . 00 0 . 0 2 9 33484 . 47 3 5 0 6 6 7 . 5 0 0 . 004 1367 .30 TOTAL 0 . 010 8 0 4 3 8 0 . 50 0 . 0 4 0 32117 . 18 2 5 0 9 3 6 . 4 4 0 . 015 3724 .24 TOTAL 0 . 020 553444 . 06 0 . 0 5 1 28392 . 94 2 5 3 9 8 8 . 2 5 0 . 027 6754 .20 TOTAL 0 . 035 2 9 9 4 5 5 . 81 0 . 0 7 2 2 1 6 3 8 . 73 127671 .44 0 . 042 5303 .95 TOTAL 0 . 050 171784 . 37 0 . 0 9 5 16334 . 79 171784 .37 0 . 095 16334 .79 BLOCK MODEL: BUCK 2 0 ' BLOCKS -• NO ORE OUTLINE METHOD: BH20 BLASTHOLE POLYGON WEIGHTED RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 610972 . 06 0 . 0 3 2 19297 . 97 1 3 9 9 2 7 . 7 5 0 . 005 671 .59 6 8 4 0 . 0 . 010 4 7 1 0 4 4 . 31 0 . 0 4 0 18626 . 38 130005 .12 0 . 015 1934 . 19 6 8 4 0 . 0 . 020 341039 . 19 0 . 0 4 9 16692 . 19 159642 .31 0 . 026 4230 .44 6 8 4 0 . 0 . 035 181396 . 87 0 . 0 6 9 1 2 4 6 1 . 75 77585 .31 0 . 042 3291 .48 6 8 4 0 . 0 . 050 1 0 3 8 1 1 . 56 0 . 0 8 8 9170 . 27 103811 .56 0 . 088 9170 .27 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 6 14182 . 02 171082 .62 0 . 004 713 .67 6 8 6 0 . 0 . 010 3 7 2 9 9 3 . 75 0 . 0 3 6 13468 . 36 117765 .19 0 . 015 1792 . 14 6 8 6 0 . 0 . 020 255228 . 56 0 . 0 4 6 11676 . 21 1 2 5 5 9 8 . 7 5 0 . 027 3371 .29 6 8 6 0 . 0 . 035 129629 . 81 0 . 0 6 4 8 3 0 4 . 92 5 8 3 1 1 . 4 4 0 . 042 2425 .91 6 8 6 0 . 0 . 050 7 1 3 1 8 . 37 0 . 0 8 2 5 8 7 9 . 01 71318 .37 0 . 082 5879 .01 TOTAL 0 . 000 1155048 . 00 0 . 0 2 9 33479 . 98 3 1 1 0 0 9 . 8 7 0 . 004 1385 .24 TOTAL 0 . 010 8 4 4 0 3 8 . 12 0 . 0 3 8 32094 . 74 2 4 7 7 7 0 . 3 7 0 . 015 3726 .34 TOTAL 0 . 020 596267 . 75 0 . 0 4 8 28368 . 40 2 8 5 2 4 1 . 0 6 0 . 027 7601 .72 TOTAL 0 . 035 311026 . 69 0 . 0 6 7 2 0 7 6 6 . 68 1 3 5 8 9 6 . 7 5 0 . 042 5717 .40 TOTAL 0 . 050 175129 . 94 0 . 0 8 6 15049 . 28 175129 .94 0 . 086 15049 .28 BLOCK MODEL: BUCK 2 0 ' BLOCKS - NO ORE OUTLINE METHOE i : BHKRIGE BLASTHOLE KRIGING - " A C T U A L " RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 3 3 19939 . 61 107989 .44 0 . 005 574 .60 6 8 4 0 . 0 . 010 5 0 2 9 8 2 . 62 0 . 0 3 9 19365 . 01 128928 .06 0 . 015 1945 .70 6 8 4 0 . 0 . 020 374054 . 56 0 . 0 4 7 17419 . 31 177480 .12 0 . 027 4764 .41 6 8 4 0 . 0 . 035 196574 . 44 0 . 0 6 4 12654 . 91 8 5 1 0 8 . 8 1 0 . 042 3553 .40 6 8 4 0 . 0 . 050 111465 . 62 0 . 0 8 2 9 1 0 1 . 51 111465 .62 0 . 082 9101 .51 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 7 14567 . 63 1 4 4 4 6 4 . 6 9 0 . 005 669 .94 6 8 6 0 . 0 . 010 3 9 9 6 1 1 . 69 0 . 0 3 5 13897 . 69 122171 .62 0 . 015 1880 .05 6 8 6 0 . 0 . 020 2 7 7 4 4 0 . 06 0 . 0 4 3 12017 . 64 1 4 4 0 0 7 . 6 9 0 . 027 3920 .42 6 8 6 0 . 0 . 035 133432 . 37 0 . 0 6 1 8 0 9 7 . 21 6 5 1 6 5 . 8 1 0 . 042 2752 .90 6 8 6 0 . 0 . 050 6 8 2 6 6 . 56 0 . 0 7 8 5344 . 31 6 8 2 6 6 . 5 6 0 . 078 5344 .31 TOTAL 0 . 000 1155048 . 00 0 . 0 3 0 34507 . 23 2 5 2 4 5 3 . 6 9 0 . 005 1244 .52 TOTAL 0 . 010 902594 . 31 0 . 0 3 7 33262 . 70 2 5 1 0 9 9 . 6 2 0 . 015 3825 .75 TOTAL 0 . 020 651494 . 69 0 . 0 4 5 29436 . 96 3 2 1 4 8 7 . 8 7 0 . 027 8684 .84 TOTAL 0 . 035 330006 . 81 0 . 0 6 3 20752 . 12 150274 .62 0 . 042 6306 .29 TOTAL 0 . 050 179732 . 19 0 . 0 8 0 14445 . 82 1 7 9 7 3 2 . 1 9 0 . 080 14445 .82 BLOCK MODEL: BUCK 2 0 ' BLOCKS -• NO ORE OUTLINE METHOD: EX4 EXPLORATION POLYGONS RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE : BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 2 7 16613 . 69 2 1 3 3 5 1 . 4 4 0 . 005 1019 . 52 6 8 4 0 . 0 . 010 397620 . 62 0 . 0 3 9 15594 . 17 118858 .62 0 . 014 1699 . 32 6 8 4 0 . 0 . 020 2 7 8 7 6 2 . 00 0 . 0 5 0 13894 . 85 135864 .06 0 . 026 3544 . 12 6 8 4 0 . 0 . 035 142897 . 94 0 . 0 7 2 10350 . 73 6 3 9 5 8 . 0 6 0 . 043 2 7 3 0 . 02 6 8 4 0 . 0 . 050 78939 . 87 0 . 0 9 7 7620 . 71 78939 .87 0 . 097 7620 . 71 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 5 13460 . 14 2 3 6 9 0 1 . 2 5 0 . 004 1003 . 89 6 8 6 0 . 0 . 010 3 0 7 1 7 5 . 12 0 . 0 4 1 12456 . 24 9 6 7 7 7 . 6 2 0 . 014 1388 . 49 6 8 6 0 . 0 . 020 210397 . 50 0 . 0 5 3 11067 . 75 9 6 2 7 1 . 7 5 0 . 027 2 5 8 7 . 77 6 8 6 0 . 0 . 035 114125 . 75 0 . 0 7 4 8 4 7 9 . 98 4 6 6 0 9 . 9 4 0 . 040 1865 . 02 6 8 6 0 . 0 . 050 6 7 5 1 5 . 81 0 . 0 9 8 6614 . 96 6 7 5 1 5 . 8 1 0 . 098 6614 . 96 TOTAL 0 . 000 1155048 . 00 0 . 0 2 6 3 0 0 7 3 . 80 4 5 0 2 5 2 . 1 9 0 . 004 2 0 2 3 . 39 TOTAL 0 . 010 704795 . 81 0 . 0 4 0 28050 . 41 2 1 5 6 3 6 . 2 5 0 . 014 3087 . 81 TOTAL 0 . 020 4 8 9 1 5 9 . 56 0 . 0 5 1 24962 . 60 2 3 2 1 3 5 . 8 1 0 . 026 6 1 3 1 . 89 TOTAL 0 . 035 2 5 7 0 2 3 . 75 0 . 0 7 3 18830 . 71 110568 .06 0 . 042 4 5 9 5 . 04 TOTAL 0 . 050 146455 . 69 0 . 0 9 7 14235 . 67 146455 .69 0 . 097 14235 . 67 BLOCK MODEL: BUCK 2 0 ' BLOCKS -• NO ORE OUTLINE METHOD: EX20 EXPLORATION POLYGON WEIGHTED RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 2 7 16611 . 42 188071 .75 0 . 005 9 4 1 . 75 6 8 4 0 . 0 . 010 4 2 2 9 0 0 . 31 0 . 0 3 7 15669 . 67 135162 .31 0 . 014 1957. 12 6 8 4 0 . 0 . 020 287738 . 00 0 . 0 4 8 13712 . 55 143061 .19 0 . 027 3819 . 24 6 8 4 0 . 0 . 035 144676 . 81 0 .068 9 8 9 3 . 31 7 3 0 6 4 . 6 2 0 . 042 3 0 7 1 . 90 6 8 4 0 . 0 . 050 71612 . 19 0 . 0 9 5 6 8 2 1 . 41 7 1 6 1 2 . 1 9 0 . 095 6 8 2 1 . 41 6 8 6 0 . 0 . 000 5 4 4 0 7 6 . 37 0 . 0 2 5 13458 . 30 2 1 9 2 1 0 . 3 1 0 . 005 9 9 2 . .43 6 8 6 0 . 0 . 010 324866 . 06 0 . 0 3 8 12465 . 87 103942 .12 0 . 015 1510. ,69 6 8 6 0 . 0 . 020 2 2 0 9 2 3 . 94 0 . 0 5 0 10955 . 18 111335 .12 0 . 027 2965 . 61 6 8 6 0 . 0 . 035 109588 . 81 0 . 0 7 3 7989 . 58 4 6 7 4 0 . 4 6 0 . 041 1924. 91 6 8 6 0 . 0 . 050 6 2 8 4 8 . 35 0 . 0 9 6 6064 . 67 6 2 8 4 8 . 3 5 0 . 096 6064 . 67 TOTAL 0 . 000 1155048 . 00 0 . 0 2 6 30069 . 71 4 0 7 2 8 1 . 6 2 0 . 005 1934. 16 TOTAL 0 . 010 747766 . 37 0 . 0 3 8 2 8 1 3 5 . 55 2 3 9 1 0 4 . 4 4 0 . 015 3467 . 81 TOTAL 0 . 020 5 0 8 6 6 1 . 94 0 . 0 4 8 2 4 6 6 7 . 74 2 5 4 3 9 6 . 2 5 0 . 027 6784 . 85 TOTAL 0 . 035 2 5 4 2 6 5 . 69 0 . 0 7 0 17882 . 89 1 1 9 8 0 5 . 1 9 0 . 042 4 9 9 6 . 81 TOTAL 0 . 050 134460 . 50 0 . 0 9 6 12886 . 08 1 3 4 4 6 0 . 5 0 0 . 096 12886. 08 BLOCK MODEL: BUCK 2 0 ' BLOCKS -• NO ORE OUTLINE METHOD: IDIO INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 2 8 17132 . 94 170119 .75 0 . 006 9 7 1 . 94 6 8 4 0 . 0 . 010 4 4 0 8 5 2 . 31 0 . 0 3 7 1 6 1 6 1 . 00 131963 .56 0 . 014 1 9 1 1 . 33 6 8 4 0 . 0 . 020 3 0 8 8 8 8 . 75 0 . 0 4 6 14249 . 68 1 5 9 6 2 6 . 0 0 0 . 026 4 1 8 1 . 55 6 8 4 0 . 0 . 035 149262 . 75 0 . 0 6 7 10068 . 12 7 4 2 5 6 . 0 0 0 . 042 3 0 9 8 . 67 6 8 4 0 . 0 . 050 75006 . 75 0 . 0 9 3 6 9 6 9 . 46 7 5 0 0 6 . 7 5 0 . 093 6 9 6 9 . 46 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 5 13675 . 96 2 0 5 1 5 8 . 8 1 0 . 005 1059 . 93 6 8 6 0 . 0 . 010 338917 . 56 0 . 0 3 7 12616 . 04 117340 .87 0 . 014 1677. 80 6 8 6 0 . 0 . 020 221576 . 69 0 . 0 4 9 10938 . 24 110927 .06 0 . 027 3 0 1 1 . 86 6 8 6 0 . 0 . 035 110649 . 62 0 . 0 7 2 7926 . 38 5 2 5 0 1 . 4 4 0 . 042 2185 . 65 6 8 6 0 . 0 . 050 58148 . 18 0 . 0 9 9 5 7 4 0 . 73 5 8 1 4 8 . 1 8 0 . 099 5740 . 73 TOTAL 0 . 000 1155048 . 00 0 . 0 2 7 3 0 8 0 8 . 89 3 7 5 2 7 8 . 0 6 0 . 005 2 0 3 1 . 85 TOTAL 0 . 010 779769 . 94 0 . 0 3 7 2 8 7 7 7 . 05 2 4 9 3 0 4 . 4 4 0 . 014 3589 . 13 TOTAL 0 . 020 5 3 0 4 6 5 . 50 0 . 0 4 7 25187 . 91 2 7 0 5 5 3 . 1 2 0 . 027 7193 . 42 TOTAL 0 . 035 2 5 9 9 1 2 . 37 0 . 0 6 9 17994 . 50 126757 .44 0 . 042 5284 . 30 TOTAL 0 . 050 133154. 94 0 . 0 9 5 12710 . 19 133154 .94 0 . 095 12710. 19 BLOCK MODEL: BUCK 2 0 ' BLOCKS -• NO ORE OUTLINE METHOD: ID5 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE I N S I D E GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 2 9 17503 . 23 138883 .25 0 .006 824 .06 6 8 4 0 . 0 . 010 4 7 2 0 8 8 . 81 0 . 0 3 5 16679 . 17 136451 .56 0 . 015 1995 .50 6 8 4 0 . 0 . 020 335637 . 25 0 . 0 4 4 14683 . 68 1 8 1 0 5 4 . 1 9 0 .026 4764 .59 6 8 4 0 . 0 . 035 154583 . 06 0 . 0 6 4 9 9 1 9 . 09 78760 .31 0 .041 3252 .19 6 8 4 0 . 0 . 050 75822 . 75 0 . 0 8 8 6 6 6 6 . 90 7 5 8 2 2 . 7 5 0 .088 6666 .90 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 5 13500 . 41 176925 .19 0 .006 979 .37 6 8 6 0 . 0 . 010 3 6 7 1 5 1 . 19 0 . 0 3 4 1 2 5 2 1 . 04 139405 .50 0 .014 2006 .84 6 8 6 0 . 0 . 020 2 2 7 7 4 5 . 69 0 . 0 4 6 10514 . 20 121453 .50 0 .027 3302 .89 6 8 6 0 . 0 . 035 106292 . 19 0 . 0 6 8 7 2 1 1 . 31 5 0 5 9 2 . 0 0 0 .041 2079 .86 6 8 6 0 . 0 . 050 5 5 7 0 0 . 18 0 . 0 9 2 5 1 3 1 . 45 5 5 7 0 0 . 1 8 0 .092 5131 .45 TOTAL 0 . 000 1155048 . 00 0 . 0 2 7 3 1 0 0 3 . 63 3 1 5 8 0 8 . 0 0 0 .006 1803 .41 TOTAL 0 . 010 8 3 9 2 4 0 . 00 0 . 0 3 5 29200 . 21 2 7 5 8 5 7 . 0 6 0 . 015 4002 .34 TOTAL 0 . 020 5 6 3 3 8 2 . 94 0 . 0 4 5 25197 . 87 3 0 2 5 0 7 . 6 2 0 .027 8067 .46 TOTAL 0 . 035 2 6 0 8 7 5 . 31 0 . 0 6 6 17130 . 41 129352 .37 0 .041 5332 .05 TOTAL 0 . 050 131522 . 94 0 . 0 9 0 11798 . 36 131522 .94 0 .090 11798 .36 BLOCK MODEL: BUCK 2 0 ' BLOCKS -• NO ORE OUTLINE METHOD: ID3 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 2 9 17892 . 36 110323 .25 0 .006 684 .20 6 8 4 0 . 0 . 010 500648 . 81 0 . 0 3 4 17208 . 15 142604 .19 0 . 015 2110 .25 6 8 4 0 . 0 . 020 358044 . 62 0 . 0 4 2 15097 . 90 199887 .44 0 .027 5309 .55 6 8 4 0 . 0 . 035 158157 . 19 0 . 0 6 2 9 7 8 8 . 36 8 0 7 0 2 . 4 4 0 .041 3340 .52 6 8 4 0 . 0 . 050 77454 . 75 0 . 0 8 3 6 4 4 7 . 84 7 7 4 5 4 . 7 5 0 .083 6447 .84 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 5 13439 . 79 152412 .56 0 .006 891 .95 6 8 6 0 . 0 . 010 3 9 1 6 6 3 . 81 0 . 0 3 2 12547 . 84 151988 .19 0 .014 2191 .75 6 8 6 0 . 0 . 020 2 3 9 6 7 5 . 62 0 . 0 4 3 10356 . 09 135178 .62 0 .027 3663 .50 6 8 6 0 . 0 . 035 104497 . 00 0 . 0 6 4 6 6 9 2 . 59 5 1 6 5 2 . 8 2 0 .041 2136 .23 6 8 6 0 . 0 . 050 52844 . 18 0 . 0 8 6 4 5 5 6 . 36 5 2 8 4 4 . 1 8 0 .086 4556 .36 TOTAL 0 . 000 1155048 . 00 0 . 0 2 7 3 1 3 3 2 . 14 2 6 2 7 3 5 . 3 1 0 .006 1576 . 14 TOTAL 0 . 010 8 9 2 3 1 2 . 69 0 . 0 3 3 2 9 7 5 6 . 00 2 9 4 5 9 2 . 4 4 0 .015 4302 .01 TOTAL 0 . 020 597720 . 25 0 . 0 4 3 2 5 4 5 3 . 99 3 3 5 0 6 6 . 0 6 0 .027 8973 .04 TOTAL 0 . 035 262654 . 19 0 . 0 6 3 16480 . 95 132355 .25 0 .041 5476 .75 TOTAL 0 . 050 130298 . 94 0 . 0 8 4 11004 . 20 130298 .94 0 .084 11004 .20 BLOCK MODEL: BUCK 2 0 ' BLOCKS -• NO ORE OUTLINE METHOE »: ID2 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 3 0 18178 . 04 92632 .31 0 .007 611 . 13 6 8 4 0 . 0 . 010 5 1 8 3 3 9 . 75 0 . 0 3 4 17566 . 91 1 4 1 4 7 8 . 1 9 0 . 015 2127 .39 6 8 4 0 . 0 . 020 3 7 6 8 6 1 . 56 0 . 0 4 1 15439 . 52 2 1 2 9 5 9 . 7 5 0 .027 5652 .74 6 8 4 0 . 0 . 035 1 6 3 9 0 1 . 81 0 . 0 6 0 9786 . 78 8 8 0 9 5 . 4 4 0 .041 3630 .66 6 8 4 0 . 0 . 050 75806 . 37 0 . 0 8 1 6156 . 12 7 5 8 0 6 . 3 7 0 .081 6156 .12 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 5 13418 . 90 135602 .94 0 .006 833 .87 6 8 6 0 . 0 . 010 4 0 8 4 7 3 . 44 0 . 0 3 1 12585 . 02 163249 .06 0 .014 2367 .10 6 8 6 0 . 0 . 020 245224 . 37 0 . 0 4 2 10217 . 93 1 3 6 7 9 4 . 2 5 0 .027 3700 .68 6 8 6 0 . 0 . 035 108430 . 12 0 . 0 6 0 6 5 1 7 . 25 5 9 8 1 2 . 8 2 0 .041 2466 .07 6 8 6 0 . 0 . 050 4 8 6 1 7 . 30 0 . 0 8 3 4 0 5 1 . 18 4 8 6 1 7 . 3 0 0 .083 4051 .18 TOTAL 0 . 000 1155048 . 00 0 . 0 2 7 31596 . 93 2 2 8 2 3 4 . 8 1 0 .006 1445 .00 TOTAL 0 . 010 9 2 6 8 1 3 . 19 0 . 0 3 3 3 0 1 5 1 . 94 3 0 4 7 2 7 . 1 9 0 . 015 4494 .49 TOTAL 0 . 020 622086 . 00 0 . 0 4 1 2 5 6 5 7 . 45 3 4 9 7 5 4 . 0 6 0 .027 9353, .41 TOTAL 0 . 035 2 7 2 3 3 1 . 94 0 . 0 6 0 16304 . 04 1 4 7 9 0 8 . 2 5 0 .041 6096, .73 TOTAL 0 . 050 124423 . 69 0 . 0 8 2 10207 . 30 124423 .69 0 .082 10207, .30 BLOCK MODEL: BUCK 2 0 ' BLOCKS - NO ORE OUTLINE METHOD: I D I INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 3 0 18474 . 07 6 8 1 0 3 . 3 7 0 . 007 4 4 7 . 27 6 8 4 0 . 0 . 010 542868 . 69 0 . 0 3 3 18026 . 80 140172 .56 0 . 015 2 1 2 1 . 19 6 8 4 0 . 0 . 020 4 0 2 6 9 6 . 12 0 . 0 3 9 15905 . 61 2 3 6 1 1 7 . 8 1 0 . 026 6 2 3 8 . 11 6 8 4 0 . 0 . 035 166578 . 31 0 . 0 5 8 9 6 6 7 . 50 8 8 5 3 6 . 0 6 0 . 041 3 6 4 5 . 70 6 8 4 0 . 0 . 050 78042 . 25 0 . 0 7 7 6 0 2 1 . 80 7 8 0 4 2 . 2 5 0 . 077 6 0 2 1 . 80 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 5 13414 . 34 111514 .62 0 . 006 7 0 6 . 81 6 8 6 0 . 0 . 010 4 3 2 5 6 1 . 75 0 . 0 2 9 12707 . 53 182686 .12 0 . 014 2 6 3 5 . 60 6 8 6 0 . 0 . 020 2 4 9 8 7 5 . 62 0 . 0 4 0 10071 . 93 140531 .62 0 . 027 3 8 0 7 . 56 6 8 6 0 . 0 . 035 109344 . 00 0 . 0 5 7 6264 . 37 6 3 2 0 7 . 3 4 0 . 042 2 6 2 8 . 49 6 8 6 0 . 0 . 050 4 6 1 3 6 . 66 0 . 0 7 9 3 6 3 5 . 89 4 6 1 3 6 . 6 6 0 . 079 3 6 3 5 . 89 TOTAL 0 . 000 1155048 . 00 0 . 0 2 8 31888 . 40 179617 .50 0 . 006 1154 . 07 TOTAL 0 . 010 975430 . 50 0 . 0 3 2 30734 . 33 3 2 2 8 5 8 . 6 9 0 . 015 4 7 5 6 . 78 TOTAL 0 . 020 6 5 2 5 7 1 . 81 0 . 0 4 0 2 5 9 7 7 . 55 3 7 6 6 4 9 . 5 0 0 . 027 10045 . 68 TOTAL 0 . 035 2 7 5 9 2 2 . 31 0 . 0 5 8 15931 . 87 151743 .44 0 . 041 6274 . 18 TOTAL 0 . 050 124178 . 87 0 . 0 7 8 9 6 5 7 . 69 124178 .87 0 . 078 9 6 5 7 . 69 BLOCK MODEL: BUCK 2 0 ' BLOCKS - NO ORE OUTLINE METHOD: IDO INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE I N S I D E GRADE 1 BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 .031 18658 . 23 5 8 9 4 7 . 8 7 0 . 007 3 9 1 . 27 6 8 4 0 . 0 . 010 552024 . 19 0 . 0 3 3 18266 . 96 138850 .56 0 . 016 2 1 6 2 . 00 6 8 4 0 . 0 . 020 4 1 3 1 7 3 . 62 0 . 0 3 9 16104. 95 2 4 5 0 4 4 . 9 4 0 . 027 6509 . 42 6 8 4 0 . 0 . 035 168128 . 69 0 . 0 5 7 9 5 9 5 . 54 9 4 1 3 3 . 8 1 0 . 042 3925 . 21 6 8 4 0 . 0 . 050 73994 . 87 0 . 0 7 7 5 6 7 0 . 32 73994 .87 0 . 077 5670 . 32 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 5 13439 . 38 102913 .94 0 . 007 6 7 4 . 73 6 8 6 0 . 0 . 010 4 4 1 1 6 2 . 44 0 . 0 2 9 12764 . 64 188039 .12 0 . 015 2 7 4 9 . 88 6 8 6 0 . 0 . 020 2 5 3 1 2 3 . 31 0 . 0 4 0 10014 . 76 150144 .12 0 . 027 4 1 1 1 . 04 6 8 6 0 . 0 . 035 102979 . 19 0 . 0 5 7 5 9 0 3 . 73 5 4 2 8 0 . 2 9 0 . 041 2 2 4 0 . 03 6 8 6 0 . 0 . 050 4 8 6 9 8 . 90 0 . 0 7 5 3 6 6 3 . 70 4 8 6 9 8 . 9 0 0 . 075 3 6 6 3 . 70 TOTAL 0 . 000 1155048 . 00 0 . 0 2 8 32097 . 59 161861 .37 0 . 007 1065 . 99 TOTAL 0 . 010 9 9 3 1 8 6 . 62 0 . 0 3 1 3 1 0 3 1 . 61 3 2 6 8 8 9 . 6 9 0 . 015 4 9 1 1 . 89 TOTAL 0 . 020 666296 . 94 0 . 0 3 9 26119 . 71 3 9 5 1 8 9 . 0 0 0 . 027 10620 . 45 TOTAL 0 . 035 271107 . 94 0 . 0 5 7 15499 . 27 148414 .12 0 . 042 6 1 6 5 . 25 TOTAL 0 . 050 122693 . 81 0 . 0 7 6 9334 . 02 122693 .81 0 . 076 9334 . 02 BLOCK MODEL: BUCK 2 0 ' BLOCKS -• NO ORE OUTLINE METHOD: KRIGE EXPLORATION KRIGED : ESTIMATE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 3 0 18052 . 25 9 0 8 6 9 . 7 5 0 . 006 557 . 58 6 8 4 0 . 0 . 010 5 2 0 1 0 2 . 31 0 . 0 3 4 17494 . 66 149785 .06 0 . 015 2276 . 53 6 8 4 0 . 0 . 020 370317 . 25 0 . 0 4 1 15218 . 14 2 0 9 8 5 9 . 0 0 0 . 027 5 5 8 2 . 90 6 8 4 0 . 0 . 035 160458 . 25 0 . 0 6 0 9 6 3 5 . 23 8 7 1 4 8 . 8 1 0 . 041 3 5 6 5 . 57 6 8 4 0 . 0 . 050 73309 . 44 0 . 0 8 3 6 0 6 9 . 66 7 3 3 0 9 . 4 4 0 . 083 6 0 6 9 . 66 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 4 12994 . 03 137789 .81 0 . 006 8 3 8 . 07 6 8 6 0 . 0 . 010 4 0 6 2 8 6 . 56 0 . 0 3 0 12155 . 95 166219 .31 0 . 015 2 4 3 6 . 57 6 8 6 0 . 0 . 020 2 4 0 0 6 7 . 25 0 . 0 4 0 9 7 1 9 . 38 1 4 0 6 2 9 . 5 0 0 . 027 3 7 7 0 . 74 6 8 6 0 . 0 . 035 9 9 4 3 7 . 75 0 . 0 6 0 5 9 4 8 . 64 5 2 0 9 3 . 4 1 0 . 041 2 1 3 7 . 92 6 8 6 0 . 0 . 050 4 7 3 4 4 . 34 0 . 0 8 0 3 8 1 0 . 72 4 7 3 4 4 . 3 4 0 . 080 3 8 1 0 . 72 TOTAL 0 . 000 1155048 . 00 0 . 0 2 7 31046 . 27 2 2 8 6 5 9 . 1 2 0 . 006 1395 . 65 TOTAL 0 . 010 926388 . 87 0 . 0 3 2 2 9 6 5 0 . 62 3 1 6 0 0 4 . 3 1 0 . 015 4 7 1 3 . 09 TOTAL 0 . 020 610384 . 56 0 . 0 4 1 2 4 9 3 7 . 52 3 5 0 4 8 8 . 5 0 0 . 027 9 3 5 3 . 64 TOTAL 0 . 035 259896 . 06 0 . 0 6 0 15583 . 88 1 3 9 2 4 2 . 2 5 0 . 041 5 7 0 3 . 50 TOTAL 0 . 050 120653 . 81 0 . 0 8 2 9 8 8 0 . 37 120653 .81 0 . 082 9 8 8 0 . 37 BLOCK MODEL: BUCK 20» BLOCKS - NO ORE OUTLINE METHOD: CPROB CONDITIONAL PROBABILITY RESERVES - ABOVE CUTOFF GRADE I N S I D E GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 030 18052 .25 141275 . 4 4 0 . 005 734. , 14 6 8 4 0 . 0 . 010 4 6 9 6 9 6 . 62 0 . 037 17318 . 10 148412 .87 0 . 015 2206. ,54 6 8 4 0 . 0 . 020 321283 . 75 0 . 047 15111 .56 154524 .25 0 .027 4 1 3 1 . ,00 6 8 4 0 . 0 . 035 166759 . 50 0 . 066 10980 .57 76548 .75 0 .042 3186. ,00 6 8 4 0 . 0 . 050 9 0 2 1 0 . 75 0 . 086 7794 .57 90210 . 75 0 .086 7794. ,57 6 8 6 0 . 0 . 000 544076 . 37 0 . 024 12994 .03 184398 .00 0 .005 919. .47 6 8 6 0 . 0 . 010 359678 . 37 0 . 034 12074 .56 138627 .19 0 .015 2027, .75 6 8 6 0 . 0 . 020 2 2 1 0 5 1 . 19 0 . 045 10046 .81 113321 .75 0 .027 3009, .57 6 8 6 0 . 0 . 035 107729 . 44 0 . 065 7037 .25 49927 .98 0 .042 2080. .40 6 8 6 0 . 0 . 050 5 7 8 0 1 . 45 0 . 086 4956 .84 57801 .45 0 .086 4956 . .84 TOTAL 0 . 000 1155048 . 00 0 . 027 31046 .27 325673 .00 0 . 005 1653. ,60 TOTAL 0 . 010 8 2 9 3 7 5 . 00 0 . 035 29392 .66 287040 .00 0 . 015 4234 . .29 TOTAL 0 . 020 5 4 2 3 3 5 . 00 0 . 046 25158 .38 267846 . 00 0 .027 7140. ,55 TOTAL 0 . 035 2 7 4 4 8 9 . 00 0 . 066 18017 .82 126476 .81 0 .042 5266. ,41 TOTAL 0 . 050 148012 . 19 0 . 086 12751 .41 148012 .19 0 .086 12751 . ,41 BLOCK MODEL: BUCKG 2 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE METHOE >: BH4 BLASTHOLE POLYGONS RESERVES - ABOVE CUTOFF GRADE I N S I D E GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 4 1 17212 . 70 4 8 5 0 3 . 0 6 0 . 0 0 5 247 .21 6 8 4 0 . 0 . 010 374397 . 25 0 . 0 4 5 16965 . 49 8 6 3 9 8 . 1 2 0 . 0 1 5 1300 .43 6 8 4 0 . 0 . 020 2 8 7 9 9 9 . 12 0 . 0 5 4 15665 . 06 1 2 4 0 6 4 . 6 9 0 . 0 2 7 3327 .88 6 8 4 0 . 0 . 035 163934 . 44 0 . 0 7 5 12337 . 18 6 6 2 4 2 . 8 7 0 . 0 4 2 2768 .82 6 8 4 0 . 0 . 050 9 7 6 9 1 . 56 0 . 0 9 8 9 5 6 8 . 37 9 7 6 9 1 . 5 6 0 . 0 9 8 9568 .37 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 .037 12279 . 08 4 2 7 4 2 . 1 2 0 . 0 0 5 224 .80 6 8 6 0 . 0 . 010 2 9 0 4 7 9 . 75 0 . 0 4 1 12054 . 28 7 7 6 3 4 . 2 5 0 . 0 1 5 1168 .28 6 8 6 0 . 0 . 020 2 1 2 8 4 5 . 50 0 . 0 5 1 10886 . 00 9 2 0 7 7 . 5 0 0 . 0 2 7 2471 .22 6 8 6 0 . 0 . 035 120768 . 00 0 . 0 7 0 8 4 1 4 . 78 5 1 8 8 1 . 2 5 0 . 0 4 1 2151 .11 6 8 6 0 . 0 . 050 68886 . 75 0 . 0 9 1 6 2 6 3 . 66 6 8 8 8 6 . 7 5 0 . 0 9 1 6263 .66 TOTAL 0 . 000 756122 . 25 0 . 0 3 9 2 9 4 9 1 . 80 9 1 2 4 5 . 1 9 0 . 0 0 5 472 .04 TOTAL 0 . 010 664877 . 06 0 . 0 4 4 29019 . 77 164032 .37 0 . 0 1 5 2468 .70 TOTAL 0 . 020 500844 . 69 0 . 0 5 3 2 6 5 5 1 . 06 2 1 6 1 4 2 . 1 9 0 . 0 2 7 5799 .09 TOTAL 0 . 035 2 8 4 7 0 2 . 50 0 . 0 7 3 2 0 7 5 1 . 98 118124 .19 0 . 0 4 2 4919 .95 TOTAL 0 . 050 166578 . 31 0 . 0 9 5 15832 . 03 166578 .31 0 . 0 9 5 15832 .03 BLOCK MODEL: BUCKG 2 0 ' BLOCKS -• WITHIN ORE ZONE OUTLINE METHOD: BH20 BLASTHOLE POLYGON WEIGHTED RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 4 1 17210 . 97 3 2 2 8 0 . 9 4 0 . 0 0 6 196 .75 6 8 4 0 . 0 . 010 390619 . 37 0 . 0 4 4 17014 . 23 75953 .37 0 . 0 1 5 1159 .88 6 8 4 0 . 0 . 020 314666 . 00 0 . 0 5 0 15854 . 34 138899 .56 0 . 0 2 7 3714 .05 6 8 4 0 . 0 . 035 175766 . 44 0 . 0 6 9 12140 . 29 7 4 1 9 0 . 7 5 0 . 0 4 2 3139 .78 6 8 4 0 . 0 . 050 101575 . 69 0 . 0 8 9 9 0 0 0 . 51 101575 .69 0 . 0 8 9 9000 .51 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 .037 12277 . 66 2 8 4 6 2 . 0 6 0 . 0 0 6 178 .27 6 8 6 0 . 0 . 010 3 0 4 7 5 9 . 81 0 . 0 4 0 12099 . 39 7 3 7 1 7 . 5 0 0 . 0 1 6 1149 .42 6 8 6 0 . 0 . 020 2 3 1 0 4 2 . 31 0 . 0 4 7 10949 . 97 105982 .12 0 . 0 2 7 2865 .48 6 8 6 0 . 0 . 035 125060 . 19 0 . 0 6 5 8 0 8 4 . 48 5 5 2 7 5 . 8 7 0 . 0 4 2 2315 .61 6 8 6 0 . 0 . 050 69784 . 31 0 . 0 8 3 5768 . 87 6 9 7 8 4 . 3 1 0 . 0 8 3 5768 .87 TOTAL 0 . 000 7 5 6 1 2 2 . 25 0 . 0 3 9 29488 . 64 6 0 7 4 3 . 0 6 0 . 0 0 6 375 .02 TOTAL 0 . 010 6 9 5 3 7 9 . 19 0 . 0 4 2 2 9 1 1 3 . 62 149670 .81 0 . 0 1 5 2309 .30 TOTAL 0 . 020 545708 . 37 0 . 0 4 9 26804 . 32 2 4 4 8 8 1 . 6 9 0 . 0 2 7 6579 .53 TOTAL 0 . 035 300826 . 69 0 . 0 6 7 20224 . 79 129466 .62 0 . 0 4 2 5455 .40 TOTAL 0 . 050 171360 . 06 0 . 0 8 6 14769 . 39 171360 .06 0 . 0 8 6 14769 .39 BLOCK MODEL: BUCKG 2 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE METHOD: BHKRIGE BLASTHOLE KRIGING - " A C T U A L " RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 4 2 17737 . 18 16483 .19 0 . 0 0 7 113 .38 6 8 4 0 . 0 . 010 4 0 6 4 1 7 . 12 0 . 0 4 3 17623 . 80 5 5 9 2 8 . 6 9 0 . 0 1 6 900 . 15 6 8 4 0 . 0 . 020 350488 . 44 0 . 0 4 8 16723 . 65 1 5 9 6 9 1 . 2 5 0 . 0 2 7 4302 .34 6 8 4 0 . 0 . 035 190797 . 19 0 . 0 6 5 12421 . 31 7 7 7 4 8 . 5 0 0 . 0 4 1 3210 .00 6 8 4 0 . 0 . 050 113048 . 69 0 . 0 8 1 9 2 1 1 . 31 113048 .69 0 . 0 8 1 9211 .31 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 0 3 8 12598 . 95 11587 .19 0 . 0 0 6 71 .21 6 8 6 0 . 0 . 010 321634 . 69 0 . 0 3 9 12527 . 74 6 9 0 0 1 . 0 0 0 . 0 1 6 1112 .00 6 8 6 0 . 0 . 020 2 5 2 6 3 3 . 69 0 . 0 4 5 11415 . 73 1 1 7 0 3 0 . 7 5 0 . 0 2 7 3185 .25 6 8 6 0 . 0 . 035 135602 . 94 0 . 0 6 1 8 2 3 0 . 49 6 5 5 9 0 . 1 2 0 . 0 4 2 2742 .25 6 8 6 0 . 0 . 050 7 0 0 1 2 . 81 0 . 0 7 8 5 4 8 8 . 24 7 0 0 1 2 . 8 1 0 . 0 7 8 5488 .24 TOTAL 0 . 000 756122 . 25 0 . 0 4 0 30336 . 14 2 8 0 7 0 . 4 4 0 . 0 0 7 184 .60 TOTAL 0 . 010 7 2 8 0 5 1 . 81 0 . 0 4 1 3 0 1 5 1 . 54 124929 .62 0 . 0 1 6 2012 .15 TOTAL 0 . 020 6 0 3 1 2 2 . 19 0 . 0 4 7 28139 . 39 2 7 6 7 2 2 . 0 6 0 . 0 2 7 7487 .60 TOTAL 0 . 035 326400 . 12 0 . 0 6 3 2 0 6 5 1 . 79 143338 .62 0 . 0 4 2 5952 .25 TOTAL 0 . 050 1 8 3 0 6 1 . 50 0 . 0 8 0 14699 . 55 1 8 3 0 6 1 . 5 0 0 . 0 8 0 14699 .55 240 BLOCK MODEL: BUCKG 2 0 ' BLOCKS -• WITHIN ORE ZONE OUTLINE METHOD: EX4 EXPLORATION POLYGONS RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 3 6 1 5 1 5 1 . 52 5 6 6 3 0 . 4 4 0 . 0 0 6 324 . 36 6 8 4 0 . 0 . 010 3 6 6 2 6 9 . 87 0 . 0 4 0 14827 . 16 9 8 4 5 8 . 5 6 0 . 0 1 4 1415 . 63 6 8 4 0 . 0 . 020 2 6 7 8 1 1 . 31 0 . 0 5 0 1 3 4 1 1 . 53 128977 .06 0 . 0 2 6 3355 . 19 6 8 4 0 . 0 . 035 138834 . 25 0 . 0 7 2 10056 . 34 6 1 3 9 5 . 8 7 0 . 0 4 3 2 6 1 9 . 04 6 8 4 0 . 0 . 050 77438 . 37 0 . 0 9 6 7437 . 31 77438 .37 0 . 0 9 6 7 4 3 7 . 31 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 0 3 6 12055 . 03 4 5 2 8 8 . 0 0 0 . 0 0 5 236 . 92 6 8 6 0 . 0 . 010 2 8 7 9 3 3 . 87 0 . 0 4 1 11818 . 11 8 7 9 1 5 . 8 7 0 . 0 1 4 1255 . 94 6 8 6 0 . 0 . 020 200018 . 00 0 . 0 5 3 10562 . 17 9 2 8 1 1 . 8 7 0 . 0 2 7 2 4 9 2 . 69 6 8 6 0 . 0 . 035 107206 . 12 0 . 0 7 5 8 0 6 9 . 48 4 4 0 9 6 . 6 6 0 . 0 4 0 1774 . 54 6 8 6 0 . 0 . 050 6 3 1 0 9 . 46 0 . 1 0 0 6294 . 95 6 3 1 0 9 . 4 6 0 . 1 0 0 6294 . 95 TOTAL 0 . 000 756122 . 25 0 . 0 3 6 27206 . 55 1 0 1 9 1 8 . 4 4 0 . 0 0 6 5 6 1 . 28 TOTAL 0 . 010 6 5 4 2 0 3 . 81 0 . 0 4 1 2 6 6 4 5 . 28 1 8 6 3 7 4 . 5 0 0 . 0 1 4 2 6 7 1 . 57 TOTAL 0 . 020 4 6 7 8 2 9 . 31 0 . 0 5 1 2 3 9 7 3 . 71 2 2 1 7 8 8 . 9 4 0 . 0 2 6 5 8 4 7 . 88 TOTAL 0 . 035 246040 . 37 0 . 0 7 4 18125 . 83 105492 .50 0 . 0 4 2 4 3 9 3 . 57 TOTAL 0 . 050 140547 . 87 0 . 0 9 8 13732 . 26 140547 .87 0 . 0 9 8 13732 . 26 BLOCK MODEL: BUCKG 2 0 ' BLOCKS -• WITHIN ORE ZONE l DUTLINE METHOD: EX20 EXPLORATION POLYGON WEIGHTED RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 3 6 15149 . 92 4 1 9 9 1 . 3 7 0 . 0 0 7 2 7 6 . 38 6 8 4 0 . 0 . 010 380908 . 94 0 . 0 3 9 14873 . 54 102293 .81 0 . 0 1 5 1515 . 27 6 8 4 0 . 0 . 020 2 7 8 6 1 5 . 12 0 . 0 4 8 13358 . 27 136304 .69 0 . 0 2 7 3 6 3 1 . 97 6 8 4 0 . 0 . 035 142310 . 44 0 . 0 6 8 9 7 2 6 . 30 71367 .37 0 . 0 4 2 3 0 0 7 . 43 6 8 4 0 . 0 . 050 7 0 9 4 3 . 06 0 . 0 9 5 6 7 1 8 . 87 7 0 9 4 3 . 0 6 0 . 0 9 5 6 7 1 8 . 87 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 0 3 6 12053 . 87 3 1 6 4 4 . 5 0 0 . 0 0 6 2 0 3 . 90 6 8 6 0 . 0 . 010 301577 . 37 0 . 0 3 9 11849. 98 9 0 8 0 4 . 5 0 0 . 0 1 5 1322 . 01 6 8 6 0 . 0 . 020 2 1 0 7 7 2 . 87 0 . 0 5 0 10527 . 96 1 0 7 6 3 0 . 4 4 0 . 0 2 7 2 8 6 7 . 71 6 8 6 0 . 0 . 035 103142 . 44 0 . 0 7 4 7660 . 25 4 2 7 5 8 . 4 1 0 . 0 4 1 1763 . 88 6 8 6 0 . 0 . 050 60384 . 02 0 . 0 9 8 5896 . 37 6 0 3 8 4 . 0 2 0 . 0 9 8 5896 . 37 TOTAL 0 . 000 7 5 6 1 2 2 . 25 0 . 0 3 6 2 7 2 0 3 . 80 73635 .87 0 . 0 0 7 4 8 0 . 28 TOTAL 0 . 010 682486 . 37 0 . 0 3 9 2 6 7 2 3 . 52 193098 .37 0 . 0 1 5 2 8 3 7 . 28 TOTAL 0 . 020 4 8 9 3 8 8 . 00 0 . 0 4 9 2 3 8 8 6 . 23 2 4 3 9 3 5 . 1 2 0 . 0 2 7 6 4 9 9 . 67 TOTAL 0 . 035 2 4 5 4 5 2 . 87 0 . 0 7 1 17386 . 56 114125 .81 0 . 0 4 2 4 7 7 1 . 32 TOTAL 0 . 050 131327 . 06 0 . 0 9 6 12615 . 24 131327 .06 0 . 0 9 6 12615 . 24 BLOCK MODEL: BUCKG 2 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE METHOD: IDIO INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 3 8 16178 . 18 1 9 2 2 4 . 9 4 0 . 0 0 7 1 3 1 . 73 6 8 4 0 . 0 . 010 4 0 3 6 7 5 . 37 0 . 0 4 0 16046 . 45 8 3 1 9 9 . 4 4 0 . 0 1 5 1260 . 13 6 8 4 0 . 0 . 020 3 2 0 4 7 5 . 94 0 . 0 4 6 14786 . 32 166235 .56 0 . 0 2 6 4 3 7 9 . 07 6 8 4 0 . 0 . 035 154240 . 37 0 . 0 6 7 10407 . 25 7 7 0 4 6 . 7 5 0 . 0 4 2 3236 . 73 6 8 4 0 . 0 . 050 7 7 1 9 3 . 62 0 . 0 9 3 7170 . 52 7 7 1 9 3 . 6 2 0 . 0 9 3 7 1 7 0 . 52 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 0 3 8 12612 . 59 2 0 1 7 1 . 5 0 0 . 0 0 6 130 . 37 6 8 6 0 . 0 . 010 313050 . 37 0 . 0 4 0 12482 . 22 8 6 6 2 6 . 6 2 0 . 0 1 5 1320 . 17 6 8 6 0 . 0 . 020 2 2 6 4 2 3 . 75 0 . 0 4 9 11162 . 05 1 1 4 3 3 8 . 0 0 0 . 0 2 7 3 0 9 2 . 50 6 8 6 0 . 0 . 035 112085 . 75 0 . 0 7 2 8 0 6 9 . 55 5 2 6 8 0 . 9 3 0 . 0 4 1 2176 . 84 6 8 6 0 . 0 . 050 59404 . 82 0 . 0 9 9 5 8 9 2 . 71 5 9 4 0 4 . 8 2 0 . 0 9 9 5 8 9 2 . 71 TOTAL 0 . 000 7 5 6 1 2 2 . 25 0 . 0 3 8 28790 . 77 3 9 3 9 6 . 5 0 0 . 0 0 7 2 6 2 . 10 TOTAL 0 . 010 7 1 6 7 2 5 . 75 0 . 0 4 0 28528 . 67 169826 .00 0 . 0 1 5 2 5 8 0 . 30 TOTAL 0 . 020 5 4 6 8 9 9 . 75 0 . 0 4 7 2 5 9 4 8 . 37 2 8 0 5 7 3 . 5 6 0 . 0 2 7 7 4 7 1 . 57 TOTAL 0 . 035 266326 . 19 0 . 0 6 9 18476 . 80 1 2 9 7 2 7 . 7 5 0 . 0 4 2 5 4 1 3 . 58 TOTAL 0 . 050 136598 . 44 0 . 0 9 6 13063 . 22 136598 .44 0 . 0 9 6 13063 . 22 BLOCK MODEL: BUCKG 2 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE METHOE 1: ID5 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 3 9 16644 .41 10608 .00 0 . 0 0 8 8 2 . 00 6 8 4 0 . 0 . 010 4 1 2 2 9 2 . 31 0 . 0 4 0 16562 .41 6 0 9 3 8 . 8 7 0 . 0 1 6 9 4 8 . 97 6 8 4 0 . 0 . 020 3 5 1 3 5 3 . 4 4 0 . 0 4 4 1 5 6 1 3 . 4 4 1 7 9 3 2 4 . 2 5 0 . 0 2 7 4 8 0 6 . 42 6 8 4 0 . 0 . 035 172029 . 19 0 . 0 6 3 10807 .02 9 0 8 6 9 . 8 1 0 . 0 4 1 3 7 4 0 . 13 6 8 4 0 . 0 . 050 8 1 1 5 9 . 37 0 . 0 8 7 7 0 6 6 . 8 9 8 1 1 5 9 . 3 7 0 . 0 8 7 7066 . 89 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 0 3 7 1 2 4 8 7 . 8 5 9 3 3 5 . 0 6 0 . 0 0 7 6 4 . 48 6 8 6 0 . 0 . 010 3 2 3 8 8 6 . 81 0 . 0 3 8 12423 .37 8 9 4 4 9 . 9 4 0 . 0 1 6 1436 . 91 6 8 6 0 . 0 . 020 2 3 4 4 3 6 . 87 0 . 0 4 7 10986 .46 1 2 2 3 3 4 . 7 5 0 . 0 2 8 3368 . 05 6 8 6 0 . 0 . 035 112102 . 12 0 . 0 6 8 7 6 1 8 . 4 1 5 3 0 2 3 . 7 0 0 . 0 4 1 2 1 9 0 . 83 6 8 6 0 . 0 . 050 5 9 0 7 8 . 43 0 . 0 9 2 5 4 2 7 . 5 7 5 9 0 7 8 . 4 3 0 . 0 9 2 5 4 2 7 . 57 TOTAL 0 . 000 756122 . 25 0 . 0 3 9 2 9 1 3 2 . 2 6 19943 .06 0 . 0 0 7 146 . 48 TOTAL 0 . 010 736179 . 19 0 . 0 3 9 2 8 9 8 5 . 7 8 150388 .87 0 . 0 1 6 2 3 8 5 . 88 TOTAL 0 . 020 5 8 5 7 9 0 . 31 0 . 0 4 5 2 6 5 9 9 . 9 0 3 0 1 6 5 9 . 0 0 0 . 0 2 7 8 1 7 4 . 46 TOTAL 0 . 035 2 8 4 1 3 1 . 31 0 . 0 6 5 18425 .43 1 4 3 8 9 3 . 5 0 0 . 0 4 1 5 9 3 0 . 96 TOTAL 0 . 050 140237 . 81 0 . 0 8 9 12494 .47 140237 .81 0 . 0 8 9 12494 . 47 BLOCK MODEL: BUCKG 2 0 ' BLOCKS - WITHIN ORE ZONE I OUTLINE METHOD: ID3 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 4 0 17060 .00 3 5 0 8 . 8 1 0 . 0 0 7 2 5 . 83 6 8 4 0 . 0 . 010 4 1 9 3 9 1 . 50 0 . 0 4 1 17034 .17 4 4 6 1 8 . 8 7 0 . 0 1 6 710 . 65 6 8 4 0 . 0 . 020 3 7 4 7 7 2 . 62 0 . 0 4 4 16323 .52 187745 .37 0 . 0 2 7 5 1 4 5 . 30 6 8 4 0 . 0 . 035 187027 . 25 0 . 0 6 0 11178 .21 101135 .06 0 . 0 4 1 4 1 5 1 . 78 6 8 4 0 . 0 . 050 8 5 8 9 2 . 19 0 . 0 8 2 7026 .43 8 5 8 9 2 . 1 9 0 . 0 8 2 7026 . 43 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 0 3 7 12469 .78 4 3 4 1 . 1 2 0 . 0 0 8 3 2 . 79 6 8 6 0 . 0 . 010 328880 . 75 0 . 0 3 8 12436 .99 7 4 0 7 6 . 5 0 0 . 0 1 7 1237 . 93 6 8 6 0 . 0 . 020 2 5 4 8 0 4 . 25 0 . 0 4 4 11199 .06 136973 .81 0 . 0 2 7 3 7 3 6 . 60 6 8 6 0 . 0 . 035 117830 . 44 0 . 0 6 3 7 4 6 2 . 4 6 5 8 7 6 8 . 3 3 0 . 0 4 1 2 4 2 0 . 30 6 8 6 0 . 0 . 050 5 9 0 6 2 . 11 0 . 0 8 5 5 0 4 2 . 1 6 5 9 0 6 2 . 1 1 0 . 0 8 5 5 0 4 2 . 16 TOTAL 0 . 000 7 5 6 1 2 2 . 25 0 . 0 3 9 2 9 5 2 9 . 7 9 7 8 4 9 . 9 4 0 . 0 0 7 5 8 . 63 TOTAL 0 . 010 748272 . 31 0 . 0 3 9 2 9 4 7 1 . 1 6 118695 .44 0 . 0 1 6 1948 . 58 TOTAL 0 . 020 6 2 9 5 7 6 . 87 0 . 0 4 4 2 7 5 2 2 . 5 8 3 2 4 7 1 9 . 1 9 0 . 0 2 7 8 8 8 1 . 89 TOTAL 0 . 035 304857 . 69 0 . 0 6 1 18640 .68 159903 .44 0 . 0 4 1 6 5 7 2 . 09 TOTAL 0 . 050 144954 . 25 0 . 0 8 3 12068 .59 144954 .25 0 . 0 8 3 12068 . 59 BLOCK MODEL: BUCKG 2 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE METHOD: ID2 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 4 1 17339 .06 1 2 2 4 . 0 0 0 . 0 0 8 9 . 75 6 8 4 0 . 0 . 010 4 2 1 6 7 6 . 31 0 . 0 4 1 17329 .31 3 1 6 1 1 . 8 7 0 . 0 1 7 5 2 5 . 27 6 8 4 0 . 0 . 020 390064 . 44 0 . 0 4 3 16804 .04 1 8 6 8 9 6 . 6 9 0 . 0 2 8 5 1 8 8 . 77 6 8 4 0 . 0 . 035 2 0 3 1 6 7 . 75 0 . 0 5 7 11615 .26 1 1 8 5 3 2 . 2 5 0 . 0 4 1 4 8 3 9 . 10 6 8 4 0 . 0 . 050 8 4 6 3 5 . 50 0 . 0 8 0 6776 . 16 8 4 6 3 5 . 5 0 0 . 0 8 0 6 7 7 6 . 16 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 0 3 7 12473 .97 1 6 3 2 . 0 0 0 . 0 0 8 1 3 . 38 6 8 6 0 . 0 . 010 3 3 1 5 8 9 . 87 0 . 0 3 8 12460 .59 6 4 2 5 1 . 8 7 0 . 0 1 7 1 1 0 7 . 20 6 8 6 0 . 0 . 020 267338 . 00 0 . 0 4 2 11353 .40 1 4 2 0 3 3 . 0 0 0 . 0 2 7 3 8 6 1 . 61 6 8 6 0 . 0 . 035 125305 . 00 0 . 0 6 0 7 4 9 1 . 7 9 6 8 0 7 0 . 6 9 0 . 0 4 1 2794 . 67 6 8 6 0 . 0 . 050 57234 . 27 0 . 0 8 2 4 6 9 7 . 1 2 5 7 2 3 4 . 2 7 0 . 0 8 2 4 6 9 7 . 12 TOTAL 0 . 000 7 5 6 1 2 2 . 25 0 . 0 3 9 2 9 8 1 3 . 0 4 2 8 5 6 . 0 0 0 . 0 0 8 2 3 . 13 TOTAL 0 . 010 753266 . 25 0 . 0 4 0 2 9 7 8 9 . 9 1 9 5 8 6 3 . 7 5 0 . 0 1 7 1632 . 46 TOTAL 0 . 020 6 5 7 4 0 2 . 50 0 . 0 4 3 2 8 1 5 7 . 4 4 3 2 8 9 2 9 . 7 5 0 . 0 2 8 9 0 5 0 . 39 TOTAL 0 . 035 3 2 8 4 7 2 . 75 0 . 0 5 8 1 9 1 0 7 . 0 5 1 8 6 6 0 2 . 9 4 0 . 0 4 1 7 6 3 3 . 77 TOTAL 0 . 050 141869 . 81 0 . 0 8 1 11473 .29 141869 .81 0 . 0 8 1 11473 . 29 BLOCK MODEL: BUCKG 2 0 ' BLOCKS -• WITHIN ORE ZONE OUTLINE METHOE I: I D I INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 4 2 17612 . 74 0 . 0 0 0 . 0 0 0 0 .00 6 8 4 0 . 0 .010 4 2 2 9 0 0 . 31 0 . 0 4 2 17612 . 74 17495 .06 0 . 0 1 7 301 .67 6 8 4 0 . 0 .020 4 0 5 4 0 5 . 25 0 . 0 4 3 1 7 3 1 1 . 07 186962 .00 0 . 0 2 8 5283 .32 6 8 4 0 . 0 . 035 2 1 8 4 4 3 . 25 0 . 0 5 5 12027 . 75 132028 .81 0 . 0 4 1 5369 .51 6 8 4 0 . 0 . 050 8 6 4 1 4 . 44 0 . 0 7 7 6 6 5 8 . 24 8 6 4 1 4 . 4 4 0 . 0 7 7 6658 .24 6 8 6 0 . 0 .000 3 3 3 2 2 1 . 87 0 . 0 3 7 12475 . 58 0 . 0 0 0 . 0 0 0 0 .00 6 8 6 0 . 0 . 010 3 3 3 2 2 1 . 87 0 . 0 3 7 12475 . 58 5 1 7 0 1 . 7 5 0 . 0 1 8 917 .42 6 8 6 0 . 0 .020 281520 . 12 0 . 0 4 1 11558 . 16 151253 .87 0 . 0 2 7 4102 .67 6 8 6 0 . 0 . 035 130266 . 25 0 . 0 5 7 7455 . 49 78025 .87 0 . 0 4 2 3260 .91 6 8 6 0 . 0 . 050 5 2 2 4 0 . 34 0 . 0 8 0 4 1 9 4 . 58 5 2 2 4 0 . 3 4 0 . 0 8 0 4194 .58 TOTAL 0 .000 756122 . 25 0 . 0 4 0 30088 . 32 0 . 0 0 0 . 0 0 0 0 .00 TOTAL 0 .010 756122 . 25 0 . 0 4 0 30088 . 32 6 9 1 9 6 . 8 7 0 . 0 1 8 1219 .09 TOTAL 0 .020 6 8 6 9 2 5 . 37 0 . 0 4 2 28869 . 23 3 3 8 2 1 5 . 8 1 0 . 0 2 8 9385 .99 TOTAL 0 .035 3 4 8 7 0 9 . 56 0 . 0 5 6 19483 . 24 2 1 0 0 5 4 . 8 1 0 . 0 4 1 8630 .42 TOTAL 0 . 050 138654 . 75 0 . 0 7 8 10852 . 82 1 3 8 6 5 4 . 7 5 0 . 0 7 8 10852 .82 BLOCK MODEL: BUCKG 2 0 ' BLOCKS -• WITHIN ORE ZONE l DUTLINE METHOD: IDO INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 4 2 17770 . 50 0 . 0 0 0 . 0 0 0 0 .00 6 8 4 0 . 0 .010 4 2 2 9 0 0 . 31 0 . 0 4 2 17770 . 50 13464 .00 0 . 0 1 8 239 .57 6 8 4 0 . 0 .020 4 0 9 4 3 6 . 31 0 . 0 4 3 17530 . 93 184008 .06 0 . 0 2 8 5232 .05 6 8 4 0 . 0 .035 225428 . 25 0 . 0 5 5 12298 . 87 143828 .25 0 . 0 4 2 5992 . 10 6 8 4 0 . 0 . 050 8 1 6 0 0 . 00 0 . 0 7 7 6306 . 77 8 1 6 0 0 . 0 0 0 . 0 7 7 6306 . 77 6 8 6 0 . 0 .000 3 3 3 2 2 1 . 87 0 . 0 3 7 12467 . 73 0 . 0 0 0 . 0 0 0 0 .00 6 8 6 0 . 0 . 010 3 3 3 2 2 1 . 87 0 . 0 3 7 12467 . 73 4 6 9 6 9 . 0 0 0 . 0 1 8 832 .79 6 8 6 0 . 0 . 020 2 8 6 2 5 2 . 87 0 . 0 4 1 11634 . 94 151710 .75 0 . 0 2 7 4138 .44 6 8 6 0 . 0 . 035 134542 . 12 0 . 0 5 6 7496 . 50 8 0 2 4 5 . 4 4 0 . 0 4 1 3316 .92 6 8 6 0 . 0 .050 5 4 2 9 6 . 66 0 . 0 7 7 4 1 7 9 . 58 5 4 2 9 6 . 6 6 0 . 0 7 7 4179 .58 TOTAL 0 . 000 756122 . 25 0 . 0 4 0 30238 . 24 0 . 0 0 0 . 0 0 0 0 .00 TOTAL 0 .010 756122 . 25 0 . 0 4 0 30238 . 24 6 0 4 3 3 . 0 0 0 . 0 1 8 1072 .37 TOTAL 0 . 020 6 9 5 6 8 9 . 25 0 . 0 4 2 2 9 1 6 5 . 87 3 3 5 7 1 8 . 8 7 0 . 0 2 8 9370 .50 TOTAL 0 . 035 359970 . 37 0 . 0 5 5 19795 . 37 2 2 4 0 7 3 . 6 9 0 . 0 4 2 9309 .02 TOTAL 0 .050 135896 . 69 0 . 0 7 7 10486 . 36 135896 .69 0 . 0 7 7 10486 .36 BLOCK MODEL: BUCKG 2 0 ' BLOCKS -• WITHIN ORE ZONE l DUTLINE METHOD: KRIGE EXPLORATION KRIGED ESTIMATE RESERVES - ABOVE CUTOFF GRADE I N S I D E GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 4 1 17383 . 05 4 0 8 . 0 0 0 . 0 0 9 3 .73 6 8 4 0 . 0 . 010 4 2 2 4 9 2 . 31 0 . 0 4 1 17379 . 32 2 5 1 6 5 . 4 4 0 . 0 1 7 430 .02 6 8 4 0 . 0 . 020 397326 . 87 0 . 0 4 3 16949 . 30 2 0 1 9 4 3 . 7 5 0 . 0 2 8 5654 .53 6 8 4 0 . 0 . 035 195383 . 12 0 . 0 5 8 11294 . 77 1 1 1 3 5 1 . 4 4 0 . 0 4 1 4550 .21 6 8 4 0 . 0 . 050 8 4 0 3 1 . 69 0 . 0 8 0 6744 . 56 8 4 0 3 1 . 6 9 0 . 0 8 0 6744 .56 6 8 6 0 . 0 .000 3 3 3 2 2 1 . 87 0 . 0 3 6 12140 . 83 0 . 0 0 0 . 0 0 0 0 .00 6 8 6 0 . 0 . 010 3 3 3 2 2 1 . 87 0 . 0 3 6 12140 . 83 6 1 0 2 0 . 5 0 0 . 0 1 8 1070 .23 6 8 6 0 . 0 . 020 2 7 2 2 0 1 . 37 0 . 0 4 1 11070 . 59 148871 .12 0 . 0 2 7 3999 . 77 6 8 6 0 . 0 .035 123330 . 25 0 . 0 5 7 7070 . 83 7 1 6 4 4 . 7 5 0 . 0 4 2 2980, .93 6 8 6 0 . 0 . 050 5 1 6 8 5 . 46 0 . 0 7 9 4 0 8 9 . 89 5 1 6 8 5 . 4 6 0 . 0 7 9 4089 .89 TOTAL 0 .000 756122 . 25 0 . 0 3 9 2 9 5 2 3 . 88 4 0 8 . 0 0 0 . 0 0 9 3, .73 TOTAL 0 . 010 755714 . 25 0 . 0 3 9 2 9 5 2 0 . 15 8 6 1 8 6 . 0 0 0 . 0 1 7 1500. .25 TOTAL 0 . 020 669528 . 25 0 . 0 4 2 28019 . 90 3 5 0 8 1 4 . 8 7 0 . 0 2 8 9654, .29 TOTAL 0 . 035 3 1 8 7 1 3 . 37 0 . 0 5 8 18365 . 61 1 8 2 9 9 6 . 2 5 0 . 0 4 1 7531, .16 TOTAL 0 .050 135717 . 12 0 . 0 8 0 10834 . 45 135717 .12 0 . 0 8 0 10834, .45 BLOCK MODEL: METHOD: RESERVES - BENCH CUTOFF BUCKG 2 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE CPROB CONDITIONAL PROBABILITY ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 041 17383 . 05 6261 .19 0 .008 52. ,94 6 8 4 0 . 0 . 010 4 1 6 6 3 9 . 12 0 . 042 17330 . 11 70203 .81 0 .016 1117, .34 6 8 4 0 . 0 . 020 3 4 6 4 3 5 . 31 0 . 047 16212 . 77 156921 . 25 0 .027 4265 , .10 6 8 4 0 . 0 . 035 189514 . 06 0 . 063 11947 . 67 90029 .56 0 .042 3741 , .62 6 8 4 0 . 0 . 050 99484 . 50 0 . 082 8 2 0 6 . 05 99484 .50 0 .082 8206, .05 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 036 12140 . 83 8502 .37 0 .008 72. ,02 6 8 6 0 . 0 . 010 3 2 4 7 1 9 . 50 0 . 037 12068 . 81 82564 .62 0 .016 1288. ,20 6 8 6 0 . 0 . 020 242154 . 87 0 . 045 10780 . 61 122275 .81 0 .027 3269 . ,89 6 8 6 0 . 0 . 035 119879 . 06 0 . 063 7510 . 72 57832 .39 0 .042 2404. ,70 6 8 6 0 . 0 . 050 6 2 0 4 6 . 67 0 . 082 5106 . 02 62046 .67 0 .082 5106. ,02 TOTAL 0 . 000 7 5 6 1 2 2 . 25 0 . 039 2 9 5 2 3 . 88 14763 .62 0 .008 124, .95 TOTAL 0 . 010 741358 . 62 0 . 040 2 9 3 9 8 . 93 152768 .44 0 .016 2405, .55 TOTAL 0 . 020 588590 . 19 0 . 046 2 6 9 9 3 . 38 279197 .00 0 .027 7535. ,00 TOTAL 0 . 035 3 0 9 3 9 3 . 19 0 . 063 19458 . 38 147862 .06 0 .042 6146. .30 TOTAL 0 . 050 1 6 1 5 3 1 . 12 0 . 082 13312 . 07 161531 . 12 0 .082 13312. ,07 BLOCK MODEL: BUCK60 60* BLOCKS - NO ORE OUTLINE METHOD: BH4 BLASTHOLE POLYGONS RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 0 6 0 . 0 3 2 19300 .41 1 6 3 6 5 7 . 0 0 0 . 004 688 .05 6 8 4 0 . 0 . 010 4 4 7 3 1 5 . 0 6 0 . 0 4 2 18612 .36 1 3 1 2 4 5 . 5 0 0 . 015 1934 .85 6 8 4 0 . 0 . 020 3 1 6 0 6 9 . 5 6 0 . 0 5 3 16677 .51 144481 .06 0 . 027 3848 .28 6 8 4 0 . 0 . 035 171588 .50 0 . 0 7 5 12829 .23 70828 .81 0 . 042 2952 .16 6 8 4 0 . 0 . 050 100759 .69 0 . 0 9 8 9877 .07 100759 .69 0 . 098 9877 .07 6 8 6 0 . 0 . 000 5 4 4 0 7 6 . 3 7 0 . 0 2 6 14184 .09 187010 .94 0 . 004 679 .27 6 8 6 0 . 0 . 010 3 5 7 0 6 5 . 4 4 0 . 0 3 8 13504 .82 119690 .94 0 . 015 1789 .39 6 8 6 0 . 0 . 020 2 3 7 3 7 4 . 5 0 0 . 0 4 9 11715 .43 109507 .25 0 . 027 2905 .93* 6 8 6 0 . 0 . 035 1 2 7 8 6 7 . 2 5 0 . 0 6 9 8809 .50 5 6 8 4 2 . 6 2 0 . 041 2351 .80 6 8 6 0 . 0 . 050 7 1 0 2 4 . 6 2 0 . 0 9 1 6457 .70 7 1 0 2 4 . 6 2 0 . 091 6457 .70 TOTAL 0 . 000 1155048 .00 0 . 0 2 9 33484 .47 3 5 0 6 6 7 . 5 0 0 . 004 1367 .30 TOTAL 0 . 010 8 0 4 3 8 0 . 5 0 0 . 0 4 0 32117 .18 2 5 0 9 3 6 . 4 4 0 . 015 3724 .24 TOTAL 0 . 020 5 5 3 4 4 4 . 0 6 0 . 0 5 1 28392 .94 2 5 3 9 8 8 . 2 5 0 . 027 6754 .20 TOTAL 0 . 035 2 9 9 4 5 5 . 8 1 0 . 0 7 2 21638 .73 127671 .44 0 . 042 5303 .95 TOTAL 0 . 050 171784 .37 0 . 0 9 5 16334 .79 171784 .37 0 . 095 16334 .79 BLOCK MODEL: BUCK60 6 0 ' BLOCKS • - NO ORE OUTLINE METHOD: BH60 BLASTHOLE POLYGON WEIGHTED RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE : BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 0 6 0 . 0 3 2 19300 .17 108071 .06 0 . 005 572 .45 6 8 4 0 . 0 . 010 5 0 2 9 0 1 . 0 0 0 . 0 3 7 18727 .71 117650 .94 0 . 016 1834 . 18 6 8 4 0 . 0 . 020 3 8 5 2 5 0 . 0 6 0 . 0 4 4 16893 .54 184187 .62 0 . 027 4978 .32 6 8 4 0 . 0 . 035 2 0 1 0 6 2 . 4 4 0 . 0 5 9 11915 .21 1 0 1 3 4 7 . 2 5 0 . 042 4228 . 17 6 8 4 0 . 0 . 050 9 9 7 1 5 . 1 9 0 . 0 7 7 7687 .04 9 9 7 1 5 . 1 9 0 . 077 7687 .04 6 8 6 0 . 0 . 000 5 4 4 0 7 6 . 3 7 0 . 0 2 6 14183 .92 142767 .44 0 . 005 690 .74 6 8 6 0 . 0 . 010 4 0 1 3 0 8 . 9 4 0 . 0 3 4 13493 . 18 113407 .75 0 . 015 1687 . 73 6 8 6 0 . 0 . 020 2 8 7 9 0 1 . 1 9 0 .041 11805 .45 144366 .75 0 . 027 3830 .37 6 8 6 0 . 0 . 035 143534 .44 0 . 0 5 6 7975 .07 8 2 3 3 4 . 3 7 0 . 041 3360 .28 6 8 6 0 . 0 . 050 6 1 2 0 0 . 0 3 0 . 0 7 5 4614 . 79 6 1 2 0 0 . 0 3 0 . 075 4614 .79 TOTAL 0 . 000 1155048 .00 0 . 0 2 9 33484 .07 2 5 0 8 3 8 . 0 0 0 . 005 1263 . 18 TOTAL 0 . 010 9 0 4 2 1 0 . 0 0 0 . 0 3 6 32220 .90 2 3 1 0 5 8 . 6 9 0 . 015 3521 .91 TOTAL 0 . 020 6 7 3 1 5 1 . 3 1 0 . 0 4 3 28698 .99 3 2 8 5 5 4 . 3 7 0 . 027 8808 .70 TOTAL 0 . 035 3 4 4 5 9 6 . 9 4 0 . 0 5 8 19890 .29 183681 .69 0 . 041 7588 .45 TOTAL 0 . 050 1 6 0 9 1 5 . 2 5 0 . 0 7 6 12301 .84 1 6 0 9 1 5 . 2 5 0 . 076 12301 .84 BLOCK MODEL: BUCK60 6 0 ' BLOCKS - NO ORE OUTLINE METHOD: BHKRIGE BLASTHOLE KRIGING - " A C T U A L " RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 0 6 0 . 0 3 3 20033 .43 8 9 5 3 1 . 5 6 0 . 006 494 . 13 6 8 4 0 . 0 . 010 5 2 1 4 4 0 . 5 0 0 . 0 3 7 19539 .30 1 1 9 5 4 4 . 0 0 0 . 015 1808 .67 6 8 4 0 . 0 . 020 4 0 1 8 9 6 . 5 0 0 . 0 4 4 17730 .63 1 9 2 2 4 9 . 6 9 0 . 027 5194 .79 6 8 4 0 . 0 . 035 2 0 9 6 4 6 . 8 1 0 . 0 6 0 12535 .84 109931 .62 0 . 042 4652 .30 6 8 4 0 . 0 . 050 9 9 7 1 5 . 1 9 0 . 0 7 9 7883 .54 9 9 7 1 5 . 1 9 0 . 079 7883 .54 6 8 6 0 . 0 . 000 5 4 4 0 7 6 . 3 7 0 . 0 2 7 14425 .90 133187 .56 0 . 005 661 .96 6 8 6 0 . 0 . 010 4 1 0 8 8 8 . 8 1 0 . 0 3 3 13763 . 95 1 1 2 9 3 4 . 5 0 0 . 015 1692 . 16 6 8 6 0 . 0 . 020 2 9 7 9 5 4 . 3 1 0 . 0 4 1 12071 .79 163167 .37 0 . 027 4411 .92 6 8 6 0 . 0 . 035 134786 .94 0 . 0 5 7 7659 .87 6 8 9 3 5 . 7 5 0 . 041 2860 .61 6 8 6 0 . 0 . 050 6 5 8 5 1 . 1 9 0 . 0 7 3 4799 .26 6 5 8 5 1 . 1 9 0 . 073 4799 .26 TOTAL 0 . 000 1155048 .00 0 . 0 3 0 34459 .32 2 2 2 7 1 8 . 6 2 0 . 005 1156 .07 TOTAL 0 . 010 9 3 2 3 2 9 . 3 7 0 . 0 3 6 33303 .25 2 3 2 4 7 8 . 5 6 0 . 015 3500, .83 TOTAL 0 . 020 6 9 9 8 5 0 . 8 1 0 . 0 4 3 29802 .42 3 5 5 4 1 7 . 0 6 0 . 027 9606 .71 TOTAL 0 . 035 3 4 4 4 3 3 . 7 5 0 . 0 5 9 20195 .71 178867 .31 0 . 042 7512, . 90 TOTAL 0 . 050 165566 .44 0 . 0 7 7 12682 .80 165566 .44 0 . 077 12682, .80 BLOCK MODEL: BUCK60 6 0 ' BLOCKS -• NO ORE OUTLINE METHOD: EX4 EXPLORATION POLYGONS RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 0 6 0 . 0 2 7 16613 . 69 2 1 3 3 5 1 . 4 4 0 . 005 1019 . 52 6 8 4 0 . 0 . 010 3 9 7 6 2 0 . 6 2 0 . 0 3 9 15594 . 17 118858 .62 0 .014 1699 . 32 6 8 4 0 . 0 . 020 2 7 8 7 6 2 . 0 0 0 . 0 5 0 13894 . 85 135864 .06 0 .026 3544 . 12 6 8 4 0 . 0 . 035 142897 .94 0 . 0 7 2 10350 . 73 6 3 9 5 8 . 0 6 0 .043 2 7 3 0 . 02 6 8 4 0 . 0 . 050 78939 .87 0 . 0 9 7 7 6 2 0 . 71 7 8 9 3 9 . 8 7 0 .097 7620 . 71 6 8 6 0 . 0 . 000 5 4 4 0 7 6 . 3 7 0 . 0 2 5 13460 . 14 2 3 6 9 0 1 . 2 5 0 . 004 1003 . 89 6 8 6 0 . 0 . 010 3 0 7 1 7 5 . 1 2 0 . 0 4 1 12456 . 24 9 6 7 7 7 . 6 2 0 .014 1388 . 49 6 8 6 0 . 0 . 020 2 1 0 3 9 7 . 5 0 0 . 0 5 3 11067 . 75 9 6 2 7 1 . 7 5 0 .027 2 5 8 7 . 77 6 8 6 0 . 0 . 035 1 1 4 1 2 5 . 7 5 0 . 0 7 4 8 4 7 9 . 98 4 6 6 0 9 . 9 4 0 . 0 4 0 1865 . 02 6 8 6 0 . 0 . 050 6 7 5 1 5 . 8 1 0 . 0 9 8 6614 . 96 6 7 5 1 5 . 8 1 0 .098 6614 . 96 TOTAL 0 . 000 1155048 .00 0 . 0 2 6 3 0 0 7 3 . 80 4 5 0 2 5 2 . 1 9 0 .004 2 0 2 3 . 39 TOTAL 0 . 010 7 0 4 7 9 5 . 8 1 0 . 0 4 0 2 8 0 5 0 . 41 2 1 5 6 3 6 . 2 5 0 .014 3 0 8 7 . 81 TOTAL 0 . 020 4 8 9 1 5 9 . 5 6 0 .051 2 4 9 6 2 . 60 2 3 2 1 3 5 . 8 1 0 .026 6 1 3 1 . 89 TOTAL 0 . 035 2 5 7 0 2 3 . 7 5 0 . 0 7 3 18830 . 71 110568 .06 0 .042 4 5 9 5 . 04 TOTAL 0 . 050 1 4 6 4 5 5 . 6 9 0 . 0 9 7 14235 . 67 146455 .69 0 .097 14235 . 67 BLOCK MODEL: BUCK60 6 0 ' BLOCKS - NO ORE OUTLINE METHOD: EX60 EXPLORATION POLYGON WEIGHTED RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 0 6 0 . 0 2 7 16613 . 35 150193 .00 0 .006 8 5 6 . 76 6 8 4 0 . 0 . 010 4 6 0 7 7 9 . 0 6 0 . 0 3 4 15756 . 59 149670 .81 0 .015 2 1 9 9 . 74 6 8 4 0 . 0 . 020 3 1 1 1 0 8 . 2 5 0 . 0 4 4 13556 . 84 166039 .75 0 .027 4 4 1 7 . 37 6 8 4 0 . 0 . 035 1 4 5 0 6 8 . 5 0 0 . 0 6 3 9 1 3 9 . 47 8 0 5 2 2 . 8 1 0 .041 3 3 3 3 . 88 6 8 4 0 . 0 . 050 6 4 5 4 5 . 6 3 0 . 0 9 0 5 8 0 5 . 59 6 4 5 4 5 . 6 3 0 .090 5805 . 59 6 8 6 0 . 0 . 000 5 4 4 0 7 6 . 3 7 0 . 0 2 5 13459 . 68 159299 .56 0 .004 6 8 7 . 82 6 8 6 0 . 0 . 010 3 8 4 7 7 6 . 8 1 0 . 0 3 3 12771 . 87 152624 .75 0 .015 2 2 4 1 . 86 6 8 6 0 . 0 . 020 2 3 2 1 5 2 . 0 6 0 . 0 4 5 10530 . 01 119119 .75 0 .027 3 2 2 5 . 09 6 8 6 0 . 0 . 035 113032 .31 0 . 0 6 5 7304 . 92 5 5 4 8 7 . 9 7 0 .043 2 3 9 3 . 77 6 8 6 0 . 0 . 050 5 7 5 4 4 . 3 4 0 . 0 8 5 4 9 1 1 . 15 5 7 5 4 4 . 3 4 0 .085 4 9 1 1 . 15 TOTAL 0 . 000 1155048 .00 0 . 0 2 6 3 0 0 7 3 . 02 3 0 9 4 9 2 . 1 2 0 . 005 1544 . 57 TOTAL 0 . 010 8 4 5 5 5 5 . 8 7 0 . 0 3 4 28528 . 46 3 0 2 2 9 5 . 5 0 0 . 015 4 4 4 1 . 60 TOTAL 0 . 020 5 4 3 2 6 0 . 3 7 0 . 0 4 4 24086 . 86 2 8 5 1 5 9 . 5 0 0 .027 7 6 4 2 . 46 TOTAL 0 . 035 2 5 8 1 0 0 . 8 7 0 . 0 6 4 16444 . 40 136010 .94 0 .042 5 7 2 7 . 65 TOTAL 0 . 050 1 2 2 0 8 9 . 9 4 0 . 0 8 8 10716 . 75 122089 .94 0 .088 10716 . 75 BLOCK MODEL: BUCK60 6 0 ' BLOCKS -• NO ORE OUTLINE METHOD: IDIO INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 0 6 0 . 0 2 6 15911 . 70 1 8 2 6 3 7 . 1 9 0 .006 1004 . 65 6 8 4 0 . 0 . 010 4 2 8 3 3 4 . 8 7 0 . 0 3 5 14907 . 05 117553 .00 0 .015 1739 . 86 6 8 4 0 . 0 . 020 3 1 0 7 8 1 . 8 7 0 . 0 4 2 13167 . 20 172943 .12 0 .026 4 4 6 2 . 40 6 8 4 0 . 0 . 035 1 3 7 8 3 8 . 7 5 0 . 0 6 3 8 7 0 4 . 79 7 3 2 9 3 . 0 6 0 .042 3 0 8 1 . 34 6 8 4 0 . 0 . 050 6 4 5 4 5 . 6 3 0 . 0 8 7 5 6 2 3 . 46 6 4 5 4 5 . 6 3 0 .087 5 6 2 3 . 46 6 8 6 0 . 0 . 000 5 4 4 0 7 6 . 3 7 0 . 0 2 3 12536 . 46 2 1 3 1 7 1 . 9 4 0 .005 1086 . 34 6 8 6 0 . 0 . 010 3 3 0 9 0 4 . 4 4 0 . 0 3 5 11450 . 12 116769 .62 0 . 014 1662 . 68 6 8 6 0 . 0 . 020 2 1 4 1 3 4 . 8 1 0 . 0 4 6 9 7 8 7 . 45 119609 .37 0 .027 3 2 1 4 . 55 6 8 6 0 . 0 . 035 9 4 5 2 5 . 4 4 0 . 0 7 0 6 5 7 2 . 90 4 9 3 6 7 . 9 8 0 .042 2 0 9 0 . 43 6 8 6 0 . 0 . 050 4 5 1 5 7 . 4 6 0 . 0 9 9 4 4 8 2 . 46 4 5 1 5 7 . 4 6 0 . 0 9 9 4 4 8 2 . 46 TOTAL 0 . 000 1155048 .00 0 . 0 2 5 2 8 4 4 8 . 16 3 9 5 8 0 8 . 6 2 0 . 005 2 0 9 0 . 97 TOTAL 0 . 010 759239 .37 0 . 0 3 5 26357 . 18 2 3 4 3 2 2 . 6 9 0 . 015 3 4 0 2 . 54 TOTAL 0 . 020 5 2 4 9 1 6 . 6 9 0 . 0 4 4 22954 . 64 2 9 2 5 5 2 . 4 4 0 .026 7676 . 94 TOTAL 0 . 035 2 3 2 3 6 4 . 2 5 0 . 0 6 6 15277 . 70 1 2 2 6 6 1 . 1 9 0 .042 5 1 7 1 . 79 TOTAL 0 . 050 109703 .06 0 . 0 9 2 10105 . 91 109703 .06 0 .092 10105 . 91 BLOCK MODEL: BUCK60 6 0 ' BLOCKS - NO ORE OUTLINE METHOD: ID5 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE 1 GRADE : BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 2 7 16617 . 16 160197 . 19 0 . 006 960 .51 6 8 4 0 . 0 . 010 4 5 0 7 7 4 . 87 0 . 0 3 5 15656 . 65 106634 . 94 0 . 014 1524 .40 6 8 4 0 . 0 .020 3 4 4 1 3 9 . 94 0 . 0 4 1 14132 . 25 188039 . 12 0 . 026 4817 .10 6 8 4 0 . 0 .035 156100 . 81 0 . 0 6 0 9 3 1 5 . 15 8 7 8 8 3 . 19 0 . 041 3596 .41 6 8 4 0 . 0 . 050 6 8 2 1 7 . 62 0 . 0 8 4 5 7 1 8 . 74 6 8 2 1 7 . 62 0 . 084 5718 .74 6 8 6 0 . 0 .000 544076 . 37 0 . 0 2 3 12448 . 25 182865 . 69 0 . 005 962 .66 6 8 6 0 . 0 .010 361210 . 69 0 . 0 3 2 11485 . 59 139062 . 75 0 . 014 1963 .08 6 8 6 0 . 0 .020 2 2 2 1 4 7 . 94 0 . 0 4 3 9 5 2 2 . 51 127622 . 50 0 . 026 3364 .81 6 8 6 0 . 0 . 035 9 4 5 2 5 . 44 0 . 0 6 5 6 1 5 7 . 70 5 3 0 3 9 . 98 0 . 041 2196 .64 6 8 6 0 . 0 .050 4 1 4 8 5 . 46 0 . 0 9 5 3 9 6 1 . 06 4 1 4 8 5 . 46 0 . 095 3961 .06 TOTAL 0 .000 1155048 . 00 0 . 0 2 5 2 9 0 6 5 . 41 3 4 3 0 6 2 . 37 0 . 006 1923 .16 TOTAL 0 .010 8 1 1 9 8 5 . 62 0 . 0 3 3 27142 . 25 2 4 5 6 9 7 . 75 0 . 014 3487 .49 TOTAL 0 . 020 566287 . 87 0 . 0 4 2 23654 . 76 3 1 5 6 6 1 . 56 0 . 026 8181 .91 TOTAL 0 . 035 2 5 0 6 2 6 . 31 0 . 0 6 2 15472 . 85 140923 . 25 0 . 041 5793 .06 TOTAL 0 .050 109703 . 06 0 . 0 8 8 9 6 7 9 . 79 109703 . 06 0 . 088 9679 .79 BLOCK MODEL: BUCK60 6 0 ' BLOCKS -• NO ORE OUTLINE METHOD: ID3 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE I GRADE ! BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 2 8 17326 . 97 133938 . 25 0 . 007 879 .78 6 8 4 0 . 0 . 010 4 7 7 0 3 3 . 81 0 . 0 3 4 16447 . 20 1 1 5 7 4 1 . 50 0 . 015 1692 .46 6 8 4 0 . 0 .020 3 6 1 2 9 2 . 31 0 . 0 4 1 14754 . 73 205044 . 56 0 . 026 5309 .41 6 8 4 0 . 0 .035 156247 . 75 0 . 0 6 0 9 4 4 5 . 33 77014 . 12 0 . 042 3226 .20 6 8 4 0 . 0 . 050 79233 . 62 0 . 0 7 8 6 2 1 9 . 13 79233 . 62 0 . 078 6219 .13 6 8 6 0 . 0 .000 544076 . 37 0 . 0 2 3 12592 . 44 160523 . 62 0 . 006 915 .39 6 8 6 0 . 0 . 010 3 8 3 5 5 2 . 75 0 . 0 3 0 11677 . 05 156655 . 75 0 . 014 2244 .30 6 8 6 0 . 0 .020 226897 . 00 0 . 0 4 2 9 4 3 2 . 75 1 4 0 8 4 1 . 62 0 . 027 3860 .05 6 8 6 0 . 0 .035 8 6 0 5 5 . 37 0 . 0 6 5 5 5 7 2 . 69 3 7 9 1 1 . 36 0 . 041 1549 .31 6 8 6 0 . 0 . 050 4 8 1 4 4 . 02 0 . 0 8 4 4 0 2 3 . 38 4 8 1 4 4 . 02 0 . 084 4023 .38 TOTAL 0 .000 1155048 . 00 0 . 0 2 6 29919 . 41 2 9 4 4 6 1 . 37 0 . 006 1795 . 16 TOTAL 0 .010 8 6 0 5 8 6 . 62 0 . 0 3 3 28124 . 25 272397 . 25 0 . 014 3936 .76 TOTAL 0 . 020 5 8 8 1 8 9 . 37 0 . 0 4 1 2 4 1 8 7 . 49 345886 . 25 0 . 027 9169 .46 TOTAL 0 . 035 2 4 2 3 0 3 . 12 0 . 0 6 2 15018 . 02 114925 . 50 0 . 042 4775 .52 TOTAL 0 . 050 127377 . 62 0 . 0 8 0 10242 . 51 127377 . 62 0 . 080 10242 .51 BLOCK MODEL: BUCK60 6 0 ' BLOCKS - NO ORE OUTLINE METHOD: ID2 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE I GRADE 1 BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 0 2 9 17832 . 84 9 6 1 0 8 . 50 0 . 007 647 .62 6 8 4 0 . 0 .010 5 1 4 8 6 3 . 56 0 . 0 3 3 17185 . 22 135439 . 75 0 . 014 1914 .53 6 8 4 0 . 0 .020 3 7 9 4 2 3 . 81 0 . 0 4 0 15270 . 69 223176 . 06 0 . 026 5897 .93 6 8 4 0 . 0 .035 156247 . 75 0 . 0 6 0 9 3 7 2 . 76 6 9 6 7 0 . 12 0 . 041 2859 .58 6 8 4 0 . 0 .050 8 6 5 7 7 . 62 0 . 0 7 5 6 5 1 3 . 18 8 6 5 7 7 . 62 0 . 075 6513 .18 6 8 6 0 . 0 . 000 544076 . 37 0 . 0 2 4 12820 . 79 147157 . 50 0 . 006 923 .52 6 8 6 0 . 0 .010 396918 . 87 0 . 0 3 0 11897 . 27 159005 . 81 0 . 014 2276 .62 6 8 6 0 . 0 .020 2 3 7 9 1 3 . 06 0 . 0 4 0 9 6 2 0 . 65 144970 . 62 0 . 028 4004 .55 6 8 6 0 . 0 . 035 9 2 9 4 2 . 44 0 . 0 6 0 5616 . 09 4 3 8 5 1 . 86 0 . 040 1766 .41 6 8 6 0 . 0 . 050 4 9 0 9 0 . 58 0 . 0 7 8 3 8 4 9 . 69 4 9 0 9 0 . 58 0 . 078 3849 .69 TOTAL 0 . 000 1155048 . 00 0 . 0 2 7 3 0 6 5 3 . 62 2 4 3 2 6 5 . 56 0 . 006 1571 .12 TOTAL 0 . 010 9 1 1 7 8 2 . 44 0 . 0 3 2 2 9 0 8 2 . 50 2 9 4 4 4 5 . 56 0 . 014 4191 .16 TOTAL 0 . 020 617336 . 87 0 . 0 4 0 2 4 8 9 1 . 34 368146 . 69 0 . 027 9902 .48 TOTAL 0 . 035 249190 . 19 0 . 0 6 0 14988 . 86 113522 . 00 0 . 041 4625 .99 TOTAL 0 . 050 135668 . 19 0 . 0 7 6 10362 . 86 135668 . 19 0 . 076 10362 .86 BLOCK MODEL: BUCK60 6 0 ' BLOCKS - NO ORE OUTLINE METHOD: I D I INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 0 6 0 . 0 3 0 18457 . 41 5 8 2 9 5 . 0 6 0 . 006 363 .42 6 8 4 0 . 0 . 010 5 5 2 6 7 7 . 0 0 0 . 0 3 3 18093 . 99 151922 .94 0 . 015 2240 .08 6 8 4 0 . 0 . 020 4 0 0 7 5 4 . 0 6 0 . 0 4 0 15853 . 91 2 3 7 1 6 2 . 3 1 0 . 026 6284 .63 6 8 4 0 . 0 . 035 1 6 3 5 9 1 . 7 5 0 . 0 5 8 9 5 6 9 . 28 7 9 0 7 0 . 4 4 0 . 042 3290 .36 6 8 4 0 . 0 . 050 8 4 5 2 1 . 3 1 0 . 0 7 4 6 2 7 8 . 91 8 4 5 2 1 . 3 1 0 . 074 6278 .91 6 8 6 0 . 0 . 000 5 4 4 0 7 6 . 3 7 0 . 0 2 4 13224 . 52 111416 .69 0 . 006 713 .00 6 8 6 0 . 0 . 010 4 3 2 6 5 9 . 6 9 0 . 0 2 9 12511 . 52 1 8 6 6 6 8 . 2 5 0 . 014 2665 .45 6 8 6 0 . 0 . 020 2 4 5 9 9 1 . 4 4 0 . 0 4 0 9846 . 07 135635 .56 0 . 027 3688 .43 6 8 6 0 . 0 . 035 110355 .87 0 . 0 5 6 6 1 5 7 . 63 7 2 6 8 9 . 2 5 0 . 042 3064 .47 6 8 6 0 . 0 . 050 3 7 6 6 6 . 5 7 0 . 0 8 2 3 0 9 3 . 16 3 7 6 6 6 . 5 7 0 . 082 3093 .16 TOTAL 0 . 000 1 1 5 5 0 4 8 . 0 0 0 . 0 2 7 3 1 6 8 1 . 93 1 6 9 7 1 1 . 2 5 0 . 006 1076 .41 TOTAL 0 . 010 9 8 5 3 3 6 . 7 5 0 . 0 3 1 3 0 6 0 5 . 51 3 3 8 5 9 1 . 1 9 0 . 014 4905 .53 TOTAL 0 . 020 6 4 6 7 4 5 . 5 6 0 . 0 4 0 2 5 6 9 9 . 98 3 7 2 7 9 7 . 9 4 0 . 027 9973 .07 TOTAL 0 . 035 2 7 3 9 4 7 . 6 2 0 . 0 5 7 15726 . 91 1 5 1 7 5 9 . 7 5 0 . 042 6354 .85 TOTAL 0 . 050 122187 .87 0 . 0 7 7 9 3 7 2 . 07 122187 .87 0 . 077 9372 .07 BLOCK MODEL: BUCK60 6 0 ' BLOCKS -• NO ORE OUTLINE METHOD: IDO INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 0 6 0 . 0 3 1 18924 . 66 4 9 7 2 7 . 0 6 0 . 006 320 .41 6 8 4 0 . 0 . 010 5 6 1 2 4 5 . 0 0 0 . 0 3 3 18604 . 24 145101 .19 0 . 016 2265 .37 6 8 4 0 . 0 . 020 4 1 6 1 4 3 . 8 1 0 . 0 3 9 16338 . 87 2 5 2 5 6 8 . 4 4 0 . 027 6716 .43 6 8 4 0 . 0 . 035 163575 .37 0 . 0 5 9 9 6 2 2 . 45 9 0 4 2 9 . 1 2 0 . 043 3847 . 75 6 8 4 0 . 0 . 050 7 3 1 4 6 . 2 5 0 . 0 7 9 5774 . 70 7 3 1 4 6 . 2 5 0 . 079 5774 .70 6 8 6 0 . 0 . 000 544076 .37 0 . 0 2 5 13591 . 05 106357 .50 0 . 007 745 .62 6 8 6 0 . 0 . 010 4 3 7 7 1 8 . 8 7 0 . 0 2 9 12845 . 43 1 8 7 0 7 6 . 2 5 0 . 014 2678 .77 6 8 6 0 . 0 . 020 2 5 0 6 4 2 . 6 2 0 .041 10166 . 66 146716 .87 0 . 028 4072 .28 6 8 6 0 . 0 . 035 1 0 3 9 2 5 . 7 5 0 . 0 5 9 6094 . 39 5 2 5 1 7 . 7 3 0 . 042 2204 .86 6 8 6 0 . 0 . 050 5 1 4 0 8 . 0 2 0 . 0 7 6 3 8 8 9 . 53 5 1 4 0 8 . 0 2 0 . 076 3889 .53 TOTAL 0 . 000 1155048 .00 0 . 0 2 8 3 2 5 1 5 . 70 156084 .06 0 . 007 1066 .02 TOTAL 0 . 010 9 9 8 9 6 3 . 9 4 0 . 0 3 1 31449 . 68 3 3 2 1 7 7 . 4 4 0 . 015 4944 . 14 TOTAL 0 . 020 6 6 6 7 8 6 . 5 0 0 . 0 4 0 2 6 5 0 5 . 54 3 9 9 2 8 5 . 3 1 0 . 027 10788 . 70 TOTAL 0 . 035 2 6 7 5 0 1 . 1 9 0 . 0 5 9 15716 . 84 1 4 2 9 4 6 . 9 4 0 . 042 6052 .61 TOTAL 0 . 050 1 2 4 5 5 4 . 2 5 0 . 0 7 8 9 6 6 4 . 23 1 2 4 5 5 4 . 2 5 0 . 078 9664 .23 BLOCK MODEL: BUCK60 6 0 ' BLOCKS - NO ORE OUTLINE METHOD: KRIGE EXPLORATION KRIGING RESERVES - ABOVE CUTOFF GRADE I N S I D E GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 0 6 0 . 0 3 0 18042 . 68 7 7 3 7 3 . 1 2 0 . 006 480 .54 6 8 4 0 . 0 . 010 5 3 3 5 9 8 . 9 4 0 . 0 3 3 17562 . 14 153734 .50 0 . 015 2329 . 79 6 8 4 0 . 0 . 020 3 7 9 8 6 4 . 4 4 0 . 0 4 0 15232 . 35 2 0 7 4 7 6 . 2 5 0 . 026 5363 .81 6 8 4 0 . 0 . 035 1 7 2 3 8 8 . 1 9 0 . 0 5 7 9 8 6 8 . 54 109800 .94 0 . 042 4617 .30 6 8 4 0 . 0 . 050 6 2 5 8 7 . 2 3 0 . 0 8 4 5 2 5 1 . 24 6 2 5 8 7 . 2 3 0 . 084 5251 .24 6 8 6 0 . 0 . 000 5 4 4 0 7 6 . 3 7 0 . 0 2 4 12860 . 89 124668 .56 0 . 006 788 .38 6 8 6 0 . 0 . 010 4 1 9 4 0 7 . 8 1 0 . 0 2 9 12072 . 50 1 6 7 7 2 0 . 6 9 0 . 014 2418 .86 6 8 6 0 . 0 . 020 2 5 1 6 8 7 . 1 2 0 . 0 3 8 9 6 5 3 . 65 149980 .87 0 . 026 3909 .45 6 8 6 0 . 0 . 035 101706 .25 0 . 0 5 6 5 7 4 4 . 20 6 4 0 2 3 . 3 6 0 . 042 2668, .53 6 8 6 0 . 0 . 050 3 7 6 8 2 . 8 9 0 . 0 8 2 3 0 7 5 . 67 3 7 6 8 2 . 8 9 0 . 082 3075 .67 TOTAL 0 . 000 1155048 .00 0 . 0 2 7 3 0 9 0 3 . 56 2 0 2 0 4 1 . 1 9 0 . 006 1268 .91 TOTAL 0 . 010 9 5 3 0 0 6 . 8 1 0 . 0 3 1 29634 . 65 3 2 1 4 5 5 . 1 9 0 . 015 4748, .65 TOTAL 0 . 020 6 3 1 5 5 1 . 6 2 0 . 0 3 9 2 4 8 8 6 . 00 3 5 7 4 5 7 . 1 2 0 . 026 9273, .26 TOTAL 0 . 035 2 7 4 0 9 4 . 5 0 0 . 0 5 7 15612 . 74 173824 .37 0 . 042 7285 .83 TOTAL 0 . 050 100270 .12 0 . 0 8 3 8 3 2 6 . 91 100270 .12 0 . 083 8326, .91 248 BLOCK MODEL: BUCK60 6 0 ' BLOCKS - NO ORE OUTLINE METHOD: CPROB CONDITIONAL PROBABILITY RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 6 1 0 9 7 2 . 06 0 . 030 18042 .68 113827 . 25 0 . 006 633 .06 6 8 4 0 . 0 . 010 4 9 7 1 4 4 . 81 0 . 035 17409 .62 1 5 6 2 3 1 . 87 0 . 015 2332 .91 6 8 4 0 . 0 . 020 3 4 0 9 1 2 . 94 0 . 044 15076 .71 170762 . 44 0 . 027 4564 .67 6 8 4 0 . 0 . 035 170150 . 50 0 . 062 10512 .04 8 3 8 7 6 . 00 0 . 042 3489 .61 6 8 4 0 . 0 . 050 8 6 2 7 4 . 50 0 . 081 7022 .43 8 6 2 7 4 . 50 0 . 081 7022 .43 6 8 6 0 . 0 . 000 544076 . 37 0 . 024 12860 .89 161263 . 56 0 . 005 884 .77 6 8 6 0 . 0 . 010 3 8 2 8 1 2 . 81 0 . 031 11976 .12 151008 . 25 0 . 015 2213 .35 6 8 6 0 . 0 . 020 231804 . 56 0 . 042 9762 .77 125040 . 81 0 . 027 3318 .82 6 8 6 0 . 0 . 035 106763 . 75 0 . 060 6443 .95 5 4 7 6 2 . 33 0 . 042 2277 .93 6 8 6 0 . 0 . 050 5 2 0 0 1 . 42 0 . 080 4166 .02 5 2 0 0 1 . 42 0 . 080 4166 .02 TOTAL 0 . 000 1155048 . 00 0 . 027 30903 .56 275090 . 31 0 . 006 1517 .82 TOTAL 0 . 010 8 7 9 9 5 7 . 69 0 . 033 29385 .74 307240 . 12 0 . 015 4546 .25 TOTAL 0 . 020 572717 . 56 0 . 043 24839 .49 2 9 5 8 0 3 . 25 0 . 027 7883 .49 TOTAL 0 . 035 276914 . 31 0 . 061 16956 .00 138638 . 44 0 . 042 5767 .54 TOTAL 0 . 050 138275 . 87 0 . 081 11188 .45 138275 . 87 0 . 081 11188 .45 249 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS -• WITHIN ORE ZONE 1 DUTLINE METHOE I: BH4 BLASTHOLE POLYGONS RESERVES - ABOVE CUTOFF GRADE I N S I D E GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 3 1 0 . 0 4 1 17212 . 70 4 8 5 0 3 . 0 6 0 . 0 0 5 247 . 21 6 8 4 0 . 0 . 010 3 7 4 3 9 7 . 2 5 0 . 0 4 5 16965 . 49 8 6 3 9 8 . 1 2 0 . 0 1 5 1300 . 43 6 8 4 0 . 0 . 020 2 8 7 9 9 9 . 1 2 0 . 0 5 4 15665 . 06 1 2 4 0 6 4 . 6 9 0 . 0 2 7 3 3 2 7 . 88 6 8 4 0 . 0 . 035 1 6 3 9 3 4 . 4 4 0 . 0 7 5 12337 . 18 6 6 2 4 2 . 8 7 0 . 0 4 2 2 7 6 8 . 82 6 8 4 0 . 0 . 050 9 7 6 9 1 . 5 6 0 . 0 9 8 9 5 6 8 . 37 9 7 6 9 1 . 5 6 0 . 0 9 8 9 5 6 8 . 37 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 8 7 0 . 0 3 7 12279 . 08 4 2 7 4 2 . 1 2 0 . 0 0 5 2 2 4 . 80 6 8 6 0 . 0 . 010 2 9 0 4 7 9 . 7 5 0 . 0 4 1 12054 . 28 7 7 6 3 4 . 2 5 0 . 0 1 5 1168 . 28 6 8 6 0 . 0 . 020 2 1 2 8 4 5 . 5 0 0 . 0 5 1 10886 . 00 9 2 0 7 7 . 5 0 0 . 0 2 7 2 4 7 1 . 22 6 8 6 0 . 0 . 035 120768 .00 0 . 0 7 0 8 4 1 4 . 78 5 1 8 8 1 . 2 5 0 . 0 4 1 2 1 5 1 . 11 6 8 6 0 . 0 . 050 6 8 8 8 6 . 7 5 0 . 0 9 1 6 2 6 3 . 66 6 8 8 8 6 . 7 5 0 . 0 9 1 6 2 6 3 . 66 TOTAL 0 . 000 7 5 6 1 2 2 . 2 5 0 . 0 3 9 2 9 4 9 1 . 80 9 1 2 4 5 . 1 9 0 . 0 0 5 4 7 2 . 04 TOTAL 0 . 010 6 6 4 8 7 7 . 0 6 0 . 0 4 4 29019 . 77 164032 .37 0 . 0 1 5 2 4 6 8 . 70 TOTAL 0 . 020 5 0 0 8 4 4 . 6 9 0 . 0 5 3 2 6 5 5 1 . 06 2 1 6 1 4 2 . 1 9 0 . 0 2 7 5 7 9 9 . 09 TOTAL 0 . 035 2 8 4 7 0 2 . 5 0 0 . 0 7 3 2 0 7 5 1 . 98 1 1 8 1 2 4 . 1 9 0 . 0 4 2 4 9 1 9 . 95 TOTAL 0 . 050 166578 .31 0 . 0 9 5 15832 . 03 166578 .31 0 . 0 9 5 15832 . 03 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS -• WITHIN ORE ZONE 1 DUTLINE METHOD: BH60 BLASTHOLE POLYGON WEIGHTED RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 3 1 0 . 0 4 1 17212 . 47 1 3 3 4 9 . 7 5 0 . 0 0 5 7 0 . 79 6 8 4 0 . 0 . 010 4 0 9 5 5 0 . 5 6 0 . 0 4 2 17141 . 68 51832 .37 0 . 0 1 7 8 9 1 . 49 6 8 4 0 . 0 . 020 3 5 7 7 1 8 . 1 9 0 . 0 4 5 16250 . 20 165811 .25 0 . 0 2 7 4 5 4 1 . 51 6 8 4 0 . 0 . 035 191906 .94 0 . 0 6 1 11708. 68 8 3 2 3 2 . 0 6 0 . 0 4 2 3474 . 77 6 8 4 0 . 0 . 050 108674 .87 0 . 0 7 6 8 2 3 3 . 92 108674 .87 0 . 0 7 6 8 2 3 3 . 92 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 8 7 0 . 0 3 7 12278 . 81 9 0 5 7 . 6 2 0 . 0 0 6 5 7 . 66 6 8 6 0 . 0 . 010 3 2 4 1 6 4 . 2 5 0 . 0 3 8 12221 . 14 6 8 4 6 2 . 4 4 0 . 0 1 6 1094 . 43 6 8 6 0 . 0 . 020 2 5 5 7 0 1 . 8 1 0 . 0 4 4 11126 . 71 111841 .00 0 . 0 2 7 3 0 0 9 . 38 6 8 6 0 . 0 . 035 143860 .81 0 . 0 5 6 8 1 1 7 . 33 74223 .37 0 . 0 4 1 3 0 3 1 . 89 6 8 6 0 . 0 . 050 6 9 6 3 7 . 4 4 0 . 0 7 3 5 0 8 5 . 44 6 9 6 3 7 . 4 4 0 . 0 7 3 5 0 8 5 . 44 TOTAL 0 . 000 7 5 6 1 2 2 . 2 5 0 . 0 3 9 2 9 4 9 1 . 28 2 2 4 0 7 . 3 7 0 . 0 0 6 128 . 45 TOTAL 0 . 010 7 3 3 7 1 4 . 8 7 0 . 0 4 0 29362 . 83 120294 .81 0 . 0 1 7 1985 . 92 TOTAL 0 . 020 6 1 3 4 2 0 . 0 6 0 . 0 4 5 2 7 3 7 6 . 91 2 7 7 6 5 2 . 2 5 0 . 0 2 7 7 5 5 0 . 89 TOTAL 0 . 035 3 3 5 7 6 7 . 8 1 0 . 0 5 9 19826 . 02 1 5 7 4 5 5 . 4 4 0 . 0 4 1 6 5 0 6 . 65 TOTAL 0 . 050 178312 .37 0 . 0 7 5 13319 . 37 178312 .37 0 . 0 7 5 13319 . 37 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS -• WITHIN ORE ZONE 1 DUTLINE METHOD: BHKRIGE BLASTHOLE KRIGING - " A C T U A L " RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 3 1 0 . 0 4 2 17779 . 30 1 2 7 7 8 . 5 6 0 . 0 0 6 8 2 . 46 6 8 4 0 . 0 . 010 4 1 0 1 2 1 . 7 5 0 . 0 4 3 17696 . 84 3 4 4 5 1 . 5 6 0 . 0 1 7 5 7 1 . 64 6 8 4 0 . 0 . 020 3 7 5 6 7 0 . 1 9 0 . 0 4 6 17125 . 20 174819 .87 0 . 0 2 7 4 7 6 2 . 26 6 8 4 0 . 0 . 035 2 0 0 8 5 0 . 3 1 0 . 0 6 2 12362 . 94 9 5 8 6 3 . 7 5 0 . 0 4 3 4 0 8 7 . 16 6 8 4 0 . 0 . 050 104986 .56 0 . 0 7 9 8 2 7 5 . 78 104986 .56 0 . 0 7 9 8 2 7 5 . 78 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 8 7 0 . 0 3 7 12403 . 29 8 4 5 3 . 7 5 0 . 0 0 7 5 9 . 14 6 8 6 0 . 0 . 010 3 2 4 7 6 8 . 1 2 0 . 0 3 8 12344 . 15 5 4 1 4 9 . 8 1 0 . 0 1 6 8 6 2 . 18 6 8 6 0 . 0 . 020 2 7 0 6 1 8 . 3 1 0 . 0 4 2 1 1 4 8 1 . 96 133954 .62 0 . 0 2 7 3 6 3 3 . 92 6 8 6 0 . 0 . 035 136663 .69 0 . 0 5 7 7848 . 04 6 6 3 5 7 . 1 2 0 . 0 4 2 2 7 7 1 . 85 6 8 6 0 . 0 . 050 7 0 3 0 6 . 5 6 0 . 0 7 2 5076 . 20 7 0 3 0 6 . 5 6 0 . 0 7 2 5076 . 20 TOTAL 0 . 000 7 5 6 1 2 2 . 2 5 0 . 0 4 0 30182 . 59 2 1 2 3 2 . 3 7 0 . 0 0 7 1 4 1 . 59 TOTAL 0 . 010 734889 .87 0 . 0 4 1 3 0 0 4 1 . 00 8 8 6 0 1 . 3 1 0 . 0 1 6 1433 . 82 TOTAL 0 . 020 6 4 6 2 8 8 . 5 6 0 . 0 4 4 28607 . 17 3 0 8 7 7 4 . 5 0 0 . 0 2 7 8 3 9 6 . 19 TOTAL 0 . 035 3 3 7 5 1 4 . 0 6 0 . 0 6 0 20210 . 98 162220 .87 0 . 0 4 2 6 8 5 9 . 00 TOTAL 0 . 050 1 7 5 2 9 3 . 1 9 0 . 0 7 6 1 3 3 5 1 . 98 1 7 5 2 9 3 . 1 9 0 . 0 7 6 13351 . 98 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE METHOD: EX4 EXPLORATION POLYGONS RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 3 6 1 5 1 5 1 . 52 5 6 6 3 0 . 4 4 0 . 0 0 6 324 . 36 6 8 4 0 . 0 . 010 3 6 6 2 6 9 . 87 0 . 0 4 0 14827 . 16 9 8 4 5 8 . 5 6 0 . 014 1415 . 63 6 8 4 0 . 0 . 020 2 6 7 8 1 1 . 31 0 . 0 5 0 13411 . 53 128977 .06 0 . 026 3 3 5 5 . 19 6 8 4 0 . 0 . 035 138834 . 25 0 . 0 7 2 10056 . 34 6 1 3 9 5 . 8 7 0 . 043 2 6 1 9 . 04 6 8 4 0 . 0 . 050 77438 . 37 0 . 0 9 6 7437 . 31 77438 .37 0 . 096 7437 . 31 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 0 3 6 12055 . 03 4 5 2 8 8 . 0 0 0 . 005 2 3 6 . 92 6 8 6 0 . 0 . 010 2 8 7 9 3 3 . 87 0 . 0 4 1 11818 . 11 8 7 9 1 5 . 8 7 0 . 014 1255 . 94. 6 8 6 0 . 0 . 020 200018 . 00 0 . 0 5 3 10562 . 17 9 2 8 1 1 . 8 7 0 . 027 2 4 9 2 . 69 6 8 6 0 . 0 . 035 107206 . 12 0 . 0 7 5 8 0 6 9 . 48 4 4 0 9 6 . 6 6 0 . 040 1774 . 54 6 8 6 0 . 0 . 050 6 3 1 0 9 . 46 0 . 1 0 0 6294 . 95 6 3 1 0 9 . 4 6 0 . 100 6 2 9 4 . 95 TOTAL 0 . 000 756122 . 25 0 . 0 3 6 27206 . 55 101918 .44 0 . 006 5 6 1 . 28 TOTAL 0 . 010 6 5 4 2 0 3 . 81 0 . 0 4 1 2 6 6 4 5 . 28 186374 .50 0 . 014 2 6 7 1 . 57 TOTAL 0 . 020 4 6 7 8 2 9 . 31 0 .051 2 3 9 7 3 . 71 2 2 1 7 8 8 . 9 4 0 . 026 5 8 4 7 . 88 TOTAL 0 . 035 246040 . 37 0 . 0 7 4 18125 . 83 1 0 5 4 9 2 . 5 0 0 . 042 4 3 9 3 . 57 TOTAL 0 . 050 140547 . 87 0 . 0 9 8 13732 . 26 140547 .87 0 . 098 13732 . 26 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS -• WITHIN ORE ZONE OUTLINE METHOD: EX60 EXPLORATION POLYGON WEIGHTED RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 3 6 15151 . 29 2 0 3 6 7 . 3 7 0 . 008 164 . 72 6 8 4 0 . 0 . 010 4 0 2 5 3 2 . 94 0 . 0 3 7 14986 . 57 9 3 7 9 1 . 0 6 0 . 015 1408 . 72 6 8 4 0 . 0 . 020 3 0 8 7 4 1 . 87 0 . 0 4 4 13577 . 85 1 5 5 2 0 3 . 2 5 0 . 026 4 1 0 2 . 15 6 8 4 0 . 0 . 035 153538 . 62 0 . 0 6 2 9 4 7 5 . 70 8 8 6 9 9 . 1 9 0 . 041 3 6 4 0 . 17 6 8 4 0 . 0 . 050 6 4 8 3 9 . 39 0 . 0 9 0 5 8 3 5 . 53 6 4 8 3 9 . 3 9 0 . 090 5 8 3 5 . 53 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 0 3 6 12054 . 71 4 6 3 4 . 8 7 0 . 007 3 1 . 89 6 8 6 0 . 0 . 010 328587 . 00 0 .037 12022 . 81 9 7 6 0 9 . 9 4 0 . 015 1509 . 67 6 8 6 0 . 0 . 020 230977 . 06 0 . 0 4 6 10513 . 14 1 2 1 4 3 7 . 1 9 0 . 027 3332 . 18 6 8 6 0 . 0 . 035 109539 . 87 0 . 0 6 6 7180 . 96 5 3 7 0 9 . 1 3 0 . 043 2314 . 40 6 8 6 0 . 0 . 050 5 5 8 3 0 . 74 0 . 0 8 7 4 8 6 6 . 56 5 5 8 3 0 . 7 4 0 . 087 4 8 6 6 . 56 TOTAL 0 . 000 756122 . 25 0 . 0 3 6 27206 . 00 2 5 0 0 2 . 2 5 0 . 008 196 . 61 TOTAL 0 . 010 731120 . 00 0 . 0 3 7 2 7 0 0 9 . 39 191401 .06 0 . 015 2 9 1 8 . 39 TOTAL 0 . 020 539718 . 94 0 . 0 4 5 2 4 0 9 1 . 00 2 7 6 6 4 0 . 4 4 0 . 027 7434 . 35 TOTAL 0 . 035 263078 . 50 0 . 0 6 3 16656 . 65 142408 .37 0 . 042 5954 . 55 TOTAL 0 . 050 120670 . 12 0 . 0 8 9 10702 . 09 120670 .12 0 . 089 10702 . 09 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS -• WITHIN ORE ZONE OUTLINE METHOD: IDIO INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 3 5 14955 . 87 18180 .50 0 . 006 112 . 66 6 8 4 0 . 0 . 010 4 0 4 7 1 9 . 81 0 . 0 3 7 14843 . 20 8 5 7 1 2 . 6 9 0 . 015 1318 . 86 6 8 4 0 . 0 . 020 319007 . 12 0 . 0 4 2 13524 . 34 178442 .94 0 . 026 4 6 6 7 . 20 6 8 4 0 . 0 . 035 140564 . 19 0 . 0 6 3 8 8 5 7 . 14 7 3 2 1 1 . 5 6 0 . 042 3 0 7 3 . 03 6 8 4 0 . 0 . 050 67352 . 62 0 . 0 8 6 5784 . 12 6 7 3 5 2 . 6 2 0 . 086 . 5784 . 12 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 0 3 5 11797 . 02 2 0 1 3 8 . 8 7 0 . 006 119 . 81 6 8 6 0 . 0 . 010 313083 . 00 0 . 0 3 7 11677 . 21 8 1 6 1 6 . 3 7 0 . 016 1282 . 29 6 8 6 0 . 0 . 020 231466 . 62 0 . 0 4 5 10394 . 92 133383 .44 0 . 027 3 5 8 8 . 45 6 8 6 0 . 0 . 035 9 8 0 8 3 . 19 0 . 0 6 9 6 8 0 6 . 46 4 6 7 2 4 . 1 2 0 . 042 1954 . 94 6 8 6 0 . 0 . 050 5 1 3 5 9 . 06 0 . 0 9 4 4 8 5 1 . 53 5 1 3 5 9 . 0 6 0 . 094 4 8 5 1 . 53 TOTAL 0 . 000 756122 . 25 0 . 0 3 5 2 6 7 5 2 . 89 3 8 3 1 9 . 3 7 0 . 006 2 3 2 . 48 TOTAL 0 . 010 717802 . 87 0 . 0 3 7 26520 . 41 167329 .06 0 . 016 2 6 0 1 . 14 TOTAL 0 . 020 550473 . 81 0 . 0 4 3 2 3 9 1 9 . 27 3 1 1 8 2 6 . 3 7 0 . 026 8 2 5 5 . 66 TOTAL 0 . 035 238647 . 44 0 . 0 6 6 15663 . 61 1 1 9 9 3 5 . 7 5 0 . 042 5 0 2 7 . 96 TOTAL 0 . 050 118711 . 69 0 . 0 9 0 10635 . 65 1 1 8 7 1 1 . 6 9 0 . 090 10635 . 65 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE METHOD: ID5 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 3 1 0 . 0 3 7 15764 . 52 1 6 1 8 9 . 4 4 0 . 0 0 8 122 . 47 6 8 4 0 . 0 . 010 4 0 6 7 1 0 . 8 7 0 . 0 3 8 15642 . 05 5 1 9 4 6 . 5 6 0 . 0 1 6 8 2 6 . 61 6 8 4 0 . 0 . 020 3 5 4 7 6 4 . 3 1 0 . 0 4 2 14815 . 45 1 8 1 8 7 0 . 1 9 0 . 0 2 6 4 7 5 5 . 66 6 8 4 0 . 0 . 035 172894 .12 0 . 0 5 8 10059 . 79 9 8 6 7 0 . 7 5 0 . 0 4 0 3 9 9 1 . 79 6 8 4 0 . 0 . 050 74223 .37 0 . 0 8 2 6 0 6 8 . 00 74223 .37 0 . 0 8 2 6 0 6 8 . 00 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 8 7 0 . 0 3 5 11749 . 78 1 4 9 6 5 . 4 4 0 . 0 0 6 9 6 . 54 6 8 6 0 . 0 . 010 3 1 8 2 5 6 . 4 4 0 . 0 3 7 11653 . 23 7 7 9 2 8 . 0 6 0 . 0 1 7 1297 . 48 6 8 6 0 . 0 . 020 2 4 0 3 2 8 . 3 7 0 . 0 4 3 10355 . 75 141690 .31 0 . 0 2 7 3 8 1 8 . 07 6 8 6 0 . 0 . 035 9 8 6 3 8 . 0 6 0 . 0 6 6 6 5 3 7 . 68 5 1 5 2 2 . 2 0 0 . 0 4 2 2 1 7 1 . 55 6 8 6 0 . 0 . 050 4 7 1 1 5 . 8 6 0 . 0 9 3 4 3 6 6 . 13 4 7 1 1 5 . 8 6 0 . 0 9 3 4 3 6 6 . 13 TOTAL 0 . 000 7 5 6 1 2 2 . 2 5 0 . 0 3 6 27514 . 30 3 1 1 5 4 . 9 4 0 . 0 0 7 2 1 9 . 01 TOTAL 0 . 010 724967 .31 0 . 0 3 8 2 7 2 9 5 . 29 129874 .62 0 . 0 1 6 2 1 2 4 . 09 TOTAL 0 . 020 5 9 5 0 9 2 . 6 9 0 . 0 4 2 2 5 1 7 1 . 20 3 2 3 5 6 0 . 4 4 0 . 0 2 6 8 5 7 3 . 71 TOTAL 0 . 035 2 7 1 5 3 2 . 2 5 0 . 0 6 1 16597 . 48 150193 .00 0 . 0 4 1 6 1 6 3 . 35 TOTAL 0 . 050 1 2 1 3 3 9 . 2 5 0 . 0 8 6 10434 . 14 1 2 1 3 3 9 . 2 5 0 . 0 8 6 10434 . 14 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE METHOD: ID3 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 3 1 0 . 0 3 9 16487 . 60 1 2 5 1 7 . 4 4 0 . 0 0 8 106 . 06 6 8 4 0 . 0 . 010 4 1 0 3 8 2 . 8 7 0 . 0 4 0 16381 . 54 3 6 4 9 1 . 5 6 0 . 0 1 6 5 8 6 . 85 6 8 4 0 . 0 . 020 3 7 3 8 9 1 . 3 1 0 . 0 4 2 15794 . 69 194779 .25 0 . 0 2 7 5 2 9 5 . 65 6 8 4 0 . 0 . 035 179112 .06 0 . 0 5 9 10499 . 04 9 4 3 4 6 . 0 0 0 . 0 4 1 3904 . 74 6 8 4 0 . 0 . 050 8 4 7 6 6 . 0 6 0 . 0 7 8 6594 . 30 8 4 7 6 6 . 0 6 0 . 0 7 8 6594 . 30 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 8 7 0 . 0 3 6 11894 . 65 9 3 1 8 . 7 5 0 . 0 0 6 6 0 . 24 6 8 6 0 . 0 . 010 3 2 3 9 0 3 . 1 2 0 .037 11834 . 41 6 5 3 2 8 . 9 4 0 . 0 1 7 1096 . 15 6 8 6 0 . 0 . 020 2 5 8 5 7 4 . 1 9 0 . 0 4 2 10738 . 26 1 6 2 3 0 2 . 5 0 0 . 0 2 8 4 4 7 6 . 30 6 8 6 0 . 0 . 035 9 6 2 7 1 . 6 9 0 . 0 6 5 6 2 6 1 . 96 4 4 6 0 2 . 5 5 0 . 0 4 2 1856 . 47 6 8 6 0 . 0 . 050 5 1 6 6 9 . 1 4 0 . 0 8 5 4 4 0 5 . 49 5 1 6 6 9 . 1 4 0 . 0 8 5 4 4 0 5 . 49 TOTAL 0 . 000 7 5 6 1 2 2 . 2 5 0 . 0 3 8 28382 . 26 2 1 8 3 6 . 1 9 0 . 0 0 8 166 . 30 TOTAL 0 . 010 7 3 4 2 8 6 . 0 6 0 . 0 3 8 2 8 2 1 5 . 96 101820 .50 0 . 0 1 7 1 6 8 3 . 00 TOTAL 0 . 020 6 3 2 4 6 5 . 5 6 0 . 0 4 2 26532 . 96 3 5 7 0 8 1 . 8 1 0 . 0 2 7 9771 . 95 TOTAL 0 . 035 2 7 5 3 8 3 . 7 5 0 . 0 6 1 16761 . 01 1 3 8 9 4 8 . 5 0 0 . 0 4 1 5 7 6 1 . 21 TOTAL 0 . 050 1 3 6 4 3 5 . 2 5 0 . 0 8 1 10999 . 80 136435 .25 0 . 0 8 1 10999 . 80 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS -• WITHIN ORE ZONE OUTLINE METHOD: ID2 INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 3 1 0 . 0 4 0 16946 . 35 3 6 7 2 . 0 0 0 . 0 1 0 3 4 . 96 6 8 4 0 . 0 . 010 4 1 9 2 2 8 . 3 1 0 . 0 4 0 16911 . 39 3 0 3 3 8 . 8 7 0 . 0 1 6 4 7 7 . 14 6 8 4 0 . 0 . 020 3 8 8 8 8 9 . 4 4 0 . 0 4 2 16434 . 25 2 0 1 0 6 2 . 5 0 0 . 0 2 8 5 6 0 3 . 50 6 8 4 0 . 0 . 035 187826 .94 0 . 0 5 8 10830 . 75 9 4 3 6 2 . 3 1 0 . 0 4 1 3 8 2 7 . 71 6 8 4 0 . 0 . 050 9 3 4 6 4 . 6 2 0 . 0 7 5 7 0 0 3 . 05 9 3 4 6 4 . 6 2 0 . 0 7 5 7 0 0 3 . 05 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 8 7 0 . 0 3 6 1 2 0 7 1 . 93 4 7 9 8 . 0 6 0 . 0 0 9 4 2 . 77 6 8 6 0 . 0 . 010 3 2 8 4 2 3 . 8 1 0 . 0 3 7 12029 . 16 6 1 8 0 3 . 8 7 0 . 0 1 7 1054 . 77 6 8 6 0 . 0 . 020 2 6 6 6 1 9 . 9 4 0 . 0 4 1 10974 . 40 1 4 8 9 0 3 . 7 5 0 . 0 2 7 4 0 7 6 . 49 6 8 6 0 . 0 . 035 1 1 7 7 1 6 . 1 9 0 . 0 5 9 6 8 9 7 . 91 6 3 5 9 9 . 0 5 0 . 0 4 0 2 5 2 6 . 18 6 8 6 0 . 0 . 050 5 4 1 1 7 . 1 4 0 . 0 8 1 4 3 7 1 . 73 5 4 1 1 7 . 1 4 0 . 0 8 1 4 3 7 1 . 73 TOTAL 0 . 000 7 5 6 1 2 2 . 2 5 0 . 0 3 8 29018 . 29 8 4 7 0 . 1 2 0 . 0 0 9 7 7 . 72 TOTAL 0 . 010 7 4 7 6 5 2 . 1 2 0 . 0 3 9 2 8 9 4 0 . 56 9 2 1 4 2 . 7 5 0 . 0 1 7 1 5 3 1 . 91 TOTAL 0 . 020 6 5 5 5 0 9 . 3 7 0 . 0 4 2 2 7 4 0 8 . 65 3 4 9 9 6 6 . 2 5 0 . 0 2 8 9 6 7 9 . 98 TOTAL 0 . 035 3 0 5 5 4 3 . 1 2 0 . 0 5 8 17728 . 67 157961 .31 0 . 0 4 0 6 3 5 3 . 88 TOTAL 0 . 050 147581 .81 0 . 0 7 7 11374 . 79 147581 .81 0 . 0 7 7 11374 . 79 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE METHOD: I D I INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE INSIDE GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 3 1 0 . 0 4 1 17483 . 48 0 . 0 0 0 . 0 0 0 0 . 00 6 8 4 0 . 0 . 010 4 2 2 9 0 0 . 3 1 0 . 0 4 1 17483 . 48 2 0 3 1 8 . 3 7 0 . 0 1 7 339 . 06 6 8 4 0 . 0 . 020 4 0 2 5 8 1 . 9 4 0 . 0 4 3 17144 . 42 195725 .87 0 . 0 2 9 5626 . 14 6 8 4 0 . 0 . 035 2 0 6 8 5 6 . 0 6 0 . 0 5 6 11518 . 27 111220 .87 0 . 0 4 0 4 4 9 1 . 75 6 8 4 0 . 0 .050 9 5 6 3 5 . 1 9 0 . 0 7 3 7026 . 53 9 5 6 3 5 . 1 9 0 . 0 7 3 7026 . 53 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 8 7 0 . 0 3 7 12375 . 63 0 . 0 0 0 . 0 0 0 0 . 00 6 8 6 0 . 0 .010 3 3 3 2 2 1 . 8 7 0 . 0 3 7 12375 . 63 3 8 1 7 2 . 5 0 0 . 0 1 7 6 4 9 . 23 6 8 6 0 . 0 . 020 2 9 5 0 4 9 . 3 7 0 . 0 4 0 11726 . 40 169336 .37 0 . 0 2 7 4 5 6 3 . 92 6 8 6 0 . 0 .035 1 2 5 7 1 3 . 0 0 0 . 0 5 7 7 1 6 2 . 48 8 1 2 5 7 . 2 5 0 . 0 4 2 3436 . 90 6 8 6 0 . 0 .050 4 4 4 5 5 . 7 0 0 . 0 8 4 3 7 2 5 . 58 4 4 4 5 5 . 7 0 0 . 0 8 4 3 7 2 5 . 58 TOTAL 0 .000 7 5 6 1 2 2 . 2 5 0 . 0 3 9 29859 . 12 0 . 0 0 0 . 0 0 0 0 . 00 TOTAL 0 . 010 7 5 6 1 2 2 . 2 5 0 . 0 3 9 29859 . 12 5 8 4 9 0 . 9 4 0 . 0 1 7 9 8 8 . 30 TOTAL 0 . 020 6 9 7 6 3 1 . 3 1 0 . 0 4 1 2 8 8 7 0 . 82 3 6 5 0 6 2 . 2 5 0 . 0 2 8 10190 . 06 TOTAL 0 .035 3 3 2 5 6 9 . 0 6 0 . 0 5 6 18680 . 76 192478 .12 0 . 0 4 1 7928 . 65 TOTAL 0 .050 1 4 0 0 9 0 . 9 4 0 . 0 7 7 10752 . 11 140090 .94 0 . 0 7 7 10752 . 11 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS -• WITHIN ORE ZONE OUTLINE METHOE ): IDO INVERSE DISTANCE RESERVES - ABOVE CUTOFF GRADE I N S I D E GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 3 1 0 . 0 4 2 17864 . 58 0 . 0 0 0 . 0 0 0 0 . 00 6 8 4 0 . 0 . 010 4 2 2 9 0 0 . 3 1 0 . 0 4 2 17864 . 58 1 5 9 7 7 . 2 5 0 . 0 1 8 2 8 7 . 56 6 8 4 0 . 0 .020 4 0 6 9 2 3 . 0 6 0 . 0 4 3 17577 . 02 1 8 9 2 7 9 . 5 0 0 . 0 2 9 5 4 7 2 . 30 6 8 4 0 . 0 .035 2 1 7 6 4 3 . 5 6 0 . 0 5 6 12104 . 72 144611 .56 0 . 0 4 2 6 1 3 9 . 39 6 8 4 0 . 0 . 050 7 3 0 3 2 . 0 0 0 . 0 8 2 5 9 6 5 . 32 7 3 0 3 2 . 0 0 0 . 0 8 2 5 9 6 5 . 32 6 8 6 0 . 0 .000 3 3 3 2 2 1 . 8 7 0 . 0 3 8 12671 . 93 0 . 0 0 0 . 0 0 0 0 . 00 6 8 6 0 . 0 .010 3 3 3 2 2 1 . 8 7 0 . 0 3 8 12671 . 93 3 8 8 9 0 . 5 6 0 . 0 1 7 6 7 1 . 32 6 8 6 0 . 0 . 020 2 9 4 3 3 1 . 3 1 0 .041 12000 . 61 156965 .81 0 . 0 2 7 4 2 8 5 . 69 6 8 6 0 . 0 . 035 1 3 7 3 6 5 . 5 0 0 . 0 5 6 7714 . 92 7 7 9 2 8 . 0 0 0 . 0 4 1 3 2 1 3 . 84 6 8 6 0 . 0 .050 5 9 4 3 7 . 4 6 0 . 0 7 6 4 5 0 1 . 09 5 9 4 3 7 . 4 6 0 . 0 7 6 4 5 0 1 . 09 TOTAL 0 . 000 7 5 6 1 2 2 . 2 5 0 . 0 4 0 30536 . 51 0 . 0 0 0 . 0 0 0 0 . 00 TOTAL 0 . 010 7 5 6 1 2 2 . 2 5 0 . 0 4 0 30536 . 51 5 4 8 6 7 . 8 7 0 . 0 1 7 958 . 89 TOTAL 0 .020 701254 .37 0 . 0 4 2 29577 . 62 3 4 6 2 4 5 . 3 1 0 . 0 2 8 9 7 5 7 . 98 TOTAL 0 .035 3 5 5 0 0 9 . 0 6 0 . 0 5 6 19819 . 64 2 2 2 5 3 9 . 6 2 0 . 0 4 2 9 3 5 3 . 23 TOTAL 0 . 050 1 3 2 4 6 9 . 4 4 0 . 0 7 9 10466 . 41 1 3 2 4 6 9 . 4 4 0 . 0 7 9 10466 . 41 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS - WITHIN ORE ZONE OUTLINE METHOE K R I G E EXPLORATION KRIGING RESERVES - ABOVE CUTOFF GRADE I N S I D E GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 .000 4 2 2 9 0 0 . 3 1 0 . 0 4 0 17120 . 96 0 . 0 0 0 . 0 0 0 0 . 00 6 8 4 0 . 0 . 010 4 2 2 9 0 0 . 3 1 0 . 0 4 0 17120 . 96 2 2 7 8 2 . 7 5 0 . 0 1 6 3 5 4 . 04 6 8 4 0 . 0 . 020 4 0 0 1 1 7 . 5 6 0 . 0 4 2 16766 . 92 2 0 1 3 0 7 . 2 5 0 . 0 2 8 5 5 8 2 . 57 6 8 4 0 . 0 . 035 198810 .31 0 . 0 5 6 11184 . 35 118418 .00 0 . 0 4 1 4 8 2 6 . 31 6 8 4 0 . 0 . 050 8 0 3 9 2 . 3 1 0 . 0 7 9 6 3 5 8 . 04 8 0 3 9 2 . 3 1 0 . 0 7 9 6 3 5 8 . 04 6 8 6 0 . 0 . 0 0 0 3 3 3 2 2 1 . 8 7 0 . 0 3 5 11716 . 03 0 . 0 0 0 . 0 0 0 0 . 00 6 8 6 0 . 0 . 010 3 3 3 2 2 1 . 8 7 0 . 0 3 5 11716 . 03 6 4 3 8 2 . 4 4 0 . 0 1 8 1129 . 20 6 8 6 0 . 0 . 020 2 6 8 8 3 9 . 4 4 0 . 0 3 9 10586 . 83 155692 .87 0 . 0 2 7 4 2 7 4 . 99 6 8 6 0 . 0 . 035 113146 .56 0 . 0 5 6 6 3 1 1 . 84 7 4 5 3 3 . 3 7 0 . 0 4 2 3 1 2 8 . 55 6 8 6 0 . 0 . 050 3 8 6 1 3 . 1 4 0 . 0 8 2 3 1 8 3 . 29 3 8 6 1 3 . 1 4 0 . 0 8 2 3 1 8 3 . 29 TOTAL 0 . 0 0 0 7 5 6 1 2 2 . 2 5 0 . 0 3 8 28837 . 00 0 . 0 0 0 . 0 0 0 0 . 00 TOTAL 0 . 010 7 5 6 1 2 2 . 2 5 0 . 0 3 8 28837 . 00 8 7 1 6 5 . 1 9 0 . 0 1 7 1 4 8 3 . 24 TOTAL 0 . 020 6 6 8 9 5 7 . 0 6 0 . 0 4 1 2 7 3 5 3 . 75 3 5 7 0 0 0 . 1 2 0 . 0 2 8 9 8 5 7 . 56 TOTAL 0 . 035 3 1 1 9 5 6 . 9 4 0 . 0 5 6 17496 . 20 1 9 2 9 5 1 . 5 0 0 . 0 4 1 7954 . 87 TOTAL 0 . 050 119005 .44 0 . 0 8 0 9 5 4 1 . 32 119005 .44 0 . 0 8 0 9 5 4 1 . 32 253 BLOCK MODEL: BUCK60G 6 0 ' BLOCKS -• WITHIN ORE ZONE OUTLINE METHOD: CPROB CONDITIONAL PROBABILITY RESERVES - ABOVE CUTOFF GRADE INSIDE 1 GRADE BOUNDARIES BENCH CUTOFF TONS GRADE OUNCES TONS GRADE OUNCES 6 8 4 0 . 0 . 000 4 2 2 9 0 0 . 31 0 . 0 4 0 17120 . 96 4 5 3 4 . 00 0 . 0 0 9 39 .94 6 8 4 0 . 0 . 010 4 1 8 3 6 6 . 31 0 . 0 4 1 17081 . 02 6 4 4 4 7 . 19 0 . 0 1 6 1030 .20 6 8 4 0 . 0 . 020 3 5 3 9 1 9 . 12 0 . 0 4 5 16050 . 83 162382 . 25 0 . 0 2 7 4438 .71 6 8 4 0 . 0 . 035 191536 . 87 0 . 0 6 1 11612 . 12 97680 . 50 0 . 0 4 1 4050 .96 6 8 4 0 . 0 . 050 9 3 8 5 6 . 37 0 . 0 8 1 7 5 6 1 . 16 9 3 8 5 6 . 37 0 . 0 8 1 7561 . 16 6 8 6 0 . 0 . 000 3 3 3 2 2 1 . 87 0 . 0 3 5 11716 . 03 5 6 1 3 . 75 0 . 0 0 9 48 .77 6 8 6 0 . 0 . 010 327608 . 12 0 . 0 3 6 11667 . 26 8 0 9 0 0 . 75 0 . 0 1 6 1277 .23 6 8 6 0 . 0 . 020 2 4 6 7 0 7 . 37 0 . 0 4 2 10390 . 03 131230 . 44 0 . 0 2 7 3520 . 76 6 8 6 0 . 0 . 035 115476 . 94 0 . 0 5 9 6 8 6 9 . 27 62086 . 79 0 . 0 4 1 2573 .35 6 8 6 0 . 0 . 050 5 3 3 9 0 . 14 0 . 0 8 0 4 2 9 5 . 92 53390 . 14 0 . 0 8 0 4295 .92 TOTAL 0 . 000 756122 . 25 0 . 0 3 8 2 8 8 3 7 . 00 10147 . 81 0 . 0 0 9 88 .71 TOTAL 0 . 010 745974 . 44 0 . 0 3 9 28748 . 28 145347 . 87 0 . 0 1 6 2307 .41 TOTAL 0 . 020 600626 . 56 0 . 0 4 4 26440 . 87 2 9 3 6 1 2 . 69 0 . 0 2 7 7959 .47 TOTAL 0 . 035 307013 . 87 0 . 0 6 0 18481 . 39 159767 . 31 0 . 0 4 1 6624 .31 TOTAL 0 . 050 147246 . 56 0 .081 11857 . 09 147246 . 56 0 . 0 8 1 11857 .09 254 APPENDIX D LISTING OF CALCULATED SEMI-VARIOGRAM VALUES n o t e : raw grades were m u l t i p l i e d by 100 LEGEND: LAG Lag d i s t a n c e . N Number o f p a i r s f o r a r i t h m e t i c and r e l a t i v e v a r i o g r a m s . LN Number o f samples f o r l o g n o r m a l v a r i o g r a m , AR MEAN A r i t h m e t i c mean grade o f samples . LG MEAN Lognormal mean grade o f samples . VG C a l c u l a t e d v a r i o g r a m v a l u e . LOG VG Lognormal v a r i o g r a m . REL VG R e l a t i v e v a r i o g r a m . 255 FILE= BEX ANGLE 90 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 30 831 819 48.7 1.4211 2476 . 1 0.1675 1.0458 57 5553 5410 39.5 1.3067 2775. 8 0.2186 1.7757 105 11622 11326 36.8 1.2981 2634. 6 0.2402 1.9432 137 6235 6104 37.3 1.2750 2818. 6 0.3011 2.0308 FILE= BEX ANGLE 45 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 29 578 567 49.2 1.3704 2785. 0 0.2100 1.1516 66 5289 5166 39.0 1.3163 2576 . 6 0.2109 1.6900 105 9457 9224 37.2 1.2911 2791. 5 0.2416 2.0173 137 6758 6625 36.8 1.2872 2595. 1 0.2661 1.9209 FILE= BEX ANGLE 0 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 31 527 524 46.0 1.3760 2578 . 0 0 .1858 1.2172 57 5707 5561 38.9 1.3176 2378. 7 0.1881 1 .5684 105 11524 11230 36.7 1.2958 2459. 2 0.2134 1.8283 139 4969 4879 37.3 1.2816 2516 . 1 0.2395 1.8044 FILE= BEX ANGLE l _ 135 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 32 554 547 45 .5 1.3027 2556 . 0 0.2498 1.2367 66 5538 5417 38.1 1.3039 2219. 3 0.2039 1.5268 106 9010 8791 36.9 1.2848 2685. 9 0.2285 1.9704 137 6885 6746 36.8 1.2913 2549 . 8 0.2539 1.8832 FILE= BEX ANGLE 0 VERT ANG= 90 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 21 2020 1970 32.4 1.2164 1134 . 7 0.0883 1.0778 41 1591 1547 32.9 1.2200 1799. 8 0.1421 1.6602 61 1185 1144 32.0 1.2133 1812. 1 0.1744 1.7701 81 825 788 32.1 1.2107 2095. 1 0.2117 2.0325 101 530 501 31.0 1.1830 2242. 3 0.2300 2.3290 256 FILE= BEXG ANGLE= 90 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 29 329 327 49.8 1.5063 2510 . 9 0.1451 1.0130 56 2278 2269 46.8 1.4751 3665. 6 0.1523 1.6755 105 4759 4730 44.8 1.4678 2984 . 2 0.1606 1.4886 137 2215 2210 46.2 1.4765 3105. 2 0.1819 1.4520 FILE= BEXG • ANGLE 45 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 26 191 190 47 . 3 1.4501 2827 . 0 0.1911 1.2648 67 2172 2159 45.4 1.4727 3070 . 3 0.1475 1.4878 106 3781 3769 45.3 1.4629 3344. 6 0.1646 1.6322 137 2586 2576 45.5 1.4742 2985. 6 0.1631 1.4431 FILE= BEXG ANGLE 0 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 27 167 166 52.4 1.5412 2795. 7 0.1403 1 .0171 55 2575 2559 46 .7 1.4829 2991. 9 0.1445 1 . 3695 106 5067 5038 45.9 1.4704 3198. 2 0.1608 1.5196 140 1923 1914 49.1 1.4947 3686 . 8 0.1752 1.5318 FILE= BEXG ANGLE 135 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 29 165 164 58.8 1.5707 2549. 7 0.1790 0.7364 66 2408 2395 43.9 1.4626 2401. 2 0.1425 1.2486 108 3704 3676 46.2 1.4725 3449 . 1 0.1627 1.6171 138 2681 2671 45.7 1.4799 2899 . 3 0.1732 1.3868 FILE= BEXG ANGLE 0 VERT ANG= 90 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 21 759 755 45.9 1.4864 1835. 2 0 .0741 0.8717 41 530 526 45.7 1.4856 2779. 5 0.1068 1. 3308 61 337 332 44.3 1.4741 2481. 4 0.1203 1.2622 81 179 174 43.3 1.4663 1915. 6 0.1115 1.0237 101 55 53 42 .5 1.4773 1086. 8 0.1200 0 .6012 257 FILE= BBH ANGLE= 90 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 14 6891 6874 36 .7 1. 3012 1560. 6 0 .0739 1 .1590 32 43651 43538 39 .5 1. 3139 2636. 9 0 .1381 1 .6904 51 78256 77990 39 .7 1. 3211 2872. 5 0 .1759 1 .8234 70 105621 105302 39 .9 1. 3288 3084. 2 0 .2087 1 .9378 90 130096 129677 40 .2 1. 3359 3261. 3 0 .2387 2 .0223 110 155677 155142 40 .1 1. 3363 3302. 3 0 .2640 2 .0535 130 177403 176798 39 .7 1. 3360 3140. 7 0 .2789 1 .9952 145 96894 96539 39 .7 1. 3375 3126. 9 0 .2863 1 .9837 F I L E i BBH ANGLE= 45 VERT 1 ANG= 0 LAG N LN AR MEAN LG 1 MEAN VG LOG VG REL VG 15 5854 5838 36 .2 1. 2780 1610 . 8 0 .0777 1 .2309 32 41865 41743 39 .3 1. 3077 2589 . 2 0 .1343 1 .6790 51 76334 76108 39 . 7 1. 3177 2800 . 5 0 .1649 1 .7799 70 104405 104079 39 .6 1. 3242 2867 . 4 0 .1920 1 .8309 90 128193 127825 39 .7 1. 3261 3121. 0 0 .2205 1 . 9812 110 152144 151671 39 .5 1. 3282 3131. 9 0 .2414 2 .0054 130 171886 171339 39 .1 1. 3271 3054. 7 0 .2578 1 .9953 145 92933 92630 39 .1 1. 3276 3086. 7 0 .2678 2 .0241 F I L E l — BBH ANGLE= 0 VERT 1 ANG= 0 LAG N LN AR MEAN LG I MEAN VG LOG VG REL VG 14 6822 6793 36 .1 1. 2619 1440 . 2 0 .0638 1 . 1043 32 43712 43571 39 .0 1. 2983 2475. 1 0 . 1119 1 .6283 51 77950 77710 39 .2 1. 3086 2546 . 9 0 .1320 1 .6533 70 105823 105514 39 .3 1 . 3110 2796. 7 0 .1507 1 .8070 90 129943 129529 39 .2 1. 3106 2966 . 2 0 .1675 1 .9287 110 154452 153922 39 .3 1. 3143 3052. 7 0 .1823 1 .9721 130 172351 171765 38 .7 1. 3102 2995. 9 0 .1934 1 .9977 145 92854 92510 38 .8 1. 3110 3070 . 2 0 .2001 2 .0443 FILE= BBH ANGLE= 135 VERT ANG= 0 LAG N LN AR MEAN LG - MEAN VG LOG VG REL VG 15 5888 5872 36 .4 1. 2870 1468. 5 0 .0660 1 .1097 32 42168 42053 38 .9 1. 3021 2348. 8 0 .1202 1 .5528 51 76343 76119 39 .5 1. 3151 2623. 4 0 .1470 1 .6824 70 106062 105723 39 .6 1. 3191 2943. 9 0 .1713 1 .8756 90 130890 130458 39 .8 1. 3238 3116. 9 0 .1927 1 .9705 110 155512 154958 39 .7 1. 3265 3124. 7 0 .2124 1 .9832 130 177977 177307 39 .7 1. 3285 3250. 2 0 .2282 2 .0628 145 96231 95874 39 .6 1. 3300 3186. 5 0 .2381 2 .0345 F I L E I BBH ANGLE= 0 VERT 1 ANG= 90 LAG N LN AR MEAN LG 1 MEAN VG LOG VG REL VG 21 3257 3248 40 .6 1. 3264 2433. 6 0 .1048 1 .4742 41 2022 2013 43 .7 1. 3672 3236. 9 0 .1615 1 .6928 61 958 956 48 .1 1. 4342 3956. 4 0 .1824 1 .7098 81 295 295 50 .4 1. 5066 2887 . 7 0 .1425 1 .1376 101 10 10 43 .2 1. 6039 294. 9 0 .0377 0 .1580 259 FILE= BBHG ANGLE= 90 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 14 4889 4882 46 .3 1 .4958 2003. 6 0 .0675 0 .9335 32 29179 29148 51 .1 1 .5216 3533. 6 0 .1182 1 . 3529 51 50550 50478 51 .2 1 .5234 3800. 3 0 .1367 1 .4523 70 66620 66515 50 .4 1 .5180 3879. 9 0 .1442 1 .5272 90 79856 79708 49 .8 1 .5128 3891. 3 0 .1528 1 .5707 110 92777 92611 49 .3 1 .5071 3916. 0 0 .1599 1 .6081 130 102971 102784 48 .6 1 .5030 3714. 5 0 .1567 1 .5734 145 55137 55029 48 .7 1 .5062 3716. 9 0 .1530 1 .5644 F I L E = BBHG ANGLE= 45 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 15 4030 4023 46 .7 1 .4896 2193. 6 0 .0683 1 .0038 32 28023 27982 51 .1 1 .5209 3552. 1 0 .1155 1 .3586 51 50309 50233 51 .2 1 .5240 3739. 1 0 .1342 1 .4263 70 67296 67186 50 .5 1 .5215 3663. 4 0 .1440 1 .4354 90 80422 80297 50 .2 1 .5176 3915. 5 0 .1540 1 .5523 110 93246 93108 49 .4 1 .5119 3802. 8 0 .1577 1 .5553 130 102624 102475 48 .6 1 .5056 3658. 2 0 .1570 1 .5469 145 54439 54356 48 .6 1 .5051 3703. 1 0 .1562 1 .5702 F I L E BBHG ANGLE= 0 VERT ANG= 0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 14 4664 4649 47 .4 1 .4878 1989. 6 0 .0571 0 .8858 32 29092 29029 51 .3 1 .5204 3430. 3 0 .1016 1 .3028 51 51551 51443 51 .4 1 .5272 3536. 2 0 . 1170 1 . 3372 70 68941 68825 51 .5 1 .5274 3868. 0 0 .1314 1 .4593 90 82601 82461 51 .4 1 .5273 4102. 0 0 .1441 1 .5535 110 96665 96525 51 .2 1 .5265 4106 . 9 0 .1517 1 .5684 130 105743 105572 50 .2 1 .5199 3967 . 8 0 .1546 1 .5756 145 56167 56078 50 .1 1 .5182 4012. 8 0 .1561 1 .5995 260 F I L E BBHG ANGLE= 135 VERT ANG= 0 LAG N LN AR MEAN LG 1 MEAN VG LOG VG REL VG 15 4086 4079 46.4 1. 4894 1858. 4 0.0589 0 .8632 32 27954 27921 50.9 1. 5216 3142. 4 0.1070 1 .2112 51 49847 49780 51.4 1. 5247 3635. 6 0.1266 1 .3759 70 67564 67466 51.1 1. 5217 3959. 6 0.1387 1 .5165 90 81719 81592 50.7 1. 5194 4073. 6 0.1473 1 .5831 110 94394 94257 50.1 1. 5166 3860. 2 0.1525 1 .5400 130 106126 105939 49 .6 1. 5137 3930. 2 0.1546 1 .5961 145 56604 56511 49 .0 1. 5110 3730. 9 0.1557 1 .5509 F I L E BBHG ANGLE= 0 VERT ANG= 90 LAG N LN AR MEAN LG 1 MEAN VG LOG VG REL VG 21 2204 2200 53.0 1. 5384 3445. 6 0.0951 1 .2278 41 1397 1391 55.0 1. 5620 4013 . 2 0.1404 1 . 3262 61 743 741 54.9 1. 5644 4621. 7 0.1399 1 .5354 81 241 241 54.6 1. 5696 3371. 3 0.1391 1 .1319 101 10 10 43.2 1. 6039 294. 9 0.0377 0 .1580 261 APPENDIX E LISTING OF VARIOGRAMS GENERATED BY MAXIMUM DIFFERENCE METHOD These v a r i o g r a m s were c r e a t e d from the BEXG d a t a s e t . Any sample p a i r d i f f e r e n c e ( r e g a r d l e s s o f g r a d e s ) , a t a g i v e n l a g , was examined and i f the a b s o l u t e d i f f e r e n c e exceeded the maximum v a l u e shown f o r each v a r i o g r a m , i t was no t used i n the c o m p u t a t i o n o f y(h). R e s u l t s show t h a t the o n l y v a r i o g r a m s which showed the 1 3 5 ° a n i s o t r o p y were the ones t h a t used a l l sample p a i r s . T h i s was de termined by examin ing the lowes t f i r s t l a g v a l u e . In most o f the o t h e r c a s e s , the lowes t v a l u e o f y a t the f i r s t l a g was e i t h e r i n the 0 ° (N-S) or the 4 5 ° d i r e c t i o n . Note t h a t a p p r o x i m a t e l y 50% o f a l l sample p a i r s had a b s o l u t e d i f f e r e n c e s o f l e s s than 0.020 o p t . (raw grades were m u l t i p l i e d by 100. t o produce these r e p o r t s ) . A lmost 90% o f a l l p a i r s had a b s o l u t e d i f f e r e n c e s o f l e s s than 0.080 o p t . F o r h o r i z o n t a l d i r e c t i o n s , the l owes t v a l u e s o f y(l) f o r the v a r i o g r a m t h a t used a l l sample p a i r s was i n the 1 3 5 ° d i r e c t i o n f o r a c t u a l , l o g n o r m a l and r e l a t i v e v a r i o g r a m s . In the o t h e r c a s e s , the l o g n o r m a l v a r i o g r a m c o n s i s t e n t l y i n d i c a t e d t h a t a n i s o t r o p y was i n the 4 5 ° d i r e c t i o n . The a c t u a l and r e l a t i v e v a r i o g r a m s showed lowes t yd) i n the N-S d i r e c t i o n f o r the lowes t grade d i f f e r e n c e s and v a r i e d f o r the nex t 2 v a r i o g r a m s . Only the a c t u a l v a r i o g r a m w i t h maximum p a i r d i f f e r e n c e s o f 0.080 o p t . showed the 1 3 5 ° d i r e c t i o n as l o w e s t . Lowest s e m i - v a r i o g r a m v a l u e s a t the f i r s t l a g f o r each h o r i z o n t a l v a r i o g r a m a r e u n d e r l i n e d i n the l i s t i n g s . N o t i c e a l s o how much lower the i n d i c a t e d v a r i a n c e o f the d a t a i s when the maximum p a i r d i f f e r e n c e s d e c r e a s e . The r e l a t i v e v a r i o g r a m s i l l s d e c r e a s e from about 1.5 t o l e s s than 0.4 f o r sample p a i r s which v a r y by l e s s t h a n 0.08 o p t . — t h i s r e p r e s e n t s n e a r l y 90% o f a l l p a i r s . 262 FILE= ANGLE VERT ANG= BEXG 90 0 - MAXIMUM SAMPLE PAIR DIFFERENCE - 2.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 54 105 146 1122 2289 2123 1117 2279 2114 27.3 1.3564 27.4 1.3605 27.5 1.3623 58. 59 . 61. 9 7 6 0.0409 0.0340 0.0391 0.0787 0.0793 0.0816 FILE= ANGLE VERT ANG= BEXG 45 0 - MAXIMUM SAMPLE PAIR DIFFERENCE = 2.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 67 106 145 1103 1827 2098 1099 1820 2088 27.7 1.3612 26.3 1.3410 27.5 1.3603 59. 59. 61. 4 1 1 0.0363 0.0387 0.0401 0.0771 0.0857 0.0806 FILE= ANGLE VERT ANG= BEXG 0 0 - MAXIMUM SAMPLE PAIR DIFFERENCE = 2.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 54 106 148 1283 2471 1992 1276 2461 1984 28.7 1.3725 27.1 1.3507 28.3 1.3724 57 . 59. 58. 6 2 1 0.0397 0 .0403 0.0351 0.0699 0.0806 0.0727 FILE= ANGLE VERT ANG= BEXG 135 0 - MAXIMUM SAMPLE PAIR DIFFERENCE = 2.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 66 108 145 1216 1768 2104 1209 1762 2099 27.6 1.3581 27.7 1.3584 28.7 1.3769 60 . 60. 60. 8 3 3 0.0399 0.0396 0 .0362 0 .0798 0.0785 0.0734 FILE= ANGLE VERT ANG= BEXG 0 90 - MAXIMUM SAMPLE PAIR DIFFERENCE - 2.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 20 457 456 28.8 1.3597 50.7 0.0276 0.0612 40 285 284 28.0 1.3606 54 .5 0.0312 0.0693 60 148 147 25.1 1.3057 49.6 0.0363 0.0790 263 FILE= ANGLE VERT . ANG= BEXG 90 0 - MAXIMUM SAMPLE PAIR DIFFERENCE = 3.5 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 55 105 147 1564 3173 3013 1558 3158 2994 29.4 1.3783 29.9 1.3846 29.7 1.3839 147 150 155 .2 .0 .2 0.0694 0.0641 0.0706 0.1700 0.1683 0.1761 FILE= ANGLE VERT ANG= BEXG 45 0 - MAXIMUM SAMPLE PAIR DIFFERENCE = 3.5 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 67 106 145 1495 2497 3007 1485 2489 2989 30.2 1.3872 28.6 1.3678 30.1 1.3848 143 146 158 .8 .0 .4 0.0610 0.0665 0.0705 0.1575 0.1778 0.1753 FILE= ANGLE VERT ANG= BEXG 0 0 - MAXIMUM SAMPLE PAIR DIFFERENCE = 3.5 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 54 106 148 1751 3353 2831 1743 3336 2819 30.8 1.3901 29.5 1.3786 30.6 1.3926 141 143 154 .5 .2 .2 0.0707 0.0633 0.0670 0.1490 0.1640 0 .1652 FILE= ANGLE VERT ANG= BEXG 135 0 - MAXIMUM SAMPLE PAIR DIFFERENCE = 3.5 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 66 107 145 1706 2451 2997 1698 2437 2982 30.1 1.3810 29.9 1.3828 30.7 1.3971 155 149 156 .0 .8 .9 0 .0743 0.0674 0.0674 0.1714 0.1674 0.1663 FILE= ANGLE VERT ANG= BEXG 0 90 - MAXIMUM SAMPLE PAIR DIFFERENCE = 3.5 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 20 593 591 32.8 1.4055 124.2 0.0407 0.1157 40 372 370 30.7 1.3934 134.5 0.0492 0.1423 60 222 220 30.0 1.3736 166.9 0.0552 0.1857 264 FILE= ANGLE VERT . ANG= BEXG 90 0 - MAXIMUM SAMPLE PAIR DIFFERENCE = 5.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 55 105 146 1758 3717 3569 1751 3695 3548 31.4 32.0 31.9 1.3978 1.4034 1.4037 231 258 269 .0 . 3 .7 0.0814 0 .0854 0.0920 0.2347 0.2525 0.2647 FILE= ANGLE VERT ANG= BEXG 45 0 - MAXIMUM 1 SAMPLE PAIR DIFFERENCE = 5.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 67 106 145 1710 2891 3530 1697 2881 3507 32.2 30.7 32.1 1.4062 1.3871 1.4026 239 246 267 .4 .2 .0 0.0767 0.0866 0.0920 0.2316 0.2610 0.2598 FILE= ANGLE VERT ANG= BEXG 0 0 - MAXIMUM I SAMPLE PAIR DIFFERENCE = 5.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 54 106 148 2029 3889 3336 2020 3866 3317 33.2 31.6 32.4 1.4124 1.3976 1.4087 243 245 266 .0 .1 .3 0.0872 0.0832 0.0911 0.2206 0.2460 0.2532 FILE= ANGLE VERT ANG= BEXG 135 0 - MAXIMUM SAMPLE PAIR DIFFERENCE = 5.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 66 107 145 1944 2852 3521 1935 2832 3500 32. 3 31.8 32.7 1.4004 1.3997 1.4143 247 253 267 .1 .4 .3 0 .0912 0 .0878 0.0887 0.2375 0.2502 0.2499 FILE= ANGLE VERT ANG= BEXG 0 90 - MAXIMUM SAMPLE PAIR DIFFERENCE = 5.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 20 40 60 652 425 260 649 422 256 34.7 32.7 31.5 1.4249 1.4141 1.3926 195 232 277 .4 . 3 .9 0.0493 0.0614 0.0716 0.1626 0.2174 0.2803 265 FILE= ANGLE VERT . ANG= BEXG 90 0 - MAXIMUM ! SAMPLE PAIR DIFFERENCE = 8.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 55 105 146 1991 4184 4099 1984 4157 4077 34.2 34.5 34.8 1.4196 1.4222 1.4248 441 462 498 .0 .8 .8 0.1057 0.1099 0.1199 0.3770 0.3895 0.4113 FILE= ANGLE VERT ANG= BEXG 45 0 - MAXIMUM I SAMPLE PAIR DIFFERENCE = 8.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 66 106 144 1924 3306 3993 1911 3294 3969 34.9 33.8 34.8 1.4276 1.4121 1.4229 438 468 463 .5 .9 .4 0.0990 0.1117 0.1155 0.3606 0.4095 0.3836 FILE= ANGLE VERT ANG= BEXG 0 0 - MAXIMUM SAMPLE PAIR DIFFERENCE = 8.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 55 106 148 2294 4429 3827 2278 4402 3806 36.0 34.6 35. 3 1.4340 1.4200 1.4321 453 459 488 .0 . 3 .1 0.1095 0.1103 0.1131 0.3488 0.3837 0.3912 FILE= ANGLE VERT ANG= BEXG 135 0 - MAXIMUM SAMPLE PAIR DIFFERENCE = 8.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 66 107 145 2175 3232 4014 2165 3208 3990 34.9 34.5 35.4 1.4207 1.4222 1.4350 435 461 482 .7 .4 .8 0.1122 0.1088 0.1125 0.3584 0.3872 0.3843 FILE= ANGLE VERT ANG= BEXG 0 90 - MAXIMUM SAMPLE PAIR DIFFERENCE = 8.0 LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 20 40 60 703 475 295 700 471 290 37.5 35.8 35.0 1.4460 1.4371 1.4239 321 423 478 .2 .4 .9 0.0587 0.0802 0.0865 0.2283 0.3310 0. 3900 266 FILE= ANGLE VERT ANG= BEXG 90 0 - ALL SAMPLE PAIRS LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 56 105 137 2278 4759 2215 2269 4730 2210 46.8 1.4751 3665. 44.8 1.4678 2984. 46.2 1.4765 3105. 6 2 2 0.1523 0.1606 0.1819 1.6755 1.4886 1.4520 FILE= ANGLE VERT ANG= BEXG 45 0 - ALL SAMPLE PAIRS LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 67 106 137 2172 3781 2586 2159 3769 2576 45.4 1.4727 3070. 45.3 1.4629 3344. 45.5 1.4742 2985. 3 6 6 0.1475 0.1646 0.1631 1.4878 1.6322 1.4431 FILE= ANGLE VERT ANG= BEXG 0 0 - ALL SAMPLE PAIRS LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 55 106 140 2575 5067 1923 2559 5038 1914 46.7 1.4829 2991. 45.9 1.4704 3198. 49.1 1.4947 3686. 9 2 8 0.1445 0.1608 0.1752 1.3695 1.5196 1.5318 FILE= ANGLE VERT i ANG= BEXG 135 0 - ALL SAMPLE PAIRS LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 66 108 138 2408 3704 2681 2395 3676 2671 43.9 1.4626 2401. 46.2 1.4725 3449. 45.7 1.4799 2899. 2 1 3 0 .1425 0.1627 0.1732 1.2486 1 .6171 1.3868 FILE= ANGLE VERT ANG= BEXG 0 90 - ALL SAMPLE PAIRS LAG N LN AR MEAN LG MEAN VG LOG VG REL VG 41 61 81 530 337 179 526 332 174 45.7 1.4856 2779. 44.3 1.4741 2481. 43.3 1.4663 1915. 5 4 6 0.1068 0.1203 0.1115 1.3308 1.2622 1.0237 267 APPENDIX F SCATTERGRAMS LEGEND; B l o c k Models BUCK 20' B l o c k s , no o u t l i n e . BUCKG 20' B l o c k s , w i t h "ore zone" o u t l i n e , BUCK60 60' B l o c k s , no o u t l i n e . BUCK60G 60' B l o c k s , w i t h "ore zone" o u t l i n e , Method BHK B l a s t h o l e K r i g i n g - - " A c t u a l " . EX20 E x p l o r a t i o n Po lygon o r EX60 Weighted (20' & 60') ID10 ID5 ID3 ID2 IDI IDO I n v e r s e D i s t a n c e to t h e i n d i c a t e d power, KRIG E x p l o r a t i o n K r i g e d E s t i m a t e . n o t e : r e s u l t s from c o n d i t i o n a l p r o b a b i l i t y cannot be compared on a b l o c k by b l o c k b a s i s u s i n g s c a t t e r g r a m s . 268 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L « B U C K 0.240 O X 0.200 LU O " 0.160 l — < or o ^ 0.120 x 0.080 0.040 0.000 — i 1 1 i i 1 0.000 0.040 0.080 0-120 0-160 0.200 0.240 0.280 0-320 B H K ( A C T U A L ) 0.280 . 0.240 D •— 0-160 . < DC O 0.120 X LU A C T U A L V S . E S T I M A T E D - B L O C K M O D E L : B U C K T~. Tr, i . • r 0-000 1 1 1 1 1 1 0.000 0.040 0.080 0.120 0.160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ' B U C K 0.240 O 0.200 . < CC o _ l <̂  0.120 . UJ 0.080 . 0.000 — r 1 1 i 1 1 1 0.000 0.040 0.080 0.120 0.160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) 269 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L : B U C K 0.240. r-> Q 0.200. ,_ 0.160. < or o i °j 0.120. 0.040 **1 1 1 I : 1 1 1 0.000 0.040 0.080 0.120 0-160 0-200 0-240 0-280 0.320 B H K ( A C T U A L ) 270 0.320 A C T U A L VS . E S T I M A T E D - B L O C K MODEL 1 B U C K 0.280. i 1 i . i 1 i i 0.240 . <\l Q 0-200 . - Z o • 0.160 . < or o _ i o_ 0.120. * X L U 0.080 . • . : •S*&':-:v 0.040 . 0.000 B^^* -~; 0. r 1 i 000 0.040 o. i i i 080 0.120 0.160 0.200 BHK ( A C T U A L ) i i 0-240 0.280 0 320 0.320. Q 0.200. ,_ 0.160, < or o _ i 0̂  0.120 L U 0.080 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ' BUCK 1 — T T " -r 0.000 —I 1 1 1 I 1 1 0.000 0.040 0.080 0.120 0.160 0.200 0.240 0.280 0 BHK ( A C T U A L ) 271 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ' B U C K 0.320. 0.240. O Q 0. z o 0. 160 < or o UJ 120 . 0.080 . ! 1 1 1 1 1 1 0.000 0.040 0.080 0.120 0-160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L : B U C K 0.2B0 . 0-240 UJ O — 0.200 or 2 0.160 < or o _j 0_ X UJ 0-080 0-040 o.ooo — i i i i 1 i i 0-000 0.040 0.080 0.120 0-160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) 272 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L 1 B U C K G 0.320. 0.280. 0.240. O X 0.200. LU < or o a ! 0 . 1 2 0 . x LU 0 .080. r. .• —I I 1 I 1 I 0-000 0.040 0.080 0.120 0.160 0-200 0.240 0-280 0.320 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L = B U C K G 0-280 . O —' 0.160 . i — < or o rx o . 120 X 0.080 0-000 —i 1 i 1 1 1 — 0.000 0.040 0.080 0.120 0.160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ! B U C K G 0.280 J 0.240 J i n Q 0. 0.160J < or o UJ 0.080 0.040J I I 1 1 I 1 0.000 0.040 0.080 0.120 0.160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L : B U C K G 0.240 J ro Q 0-200 < or o _i Q- 0-120-1 0.080 0.040J: 0.000 n r i r 1 1 1 1 1 1 1 0-000 0.040 0.080 0.120 0.160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L - B U C K G 0.240 . C M Q 0-200J , _ 0.160 . < o _1 ^ 0.120. 0.000 1 , , , ! p 1 ! 0.000 0.040 0.080 0.120 0.160 0.200 0-240 0-280 0.320 B H K ( A C T U A L ) 274 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L " B U C K G 0.280 . Q 0.200 . < OC o _ l ^ 0.120 1 1 1 1 1 1 1 . 0.000 0.040 0.080 0.120 0.160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ' B U C K G 0.320. 0.240 . o Q 0.200 ,_ 0.160 < or o 0.120 0.080 0.040 . 0.000 I 1 1 1 1 I 1 0.000 0.040 0.080 0.120 0.160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) 275 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L : B U C K G 0.320 0.240 0.200 . or 2 0.160. < or o —1 0.120 . Q_ X 0.080 0.040 . .000 0.040 0-080 0.120 0.160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) 276 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L 1 B U C K 6 0 0 . 2 8 0 0 . 2 4 0 O <o X 0 - 2 0 0 LL) o *-• 0 . 1 6 0 i — < cr CD CL 0 . 1 2 0 . X UJ 0 . 0 4 0 . I 1 1 1 1 1 1 0 . 0 0 0 0 . 0 4 0 0 . 0 8 0 0 . 1 2 0 0-160 0 . 2 0 0 0 . 2 4 0 0 . 2 8 0 0 . 3 2 0 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L » B U C K 6 0 o 5 0 . 2 0 0 . — 0 . 1 6 0 . i — < or o CL 0 . 1 2 0 . X 0 . 0 8 0 . 0 . 0 0 0 ••-v.".*j?5r--?-.-.; — i 1 1 1 1 1 0 . 0 0 0 0 . 0 4 0 0 . 0 8 0 0 . 1 2 0 0.160 0 . 2 0 0 0 . 2 4 0 0 . 2 8 0 0 . 3 2 0 B H K ( A C T U A L ) 277 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ' B U C K 6 0 0 . 240 - to O 0 . 2 0 0 . < or o _ i ^ 0 . 1 20 LU ~ i 1 1 r o.ooo 0 .000 0 .040 0 . 080 0 . 120 0 . 160 0 . 2 00 0 . 2 4 0 0 . 280 0 . 320 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ' B U C K 6 0 ro Q 0 . 200 < or o _ i 0.120 L U 0 -080 0 . 0 4 0 ~1 I I 1 I T" 0.000 0 . 000 0 . 040 0 . 0 8 0 0.' 120 0 -160 0 . 2 00 0 . 240 0 . 280 0 . 3 20 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L « B U C K 6 0 0.280 CM Q 0.200 < 0T o _ l x 0.120. LU 0.080 0-040 . "T 1 I 1 I r \^.vK>'.' 1 1 1 1 1 1 1 0.000 0-040 0-080 0.120 0.160 0-200 0.240 0-280 0-320 B H K ( A C T U A L ) 278 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ' B U C K 6 0 0.320. 0-280 J Q 0.200. z o 0.160. < or o _ i 0j 0.120. UJ 0.040 J T r 1 1 1 1 1 1 1 0.000 0.040 0.080 0.120 0.160 0-200 0.240 0.280 0.320 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ' B U C K 6 0 0.280 0.240 J O Q 0.200 , _ 0.160 _| < K O _ l 0.120 0.080. 0.040 J 0.000 0.040 0.080 0.120 0.160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L : B U C K 6 0 0.320 0.000 B H K ( A C T U A L ) 280 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ' B U C K 6 0 G 0 . 2 8 0 . o CD X 0 . 2 0 0 . < or o CL 0 . I 2 0 J X 0 . 0 8 0 . 1 1 1 1 1 1 1 0 - 000 0 -040 0 .080 0 . 1 20 0 . 160 0 . 200 0 . 240 0 . 2 8 0 0 . 3 20 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L « B U C K 6 0 G 0 - 2 8 0 . O 5 0 . 2 0 0 . z o - * 0 . 1 6 0 . •— < or o CL 0 . 1 2 0 . X LU 0.080-1 0 . 0 0 0 1 1 1 1 1 1 1 0 . 0 0 0 0 .040 0 . 080 0 . 1 2 0 0 . 160 0 . 200 0 . 240 0 . 280 0 . 3 20 B H K ( A C T U A L ) 281 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L : B U C K 6 0 G 0.320 0.280 0.240 in Q 0.200 < CC o _1 CL 0.120 LU 0.080 ~ i 1 1 1 1 r i i i i 1 1 \ 0.000 0.040 0.080 0.120 0.160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) A C T U A L V S . E S T I M A T E D - B L O C K M O D E L : B U C K 6 0 G 0.240 to Q 0.200 ,_ 0.160 < or o _ i 0^ 0.120 LU 0.080 0.040 , 0.000 "i 1 i r 1 I 1 1 I 1 1 . 0.000 0.040 0.080 0.120 0.160 0.200 0.240 0.280 0.320 B H K ( A C T U A L ) 282 0.320 ACTUAL V S . ESTIMATED - BLOCK MODEL 1 BUCK60G 0.280 . i i i i i i i 0.240 . CM I D  0.200 . z o t— 0.160. < or o _ J 0- x 0.120 . UJ * 0.080 . 0.040 . - JeJr >.'*' ' .: 0.000 0 1 1 1 1 1 1 1 000 0.040 0.080 0.120 0.160 0.200 0-240 0-280 0 BHK (ACTUAL) 320 ACTUAL V S . ESTIMATED - BLOCK MODEL" BUCK60G 0.240 J Q 0.200 ,_ 0.160 < or o _ i % 0.120-1 0.080 . 0-000 "T" T ~T~ 1 1 1 1 1 1 1 0.000 0.040 0.080 0.120 0.160 0.200 0.240 0.2B0 0.320 BHK (ACTUAL) 283 0.320 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ' B U C K 6 0 G 0.280 . i i i i i i i 0.240 . O Q 0.200 _ E X P L O R A T IO N  Q O o  o  • 0.080 . 0.040 _ - 0.000 0. 1 1 1 1 1 1 000 0.040 0.080 0.120 0.160 0.200 0.240 BHK ( A C T U A L ) 0.280 0. 320 0.320 A C T U A L V S . E S T I M A T E D - B L O C K M O D E L ' B U C K 6 0 G 0.280 . i i i i i i i 0.240 . - LU O — 0.200. or - E X P L O R A T IO N  o  o  0 o  1 i - 0.080 _ ** * - 0.040 . 0.000 v."••'"'j'i-- :"• • •• - 0. 000 0-'040 0.080 0.'l20 0.'l60 0.'200 0.240 BHK ( A C T U A L ) 0.280 0. 320

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