Report project fernando saez cfsg

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ACKNOWLEDGEMENT

I would like to express my sincere gratitude to CFSG teachers and administrative in helping me to

broaden my view and knowledge.

Also I would to thank to Supervisor Seguret for his guidance.

My deepest appreciation to Yanacocha Mining in helping me collecting information.

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1. ABSTRACT

El Tapado ore deposit is an epithermal gold high sulfidation deposit that belongs to Yanacocha District,

north of Peru. The principal control of mineralization of gold are: the lithology control must be inside

permeable pyroclastic rock, the structural control is for gold high grade in direction North West and

North East for low grade, alteration control must be in the advance argillic alteration (silica, alunite,

pyrophilite).

El Tapado ore deposit contains 211 drillholes, there are 80% of DDH (Diamond drilling Hole) and 20%

RCD (Reverse circulation drilling). There are 22202 samples regularized to 3 meters. There are five

continuous variables: gold fire assay (total gold), gold cyanide (recoverable gold by cyanide), silver,

copper cyanide (copper that do react with cyanide) and sulphide sulphur (sulphur of sulphide

mineralogy).

The domain for gold estimation (Goldshape) is a deterministic model, where the gold is higher than 0.1

gpt. Moreover the domain for gold cyanide estimation has been divided in two domains (Oxide and

sulphide), that is defined taking into account the mineralogy (qualitative reason). The gold has been top

cut to 20 gpt, this gives a 2% lower average than raw data (from 1.07 to 1.05 gpt), but the standard

deviation has been reduced by 30%. The gold cyanide has been capped to 20 gpt and has 2.5% lower

average than the previous one (from 1.15 to 1.12 gpt), but the standard deviation has been reduced by

30%.

There are three different Ordinary kriging models, each model have different variography and

neighbourhood parameters; the first model has been made with variography directly of capped gold,

the second model has been done from variogram parameters of logarithmic gold ; the last model has

been made from variogram parameters of Gaussian gold . The first gold model (by gold variogram) has

lower range than the other models, therefore the estimation result shows higher mean value

(overestimated).

There are two study for Indicator Kriging, the first study has given more details to variography

parameters and idea about the behavior of gold in the different indicators; the second study has shown

that it is necessary to divided the indicator of gold in nearest indicator, moreover the estimation result

of this preliminary study is lesser than the results by ordinary kriging . The Indicator Kriging took into

account that the indicator give nested sets, therefore the choice estimation is indicator Cokriging; after

that, the estimated Indicator is converted from cumulated classes 1 x>cut-off to 1cut-off1<x≤cut-off2; finally

in order to find the grade value is used the formula: sum of each cut-off multiply by his estimated

indicator (1 Y(x)=i)k .

The gold cyanide has been estimated by Cokriging because of the good correlation with gold in both

domains (oxide and sulphide). In order to make a good comparison with the gold cyanide by Cokriging

has been found one relation between gold cyanide, gold and residual in both domains (oxide and

sulphide), where the regression line formula for residual in oxide is: Residual = AuCN -0.91Au + 0.01; and

the regression line formula in sulphide is: Residual = AuCN -0.38 Au - 0.04. Two variables are simulated

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(gold and residual); of 100 simulation values the mean value in each block has been extracted. In order

to get the gold cyanide result, the same residual formula has been used in each domain (oxide and

sulphide) using the simulated mean for gold and residual. The simulated gold cyanide result higher

values than the cokriged gold cyanide. The same way, the simulated gold has higher values than the

previous kriged result.

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2. INDEX

1. ABSTRACT .............................................................................................................................................. 2

2. INDEX .................................................................................................................................................... 4

2.1 FIGURE INDEX................................................................................................................................ 6

2.2 TABLE INDEX ................................................................................................................................. 9

3. OBJECTIVE and INTRODUCTION .......................................................................................................... 11

4. GEOLOGY ............................................................................................................................................. 11

4.1 Regional Geology Setting ............................................................................................................ 12

4.2 Alteration of Epithermal Ore Deposit ......................................................................................... 12

4.3 Mineralisation Epithermal Ore Deposit ...................................................................................... 12

4.4 Mineralisation Controls of Epithermal Ore Deposit ................................................................... 13

5. MULTIVARIATE ESTIMATION and simulation ...................................................................................... 17

5.1 Database of Samples ................................................................................................................... 17

5.2 Domains for Estimation: ............................................................................................................. 19

5.3 Gold Fire Assay ............................................................................................................................ 20

5.3.1 Statistics gold fire assay by domain .................................................................................... 20

5.3.2 Comparison Gold and Logarithm Gold ................................................................................ 27

5.3.3 Comparison Gold and Gaussian Gold .................................................................................. 33

5.3.4 Declustering analysis for gold fire assay ............................................................................. 38

5.3.5 Preliminar Study Indicator Gold Fire assay (5 cut-off) ........................................................ 46

5.3.6 Final Study of Indicators (25 different cut-off) of Gold Fire Assay...................................... 59

5.4 Gold Cyanide ............................................................................................................................... 68

5.4.1 Bivariate Statistics between Gold Fire Assay and Gold Cyanide: ........................................ 69

5.4.2 Gold Cyanide in Oxide Domain: .......................................................................................... 70

5.4.3 Residual of Gold Cyanide in Oxide Domain:........................................................................ 74

5.4.4 Gold Cyanide in Sulphide Domain: ...................................................................................... 77

5.4.5 Residual of Gold Cyanide in Sulphide Domain: ................................................................... 81

5.5 Discussion of Results ................................................................................................................... 84

5.5.1 AuFA by Ordinary Kriging .................................................................................................... 84

5.5.2 AuFa by Indicator Ordinary CoKriging ................................................................................. 88

5.5.3 AuCN by Cokriging (AuFA and AuCN) .................................................................................. 91

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5.5.4 AuFA by Turning Band Conditional Simulation ................................................................... 92

5.5.5 Residual by Turning Band Conditional Simulation .............................................................. 94

5.5.6 AuCN by Simulation of Residual and Simulation of AuFA ................................................... 96

5.5.7 Comparison Different Gold block model results ................................................................. 97

5.5.8 Comparison Different Gold Cyanide block model results ................................................... 98

6. CONCLUSION and recommendation ................................................................................................... 99

7. REFERENCE ........................................................................................................................................ 100

8. ANNEX ............................................................................................................................................... 102

8.1 GOLD STATISTICS....................................................................................................................... 102

8.2 AUCN STATISTICS ...................................................................................................................... 109

8.3 SILVER STATISTICS ..................................................................................................................... 112

8.4 Copper Cyanide STATISTICS ...................................................................................................... 114

8.5 SULPHIDE SULPHUR STATISTICS ................................................................................................ 115

8.6 RECONCILIATION APPROACH .................................................................................................... 118

8.7 Table of Statistics of Gold block model by Conditional Simulation with turning bands ........... 120

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2.1 FIGURE INDEX

Figure 1 Regional Geologic Setting of the Yanacocha District. . .................................................................................. 15

Figure 2 Generalized Stratigraphical Column for the Yanacocha District. ................................................................... 15

Figure 4 Localisation of Ore Deposits and Alteration in the Yanacocha District.. ....................................................... 16

Figure 3 Conceptual Model of Epithermal High Sulfidation Deposit. .......................................................................... 16

Figure 5 Map of AuFA (gold fire assay).. ...................................................................................................................... 18

Figure 6 Histogram and Cumulative plot (logarithm scale) of Gold Fire Assay ........................................................... 19

Figure 7 Goldshape divided on Oxide and Sulphide .................................................................................................... 19

Figure 10 Histogram of Capped Gold Fire Assay (top cut to 20 gpt), and reduced Histogram of Capped Gold in

Goldshape ................................................................................................................................................................... 21

Figure 9 Reduced Histogram and Reduced Cumulative plot (logarithm scale) of Gold fire assay in Goldshape......... 21

Figure 11 Mathematician Rotation in Isatis Software ................................................................................................. 22

Figure 12 Geologist Rotation in Isatis Software: ......................................................................................................... 22

Figure 13 : Variogram Map of capped gold fire assay in goldshape ............................................................................ 23

Figure 14 Variogram Model of capped gold fire assay in goldshape ........................................................................... 24

Figure 16 Downhole Variogram and Variogram in Short Range of capped gold fire assay inside goldshape. ............ 24

Figure 15 Variogram in long range and in perpendicular range of capped gold fire assay in goldshape.. .................. 24

Figure 17 Comparison between different Block Discretization and the standard deviation of Cvv values ................. 26

Figure 18 Histogram of logarithm Gold fire assay in Goldshape and Q-Q plot of gold in theoretical Lognormal

distribution. ................................................................................................................................................................. 27

Figure 19 Variogram Map of logarithm gold fire assay in goldshape .......................................................................... 28

Figure 20 Variogram Model of logarithm gold fire assay in goldshape ....................................................................... 29

Figure 21 Variogram in short range and in long range of capped gold fire assay in goldshape .................................. 29

Figure 22: Downhole Variogram and Variogram in Perpendicular range of Gaussian capped gold fire assay inside

the goldshape domain.. ............................................................................................................................................... 29

Figure 23 Square root of Variogram over Madogram of Logarithm gold. ................................................................... 30

Figure 24 Variogram Model of gold fire assay (from logarithm gold parameters) ...................................................... 31

Figure 25 Variogram in short range and in long range of capped gold fire assay (from logarithm gold parameters).

..................................................................................................................................................................................... 31

Figure 26 Downhole Variogram and Variogram in Perpendicular range of Gaussian capped gold fire assay inside the

goldshape domain.. ..................................................................................................................................................... 31

Figure 28 Gaussian Gold Model with 50 Hermite polynomials .................................................................................. 33

Figure 27 Histogram of Gold fire assay in Goldshape and Q-Q plot of gold Logarithm in theoretical Gaussian

distribution. ................................................................................................................................................................. 33

Figure 29 Variogram Map of Gaussian gold in goldshape ........................................................................................... 34

Figure 30 Variogram Model of Gaussian gold fire assay in goldshape ........................................................................ 35

Figure 31 Variogram in short range and in long range of gold fire assay in goldshape ............................................... 35

Figure 32 Downhole Variogram and Variogram in Perpendicular range of Gaussian gold fire assay inside the

goldshape domain.. ..................................................................................................................................................... 35

Figure 33 Square root of Variogram divide by Madogram of Gaussian gold............................................................... 36

Figure 34 Variogram Model of Gold and with experimental values (from of Gaussian gold) ..................................... 36

Figure 35 Variogram Block Model of Gold (from of Gaussian gold) ............................................................................ 37

Figure 36 Declustering statistics of gold fire assay ...................................................................................................... 38

Figure 37 Histogram and Cumulative plot (logarithm scale) of declustered Gold Fire Assay in Goldshape ............... 39

Figure 38 Gaussian Model with 50 Hermite polynomials ............................................................................................ 40

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Figure 39 Variogram Map of Gaussian declustered gold in goldshape ....................................................................... 41

Figure 40 Variogram Model of Gaussian declustered gold fire assay in goldshape .................................................... 42

Figure 41 Variogram in short range and in long range of Gaussian gold in goldshape ............................................... 42

Figure 42 Downhole Variogram and variogram in Perpendicular range of Gaussian gold inside the goldshape

domain.. ....................................................................................................................................................................... 42

Figure 43 Square root of Variogram divide by Madogram of Gaussian declustered gold ........................................... 43

Figure 44 Variogram Model of Gold (from of Gaussian declustered gold) .................................................................. 44

Figure 45 Comparison between different Block Discretization and the standard deviation of 10 Cvv values (mean

Block Covariances) ....................................................................................................................................................... 45

Figure 46 Cumulative plot and Histogram of Indicator to cut-off 0.2 gpt of gold fire assay. ...................................... 46

Figure 47 Histograms of Indicator to cut-off 0.4 and 0.7 gpt of gold fire assay. ......................................................... 46

Figure 48 Histograms of Indicator to cut-off 1.0 and 2.0 gpt of gold fire assay. ......................................................... 47

Figure 49 Variogram Map of Indicator of gold to cut-off 0.2 gpt ................................................................................ 48

Figure 50 Variogram Model of Indicator of gold fire assay to cut-off 0.2 gpt ............................................................. 49

Figure 51 Variogram in direction to short range and to long range of Indicator of gold fire assay to cut-off 0.2 gpt in

goldshape.. .................................................................................................................................................................. 49

Figure 52 Variogram in direction to perpendicular range and downhole Variograms of Indicator of gold fire assay to

cut-off 0.2 gpt in goldshape.. ....................................................................................................................................... 49



Figure 55 Variogram in short range and in long range of Indicator of gold fire assay to cut-off 0.4 gpt in goldshape..

..................................................................................................................................................................................... 51

Figure 56 Variogram in perpendicular range and downhole Variogram of Indicator of gold fire assay to cut-off 0.4

gpt in goldshape.. ........................................................................................................................................................ 51

Figure 57 Variogram Map of Indicator of gold to cut-off 0.7 gpt in goldshape ........................................................... 52



..................................................................................................................................................................................... 53


gpt in goldshape.. ........................................................................................................................................................ 53


Figure 62 Variogram Model of Indicator of gold fire assay to cut-off 1.0 gpt in goldshape. ....................................... 55

Figure 63 Variogram in short range and in long range of Indicator of gold fire assay to cut-off 1.0 gpt in goldshape.

..................................................................................................................................................................................... 55


gpt in goldshape.. ........................................................................................................................................................ 55


Figure 66: Variogram Model of Indicator of gold fire assay to cut-off 2.0 gpt ............................................................ 57


..................................................................................................................................................................................... 57


gpt in goldshape.. ........................................................................................................................................................ 57

Figure 69 Cross Variograms Models of Indicators (cut-off of gold: 0.1, 0.2, 0.3, 0.4 and 0.5 gpt), ............................. 60

Figure 70 Cross Variograms Models of Indicators (cut-off of gold: 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0 gpt) ....................... 61

Figure 71 Cross Variograms Models of Indicators (cut-off of gold: 1.0, 1.2, 1.5, 1.7 and 2.0 gpt) .............................. 62

Figure 72 Cross Variograms Models of Indicators (cut-off of gold: 2.0, 2.5, 3.0, 3.5, 4.0 and 5.0 gpt) ....................... 63

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Figure 73 Cross Variograms Models of Indicators (cut-off of gold: 5.0, 6.0, 7.0 and 8.0 gpt) ..................................... 64

Figure 74 Cross Variograms Models of Indicators (cut-off of gold: 8.0, 10.0, 12.0 and 15.0 gpt) ............................... 65


Block Covariances) for 5 different indicators (from 0.1 to 0.5 of cut-off gold) ........................................................... 67


Block Covariances) for 5 different indicators (from 1 to 2 of cut-off gold) ................................................................. 67

Figure 77 Histogram and Cumulative plot (logarithm scale) of Gold Cyanide. ............................................................ 68

Figure 78: Histogram of Capped Gold Cyanide in Gold Shape ..................................................................................... 69

Figure 79 ScatterPlot between Gold FireAssay and Gold Cyanide and between Ln(Gold) and Ln(Gold Cyanide). .... 69

Figure 81: Scatterplot between Gold and Ratio in Oxide Zone and Scatterplot between Gold and Gold Cyanide in

Oxide Zone.. ................................................................................................................................................................. 70

Figure 80 Histogram of Capped Gold Cyanide in Oxide Zone and Scatterplot between Gold and Gold Cyanide in

Oxide Zone. .................................................................................................................................................................. 70

Figure 82 Variogram Map of Cross variogram of gold and gold cyanide in oxide goldshape ...................................... 71

Figure 83 Cross Variogram Model of Gold Fire assay and Gold Cyanide ..................................................................... 72

Figure 84 Comparison between different Block Discretization and the standard deviation of Cvv values. ................ 73

Figure 85 Histogram of Residual of gold and gold Cyanide in Oxide Zone (5453 samples), and Scatterplot between

residual (au-aucn) and Gold (au). ................................................................................................................................ 74

Figure 86 Anamorphosis of residual (Au and AuCN) in oxide, and Scatterplot between Gaussian residual and

Gaussian Gold (au) in oxide. ........................................................................................................................................ 74

Figure 87: Variogram Model of Gaussian residual in oxide: the Mathematical rotation parameters is: 20°, Y-Right = -

20°, and X-right =5°, nugget effect (S1): 0.13, First Structure - Spherical (S2): sill=0.20, U=20m V=60m W=45m;

Second Structure-Exponential (S3): sill=0.63, U=45m V=160m W=70m. .................................................................... 75

Figure 88 Variogram in direction of short range and direction of long range of gaussian residual in oxide. Short

range =45m, and long range = 160m. .......................................................................................................................... 75

Figure 89 Downhole Variogram and variogram in direction of Perpendicular range of Gaussian residual inside the

oxide domain ............................................................................................................................................................... 75

Figure 90 Comparison between different Block Discretization and the standard deviation of Cvv values ................. 76

Figure 91 Histogram of Capped Gold Cyanide in Sulphide Zone; and Scatterplot between Gold and Gold Cyanide in

Sulphide Zone .............................................................................................................................................................. 77

Figure 92 Scatterplot between Gold and Ratio in Sulphide Zone and Scatterplot between Gold and Gold Cyanide in

Sulphide Zone. ............................................................................................................................................................. 77

Figure 93 Variogram Map of Cross variogram of gold and gold cyanide in sulphide goldshape ................................. 78

Figure 94 Cross Variogram Model of Gold Fire assay and Gold Cyanide in sulphide .................................................. 79

Figure 95 Comparison between different Block Discretization and the standard deviation of Cvv values. ................ 80

Figure 96 Histogram of Residual of gold and gold Cyanide in Sulphide Zone and Scatterplot between residual

(aucn-au) and gold (au) in sulphide. ............................................................................................................................ 81

Figure 97 Anamorphosis of residual (Au and AuCN) in sulphide, and Scatterplot between Gaussian residual and

Gaussian Gold (au) in sulphide. ................................................................................................................................... 81

Figure 98 Variogram Model of Gaussian residual in sulphide ..................................................................................... 82

Figure 99 Variogram in short range and in long range of Gaussian residual in sulphide ............................................ 82

Figure 100 Downhole Variogram and variogram in Perpendicular range of Gaussian residual inside the sulphide

domain. ........................................................................................................................................................................ 82

Figure 101 Comparison between different Block Discretization and the standard deviation of Cvv values. .............. 83

Figure 102 Block Model of estimated gold by ordinary kriging (variography of gold), bench (left) and section YoZ

(right) ........................................................................................................................................................................... 85

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Figure 103 Block Model of Standard deviation of gold by ordinary kriging (variography of gold), bench (left) and

section YoZ (right) ........................................................................................................................................................ 85

Figure 104 Block Model of estimated gold by ordinary kriging (variography from logarithm gold), bench (left) and

section YoZ (right) ........................................................................................................................................................ 86

Figure 105 Block Model of Standard deviation of gold by ordinary kriging (variography from logarithm gold) bench

(left) and section YoZ (right) ........................................................................................................................................ 86

Figure 106 Block Model of estimated gold by ordinary kriging (variography from gaussian gold), bench (left) and

section YoZ (right). ....................................................................................................................................................... 87

Figure 107 Block Model of Standard deviation of gold by ordinary kriging (variography from gaussian gold) bench

(left) and section YoZ (right) ........................................................................................................................................ 87

Figure 108 Diagram of all post processing indicator ................................................................................................... 90

Figure 109 Block Model of estimated gold by Indicator kriging (25 cutoff) bench (left) and section YoZ (right)........ 90

Figure 110 Block Model of estimated gold cyanide by ordinary Cokriging, bench (left) and section YoZ (right) ........ 91

Figure 111 Block Model of Standard deviation of gold by ordinary Cokriging, bench (left) and section YoZ (right) .. 91

Figure 112 Block Model of Conditioning Simulation of gold by Turning Band, bench with 5th

Simulation (left) and

bench with 25th

Simulation (right). .............................................................................................................................. 92



bench with 75th

Simulation (right) ............................................................................................................................... 92

Figure 114 Block Model of mean gold of 100 Simulations; bench (left) and section YoZ (right), the blocks with gold

value (Mean of 100 Simulations) and drillholes in black points. ................................................................................. 93

Figure 115 Block Model of Standard deviation gold of 100 Simulations; bench (left) and section YoZ (right) ........... 93

Figure 116 Block Model of Conditioning Simulation of residual by Turning Band, bench with 5th


bench with 25th

Simulation (right). .............................................................................................................................. 94


Simulation (left)

and bench with 75th

Simulation (right) ........................................................................................................................ 94

Figure 118 Block Model of mean residual of 100 Simulations; bench (left) and section YoZ (right), the blocks with

residual value (Mean of 100 Simulations) and drillholes in black points. ................................................................... 95

Figure 119 Block Model of Standard deviation residual of 100 Simulations; bench (left) and section YoZ (right). .... 95

Figure 120 Block Model of gold cyanide value by simulation of gold and residual (combined zones: oxide and

sulphide), bench (left) and section YoZ (right). ........................................................................................................... 96

Figure 121 Comparison between different gold block models in Tonnage and Cutoff curve (left) and Mean Grade

and Cutoff curve (right). .............................................................................................................................................. 97

Figure 122 Comparison between different gold cyanide block models in Tonnage and Cutoff curve (left) and Mean

Grade and Cutoff curve (right)..................................................................................................................................... 98

2.2 TABLE INDEX

Table 1 Comparison between Blasthole and Core (Drillhole) closer than 9 meters and between RCD

(RCD+BBH) and Blasthole closer than 9 meters ........................................................................................ 17

Table 2 Statistics Summary of Gold Fire Assay: Oxide and Sulphide Zones in Goldshape Domain ......... 20

Table 3 Comparison of different Methods of top-cutting or capping. .......................................................... 21

Table 4 Statistics Summary of Capped Gold Fire Assay: Oxide and Sulphide Zones in Goldshape Domain

.................................................................................................................................................................... 21

Table 5 Comparison between different variography parameters of capped gold fire assay in goldshape. 25

Table 6 Comparison between different neighbourhood parameters (search and maximum of samples) .. 25

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Table 7 Cross validation Parameters of variography gold fire assay (from logarithm gold parameters) in

goldshape.. .................................................................................................................................................. 32

Table 8 Comparison between different neighbourhood parameters .......................................................... 32

Table 9 Cross Validation of Variogram Model of Gold (from Gaussian model). ......................................... 37

Table 10 Comparison between different neighbourhood parameters (search and maximum of samples) 37

Table 11 Study of declustering to different sizes cell .................................................................................. 39

Table 12 Statistics Summary of declustered Gold Fire Assay: Oxide and Sulphide Zones in Goldshape

Domain. ....................................................................................................................................................... 40

Table 13 Comparison between different variography parameters of Gaussian declustered gold fire assay

in goldshape,. .............................................................................................................................................. 43

Table 14 Cross Validation of Variogram Model of Gold (from Gaussian model). ....................................... 44

Table 15 Comparison between different neighbourhood parameters ........................................................ 45

Table 16 Comparison between indicators statistics parameters of gold fire assay to different cut-off (0.2,

0.4, 0.7, 1.0 and 2.0 grades per tonnes or gpt)........................................................................................... 47


in goldshape.. .............................................................................................................................................. 58


in goldshape.. .............................................................................................................................................. 58

Table 19 Statistics of different indicators .................................................................................................... 59

Table 20 Correlation coefficient between different indicators ..................................................................... 59

Table 21 Comparison between different neighbourhood parameters of indicators (to cutoff: 0.1, 0.2, 0.3,

0.4, 0.5 gpt). ................................................................................................................................................ 66

Table 22 Comparison between different neighbourhood parameters of indicators (to cutoff: 1.0, 1.2, 1.5,

1.7, 2.0 gpt). ................................................................................................................................................ 66

Table 23 Comparison between different neighbourhood parameters of indicators (to cutoff: 5, 6, 7, 8 gpt)

. ................................................................................................................................................................... 66

Table 24 Statistics Summary of Gold Cyanide: Oxide and Sulphide Zones ............................................... 68

Table 25 Statistics Summary of declustered Gold Fire Assay: Oxide and Sulphide Zones . ..................... 69

Table 26 Cross validation Parameters of variography gold cyanide in oxide goldshape. .......................... 73


.................................................................................................................................................................... 76


Table 30 Cross validation Parameters of variography gold cyanide in oxide goldshape ........................... 80


Table 32 Cross validation Parameters of variography gold cyanide in oxide goldshape.. ......................... 83


Table 34 Comparison between three types of gold variograms in cross validation parameters ................ 84

Table 35 Comparison between three types of gold neighbourhood ........................................................... 84

Table 36 Comparison between the Statistics of Indicators Kriging (from 0.1 to 15) initial kriging process

(left part), and post processing kriging (minimum=0, and maximum=1) ..................................................... 88

Table 37 Comparison between the Statistics of Indicators Kriging (from 0.1 to 15) initial kriging process

(left part), and post processing kriging (minimum=0, and maximum=1) ..................................................... 89

Table 38 Comparison declustered gold and estimation results .................................................................. 90

Table 39 Comparison of Statistics between declustered gold and Mean of Simulated Gold ..................... 93

Table 40 Comparison of Statistics between declustered gold and Mean of Simulated Gold ..................... 96

Table 41 Comparison between different gold block model value by different method inside of optimize pit

.................................................................................................................................................................... 97

Table 42 Comparison between different gold cyanide block model value by different method inside of

optimize pit .................................................................................................................................................. 98

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3. OBJECTIVE AND INTRODUCTION

Improve the block models of AuFA (gold Fire Assay), AuCN (Gold Cyanide) grades of El Tapado Deposits,

because the grade Reconciliation of estimated model (by drillhole) against ore control model (true

value) for three years is 8% less tonnages, 5% higher grade and 2% less metal than predicted by the

deposit model. Otherwise, the reconciliation by year increase the uncertainty, it is +- 10% in tonnage,

+- 15% in grade, and +- 15% in metal.

Then, we will make comparison between different model in order to choose the best block models for

gold and gold cyanide, which improve the reconciliation results and decrease the uncertainty and impact

on the economic risk.

Yanacocha Mine have been considered to be the second largest gold mine in the world, is a huge open

pit gold mine spreading over a concession of about 25,000 hectares and approximately 47 kilometers by

road to the town of Cajamarca, in the Northern Andean Orogenic belt of northern Peru. (Figure 1). The

rock containing the gold is loosened by daily dynamite blasts, and then piled up and sprayed with

cyanide solution. Since the ore is porous, run-of-mine ore can be heap-leached without crushing and the

solution treated by the Merrill Crowe process, the solution that runs off is then processed to remove the

gold, nevertheless this process only can be done without sulphide and clay minerals.

Year-on-year, Yanacocha mine has usually been able to extend its oxide ore reserves faster than ore is

being mined. By the end of 1998, proven and probable reserves had grown to 20.1 Moz of gold and

peaked at 36.6 Moz by end-2000 (plus 350 Moz of silver). By end-2005, the project had a proven and

probable reserve of 1,142 Mt grading 0.9 gpt gold, for a total gold content of 32.6 Moz.

El Tapado is a bedrock-hosted deposit completely covered by the gold-bearing gravels of La Quinua

Central.

4. GEOLOGY

The district is made up of a series of epithermal, high sulfidation style gold deposits (Yanacocha

Complex, Carachugo, Maqui Maqui, El Tapado, Chaquicocha, San Jose, Cerro Negro) and one gold-rich

gravel deposit (La Quinua), aligned in a NE trend. The Yanacocha mineral belt is located along a

regional-scale disruption in this regional belt. Northwest orientations of folds and thrusts in Cretaceous

sedimentary rocks are deflected to nearly EW along the intersection of an ENE trans-Andean structural

zone (Turner, 1997). This trans-Andean zone, known as the Chicama-Yanacocha structural corridor,

trends over a length of about 200 km, beginning at the Pacific Coast. It is 30 to 40 km wide, and defined

by displacement of the Peruvian coastline, multiple parallel N50E faults, and the ENE alignment of the

Yanacocha deposits (Quiroz, 1997).

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4.1 Regional Geology Setting

The oldest rocks in the Cajamarca region are Cretaceous sedimentary rocks. A basal siliciclastic package

is overlain by platform carbonate rocks. Yanacocha high sulfidation mineralisation is known in

sedimentary rocks, but many other deposit style prospects in the region are hosted in these rocks.

The basal Tertiary volcanic rocks in the Cajamarca region are lava flows, volcanic debris flow

conglomerates and volcaniclastic strata of the Llama Formation. In the Cajamarca region the Llama

Formation has been dated as Paleocene (Noble et al, 1990). Llama Formation rocks occur to the south of

the district. Above the Llama are volcanic rocks of the Yanacocha Volcanic Complex, host for the

Yanacocha deposits (Turner, 1997). These rocks correlate with the regional Porculla Formation. The

Yanacocha Volcanic Complex is an interlayered sequence of andesitic lava flows and pyroclastic rocks

that overlie the Llama Formation along a transitional contact. Ten kilometres NE of the district the

Yanacocha Volcanic Complex is overlain by a regionally extensive andesitic to dacitic ignimbrite, the

Huambos Formation (Fraylones Member). This unit has been dated at 8.4 to 8.8 Ma (Turner, 1997).

4.2 Alteration of Epithermal Ore Deposit

Epithermal high sulfidation alteration is similar in most deposits in the district. Intense massive silica

alteration, closely associated with gold mineralisation, forms the core of each of the systems. Massive

silica alteration grades outward into a strongly acid leached zone of vuggy and granular silica. The latter

is commonly texture destructive. Beyond the leached facies there is advanced argillic alteration,

including zones of alunite, clay and weak silica, and this is normally the limit of economic grade gold

mineralisation. Advanced argillic zones grade outward to strong clay rich argillic alteration zones, then

on to propylitically altered and fresh rock. Opaline silica frequently occurs close to the surface, on the

margins of alteration cells.

The scale of alteration zoning is highly variable, with strong Lithologic and elevation control on facies

distribution causing sub horizontal alteration zone geometry. Alteration zoning may occur over

kilometres horizontally, whereas in some areas, strong massive silica alteration occurs only meters

vertically below fresh rock. Dykes and breccia bodies commonly are fresher than more porous

surrounding pyroclastic rocks, resulting in local argillic, propylitic and even fresh zones within large

silicified bodies.

4.3 Mineralisation Epithermal Ore Deposit

Typical of epithermal high sulfidation systems, the main mineralisation of the Yanacocha deposits is

localized in the silicified core facies described above. At depth mineralisation is usually related to higher

temperature advanced argillic alteration and potassic alteration that suggests proximity to gold copper

porphyry systems.

Several stages of mineralisation have been identified in the Yanacocha District. The most important

stages include: Stage 1, a low-grade gold event with development of gold copper porphyry systems at

13

depth, Stage 2, the main gold-(copper) stage, Stage 3, a late high-grade gold event, Stage 4, a late

copper-(gold) stage, and Stage 5, a late carbonate-sulphide stage (Bell et al 2005).

Stage 1, the low-grade event, is characterized by an pervasive silicification, contemporaneous with the

deposition of fine disseminated pyrite and low-grade (less than 0.2 ppm) gold (Harvey et al., 1999). At

deeper levels this stage includes the development of patchy textured silicification, grading to wormy and

A type veinlets, some banded, suggesting a transition from a high sulfidation to a copper gold porphyry

system (Pinto, 2002). Fluid inclusion data, including temperatures that range from 200 to 500 ˚C and

salinities higher than 43 per cent in some samples support this interpretation (Loayza, 2002). Secondary

biotite from potassic alteration at the Kupfertal porphyry copper prospect, using Ar39

/Ar40

, yielded an

age of 10.72 ± 0.09 Ma (Longo, in press).

Stage 2, the main gold event, post-dates the pervasive silicification. Mineralisation is characterized by

fine pyrite with minor enargite and covellite. Sulphides occur as disseminations and void and fracture

fillings. In the oxidized portion of the deposits mineralisation includes the presence of hydrothermal

breccias. Gold in this stage occurs as sub-micron grains usually closely associated with Fe-oxides (Turner,

1997).

Stage 3, a high-grade (greater than 1 ppm) gold event, is recognized by the occurrence of coarse gold

associated with blocky barite or by cross cutting creamy chalcedonic silica. The creamy silica cross-cuts

previously silicified pyroclastic rocks, phreatic breccias and occur as the matrix in some hydrothermal

breccias. Stage 3 style mineralisation is occurs in all deposits, and is especially important at the

Chaquicocha Alta, El Tapado and El Tapado Oeste deposits.

Stage 4, late copper-(gold) mineralisation, is closely associated with dacitic intrusive rocks and

phreatomagmatic breccias. It is characterized by presence of enargite, covellite and pyrite with

advanced argillic silica-alunite alteration at shallow levels and pyrophyllite-diaspore alteration at depth.

Alunite related to this stage yielded a radiometric age of 9.12 +/- 0.32 Ma (Longo, in press). This stage is

recognized at the Cerro Yanacocha deposit.

Stage 5, represented by sparsely distributed veinlets of rhodochrosite-dolomite and base metal

sulphides, is interpreted as representing a transition from acidic fluids to a more neutral pH fluid. This

suggests as a local change in the sulfidation state of the system. This latest stage has been observed at

the Cerro Yanacocha deposit.

4.4 Mineralisation Controls of Epithermal Ore Deposit

Mineralisation controls vary from one deposit to another, but most include structural and lithological

controls, including dome margins and multiphase breccias. At the district scale the location of deposits is

controlled by NE and NW structural intersections. At deposit scale the main structural controls are the

NE, NW and extensional EW faults. Structural zones of weakness controlled the emplacement of

multiple generations of breccias and intrusive rocks along NE and NW trends. These multiple events are

associated with multiple stages of alteration and gold mineralisation.

14

Lithologic control is very important in most deposits. Mineralisation occurs mainly in favourable

pyroclastic rocks. These more porous and permeable rocks localized hydrothermal fluids that produced

alteration and mineralisation. Examples of this type of control occur at the San Jose, El Tapado, Cerro

Yanacocha and Antonio Norte deposits. (Figure 2)

Dome and diatreme margins control the location of gold, especially high grade (greater than 1 ppm), in

many deposits. An example of this is at the Yanacocha Sur deposit where the highest gold grades are at

the contact of the favourable pyroclastic rocks (Ult) with a clay-altered andesitic intrusive. This setting is

duplicated at the El Tapado deposit where the high-grade gold mineralisation is at the contact between

strongly silicified pyroclastic rock and both an argillic altered phreatomagmatic pipe and an argillic

altered to fresh andesitic dome. The interpretation is that the barrier formed by impermeable rock

promoted local fluid flow changes that favoured the precipitation of gold (Bell et al 2005).

15

Figure 1 Regional Geologic Setting of the Yanacocha District. The Yanacocha District is located 20

km north of the city of Cajamarca, in the Northern Andean Orogenic belt of northern Peru.

The Lithologic control is very important in most deposits. Mineralisation occurs mainly in favourable

pyroclastic rocks. These more porous and permeable rocks localized hydrothermal fluids that produced

alteration and mineralisation.

Mineralization

La Quinua, Gravel Deposit

• ULT-Usj, The Upper Lithic Tuff Sequences:

Maqui Maqui, Antonio, Epithermal High

Sulfidation Deposits

• TEUT, Main Yanacocha Pyroclastic

Sequence:

El Tapado, El Tapado Oeste, San Jose,

Carachugo, Yanacocha, Chaquicocha,

Cerro Negro Este, HS Deposits

• TfT,Fine Tuff Sequence:

Cerro Negro Oeste, HS Deposit

• LA, Lower Andesite Sequence

Geology

Figure 2 Generalized Stratigraphical Column for the Yanacocha District.

16

Figure 4 Localisation of Ore Deposits and Alteration in the Yanacocha District. El Tapado deposit is to

the west the Yanacocha Deposit and below the La Quinua Deposit.

EL TAPADO

Figure 3 Conceptual Model of Epithermal High Sulfidation Deposit. The Structural, Alteration (Advanced

Argillic) and Lithologic (Pyroclastic rocks) are the Controls of the gold mineralisation, At deeper levels suggest a

transition from a high sulfidation to a copper gold porphyry system

17

5. MULTIVARIATE ESTIMATION AND SIMULATION

5.1 Database of Samples

All drill holes estimation has been geologically logged, initially using paper logs. Logging included

lithology, mineralogy, granulometric estimates, geotechnical, hydrological and metallurgical parameters,

and recovery percentages. Drill collars are picked up by mine survey crews. Down hole surveys are

typically taken by the drilling contractor.

In El Tapado ore deposit are 211 drillholes, there are 80% of DDH (Diamond drilling Hole) and 20% RCD

(Reverse circulation drilling).

Table 1 Comparison between Blasthole and Core (Drillhole) closer than 9 meters and between RCD

(RCD+BBH) and Blasthole closer than 9 meters

The blasthole have always higher mean grade than drillhole and RCD (BBH is RCD type) and we can have

an idea about the behaviour between drillhole and RCD where the RCD values is little bit low than

drillhole values.

The core samples can vary in length from about 0.5 m to 2 m in length; and the RC samples are typically

taken on 2 m intervals. All diamond cores are halved, with one half sent for assay, and the remainder

retained as a reference sample.

The measurements samples are: Gold Fire assay (AuFA), Gold Cyanide (AuCN), Silver (Ag), Copper

Cyanide (CuCN), Sulphide Sulphur (SS). For this study there are 22202 samples to 3 meters regularized.

Each assay sample has Quality assurance and quality control (QA/QC) measures have been undertaken

since about 1999. QA/QC includes submission of standard reference materials, blanks, and duplicate

samples. About 5% of all samples are quality-control samples.

Dataset Search No. of Ave. Min Max Mean StDev Ratio Of

Dist (m) Pairs Dist (m) Means

Blastholes 9.0 406 2.861 0.020 8.840 0.989 1.707

Core 0.004 8.720 0.890 1.377 1.11

Blastholes 9.0 1 2.053 0.020 0.020 0.020 0.000

RCD 0.010 0.010 0.010 0.000 2.00

Blastholes 9.0 483 2.970 0.020 8.840 0.593 1.109

BBH 0.006 6.560 0.495 0.822 1.20

18

Figure 5 Map of AuFA (gold fire assay). Database has local coordinates.

12000

12000

12500

12500

13000

13000

13500

13500

X (m)

X (m)

25000 25000

25500 25500

26000 26000

26500 26500

27000 27000

Y (m)

Y (m)

Au

Base Map (Au)

Isatis

19

5.2 Domains for Estimation:

The Gold Domain (Goldshape) is a deterministic model, where the gold is higher than 0.1 gpt. This was

made for the geologist area. This goldshape were interpreted on section and plan, and reconciled in

cross section, long section and level plan. , the gold fire assay has 10875 samples inside the Goldshape

domain; it is 50% of the total (Figure 6). The exploration data analysis is done in oxide and sulphide

domains, even though both domains are joined for this measurement. In contrast the gold cyanide

domain (all samples) is divided in oxide and sulphide for the mineralogy; it is a qualitative zone (Figure

7). These domains were interpreted on section and plan, and reconciled in cross section and level plan

for the geology area.

Figure 6 Histogram and Cumulative plot (logarithm scale) of Gold Fire Assay [Green=only Goldshape

(50%), Blue=outside (50%)]

Figure 7 Goldshape divided on Oxide (red blocks) and Sulphide (blue blocks) Section YOZ

OXIDE

SULPHIDE

20

5.3 Gold Fire Assay

The gold fire assay has 10875 samples inside the Goldshape domain. The exploration data analysis is

done in oxide and sulphide domains, even though both domains are joined for this measurement.

5.3.1 Statistics gold fire assay by domain

The histogram of Gold fire assay values is divided in two domains: oxide (red) and sulphide (green). It is

shown in the figure 08. The oxide samples are 75% of the total, while the sulphide zone has 25% of the

total samples.

Figure 8 Histogram and Cumulative plot (logarithm scale) of Gold fire assay in Goldshape

[Green=Sulphide (25%), Red=Oxide(75%)]

Table 2 Statistics Summary of Gold Fire Assay: Oxide and Sulphide Zones in Goldshape Domain

(Oxide and Sulphide Statistics Graphics are in the Annex)

Domain Samples Minimum Maximum Mean Std. Dev.

Oxide AuFA 8193 (75%) 0.0025 145.1557 1.14 2.76

Sulphide AuFA 2682 (25%) 0.0033 18.2601 0.86 1.34

AuFA Total 10875 0.0025 145.1557 1.07 2.49

Top cuts for gold fire assay were determined by inspection of cumulative frequency plots and

histogram (Figure 9), and by a spatial assessment of whether the highest grades in the data

were supported by surrounding composite values.

Then, the gold with top cutting to 20 gpt, which has 2% lower grades than the previous one

(from 1.07 to 1.05 gpt), but the standard deviation has been reduced in 30% (Comparison Table

2 and Table 4).

21

Table 3 Comparison of different Methods of top-cutting or capping.

Top Cutting

Method

Top Cut

value

Top Cut

Samples

Histogram 30 gpt 6

Cumulative plot 20 gpt 10

Figure 10 Histogram of Capped Gold Fire Assay (top cut to 20 gpt), and reduced Histogram of

Capped Gold in Goldshape [Green=Sulphide(25%), Blue=Oxide(75%)]

Table 4 Statistics Summary of Capped Gold Fire Assay: Oxide and Sulphide Zones in Goldshape

Domain (Oxide and Sulphide Statistics Graphics are in the Annex)


Oxide AuFA 8193 0.0025 20.000 1.11 1.85

Sulphide AuFA 2682 0.0033 18.2601 0.8593 1.34

AuFA Total 10875 0.0025 20.000 1.05 1.74

10

100

20

30

Figure 9 Reduced Histogram and Reduced Cumulative plot (logarithm scale) of Gold fire assay in

Goldshape, ([Green=Sulphide (25%), Red=Oxide(75%)]

22

3.3.3.1 Variography of Capped Gold Fire Assay in Goldshape

The variogram model is defined for behaviour near the origin, anisotropies, zones of influence, etc.

(Armstrong, 1998). First of all, we will use the variogram map and the directional variograms in order to

find the anisotropy. After that, we will define the nugget effect with the downhole variogram.

In this study we will use two types of rotation: Mathematical and Geology Rotation (Figure 11 and

Figure 12).

Figure 11 Mathematician Rotation in Isatis Software: that is X=East coordinate, Y=North Coordinate,

Z=Elevation, U=Rotated East, V=Rotated North, W=Rotated Elevation. The direction of rotation is: first Z

axis in right hand sense, second Y axis in right hand sense, third X axis in right hand sense

Figure 12 Geologist Rotation in Isatis Software: that is Y=North coordinate, X=East Coordinate,

Z=Elevation, U=Rotated North, V=Rotated West, W=Rotated Elevation. The direction of rotation is: first Z

axis in left hand sense (Azimuth), second X axis in right hand sense, third Z axis in left hand sense.

23

Figure 13 : Variogram Map of capped gold fire assay in goldshape, with the rotation Z-Right = 20°, Y-

right= -20°, and X-right = 15°(Mathematical Rotation Isatis), this is the plane that will use in the variogram

direction for anisotropy parameters. Azimuth = 122°, X-right= 25°, and Z-left = -55° (Geologist Rotation

Isatis).

Then, we will use the found rotation parameters (Figure 13) for doing 4 variogram experimental inside

the plane of this rotation (Z-Right = 20°, Y-right= -20°, and X-right = 15°), 1 experimental variogram in

direction perpendicular to the plane, and 1 downhole variogram for fixed the nugget effect (Figure 14,

Figure 15 and Figure 16).

The principal parameters of all experimental variogram are: tolerance on direction=22.5 deg, Lag

Value=35 to 50 meters, Number of Lag = 6 to 10, Slicing Height = 1.5 to 3 meters. But on downhole

variogram the parameters are: geological direction = 0° -90° -90°, Tolerance angular = 90 deg, Lag value

= 3 meters, number of Lag =6-10, and calculate along the line is activated.

N109

N289

N5

N207

N27

N60

N240

N53

N268

N88

5

N349

N169

N359

N179

N108

N288

N134

N314

0.00

0.00

0.25

0.25

0.50

0.50

0.75

0.75

1.00

1.00

1.25

1.25

Distance (m)

Distance (m)

0 0

1 1

2 2

3 3

Variogram : Au

Variogram : Au

N/A

4.2

3.7

3.2

2.7

2.2

1.7

1.2

0.7

N/A

4.8

4.3

3.8

3.3

2.8

2.3

1.8

1.3

0.8

N/A

4.1

3.6

3.1

2.6

2.1

1.6

1.1

0.6

Variogram Map - Au

Isatis

24

Figure 14 Variogram Model of capped gold fire assay in goldshape: the rotation parameters are

(Mathematical Rotation Isatis): Z-Right = 20°, Y-Right = -20°, and X-right = 15°, nugget effect (S1): 0.55,

First Structure - Spherical (S2): sill=1.2, U=30m V=25m W=25m; Second Structure-Spherical (S3):

sill=1.8, U=40m V=130m W=100m.

Figure 16 Downhole Variogram and Variogram in Short Range of capped gold fire assay inside

goldshape, below it is shown the numbers of pairs for each point of variograms. The nugget effect is

0.55, and short range = 40m.

0

0

25

25

50

50

75

75

100

100

Distance (m)

Distance (m)

0 0

1 1

2 2

3 3

Variogram : Au_cap

Variogram (Au_cap)

Figure 15 Variogram in long range and in perpendicular range of capped gold fire assay in

goldshape. Long range =130m, and perpendicular range = 100m.

25

3.3.1.2 Cross Validation for Variography parameters of gold fire assay:

The cross validation is used for validating the variograms parameters: rotation parameters (Table 5).

Taking to account that the search parameters is identical to the ranges of variogram ellipsoid and the

minimum samples = 2, and the maximum samples = 4 angular sector x 5 samples per sector = 20.

Table 5 Comparison between different variography parameters of capped gold fire assay in

goldshape, the models from 1 to 6 change the rotation. There are not high differences between the

variograms models, the best model is 1. Correlation coefficient between Estimated and true value is: Rho

Cor C.; and Correlation coefficient between Estimated and (Z-Z*)/SD is: Rho (Z-Z*)/SD.

Variogram

Model

Rotation

ZR – YR - XR

Range

U – V – W

Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)/SD

SD.

(Z-Z*)

Rho

Cor C.

Rho

(Z-Z*)/SD

Model 1 20 -20 15 40 130 100 -16.2154 10.4876 0.002 0.89 0.871 -0.098

Model 2 20 -30 20 40 130 100 -16.2217 10.5519 0.009 0.83 0.872 -0.099

Model 3 10 -20 15 40 130 100 -16.1914 10.4918 0.003 0.892 0.871 -0.098

Model 4 20 -10 5 40 130 100 -16.1052 10.6669 0.002 0.897 0.87 -0.097

Model 5 25 -20 5 40 130 100 -16.2025 10.6127 0.002 0.891 0.87 -0.099

Model 6 20 -30 5 40 130 100 -16.1875 10.5511 0.003 0.83 0.872 -0.099

3.3.1.3 Neighbourhood Choices:

We will do many comparisons the different neighbourhood parameters in the same block (Table 6); the

best neighbourhood is that have less kriging variance and slope of original data vs estimated data is

close to one.

Table 6 Comparison between different neighbourhood parameters (search and maximum of

samples), the parameters are 40 by 130 by 100 (Mathematical rotation 20 -20 15) Minimum 2 samples

and Maximum: 4 sector by 40 samples (block = 29i 44j 32k).

Au_first Mathematical Rotation: 20 -20 15 (Isatis)

search 300 x 300 x 300 300 x 300 x 300 50 x 50 x 50

parameters max: 4 sectors by 100 max: 4 sectors by 50 max: 4 sectors by 10

target Krig. Var Slope Z|Z* Krig. Var Slope Z|Z* Krig. Var Slope Z|Z*

29 x 44 x32 0.785517 0.99195 0.787089 0.98293 0.793473 0.8519

search 100 x 300 x 100 100 x 300 x 100 70 x200 x 100



29 x 44 x32 0.747002 0.98667 0.783546 0.964757 0.712535 0.987616

search 40 x 130 x100 40 x 130 x100 40 x 130 x100



29 x 44 x32 0.724377 0.964097 0.704741 0.982164 0.701748 0.981313

26

Other parameters is the size of block discretization in order to chose the best, we will make the analyses

among different size and check the less standard deviation of 10 Cvv (Mean block covariance), in our

case the best is 7 x 7 x 2 size (Figure 17).

Figure 17 Comparison between different Block Discretization and the standard deviation of Cvv

values, the best choices is 7x7x2 where it is noting the stabilization in standard deviation.

All these parameters (variography and neighbourhood parameters) we will use in order to make the

kriging estimation, and we will do different types of comparison and validation with all estimation

models together.

0

0.01

0.02

0.03

0.04

0.05

0.06

27

5.3.2 Comparison Gold and Logarithm Gold

First of all, we make the statistics of logarithm of gold fire assay; it is shown in (Figure 18). The

graphic show that oxide and sulphide have lognormal distribution.

Figure 18 Histogram of logarithm Gold fire assay in Goldshape [Green = Sulphide (25%), Red =

Oxide (75%)]; and Q-Q plot of gold in theoretical Lognormal distribution.

Then we will make the comparison the gold distribution and logarithm gold distribution with Q-Q plot

(Figure 18), the graphic shows that the logarithm gold has behaviour at lognormal distribution.

3.3.2.1 Variography of Logarithm of Gold Fire Assay in Goldshape

First of all, we will use the variogram map in order to have the principal rotation of the three axes, the

found rotation is: Z-Right = 25°, Y-right= -25°, and X-right = -5° (in Mathematical rotation) or Azimuth =

167°, X-right= 25°, and Z-left = -100° (in Geologist Rotation) in the Figure 19.

After that, we will use the found rotation and range parameters of this variography, in order to fix the

variogram parameter of experimental variogram of gold fire assay in the same rotation.

-5

-5

0

0

5

5

LnAu

LnAu

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

Frequencies

Frequencies

Nb Samples: 2682

Minimum: -5.70

Maximum: 2.90

Mean: -0.93

Std. Dev.: 1.29

Histogram (LnAu)

Isatis

28

Figure 19 Variogram Map of logarithm gold fire assay in goldshape, it has a rotation parameter with:

Z-Right = 25°, Y-right= -25°, and X-right = -5°, this plane that will use in the variogram direction for

anisotropy parameters. This parameters Azimuth = 167°, X-right= 25°, and Z-left = -100° (Geologist

Rotation Isatis).

Then, we will use the found rotation parameters for doing 4 variogram experimental inside the plane of

this rotation, an experimental variogram in direction perpendicular to the plane, and 1 downhole

variogram for fixed the nugget effect (Figure 20, Figure 21 and Figure 22).

N91

N284

N117

N309

N140

N353

N184

N16

N207

N39

U

V

N67

N248

N69

N250

N72

N80

N280

N205

N53

N239

N62

U

W

N348

N175N4

N197

N36

N90N124

N313

N141

N327

V

W

0.00

0.00

0.25

0.25

0.50

0.50

0.75

0.75

1.00

1.00

1.25

1.25

Distance (m)

Distance (m)

0.0 0.0

0.5 0.5

1.0 1.0

1.5 1.5

Variogram : LnAu

Variogram : LnAu

N/A

1.6

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

N/A

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

N/A

1.6

1.5

1.4

1.3

1.2

1.1

1.0

0.9

0.8

0.7

0.6

0.5

Variogram Map - LnAu

Isatis

29

Figure 20 Variogram Model of logarithm gold fire assay in goldshape: the rotation parameters are

(Mathematical Rotation Isatis): Z-Right = 25°, Y-Right = -25°, and X-right =-5°, nugget effect (S1): 0.1,

First Structure - Spherical (S2): sill=0.45, U=80m V=15m W=30m; Second Structure-Exponential (S3):

sill=1.05, U=170m V=270m W=180m.

Figure 21 Variogram in short range and in long range of capped gold fire assay in goldshape.

Short range =170m, and long range = 270m.

Figure 22: Downhole Variogram and Variogram in Perpendicular range of Gaussian capped gold

fire assay inside the goldshape domain. The nugget effect is 0.1 and perpendicular range =180m.

30

Figure 23 Square root of Variogram over Madogram of Logarithm gold, this kind of variogram have

been made for finding logarithm gold is bilognormal that could use to make Lognormal Kriging.

In order to use the logarithm gold for making lognormal kriging, we will need to know the logarithm gold

is bilognormal, in the figure we can see that the square root over Madogram (Figure 23) in three

principal direction (with mathematical rotation: 25 -25 -5) do not have flat behaviour for this reason this

logarithm is not bilognormal.

3.3.2.2.- Variography of Gold with variogram from Logarithm of Gold

Then, we can use the variogram parameters of logarithm gold (rotation and range, because the sill and

nugget effect are different) in gold data.

In the Figure 24, Figure 25 and Figure 26 are shown that the experimental variogram (done with

logarithm gold rotation: 25 -25 -5) is not exactly the same behaviour with the logarithm gold variogram

model, nevertheless the cross validation have better results than he cross validation of gold variogram

model.

31

Figure 24 Variogram Model of gold fire assay (from logarithm gold parameters) in goldshape: the

rotation parameters are (Mathematical Rotation Isatis): Z-Right = 25°, Y-Right = -25°, and X-right =-5°,

nugget effect (S1): 0.55, First Structure - Spherical (S2): sill=1.47, U=80m V=15m W=30m; Second

Structure-Exponential (S3): sill=1.25, U=170m V=270m W=180m.

Figure 25 Variogram in short range and in long range of capped gold fire assay (from logarithm

gold parameters) in goldshape. Short range =170m, and long range = 270m.

Figure 26 Downhole Variogram and Variogram in Perpendicular range of Gaussian capped gold fire

assay inside the goldshape domain. The nugget effect is 0.1 and perpendicular range =180m.

32

3.3.1.3 Cross Validation for Variography parameters of gold fire assay (from

logarithm gold variography parameters):

We will make a cross validation for comparison with other gold variograms models (Table 7), this is

better than the previous gold variogram models.

Table 7 Cross validation Parameters of variography gold fire assay (from logarithm gold

parameters) in goldshape. Correlation coefficient between Estimated and true value is: Rho Cor C.; and

Correlation coefficient between Estimated and (Z-Z*)/SD is: Rho (Z-Z*)/SD.

3.3.2.4. Neighbourhood Choices:


best neighbourhood is that have less kriging variance and slope of original data vs estimated data is

close to one.


samples), the parameters are 170 by 270 by 180 (Mathematical rotation 20 -25 -5) Minimum 2 samples


Au_with variogram

from lnAu Mathematical Rotation: 20 -25 -5

search 170 x 270 x 180 170 x 270 x 180 170 x 270 x 180



29 x 44 x32 0.716238 1.003595 0.716265 1.00417 0.717485 0.994648

search 120 x 220 x 120 250 x 350 x 250 250 x 350 x 250



29 x 44 x32 0.717026 1.002683 0.71694 1.003543 0.716814 1.004175

With these variograms model and neighbourhood will do other ordinary kriging that we will make

comparison with others estimations models.

Variogram

Model

Rotation

ZR – YR - XR

Range

U – V – W

Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)/SD

SD.

(Z-Z*)

Rho

Cor C.

Rho

(Z-Z*)/SD

Model 1 20 -25 -5 170 270 180 -16.2514 10.541 0.002 0.86 0.87 -0.05

33

5.3.3 Comparison Gold and Gaussian Gold

We will make the comparison the gold distribution and Gaussian distribution with Q-Q plot (Figure 27).

Then, we can use the Anamorphosis of fifty Hermite polygons for finding the relationship between the

raw data and Gaussian distribution, the Figure 28 is shown this relation.

Figure 28 Gaussian Gold Model with 50 Hermite polynomials, which is coinciding with gold fire

assay, and histogram of Gaussian gold, the mean is zero, and the standard deviation is one, it is the

typical normal Gaussian distribution.

Figure 27 Histogram of Gold fire assay in Goldshape [Green=Sulphide (25%), Red=Oxide(75%)]; and Q-Q

plot of gold Logarithm in theoretical Gaussian distribution.

34

3.3.3.1.- Variography of Gaussian Gold Fire Assay in Goldshape

First of all, we will use the variogram map in order to have the principal rotation of the three axes

(Figure 29), the found rotation is: Z-Right = -80°, Y-Right = 65°, and X-right =-45° (Mathematical

Rotation), this is the plane that will use in the variogram direction for anisotropy parameters. Azimuth =

32°, X-right= 72°, and Z-left = 108° (Geologist Rotation Isatis)

Figure 29 Variogram Map of Gaussian gold in goldshape, it has a rotation (Mathematical Rotation

Isatis): Z-Right = -80°, Y-Right = 65° and X-right =-45°, this is the plane that will use in the variogram

direction for anisotropy parameters. Azimuth = 32°, X-right= 72°, and Z-left = 108° (Geologist Rotation)


this rotation (Figure 30, Figure 31 and Figure 32), an experimental variogram in direction perpendicular

to the plane, and 1 downhole variogram for fixed the nugget effect.

50

N11

N202

N22

N209

N29

N231

N51

N249

N69

50

N44

N271

N91

N289

N109

N311

N131

N318

N138

8

N17

N356

N176

N334

N154

N274

N94

N255

N75

N57

0.00

0.00

0.25

0.25

0.50

0.50

0.75

0.75

1.00

1.00

1.25

1.25

Distance (m)

Distance (m)

0.00 0.00

0.25 0.25

0.50 0.50

0.75 0.75

1.00 1.00

Variogram : Gaussian Au


N/A

1.09

1.04

0.99

0.94

0.89

0.84

0.79

0.74

0.69

0.64

0.59

0.54

0.49

0.44

N/A

1.20

1.10

1.00

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

N/A

0.9

0.8

0.7

0.6

0.5

0.4

0.3

Variogram Map - Gaussian Au

Isatis

35

Figure 30 Variogram Model of Gaussian gold fire assay in goldshape: the rotation parameters are

(Mathematical Rotation Isatis): -80°, Y-Right = 65°, and X-right =-45°, nugget effect (S1): 0.08, First

Structure - Spherical (S2): sill=0.47, U=30m V=100m W=60m; Second Structure-Exponential (S3):

sill=0.47, U=200m V=450m W=300m. (More details in Appendix Variographies)

Figure 31 Variogram in short range and in long range of gold fire assay in goldshape. Short range

=200m, and long range = 450m.

Figure 32 Downhole Variogram and Variogram in Perpendicular range of Gaussian gold fire assay

inside the goldshape domain. The nugget effect is 0.08 and perpendicular range =300m.

0

0

50

50

100

100

150

150

200

200

Distance (m)

Distance (m)

0.0 0.0

0.5 0.5

1.0 1.0



Variogram (Gaussian Au)

Isatis

36

Figure 33 Square root of Variogram divide by Madogram of Gaussian gold, this kind of variogram

have been made for finding Gaussian gold is bigaussian.

In order to use the Gaussian gold for making Gaussian kriging, we will need to know the Gaussian gold is

bigaussian, in the figure we can see that the square root over Madogram (Figure 33) in three principal

direction (with mathematical rotation: 25 -25 -5) do not have flat behaviour for this reason this Gaussian

gold is not bigaussian, for improving this result we will use declustering Gaussian gold.

3.3.3.2.- Variography of Gold with variogram from Gaussian Gold

Then, we can use the variogram parameters of Gaussian (rotation and range, because the sill and nugget

effect are different) in gold data. In the Figure 34 is shown that the experimental variogram (done with

Gaussian gold rotation: -80 65 -45) is not exactly behaviour with the Gaussian gold variogram model, but

the cross validation have better results than the cross validation of gold variogram model (Table 9).

Figure 34 Variogram Model of Gold and with experimental values (from of Gaussian gold) in

goldshape: the rotation parameters are (Mathematical Rotation Isatis): -80°, Y-Right = 65°, and X-right =-

45°, nugget effect (S1): 0.55, First Structure - Exponential (S2): sill=4.6, U=30m V=70m W=50m; Second

Structure-Exponential (S3): sill=0.9, U=200m V=450m W=300m. Azimuth = 32°, X-right= 72°, and Z-left =

108° (Geologist Rotation Isatis)

37

Table 9 Cross Validation of Variogram Model of Gold (from Gaussian model). Correlation coefficient

between Estimated and true value is: Rho Cor C.; and Correlation coefficient between Estimated and (Z-

Z*)/SD is: Rho (Z-Z*)/SD.

Variogram

Model

Rotation

ZR – YR - XR

Range

U – V – W

Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)/SD

SD.

(Z-Z*)

Rho

Cor C.

Rho

(Z-Z*)/SD

Model 1 -80 65 -45 200 450 300 -11.279 7.2805 0.003 0.58 0.88 -0.046

3.3.3.3.- Neighbourhood Choices:

Similary to previous estimation model, we will carry on the study for getting the best neighbourhood

parameters.


samples), the parameters are 180 by 450 by 320 (Mathematical rotation -80 65 -45) Minimum 2 samples


Au_with vario from gaussian Au Mathematical Rotation: -80 65 -45

search 180 x 450 x 320 180 x 450 x 320 180 x 450 x 320



29 x 44 x32 0.732614 1.010189 0.737174 0.987077 0.74054 0.972389

search 180 x 450 x 320 180 x 450 x 320

parameters max: 4 sectors by 60 max: 4 sectors by 45

target Krig. Var Slope Z|Z* Krig. Var Slope Z|Z*

29 x 44 x32 0.731677 1.017875 0.733786 1.003528

Figure 35 Variogram Block Model of Gold (from of Gaussian gold) in goldshape: the rotation

parameters are (Mathematical Rotation Isatis): -80°, Y-Right = 65°, and X-right =-45°, First Structure -

Gaussian (S1): sill=0.43, U=45m V=95m W=70m; Second Structure-Exponential (S3): sill=0.57, U=200m

V=450m W=300m. Azimuth = 32°, X-right= 72°, and Z-left = 108° (Geologist Rotation Isatis)

38

5.3.4 Declustering analysis for gold fire assay

In order to do the simulation for gold fire assay, we will need to use the declustered gold fire assay.

The choice declustering method is the cell declustering, which consists in divided into rectangular

regions called cells. Each sample receives a weight inversely proportional to the number of samples that

fall within the same cell. Then, the clustered samples will receive lower weight with this method

because the cells in which they are located will also contain several other samples (Rivoirard 2003 and

Isaaks 1989).

First, we will use our samples to get the mean value within moving windows, and then we take these

moving windows mean and use them to get the mean of the global area.

If the cells are very small, then each sample will be into a cell of its own and all samples will therefore

receive equal weight of 1 (Isaaks 1989). Nevertheless, if the cells are as large as the entire global area, all

samples will fall into the same cell and will again receive equal weights. Somewhere between these two

extremes we must obtain an appropriate medium (it is shown in the Figure 36).

In our case the appropriate dimensions of such cell is that minimizes the estimate of the global mean

and global standard deviation, the choice value is 300 by 300 by 120 (Table 11).

Figure 36 Declustering statistics of gold fire assay, the best result is in the step 7 (350 x350 x 120 m.)

5 10 15 20

Step

.25

.50

.75

.00

.25

.50

.75

DeclusteringMean

Mean Step

Standard Dev.

Standard Dev. Step

Declustering Statistics

Isatis

39

Table 11 Study of declustering to different sizes cell: The best result of declustering is 350x350x120

meters that has the least weighted mean and the least weighted standard deviation.

The global mean of this measurement has 30% less than the mean of gold no declustered, in other way

the global standard deviation has been reduced in 26% (this is shown in the Figure 37 and Figure 6).

STEP DX DY DZ

WEIGHTED

MEAN

WEIGTHED

ST.DEV

1 50 50 17 0.4802 1.4915

2 100 100 34 0.3391 1.2052

3 150 150 51 0.2535 1.0108

4 200 200 68 0.2316 0.9877

5 250 250 85 0.2163 0.9609

6 300 300 102 0.2097 0.9355

7 350 350 119 0.2046 0.9298

8 400 400 136 0.212 0.9522

9 450 450 153 0.2201 0.9733

10 500 500 170 0.2236 0.98

11 550 550 187 0.2377 1.0181

12 600 600 204 0.2619 1.0721

13 650 650 221 0.2765 1.1127

14 700 700 238 0.2857 1.1344

15 750 750 255 0.2992 1.1682

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au

Au

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

Frequencies

Frequencies

Nb Samples: 10875

Minimum: 0.0025

Maximum: 145.1557

Mean: 0.7562

Std. Dev.: 1.8482

Histogram (Au)

Isatis

DATA/DATA(Gold)

Figure 37 Histogram and Cumulative plot (logarithm scale) of declustered Gold Fire Assay in

Goldshape [Green=Sulphide(25%), Blue=Oxide(75%)].

40

Table 12 Statistics Summary of declustered Gold Fire Assay: Oxide and Sulphide Zones in

Goldshape Domain (Oxide and Sulphide Statistics Graphics are in the Annex).


Oxide AuFA 8193 0.0025 145.1557 0.85 2.2137

Sulphide AuFA 2682 0.0033 18.2601 0.6267 1.1633

AuFA Total 10875 0.0025 145.1557 0.7562 1.8482

3.3.4.1 Gaussian Declustered Gold Fire assay

The Gaussian model of gold fire assay is made with Declustered Gold (no top cut values), in order to do

the Conditional Simulation method, it is realised with Gaussian Anamorphosis modelling of declustered

gold, we can see in the Figure 38.

The Figure 38-left is shown the statistics of Gaussian gold model with mean equal to zero, and standard

deviation equal to one.

The Gaussian Variography Model has different parameters that the capped gold variography

and gold (from logarithm gold variography) variography.

Figure 38 Gaussian Model with 50 Hermite polynomials, which is coinciding with the declustered gold

fire assay, and histogram of Gaussian declustered gold, the mean is zero, and the standard deviation

is one, it is the typical normal Gaussian distribution.

3.3.4.2 Variogram of Gaussian declustered gold fire assay

Similarly to gold fire assay variogram; we will look for the anisotropy with the variogram map

(Figure 39), after that it will use in order to make the directional variograms and fitting

variograms.

-5

-5

0

0

5

5

Gaussian values

Gaussian values

0 0

50 50

100 100

150 150

Au_raw

Au_raw

Anamorphosis

Isatis

-4

-4

-3

-3

-2

-2

-1

-1

0

0

1

1

2

2

3

3

4

4

Gaussian Au

Gaussian Au

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

Frequencies

Frequencies

Nb Samples: 10875

Minimum: -3.73

Maximum: 3.99

Mean: 0.01

Std. Dev.: 1.01

Histogram (Gaussian Au)

Isatis

41

Figure 39 Variogram Map of Gaussian declustered gold in goldshape, it has a rotation (Mathematical

Rotation Isatis): Z-Right = -80°, Y-Right = 65°, and X-right =-45°, this is the plane that will use in the

variogram direction for anisotropy parameters. Azimuth = 32°, X-right= 72°, and Z-left = 108° (Geologist

Rotation Isatis)




50

N11

N202

N22

N209

N29

N231

N51

N249

N69

50

N44

N271

N91

N289

N109

N311

N131

N318

N138

8

N17

N356

N176

N334

N154

N274

N94

N255

N75

N57

0.00

0.00

0.25

0.25

0.50

0.50

0.75

0.75

1.00

1.00

1.25

1.25

Distance (m)

Distance (m)

0.00 0.00

0.25 0.25

0.50 0.50

0.75 0.75

1.00 1.00



N/A

1.09

1.04

0.99

0.94

0.89

0.84

0.79

0.74

0.69

0.64

0.59

0.54

0.49

0.44

N/A

1.20

1.10

1.00

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

N/A

0.9

0.8

0.7

0.6

0.5

0.4

0.3

Variogram Map - Gaussian Au

Isatis

42

Figure 40 Variogram Model of Gaussian declustered gold fire assay in goldshape: the rotation

parameters are (Mathematical Rotation Isatis): -80°, Y-Right = 65°, and X-right =-45°, nugget effect (S1):

0.08, First Structure - Spherical (S2): sill=0.44, U=20m V=55m W=25m; Second Structure-Spherical (S3):


0

0

50

50

100

100

150

150

200

200

Distance (m)

Distance (m)

0.0 0.0

0.5 0.5

1.0 1.0




Isatis

Figure 41 Variogram in short range and in long range of Gaussian gold in goldshape. Short range


Figure 42 Downhole Variogram and variogram in Perpendicular range of Gaussian gold inside

the goldshape domain. The nugget effect is 0.08 and perpendicular range =320m.

43

3.3.4.3. Cross Validation for Variography parameters of Gaussian declustered gold

The cross validation is used for validating the variograms parameters: rotation parameters. Taking to

account that the search parameters is identical to the ranges of variogram ellipsoid and minimum

sample = 2, and maximum sample = 4 angular sector x 5 samples per sector = 20 (Table 13).

Table 13 Comparison between different variography parameters of Gaussian declustered gold fire

assay in goldshape, the models from 1 to 6 change the rotation. There are not higher differences between the

variograms models, but taking to account the cross validation parameters the best model is 1. Correlation coefficient

between Estimated and true value is: Rho Cor C.; and Correlation coefficient between Estimated and (Z-Z*)/SD is:

Rho (Z-Z*)/SD.

Variogram

Model

Rotation

ZR – YR - XR

Range

U – V – W

Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)

SD.

(Z-Z*)

Rho

Cor C.

Rho

(Z-Z*)/SD

Model 1 -80 65 -45 180 380 290 -5.48279 7.16158 0.011 0.88 0.905 -0.109

Model 2 -70 75 -45 180 380 290 -5.41995 7.08911 0.011 0.87 0.906 -0.106

Model 3 -90 55 -45 180 380 290 -5.6141 7.24025 0.010 0.90 0.905 -0.101

Model 4 -80 75 -55 180 380 290 -5.49784 7.07986 0.010 0.87 0.906 -0.105

Model 5 -80 55 -35 180 380 290 -5.55948 7.261 0.010 0.89 0.905 -0.101

Model 6 -80 75 -45 180 380 290 -5.49954 7.06721 0.011 0.87 0.906 -0.105

Figure 43 Square root of Variogram divide by Madogram of Gaussian declustered gold, this kind of

variogram have been made for finding Gaussian declustered gold is bigaussian.

In order to use the Gaussian gold for making Conditional Simulation method, we will need to know the

Gaussian gold is bigaussian, in the figure we can see that the square root over Madogram (Figure 43) in

three principal direction (with mathematical rotation: 25 -25 -5), which have flat behaviour for this

reason this Gaussian gold is bigaussian.

44

3.3.4.4. Variography and Cross of Gold from variogram from Gaussian declustered

gold

Then, we can use the variogram parameters of Gaussian declustered (rotation and range, because the

sill and nugget effect are different) in gold data. In the Figure 44 is shown that the experimental

variogram (done with Gaussian gold rotation: -80 65 -45) is not exactly behaviour with the Gaussian

declustered gold variogram model.

Figure 44 Variogram Model of Gold (from of Gaussian declustered gold) in goldshape: the rotation

parameters are (Mathematical Rotation Isatis): -80°, Y-Right = 65°, and X-right =-45°, nugget effect (S1):

0.55, First Structure - Exponential (S2): sill=1.95, U=25m V=45m W=25m; Second Structure-Exponential

(S3): sill=0.87, U=180m V=450m W=320m.

Table 14 Cross Validation of Variogram Model of Gold (from Gaussian model). Correlation

coefficient between Estimated and true value is: Rho Cor C.; and Correlation coefficient between

Estimated and (Z-Z*)/SD is: Rho (Z-Z*)/SD.

Variogram

Model

Rotation

ZR – YR - XR

Range

U – V – W

Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)/SD

SD.

(Z-Z*)

Rho

Cor C.

Rho

(Z-Z*)/SD

Model 1 -80 65 -45 180 450 320 -15.5917 10.199 0.009 0.806 0.879 -0.041

3.3.4.5. Neighbourhood Choices by Gaussian declustered gold

We will do many comparisons the different neighbourhood parameters in the same block; the best

neighbourhood is that have less kriging variance and slope of original data versus estimated data is close

to one (Table 15).

Other parameters is the size of block discretization in order to chose the best, we will make the analyses

among different size and check the less standard deviation of 10 Cvv (Mean block covariance), in our

case the best is 8 x 8 x 2 size (Figure 45).

45


samples), the parameters are 100 by 250 by 180 (Mathematical rotation -80 75 -55) Minimum 2 samples


Gaussian_gold Mathematical Rotation: -80 75 -55

search 300 x 300 x 300 300 x 300 x 300 50 x 50 x 50



29 x 44 x32 0.160769 1.007644 0.161035 1.015511 0.166266 0.963647

search 250 x 400 x 350 250 x 400 x 350 180 x 380 x 290



29 x 44 x32 0.160706 1.017448 0.161512 1.001256 0.160671 1.016013

search 100 x 250 x 180 100 x 250 x 180 100 x 250 x 180



29 x 44 x32 0.161591 1.000693 0.16083 1.013076 0.160677 1.016233

Figure 45 Comparison between different Block Discretization and the standard deviation of 10 Cvv

values (mean Block Covariances), the best choices is 8x8x2 where it is noting the stabilization in

standard deviation.

0

0.002

0.004

0.006

0.008

0.01

0.012

2x2x2 3x3x2 4x4x2 5x5x2 6x6x2 7x7x2 8x8x2 9x9x2 10x10x2

46

0.0

0.0

0.5

0.5

1.0

1.0

ind_0.2

ind_0.2

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

0.6 0.6

0.7 0.7

0.8 0.8

Frequencies

Frequencies

Nb Samples: 10875

Minimum: 0.00

Maximum: 1.00

Mean: 0.75

Std. Dev.: 0.43

Histogram (ind_0.2)

Isatis

DATA/DATA(Gold)

0.0

0.0

0.5

0.5

1.0

1.0

ind_0.7

ind_0.7

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

0.6 0.6

Frequencies

Frequencies

Nb Samples: 10875

Minimum: 0.00

Maximum: 1.00

Mean: 0.39

Std. Dev.: 0.49

Histogram (ind_0.7)

Isatis

0.0

0.0

0.5

0.5

1.0

1.0

ind_0.4

ind_0.4

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

0.6 0.6

Frequencies

Frequencies

Nb Samples: 10875

Minimum: 0.00

Maximum: 1.00

Mean: 0.56

Std. Dev.: 0.50

Histogram (ind_0.4)

Isatis

5.3.5 Preliminar Study Indicator Gold Fire assay (5 cut-off)

First of all, the gold fire assay is divided in 5 cut-off: 0.2, 0.4, 0.7, 1.0 and 2.0 gpt. After that we will

replace of the initial data (AuFA) by indicator data (1AuFA>cut-off). We can see the statistics of the

indicators for each cut-off in the (Figure 46, Figure 47 and Figure 48). We have the assumptions that are

Nested Set, where the area of Indicator (x>2.0 gpt) is included in the area of indicator (x>1.0 gpt), and

this is included in the area of indicator (x>0.7gpt), and this is included in the area of indicator (x>0.4 gpt),

and finally this is inside of the area of indicator (x>0.2gpt).

Figure 46 Cumulative plot and Histogram of Indicator to cut-off 0.2 gpt of gold fire assay.

Figure 47 Histograms of Indicator to cut-off 0.4 and 0.7 gpt of gold fire assay.

47

0.0

0.0

0.5

0.5

1.0

1.0

ind_2.0

ind_2.0

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

0.6 0.6

0.7 0.7

0.8 0.8

0.9 0.9

Frequencies

Frequencies

Nb Samples: 10875

Minimum: 0.00

Maximum: 1.00

Mean: 0.13

Std. Dev.: 0.34

Histogram (ind_2.0)

Isatis

0.0

0.0

0.5

0.5

1.0

1.0

ind_1.0

ind_1.0

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

0.6 0.6

0.7 0.7

Frequencies

Frequencies

Nb Samples: 10875

Minimum: 0.00

Maximum: 1.00

Mean: 0.29

Std. Dev.: 0.46

Histogram (ind_1.0)

Isatis

Table 16 Comparison between indicators statistics parameters of gold fire assay to different cut-

off (0.2, 0.4, 0.7, 1.0 and 2.0 grades per tonnes or gpt).

3.3.5.1. Variography of Indicator (cut-off > 0.2, 0.4, 0.7, 1.0, and 2.0)

First, we find the Rotation parameters with Variogram Map (Figure 49, Figure 53, Figure 57, Figure 61

and Figure 65), after that we will have 4 experimental variogram inside the plane of the choice rotation,

1 variogram in direction perpendicular to plane, and downhole variogram.

Indicator Samples Minimum Maximum Mean Std. Dev.

Cutoff 0.2 10875 0.0 1.0 0.75 0.43

Cutoff 0.4 10875 0.0 1.0 0.56 0.50

Cutoff 0.7 10875 0.0 1.0 0.39 0.49

Cutoff 1.0 10875 0.0 1.0 0.29 0.46

Cutoff 2.0 10875 0.0 1.0 0.13 0.34

Figure 48 Histograms of Indicator to cut-off 1.0 and 2.0 gpt of gold fire assay.

48

3.3.5.1.1. Variogram of Indicator of gold fire assay to cut-off 0.2 gpt.

Figure 49 Variogram Map of Indicator of gold to cut-off 0.2 gpt in goldshape, it has a rotation

(Mathematical Rotation Isatis): Z-Right = -40°, Y-Right = 35°, and X-right =-35°, this is the plane that will

use in the variogram direction for anisotropy parameters. Azimuth = 350°, X-right= 48°, and Z-left = 129°

(Geologist Rotation Isatis)


this rotation (Figure 50, Figure 51 and Figure 52), an experimental variogram in direction

perpendicular to the plane, and 1 downhole variogram for fixed the nugget effect.

10

N162

N342

N176

N356

N10

N27

N230

N50

N258

N78

U

0

N179

N359

N220

N40

N279

N99

N288

N108

98

N1

N335

N155

N301

N121

N91

N70

N235

N55

N223

N43

N31

V

0.00

0.00

0.25

0.25

0.50

0.50

0.75

0.75

1.00

1.00

1.25

1.25

Distance (m)

Distance (m)

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

Variogram : ind_0.2

Variogram : ind_0.2

N/A

0.21

0.19

0.17

0.15

0.13

0.11

0.09

0.07

0.05

0.03

N/A

0.16

0.15

0.14

0.13

0.12

0.11

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

N/A

0.22

0.20

0.18

0.16

0.14

0.12

0.10

0.08

0.06

0.04

Variogram Map - ind_0.2

Isatis

49

Figure 50 Variogram Model of Indicator of gold fire assay to cut-off 0.2 gpt in goldshape: the rotation

parameters are (Mathematical Rotation Isatis): Z-Right = -40°, Y-Right = 35°, and X-right =-35°, nugget effect (S1):

0.03, First Structure is Spherical (S2): sill=0.055, U=45m V=50m W=20m; Second Structure is Spherical (S3):


Figure 51 Variogram in direction to short range and to long range of Indicator of gold fire assay to

cut-off 0.2 gpt in goldshape. Short range =250m, and long range = 450m.

N135

N171

N203

N256

N84

dh

0

0

100

100

200

200

300

300

400

400

Distance (m)

Distance (m)

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

Variogram : ind_0.2

Variogram : ind_0.2

Variogram Model - Global Window

Figure 52 Variogram in direction to perpendicular range and downhole Variograms of

Indicator of gold fire assay to cut-off 0.2 gpt in goldshape. Perpendicular range =270m, and

nugget effect = 0.03.

50









10

N157

N337

N169

N349

N2

N20

N225

N45

N259

N79

U

10

N181

N1

N215

N35

N271

N91

N283

N103

90

N319

N139

N285

N105

N229

N49

N217

N37

N25

0.00

0.00

0.25

0.25

0.50

0.50

0.75

0.75

1.00

1.00

1.25

1.25

Distance (m)

Distance (m)

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

0.25 0.25

Variogram : ind_0.4

Variogram : ind_0.4

N/A

0.27

0.25

0.23

0.21

0.19

0.17

0.15

0.13

0.11

0.09

0.07

N/A

0.27

0.25

0.23

0.21

0.19

0.17

0.15

0.13

0.11

0.09

0.07

0.05

0.03

N/A

0.26

0.24

0.22

0.20

0.18

0.16

0.14

0.12

0.10

0.08

0.06


Isatis

51

Figure 54 Variogram Model of Indicator of gold fire assay to cut-off 0.4 gpt in goldshape: the

rotation parameters are (Mathematical Rotation Isatis): Z-Right = -40°, Y-Right = 35°, and X-right =-45°,

nugget effect (S1): 0.05, First Structure is Spherical (S2): sill=0.09, U=25m V=25m W=45m; Second

Structure is Spherical (S3): sill=0.14, U=250m V=480m W=300m.

N130

N160

N190

N250

Norm

dh

0

0

100

100

200

200

300

300

400

400

Distance (m)

Distance (m)

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

Variogram : ind_0.4

Variogram : ind_0.4


Figure 56 Variogram in perpendicular range and downhole Variogram of Indicator of gold fire

assay to cut-off 0.4 gpt in goldshape. Perpendicular range =300m, and nugget effect = 0.05.

Figure 55 Variogram in short range and in long range of Indicator of gold fire assay to cut-off 0.4

gpt in goldshape. Short range =250m, and long range = 480m.

52









10

N149

N329

N157

N337

N207

N27

N255

N75

10

N156

N336

N186

N6

N212

N32

N52

N68

N261

N81

N275

N95

N290

N110

U

W

72

N295

N115

N268

N88

N68

N53

N220

N40

N207

N27

N12

V

0.00

0.00

0.25

0.25

0.50

0.50

0.75

0.75

1.00

1.00

1.25

1.25

Distance (m)

Distance (m)

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

0.25 0.25

Variogram : ind_0.7

Variogram : ind_0.7

N/A

0.27

0.25

0.23

0.21

0.19

0.17

0.15

0.13

0.11

0.09

0.07

N/A

0.250

0.245

0.240

0.235

0.230

0.225

0.220

0.215

0.210

0.205

0.200

0.195

0.190

N/A

0.27

0.25

0.23

0.21

0.19

0.17

0.15

0.13

0.11

0.09


Isatis

53


rotation parameters are (Mathematical Rotation Isatis): Z-Right = -40°, Y-Right = 40°, and X-right =-60°,

nugget effect (S1): 0.04, First Structure is Spherical (S2): sill=0.12, U=30m V=30m W=35m; Second

Structure is Exponential (S3): sill=0.09, U=170m V=380m W=220m.

N130

N151

N172

N243

Norm

dh

0

0

100

100

200

200

300

300

400

400

500

500

Distance (m)

Distance (m)

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

0.25 0.25

Variogram : ind_0.7

Variogram : ind_0.7


Figure 59 Variogram in short range and in long range of Indicator of gold fire assay to cut-off 0.7

gpt in goldshape. Short range =170m, and long range = 380m.

Figure 60 Variogram in perpendicular range and downhole Variogram of Indicator of gold fire assay

to cut-off 0.7 gpt in goldshape. Perpendicular range =220m, and nugget effect = 0.04.

54



(Mathematical Rotation Isatis): Z-Right =35°, Y-Right =-5°, and X-right =-15°, this is the plane that will use

in the variogram direction for anisotropy parameters. Azimuth = 217°, X-right= 16°, and Z-left = -161°





35

N75

N95

N275

N115

N295

N177

N357

N196

N16

N36

U

5

N60

N67

N247

N76

N256

N207

N27

N222

N42

N49

46

N332

N152

N343

N163

N140

N320

N143

N323

0.00

0.00

0.25

0.25

0.50

0.50

0.75

0.75

1.00

1.00

1.25

1.25

Distance (m)

Distance (m)

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

Variogram : ind_1.0

Variogram : ind_1.0

N/A

0.214

0.209

0.204

0.199

0.194

0.189

0.184

0.179

0.174

0.169

0.164

0.159

0.154

0.149

0.144

0.139

N/A

0.24

0.22

0.20

0.18

0.16

0.14

0.12

0.10

0.08

0.06

N/A

0.23

0.21

0.19

0.17

0.15

0.13

0.11

0.09

0.07


Isatis

55


rotation parameters are (Mathematical Rotation Isatis): ): Z-Right =35°, Y-Right =-5°, and X-right =-15°,

nugget effect (S1): 0.04, First Structure is Exponential (S2): sill=0.12, U=25m V=50m W=60m; Second


N55

N100

N146

N192

Norm

dh

0

0

50

50

100

100

150

150

200

200

Distance (m)

Distance (m)

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

Variogram : ind_1.0

Variogram : ind_1.0




Figure 63 Variogram in short range and in long range of Indicator of gold fire assay to cut-off

1.0 gpt in goldshape. Short range =100m, and long range = 240m.

56



(Mathematical Rotation Isatis): Z-Right =35°, Y-Right =-5°, and X-right =-20°, this is the plane that will use

in the variogram direction for anisotropy parameters. Azimuth = 222°, X-right= 21°, and Z-left = -166°





35

N74

N94

N274

N115

N295

N178

N358

N197

N17

N36

5

N70

N250

N82

N262

N200

N20

N218

N38

7

N334

N154

N351

N171

N141

N321

N143

N323

N55

N147

N132

0

0

50

50

100

100

150

150

Distance (m)

Distance (m)

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

Variogram : ind_2.0

Variogram : ind_2.0

N/A

0.14

0.13

0.12

0.11

0.10

0.09

0.08

0.07

0.06

N/A

0.15

0.14

0.13

0.12

0.11

0.10

0.09

0.08

0.07

0.06

0.05

0.04

0.03

N/A

0.14

0.13

0.12

0.11

0.10

0.09

0.08

0.07

0.06

0.05

0.04


Isatis

57

Figure 66: Variogram Model of Indicator of gold fire assay to cut-off 2.0 gpt in goldshape: the

rotation parameters are (Mathematical Rotation Isatis): ): X-Right =35°, Y-Right =-5°, and X-right =-20°,

nugget effect (S1): 0.03, First Structure is Exponential (S2): sill=0.06, U=25m V=15m W=35m; Second


N55

N99

N147

N193

N312

dh

0

0

50

50

100

100

150

150

200

200

Distance (m)

Distance (m)

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

Variogram : ind_2.0

Variogram : ind_2.0

Isatis

Figure 67 Variogram in short range and in long range of Indicator of gold fire assay to cut-off

2.0 gpt in goldshape. Short range =90m, and long range = 220m.



58

3.3.5.2. Cross Validation for Variography parameters of Indicator 0.2, 0.4 and 0.7


Taking to account that the search parameters is identical to the ranges of variogram ellipsoid and

minimum sample = 2, and maximum sample = 4 angular sector x 5 samples per sector = 20.


assay in goldshape. There are not higher differences between the variograms models. Correlation coefficient


Rho (Z-Z*)/SD.

Variogram

Model

Rotation

ZR – YR - XR

Range

U – V – W

Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)

SD.

(Z-Z*)

Rho

Cor C.

Rho

(Z-Z*)/SD

Model 0.2 -40 35 -35 250 450 270 -4.70999 4.71991 0.007 1.22 0.779 0.008

Model 0.4 -40 35 -45 250 480 300 -9.6492 9.5681 0.005 1.091 0.805 -0.004

Model 0.7 -40 40 -60 170 380 220 -9.70484 9.72717 0.009 1.022 0.82 0.016

3.3.5.3. Cross Validation for Variography parameters of Indicator 1.0 and 2.0 of gold


Taking to account that the search parameters is identical to the ranges of variogram ellipsoid and

minimum sample = 2, and maximum sample = 4 angular sector x 5 samples per sector = 20.


assay in goldshape. There are not higher differences between the variograms models. Correlation coefficient


Rho (Z-Z*)/SD.

Variogram

Model

Rotation

ZR – YR - XR

Range

U – V – W

Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)

SD.

(Z-Z*)

Rho

Cor C.

Rho

(Z-Z*)/SD

Model 1.0 35 -5 -15 100 240 110 -9.72997 9.71815 0.001 0.991 0.807 0.019

Model 2.0 35 -5 -20 100 240 110 -4.48289 4.98662 0.00 0.950 0.77 0.027

The estimation result values of this preliminary study is too less to ordinary kriging results. This

has motivated the development of indicators by more cut-off (divided in 25), in order to

improve the estimation results.

59

5.3.6 Final Study of Indicators (25 different cut-off) of Gold Fire Assay

In order to improve the result of the preliminary study of Indicator of gold, we will go to divide the gold

in 25 indicators for having more details in the Estimation results. First of all, we redo the statistics of all

indicators (Table 19), and the correlation coefficient between all indicators (Table 20).

Table 19 Statistics of different indicators, for each indicator has number of samples, mean and

standard deviation.

VARIABLE Count Mean S.Dev VARIABLE Count Mean S.Dev VARIABLE Count Mean S.Dev

ind_0.1 10875 0.91 0.29 ind_1.0 10875 0.29 0.46 ind_4.0 10875 0.04 0.2

ind_0.2 10875 0.75 0.43 ind_1.2 10875 0.25 0.43 ind_5.0 10875 0.03 0.17

ind_0.3 10875 0.64 0.48 ind_1.5 10875 0.19 0.39 ind_6.0 10875 0.02 0.15

ind_0.4 10875 0.56 0.5 ind_1.7 10875 0.16 0.37 ind_7.0 10875 0.02 0.13

ind_0.5 10875 0.49 0.5 ind_2.0 10875 0.13 0.34 ind_8.0 10875 0.01 0.11

ind_0.6 10875 0.44 0.5 ind_2.5 10875 0.09 0.29 ind_10.0 10875 0.01 0.08

ind_0.7 10875 0.39 0.49 ind_3.0 10875 0.07 0.25 ind_12.0 10875 0.01 0.07

ind_0.8 10875 0.36 0.48 ind_3.5 10875 0.05 0.22 ind_15.0 10875 0.003 0.05

ind_0.9 10875 0.32 0.47

3.3.6.1.- Variography in all Indicators of Gold (cut-off from 0.1 to 15 gpt)

In order to improve the variography, we will separate the indicators by parts: from 0.1 to 0.5, from 0.5

to 1.0, from 1.0 to 2.0, from 2.0 to 5.0, from 5.0 to 8.0, and from 8.0 to 15.0).Then, we will use the found

rotation parameters (which are the rotation of the preliminary study) for doing 2 variogram

experimental inside the plane of this rotation (in direction of large and short range), an experimental

variogram in direction perpendicular to the plane, and 1 downhole variogram for fixed the nugget effect.

Table 20 Correlation coefficient between different indicators, the closer indicators has higher values than the more

distant indicators.

60

Figure 69 Cross Variograms Models of Indicators (cut-off of gold: 0.1, 0.2, 0.3, 0.4 and 0.5 gpt), with

Global Mathematical rotation: Z-Right: -40, Y-Right: 35, X-Right:-35. The Structures are:

S1 is Nugget effect with corregionalization matrix: 0.02 0.003 0.002 0 0

0.003 0.03 0.012 0.03 0

0.02 0.012 0.04 0.02 0.0065

0 0.03 0.02 0.05 0.02

0 0 0.0065 0.02 0.04

S2 is Spherical (h/30m h/30m h/40m) cor. matrix: 0.017 0.023 0.022 0.016 0.019

0.023 0.059 0.037 0.006 0.025

0.022 0.037 0.064 0.056 0.057

0.016 0.006 0.056 0.085 0.085

0.019 0.025 0.057 0.085 0.106

S3 Exponential (h/250m h/550m h/250m) cor. matrix: 0.053 0.047 0.038 0.037 0.029

0.047 0.113 0.126 0.119 0.111

0.038 0.126 0.146 0.138 0.131

0.037 0.119 0.138 0.130 0.123

0.029 0.111 0.131 0.123 0.118

1 x> 0.1

1 x> 0.2

1 x> 0.3

1 x> 0.4

1 x> 0.5

61

Figure 70 Cross Variograms Models of Indicators (cut-off of gold: 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0 gpt), with Global Mathematical rotation: Z-Right: -40, Y-Right: 40, X-Right:-60. The Structures are:

S1 is Nugget effect with corregionalization matrix: 0.05 0.03 0.015 0.01 0.006 0.003

0.03 0.05 0.03 0.02 0.01 0.006

0.015 0.03 0.045 0.03 0.018 0.01

0.01 0.02 0.03 0.045 0.03 0.018

0.006 0.01 0.018 0.03 0.04 0.027

0.003 0.006 0.01 0.018 0.027 0.038

S2 is Spherical (h/30m h/30m h/30m) cor. matrix: 0.048 0.051 0.052 0.048 0.044 0.040

0.051 0.065 0.068 0.065 0.064 0.059

0.053 0.068 0.083 0.083 0.081 0.078

0.048 0.065 0.083 0.092 0.091 0.090

0.044 0.064 0.081 0.091 0.099 0.098

0.040 0.059 0.078 0.090 0.098 0.100

S3 Exponential (h/150m h/250m h/150m) cor. matrix: 0.156 0.144 0.132 0.121 0.112 0.104

0.144 0.134 0.123 0.112 0.104 0.097

0.132 0.123 0.112 0.103 0.095 0.089

0.121 0.112 0.103 0.094 0.087 0.081

0.112 0.104 0.095 0.087 0.080 0.075

0.104 0.097 0.089 0.081 0.075 0.070

1 x> 0.5

1 x> 0.7

1 x> 0.8

1 x> 0.9

1 x> 1.0

1 x>0.6

62

Figure 71 Cross Variograms Models of Indicators (cut-off of gold: 1.0, 1.2, 1.5, 1.7 and 2.0 gpt), with

Global Mathematical rotation: Z-Right: 35, Y-Right: -5, X-Right:-15. The Structures are:

S1 is Nugget effect with corregionalization matrix: 0.04 0.022 0.01 0.005 0.002

0.022 0.04 0.017 0.01 0.0045

0.01 0.017 0.035 0.02 0.01

0.005 0.01 0.02 0.03 0.016

0.002 0.0045 0.01 0.016 0.027

S2 is Spherical (h/20m h/15m h/20m) cor. matrix: 0.006 0.002 0.000 0.000 0.000

0.002 0.008 0.004 0.001 0.001

0.000 0.004 0.012 0.014 0.014

0.000 0.001 0.014 0.019 0.020

0.000 0.001 0.014 0.020 0.028

S3 Exponential (h/60m h/90m h/65m) cor. matrix: 0.160 0.146 0.127 0.115 0.095

0.146 0.137 0.122 0.111 0.091

0.127 0.122 0.109 0.099 0.081

0.115 0.111 0.099 0.090 0.074

0.095 0.091 0.081 0.074 0.060

1 x> 1.0

1 x>1.2

1 x> 1.5

1 x> 1.7

1 x> 2.0

63

Figure 72 Cross Variograms Models of Indicators (cut-off of gold: 2.0, 2.5, 3.0, 3.5, 4.0 and 5.0 gpt), with Global Mathematical rotation: Z-Right: 35, Y-Right: -5, X-Right:-20. The Structures are:

S1 is Nugget effect with corregionalization matrix: 0.028 0.01 0.004 0.0016 0.0004 0.000

0.01 0.022 0.01 0.005 0.002 0.0008

0.004 0.01 0.045 0.009 0.0045 0.0018

0.0016 0.005 0.009 0.014 0.007 0.003

0.0004 0.01 0.045 0.007 0.01 0.0045

0.000 0.006 0.018 0.003 0.0045 0.008

S2 is Spherical (h/15m h/25m h/15m) cor. matrix: 0.0078 0.0064 0.0039 0.000 0.000 0.000

0.0064 0.0060 0.0060 0.000 0.000 0.000

0.0039 0.000 0.0058 0.0020 0.000 0.000

0.0000 0.000 0.0020 0.0037 0.0028 0.000

0.0000 0.000 0.000 0.0028 0.0039 0.0009

0.040 0.059 0.000 0.000 0.0009 0.0022

S3 Exponential (h/35m h/90m h/50m) cor. matrix: 0.0841 0.0694 0.0556 0.0495 0.0427 0.0301

0.0694 0.0624 0.0532 0.0479 0.0426 0.0326

0.0556 0.0532 0.0495 0.0447 0.0405 0.0329

0.0495 0.0479 0.0447 0.0404 0.0367 0.0300

0.0427 0.0426 0.0405 0.0367 0.0336 0.0279

0.0301 0.0326 0.0329 0.0300 0.0279 0.0241

1 x> 2.0

1 x> 3.0

1 x> 3.5

1 x> 4.0

1 x> 5.0

1 x>2.5

64

Figure 73 Cross Variograms Models of Indicators (cut-off of gold: 5.0, 6.0, 7.0 and 8.0 gpt), with


S1 is Nugget effect with corregionalization matrix: 0.006 0.0026 0.0003 0.0000

0.0026 0.0057 0.0025 0.0010

0.0003 0.0025 0.0044 0.0020

0.0000 0.001 0.0020 0.0035

S2 is Spherical (h/10m h/20m h/15m) cor. matrix: 0.0014 0.0002 0.0001 0.0000

0.0002 0.0001 0.0001 0.0001

0.0001 0.0001 0.0012 0.0013

0.0000 0.0001 0.0013 0.0020

S3 Exponential (h/30m h/70m h/30m) cor. matrix: 0.0225 0.0197 0.0161 0.0129

0.0197 0.0172 0.0141 0.0113

0.0161 0.0141 0.0116 0.0924

0.0129 0.0113 0.0924 0.0074

1 x> 5.0

1 x>6.0

1 x>7.0

1 x>8.0

65

Figure 74 Cross Variograms Models of Indicators (cut-off of gold: 8.0, 10.0, 12.0 and 15.0 gpt), with


S1 is Nugget effect with corregionalization matrix: 0.0040 0.0016 0.0006 0.0001

0.0016 0.0032 0.0016 0.0005

0.0006 0.0016 0.0021 0.0008

0.0001 0.0005 0.0008 0.0010

S2 Exponential (h/35m h/60m h/35m) cor. matrix: 0.0090 0.0061 0.0161 0.0129

0.0061 0.0047 0.0040 0.0027

0.0049 0.0040 0.0036 0.0024

0.0030 0.0027 0.0024 0.0022

The variography models (Figure 69, Figure 70, Figure 71, Figure 72, Figure 73 and Figure 74)have good

intrinsic properties among nearest indicators, similar behaviour that correlation coefficient (Table 20).

1 x> 8.0

1 x>10

1 x>12

1 x>15

66

3.3.6.2.- Neighbourhood Choices:

The neighbourhood parameters for indicator have similar behaviour than the previous parameters and

the analysis have the same criteria, with the least kriging variance and the slope value and estimated is

close to one (Table 21, Table 22 and Table 23 in block = 29i 44j 32k).

Table 21 Comparison between different neighbourhood parameters of indicators (to cutoff: 0.1,

0.2, 0.3, 0.4, 0.5 gpt) (search and maximum of samples), the parameters are 250 by 550 by 250

(Mathematical rotation -40 35 -35) Minimum 2 samples and Maximum: 4 sector by 14 samples.

search 250 x 550 x 250 250 x 550 x 250 250 x 550 x 250



ind_0.1 0.016034 1.030199 0.016075 1.02709 0.0161 1.023743

ind_0.2 0.044092 1.01664 0.04425 1.012692 0.0444 1.01002

ind_0.3 0.051306 1.021655 0.051499 1.018277 0.0517 1.015228

ind_0.4 0.058515 1.001709 0.058801 0.996594 0.059 0.992433

ind_0.5 0.066146 0.982212 0.066567 0.975931 0.06698 0.970898

Table 22 Comparison between different neighbourhood parameters of indicators (to cutoff: 1.0,

1.2, 1.5, 1.7, 2.0 gpt) (search and maximum of samples), the parameters are 80 by 120 by 80

(Mathematical rotation 35 -5 -15) Minimum 2 samples and Maximum: 4 sector by 50 samples .

search 80 x 120 x 80 80 x 120 x 80 80 x 120 x 80



ind_1.0 0.04922 0.986446 0.049593 0.97969 0.050989 0.955668

ind_1.2 0.042918 0.984209 0.043254 0.977041 0.044528 0.95113

ind_1.5 0.035334 0.980531 0.035628 0.972374 0.036748 0.942168

ind_1.7 0.030892 0.972921 0.031173 0.963395 0.032271 0.927375

ind_2.0 0.023758 0.952531 0.02402 0.939441 0.0259 0.88865

Table 23 Comparison between different neighbourhood parameters of indicators (to cutoff: 5, 6, 7,

8 gpt) (search and maximum of samples), the parameters are 200 by 300 by 200 (Mathematical rotation

35 -5 -20) Minimum 2 samples and Maximum: 4 sector by 60 samples (block = 29i 44j 32k).

search 150 x200 x 150 200 x 300 x 200 200 x 300 x 200



ind_5 0.005608 0.942426 0.005607 0.943278 0.005626 0.931034

ind_6 0.00418 0.945371 0.004179 0.946224 0.004192 0.934554

ind_7 0.002949 0.936931 0.002948 0.937755 0.002961 0.924591

ind_8 0.002017 0.921796 0.002017 0.922668 0.002028 0.906862

67


values (mean Block Covariances) for 5 different indicators (from 0.1 to 0.5 of cut-off gold), the best

choices is 7x7x2 where it is noting the stabilization in standard deviation.


values (mean Block Covariances) for 5 different indicators (from 1 to 2 of cut-off gold), the best

choices is 8x8x2 where it is noting the stabilization in standard deviation.

Other parameters is the size of block discretization in order to chose the best (Figure 75 and Figure 76),

we will make the analyses among different size and check the less standard deviation of 10 Cvv (Mean

block covariance), in our case the best is 7x7x2 (for groups indicator with cutoff 0.1 to 0.5 and 0.5 to 1

gpt)and 8 x 8 x 2 size (for other cases).

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

2x2x2 3x3x2 4x4x2 5x5x2 6x6x2 7x7x2 8x8x2 9x9x2

ind_0.5

ind_0.4

ind_0.3

ind_0.2

ind_0.1

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

ind_2.0

ind_1.7

ind_1.5

ind_1.2

ind_1.0

68

5.4 Gold Cyanide

The gold cyanide has 7180 samples (34% lesser than AuFA) inside the GoldShape domain (Figure 77).

The exploration data analysis is done in oxide and sulphide domains, this shows that there are differents

behaviour in each domain (Table 24).

Figure 77 Histogram and Cumulative plot (logarithm scale) of Gold Cyanide [Green=Sulfide(25%),

Red=Oxide(75%)].

Table 24 Statistics Summary of Gold Cyanide: Oxide and Sulphide Zones in Goldshape Domain (Oxide

and Sulphide Statistics Graphics are in the Appendix).


Oxide AuCN 5453 (75%) 0.03 132.942 1.36 2.85

Sulphide AuCN 1727 (25%) 0.03 8.13 0.50 0.82

AuCN Total 7180 0.03 132.942 1.15 2.5384

The gold cyanide has been capped values in order to decrease the uncertainty and economical risk. The

capped values is the same that gold fire assay, it is 20 gpt. The statistics of capped gold cyanide is shown

in the figure 21.

The Measurement of gold cyanide has been capped because it has high variability and economical risk.

Then it is capped to 20 gpt and has 2.5% fewer grades than the previous one (from 1.15 to 1.12 gpt), but

the standard deviation has been reduced in 30% (from 2.54 to 1.75) (Table 25 and Figure 78).

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au_CN

Au_CN

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

0.25 0.25

Frequencies

Frequencies

Nb Samples: 7180

Minimum: 0.0250

Maximum: 132.9420

Mean: 1.1504

Std. Dev.: 2.5384

Histogram (Au_CN)

Isatis

DATA/TOTAL(Gold)

69

0

0

50

50

100

100

150

150

Au

Au

0 0

50 50

100 100

150 150

Au_CN

Au_CN

rho=0.970

Scatter Diagram (Au, Au_CN)

Isatis

DATA/GOLD

-4

-4

-3

-3

-2

-2

-1

-1

0

0

1

1

2

2

3

3

4

4

5

5

LnAu

LnAu

-4 -4

-3 -3

-2 -2

-1 -1

0 0

1 1

2 2

3 3

4 4

5 5

LnAuCN

LnAuCN

rho=0.824

Scatter Diagram (LnAu, LnAuCN)

Isatis

Figure 78: Histogram of Capped Gold Cyanide in Gold Shape [Green=Sulphide(25%),

Blue=Oxide(75%)].

Table 25 Statistics Summary of declustered Gold Fire Assay: Oxide and Sulphide Zones in

Goldshape Domain (Oxide and Sulphide Statistics Graphics are in the Appendix).


Oxide AuCN 5453 (75%) 0.03 20.00 1.12 1.71

Sulphide AuCN 1727 (25%) 0.03 8.13 0.50 0.82

AuCN Total 7180 0.03 20.00 1.12 1.75

5.4.1 Bivariate Statistics between Gold Fire Assay and Gold Cyanide:

The gold fire assay and gold cyanide is shown as bivariate data in the scatterplot, which the x-coordinate

is the Gold fire assay (AuFA) and y-coordinate is the gold cyanide (AuCN). Both graphics the figure

(normal data) and figure (Logarithm of data) shows good correlation, but there are different behaviours

between oxide and sulphide zones (Figure 79) due to gold cyanide decrease in sulphide.

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

AuCN_cap

AuCN_cap

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

Frequencies

Frequencies

Nb Samples: 7180

Minimum: 0.03

Maximum: 20.00

Mean: 1.12

Std. Dev.: 1.75

Histogram (AuCN_cap)

Isatis

Figure 79 ScatterPlot between Gold FireAssay and Gold Cyanide (left side), and between

Ln(Gold) and Ln(Gold Cyanide) [Blue=Sulfide(25%), Red=Oxide(75%)] (right side).

70

5.4.2 Gold Cyanide in Oxide Domain:

The statistics of capped gold cyanide inside the oxide goldshape has 1.32 gpt of mean value. Two

variables (log of AuFA and log of AuCN) are positively correlated (Figure 80)with 0.953 of correlation

coefficient. Regression line: AuCN =0.91229 (Au)-0.009011 (figure 80 - right side)

We will define the ratio between gold cyanide and gold fire assay with: ratio=gold cyanide / gold fire

assay. But this ratio has not correlation neither gold fire assay nor gold cyanide (Figure 81).

Figure 81: Scatterplot between Gold and Ratio in Oxide Zone. Correlation coefficient is 0.085. (left

side), and Scatterplot between Gold and Gold Cyanide in Oxide Zone. Correlation coefficient is 0.163.

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

AuCN_cap

AuCN_cap

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

0.25 0.25

Frequencies

Frequencies

Nb Samples: 5453

Minimum: 0.03

Maximum: 20.00

Mean: 1.32

Std. Dev.: 1.92


Isatis

Figure 80 Histogram of Capped Gold Cyanide in Oxide Zone (left side), and Scatterplot

between Gold and Gold Cyanide in Oxide Zone. Correlation coefficient is 0.990.

71

3.4.2.1. Cross Variograms between gold cyanide and gold in oxide domain

First of all, we will use the variogram map for getting the rotation parameters (Figure 82), after that we

will use the directional variograms in order to find the anisotropy.

Figure 82 Variogram Map of Cross variogram of gold and gold cyanide in oxide goldshape, it has a

rotation (Mathematical Rotation Isatis): Z-Right =20°, Y-Right =-20° and X-right =5°, this is the plane that

will use in the variogram direction for anisotropy parameters. Azimuth = 146°, X-right= 21° and Z-left = -

77° (Geologist Rotation Isatis)

Then, we will use the found rotation parameters for doing in each case (gold, gold cyanide and

crossvariogram gold-gold cyanide): 4 variogram experimental inside the plane of this rotation, an

experimental variogram in direction perpendicular to the plane, and 1 downhole variogram for fixed the

nugget effect (Figure 83).

0

N90

N109

N289

N127

N307

N185

N5

N207

N27

N49

0

N65

N60

N240

N53

N233

N301

N121

N268

N88

N77

5

N349

N169

N359

N179

N108

N288

N134

N314

N155

N70

N32

0

0

25

25

50

50

75

75

100

100

125

125

Distance (m)

Distance (m)

0 0

1 1

2 2

3 3

4 4

5 5

Variogram : Au

Variogram : Au

N/A

4.2

3.7

3.2

2.7

2.2

1.7

1.2

0.7

N/A

6.6

6.1

5.6

5.1

4.6

4.1

3.6

3.1

2.6

2.1

1.6

1.1

0.6

N/A

4.8

4.3

3.8

3.3

2.8

2.3

1.8

1.3

0.8

0.3

Isatis

72

Figure 83 Cross Variogram Model of Gold Fire assay and Gold Cyanide, the parameters are:

Mathematical Rotation: Z-Right: 20, Y-Right: -20, X-Right: 5

Variogram (Au): 0.2 (Nug. Ef.) + 0.17 [S2: Sph.(h/20,h/60,h/45)] + 3.7 [S2: Sph.(h/45,h/160,h/70)]

Variogram (AuCN): 0.3 (Nug. Ef.) + 0.18 [S2: Sph.(h/20,h/60,h/45)] + 3.98 [S2: Sph.(h/45,h/160,h/70)]

Crossvariogram (Au-AuCN): 0.2 (Nug. Ef.)+ 0.17[S2:Sp.(h/20,h/60,h/45)]+3.8 [S2:Sp.(h/45,h/160,h/70)]

N70

N116

N158

N202

N236

dh

0

0

50

50

100

100

150

150

200

200

250

250

Distance (m)

Distance (m)

0 0

1 1

2 2

3 3

4 4

5 5

Variogram : Au

Variogram : Au

N70

N116

N158

N202

N236

dh

0

0

50

50

100

100

150

150

200

200

250

250

Distance (m)

Distance (m)

-4 -4

-3 -3

-2 -2

-1 -1

0 0

1 1

2 2

3 3

4 4

5 5

6 6

Variogram : Au_CN & Au


N70

N116

N158

N202

N236

dh

0

0

50

50

100

100

150

150

200

200

250

250

Distance (m)

Distance (m)

0 0

1 1

2 2

3 3

4 4

5 5

6 6

Variogram : Au_CN

Variogram : Au_CN

Isatis

73

3.4.2.2. Cross Validation for Variography parameters of cross variogram gold fire

assay and gold cyanide

We will make a cross validation for gold cyanide (Table 26), which make comparison with other gold

cyanide variograms models.

Table 26 Cross validation Parameters of variography gold cyanide in oxide goldshape. Correlation



Variogram

Model

Rotation

ZR – YR - XR

Range

U – V – W

Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)/SD

SD.

(Z-Z*)

Rho

Cor C.

Rho

(Z-Z*)/SD

Model 1 20 -20 5 45 160 70 -12.415 11.999 -0.094 0.986 0.87 0.169

3.4.2.3. Neighbourhood Choices

We will do many comparisons the different neighbourhood parameters in the same block (Table 27);

the best neighbourhood is that have less kriging variance and slope of original data vs estimated data is

close to one. We will make the analyses (for discretization parameter) among different blocks and check

the less standard deviation of 10 Cvv (Mean block covariance), the best is 8 x 8 x 2 size (Figure 84).


samples), the parameters are 90 by 250 by 140 (Mathematical rotation 20 -20 5) Minimum 2 samples and

Maximum: 4 sector by 30 samples (block = 29i 44j 32k).

AuCN_oxide Mathematical Rotation: 20 -20 5

search 90 x 250 x 140 90 x 250 x 140 90 x 250 x 140



29 x 44 x32 0.628943 0.990475 0.629547 0.988024 0.630963 0.985281

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08


Figure 84 Comparison between different Block Discretization and the standard deviation of

Cvv values, the best choices is 8x8x2 where it is noting the stabilization in standard deviation.

74

5.4.3 Residual of Gold Cyanide in Oxide Domain:

The residual of gold and gold cyanide was done using regression line (Figure 80-right side) and it just was

where the gold and gold cyanide values exist together (isotopic case with 5453 samples):

AuCN = a Au + b + Residual; then the values is: Residual = AuCN -0.91Au +0.01

Then, we will make the Anamorphosis to residual (Figure 86) in order to do the conditional simulation.

Figure 85 Histogram of Residual of gold and gold Cyanide in Oxide Zone (5453 samples), and

Scatterplot between residual (au-aucn) and Gold (au).

Figure 86 Anamorphosis of residual (Au and AuCN) in oxide, and Scatterplot between Gaussian

residual and Gaussian Gold (au) in oxide.

3.4.3.1. Variograms of Gaussian Residual of gold cyanide in oxide

Then, we will use the rotation parameters of crossvariogram (got with variogram map Figure 82) for

doing 4 variogram experimental inside the plane of this rotation, an experimental variogram in direction

perpendicular to the plane, and 1 downhole variogram for fixed the nugget effect (Figure 87, Figure 88

and Figure 89).

75

Figure 87: Variogram Model of Gaussian residual in oxide: the Mathematical rotation parameters is:

20°, Y-Right = -20°, and X-right =5°, nugget effect (S1): 0.13, First Structure - Spherical (S2): sill=0.20,

U=20m V=60m W=45m; Second Structure-Exponential (S3): sill=0.63, U=45m V=160m W=70m.

Figure 88 Variogram in direction of short range and direction of long range of gaussian residual in

oxide. Short range =45m, and long range = 160m.

0

0

50

50

100

100

150

150

200

200

Distance (m)

Distance (m)

0.0 0.0

0.5 0.5

1.0 1.0




Isatis

Figure 89 Downhole Variogram and variogram in direction of Perpendicular range of Gaussian

residual inside the oxide domain. The nugget effect is 0.13 and perpendicular range =70m.

76

3.4.3.2. Cross Validation of Gaussian Residual of gold cyanide in oxide






Variogram

Model

Rotation

ZR – YR - XR

Range

U – V – W

Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)/SD

SD.

(Z-Z*)

Rho

Cor C.

Rho

(Z-Z*)/SD

Model 1 20 -20 5 100 250 180 -9.0487 9.08764 0.0029 1.126 0.787 0.098

3.4.3.3. Neighbourhood Choices


the best neighbourhood is that have less kriging variance and slope of original data vs estimated data is


the less standard deviation of 10 Cvv (Mean block covariance), in our case the best is 8 x 8 x 2 size

(Figure 90).




gaussian_oxide Mathematical Rotation: 20 -20 5

search 90 x 250 x 140 90 x 250 x 140 90 x 250 x 140



29 x 44 x32 0.152216 0.982175 0.152538 0.97283 0.153173 0.961518

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018


oxide

Figure 90 Comparison between different Block Discretization and the standard deviation

of Cvv values, the best choices is 8x8x2 where it is noting the stabilization in standard

deviation.

77

5.4.4 Gold Cyanide in Sulphide Domain:

The statistics of capped gold cyanide inside the sulphide goldshape has 0.50 gpt of mean value (Figure

91-left). Two variables (log of AuFA and log of AuCN) are positively correlated with 0.705 of correlation

coefficient (Figure 91-right). Regression line: AuCN =0.381777(Au)+0.036245 (figure 91 - right side)

Figure 91 Histogram of Capped Gold Cyanide in Sulphide Zone; and Scatterplot between Gold and

Gold Cyanide in Sulphide Zone (corr. Coef. = 0.705); Regression Line: AuCN = 0.381777(Au) +

0.036245

We will define the ratio between gold cyanide and gold fire assay with: ratio=gold cyanide / gold fire

assay. But this ratio has not correlation neither gold fire assay nor gold cyanide (Figure 92).

Figure 92 Scatterplot between Gold and Ratio in Sulphide Zone. (left side), and Scatterplot

between Gold and Gold Cyanide in Sulphide Zone.

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

AuCN_cap

AuCN_cap

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

Frequencies

Frequencies

Nb Samples: 1727

Minimum: 0.03

Maximum: 8.13

Mean: 0.50

Std. Dev.: 0.82


Isatis

78

3.3.4.1.-Cross Variograms between gold cyanide and gold in sulphide domain

First of all, we will use the variogram map (Figure 93) and the directional variograms in order to find the

anisotropy; this is similarly to Variogram map in oxide domain.

Figure 93 Variogram Map of Cross variogram of gold and gold cyanide in sulphide goldshape, it

has a rotation (Mathematical Rotation Isatis): Z-Right =20°, Y-Right =-20°, and X-right =5°, this is the

plane that will use in the variogram direction for anisotropy parameters. Azimuth = 146°, X-right= 21°, and

Z-left = -77° (Geologist Rotation Isatis)

Then, we will use the found rotation parameters for doing in each case (gold, gold cyanide and

crossvariogram gold-gold cyanide): 4 variogram experimental inside the plane of this rotation, an

experimental variogram in direction perpendicular to the plane, and 1 downhole variogram for fixed the

nugget effect (Figure 94).

40

N76

N88

N268

N98

N278

N143

N323

N176

N356

N34

0

N44

N32

N212

N22

N202

N337

N157

N304

N124

N86

5

N326

N146

N341

N161

N39

N219

N67

N247

N93

0.00

0.00

0.25

0.25

0.50

0.50

0.75

0.75

1.00

1.00

1.25

1.25

Distance (m)

Distance (m)

0.0 0.0

0.5 0.5

1.0 1.0

1.5 1.5

Variogram : Au

Variogram : Au

N/A

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

N/A

3.0

2.5

2.0

1.5

1.0

0.5

0.0

N/A

2.1

1.9

1.7

1.5

1.3

1.1

0.9

0.7

0.5

0.3

0.1

Isatis

79

Figure 94 Cross Variogram Model of Gold Fire assay and Gold Cyanide in sulphide. The

parameters are:

Mathematical Rotation: Z-Right: 20, Y-Right: -20, X-Right: 5

Variogram (Au): 0.05 (Nug. Ef.) + 0.77 [S2: Sph.(h/20,h/70,h/50)] + 1.0 [S2: Sph.(h/50,h/220,h/100)]

Variogram (AuCN): 0.04 (Nug. Ef.) + 0.07 [S2: Sph.(h/20,h/70,h/50)] + 0.51 [S2: Sph.(h/50,h/220,h/100)]

Crossvariogram (Au-AuCN): 0.04 (Nug. Ef.)+ 0.08[S2:Sp.(h/20,h/70,h/50)]+0.7[S2:Sp.(h/50,h/220,h/100)]

80

3.3.4.2. Cross Validation of cross variogram between gold and gold cyanide






Variogram

Model

Rotation

ZR – YR - XR

Range

U – V – W

Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)/SD

SD.

(Z-Z*)

Rho

Cor C.

Rho

(Z-Z*)/SD

Model 1 20 -20 5 50 220 100 -8.899 6.917 -0.061 1.10 0.91 -0.004

3.3.4.3. Neighbourhood Choices:


the best neighbourhood is that have less kriging variance and slope of original data vs. estimated data is






AuCN_sulphide Mathematical Rotation: 20 -20 5

search 70 x 220 x 100 70 x 220 x 100 70 x 220 x 100



29 x 46 x25 0.077432 0.993968 0.0077893 0.9957 0.0079024 0.995286



0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09


81

5.4.5 Residual of Gold Cyanide in Sulphide Domain:

The residual of gold and gold cyanide was done using regression line (Figure 91-right) and it just was

where the gold and gold cyanide values exist together (isotopic case with 5453 samples):

AuCN = a Au + b + Residual; then the value is: Residual = AuCN -0.38Au - 0.04 (Figure 96).

Figure 96 Histogram of Residual of gold and gold Cyanide in Sulphide Zone (1727 samples), and

Scatterplot between residual (aucn-au) and gold (au) in sulphide.

Then, we will make the Anamorphosis to residual (Figure 97) in order to do the conditional simulation.

Figure 97 Anamorphosis of residual (Au and AuCN) in sulphide, and Scatterplot between

Gaussian residual and Gaussian Gold (au) in sulphide.

3.4.5.1. Variograms of Gaussian Residual of gold cyanide in sulphide

Then, we will use the rotation parameters of crossvariogram (got with variogram map Figure 93) for

doing 4 variogram experimental inside the plane of this rotation, an experimental variogram in direction

perpendicular to the plane, and 1 downhole variogram for fixed the nugget effect (Figure 98, Figure 99

and Figure 100).

82

Figure 98 Variogram Model of Gaussian residual in sulphide: the rotation parameters are

(Mathematical Rotation Isatis): 20°, Y-Right = -20°, and X-right =5°, nugget effect (S1): 0.1, First Structure

- Spherical (S2): sill=0.46, U=50m V=50m W=70m; Second Structure-Exponential (S3): sill=0.46, U=80m

V=220m W=150m.

Figure 99 Variogram in short range and in long range of Gaussian residual in sulphide. Short range


0

0

50

50

100

100

150

150

200

200

Distance (m)

Distance (m)

0.0 0.0

0.5 0.5

1.0 1.0




Isatis

Figure 100 Downhole Variogram and variogram in Perpendicular range of Gaussian residual

inside the sulphide domain. The nugget effect is 0.1 and perpendicular range =150m.

83

3.4.5.2. Cross Validation of Gaussian residual of gold cyanide in sulphide






Variogram

Model

Rotation

ZR – YR - XR

Range

U – V – W

Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)/SD

SD.

(Z-Z*)

Rho

Cor C.

Rho

(Z-Z*)/SD

Model 1 20 -20 5 120 250 180 -5.99805 6.2966 -0.0124 1.167 0.867 -0.052

3.4.5.3.- Neighbourhood Choices


best neighbourhood is that have less kriging variance and slope of original data vs. estimated data is






Gaussian sulphide Mathematical Rotation: 20 -20 5

search 70 x 220 x 100 70 x 220 x 100 70 x 220 x 100



29 x 46 x25 0.292272 0.989638 0.292441 0.987892 0.292518 0.9842



0

0.002

0.004

0.006

0.008

0.01

0.012

0.014


sulphide

84

5.5 Discussion of Results

All samples are inside of the estimation grid, and cover the benches from 2958 to 3678 meters. The

origin of the blocks has coordinate local at (11800, 25100 and 2958) meters, the grid size or mesh is 25 x

25 x 12 meters, and the number of grid is 66 x 63 x 60 blocks.

The block model is only inside of goldshape (for the gold fire assay estimation case), which is divided in

oxide and sulphide zone (for gold cyanide estimation case)

5.5.1 AuFA by Ordinary Kriging

First of all, we will estimate the gold fire assay with ordinary kriging using three different models (each

model have different variography and neighbourhood parameters) in order to define the best model by

ordinary kriging that will make comparison with Indicator kriging model.

We can see the comparison between variography, cross validation (Table 34) and neighbourhood

parameters in the same block (Table 35) for the three models (gold variography, gold (from logarithm

gold) variography and gold (from Gaussian gold) variography.

Table 34 Comparison between three types of gold variograms in cross validation parameters

Variogram

Model

Rotation Range Minimum

(Z-Z*)

Maximum

(Z-Z*)

Mean

(Z-Z*)/SD

SD.

(Z-Z*)

Rho Rho

ZR – YR - XR U – V – W Cor C. (Z-Z*)/SD

Gold 20 -20 15 40 130 100 -16.2154 10.4876 0.002 0.89 0.871 -0.098

LnGold 20 -25 -5 170 270 180 -16.2514 10.541 0.002 0.86 0.87 -0.05

GaussGold -80 65 -45 200 450 300 -11.279 7.2805 0.003 0.58 0.88 -0.046

Table 35 Comparison between three types of gold neighbourhood

Gold Ln Gold Gauss Gold

50 x 150 x 100 170 x 270 x 180 180 x 450 x 320

max: 4 sectors by 40 max: 4 sectors by 40 max: 4 sectors by 45

Krig. Var Slope Z|Z* Krig. Var Slope Z|Z* Krig. Var Slope Z|Z*

0.701748 0.981313 0.716265 1.00417 0.733786 1.003528

In the graphics we can think the best variogram is the gold variogram (from Gaussian gold) but in the

neighbourhood parameters the best results is the gold. Then, we make other comparison with

estimated results in the goldshape.

85

3.4.1.1 Estimate by Variogram of gold fire assay

We use the last parameters (Variography of gold and choice Neighbourhood of gold) for running the

Ordinary Kriging (Figure 102) and Standard Deviation Kriging (Figure 103) for gold fire assay in

goldshape.

Figure 102 Block Model of estimated gold by ordinary kriging (variography of gold), bench (left)

and section YoZ (right), the blocks with gold value and drillholes in black points

Figure 103 Block Model of Standard deviation of gold by ordinary kriging (variography of gold),

bench (left) and section YoZ (right), the blocks with standard deviation kriging value and drillholes

in black points

86

3.4.1.2 Estimate by Variogram from logarithm gold

We use the last parameters (Variography from logarithm gold and choice Neighbourhood) for running

the Ordinary Kriging (Figure 104) and Standard Deviation Kriging (Figure 105) for gold fire assay in

goldshape.

Figure 104 Block Model of estimated gold by ordinary kriging (variography from logarithm gold),

bench (left) and section YoZ (right), the blocks with gold value and drillholes in black points

Figure 105 Block Model of Standard deviation of gold by ordinary kriging (variography from

logarithm gold) bench (left) and section YoZ (right), the blocks with standard deviation kriging

value and drillholes in black points

87

3.4.1.3 Estimate by Variogram from gaussian gold

We use the last parameters (Variography from Gaussian gold and choice Neighbourhood) for running

the Ordinary Kriging (Figure 106) and Standard Deviation Kriging (Figure 107) for gold fire assay in

goldshape.

Figure 106 Block Model of estimated gold by ordinary kriging (variography from gaussian gold),

bench (left) and section YoZ (right), the blocks with gold value and drillholes in black points.

Figure 107 Block Model of Standard deviation of gold by ordinary kriging (variography from

gaussian gold) bench (left) and section YoZ (right), the blocks with standard deviation kriging

value and drillholes in black points

88

5.5.2 AuFa by Indicator Ordinary CoKriging

We use the last parameters (Variography and Neighbourhood) for running the Indicator Ordinary

Cokriging by each Indicator value. Taking to account that the indicator (1x>cut-off) kriging cannot get out

of [0,1], then we will do post processing indicator in order to take the minimum=0 and maximum=1

(Table 36).

Table 36 Comparison between the Statistics of Indicators Kriging (from 0.1 to 15) initial kriging

process (left part), and post processing kriging (minimum=0, and maximum=1)(right part)

1x>cutoff

initial kriging process

result post processing

VARIABLE Count Mini. Max. Mean Std.Dev

Mini. Max. Mean Std.Dev

ik_ind_0.1 17307 0.11 1.03 0.87 0.13

0.11 1 0.87 0.13

ik_ind_0.2 17307 0.01 1.07 0.65 0.24

0.01 1 0.65 0.24

ik_ind_0.3 17307 -0.13 1.04 0.52 0.28

0 1 0.52 0.28

ik_ind_0.4 17307 -0.14 1.03 0.43 0.28

0 1 0.44 0.28

ik_ind_0.5 17307 -0.17 1.01 0.37 0.28

0 1 0.37 0.28

ik_ind_0.6 17307 -0.06 1.03 0.33 0.27

0 1 0.33 0.27

ik_ind_0.7 17307 -0.1 1.02 0.29 0.26

0 1 0.29 0.26

ik_ind_0.8 17307 -0.11 1.01 0.26 0.25

0 1 0.26 0.25

ik_ind_0.9 17307 -0.12 1 0.23 0.24

0 1 0.23 0.23

ik_ind_1 17307 -0.12 1 0.21 0.22

0 1 0.21 0.22

ik_ind_1.2 17307 -0.04 1.01 0.17 0.21

0 1 0.17 0.21

ik_ind_1.5 17307 -0.06 0.96 0.13 0.18

0 0.96 0.13 0.18

ik_ind_1.7 17307 -0.08 0.92 0.11 0.16

0 0.92 0.11 0.16

ik_ind_2 17307 -0.09 0.85 0.09 0.14

0 0.85 0.09 0.13

ik_ind_2.5 17307 -0.02 0.96 0.06 0.11

0 0.96 0.06 0.11

ik_ind_3 17307 -0.02 0.94 0.05 0.09

0 0.94 0.05 0.09

ik_ind_3.5 17307 -0.04 0.88 0.03 0.08

0 0.88 0.03 0.08

ik_ind_4 17307 -0.04 0.81 0.03 0.07

0 0.81 0.03 0.07

ik_ind_5 17307 -0.04 0.71 0.02 0.06

0 0.71 0.02 0.06

ik_ind_6 17307 -0.01 0.72 0.01 0.04

0 0.72 0.01 0.04

ik_ind_7 17307 -0.01 0.6 0.01 0.03

0 0.6 0.01 0.03

ik_ind_8 17307 -0.01 0.49 0.01 0.03

0 0.49 0.01 0.03

ik_ind_10 17307 -0.01 0.52 0 0.02

0 0.52 0 0.02

ik_ind_12 17307 -0.01 0.46 0 0.02

0 0.46 0 0.02

ik_ind_15 17307 -0.01 0.41 0 0.01

0 0.41 0 0.01

Then, we will transform the results from indicator of x>cut-off (indicator of cumulated classes above cut-

off) to indicator of x=cut-off (Indicator of class values), the formula is:

89

We will use this formula for all Indicators of cumulated classes (1 x>cut-off), and obtain 1cut-off1<x≤cut-off2;

now, taking to account that the indicator (1cut-off1<x≤cut-off2) kriging cannot get out of [0, 1] too, then we

will do post processing indicator in order to take the minimum=0 and maximum=1 (Table 37).

Table 37 Comparison between the Statistics of Indicators Kriging (from 0.1 to 15) initial kriging

process (left part), and post processing kriging (minimum=0, and maximum=1)(right part)

1cut-off1<x≤cut-off2 initial kriging process result post processing

VARIABLE Count Mini. Max. Mean Std.Dev Mini. Max. Mean Std.Dev

ik_005 17307 0 0.89 0.13 0.13 0 0.89 0.13 0.13

ik_01 17307 -0.07 0.81 0.22 0.18 0 0.81 0.22 0.18

ik_02 17307 -0.08 0.62 0.13 0.09 0 0.62 0.13 0.09

ik_03 17307 -0.09 0.42 0.08 0.06

0 0.42 0.08 0.06

ik_04 17307 -0.08 0.41 0.06 0.05 0 0.41 0.06 0.05

ik_05 17307 -0.42 0.48 0.04 0.09 0 0.48 0.06 0.07

ik_06 17307 -0.03 0.31 0.04 0.04 0 0.31 0.04 0.04

ik_07 17307 -0.02 0.32 0.03 0.04 0 0.32 0.03 0.04

ik_08 17307 -0.02 0.26 0.03 0.03 0 0.26 0.03 0.03

ik_09 17307 -0.02 0.23 0.02 0.03 0 0.23 0.02 0.03

ik_10 17307 -0.31 0.39 0.04 0.08 0 0.39 0.05 0.06

ik_12 17307 -0.02 0.35 0.05 0.04 0 0.35 0.05 0.04

ik_15 17307 -0.03 0.16 0.02 0.02 0 0.16 0.02 0.02

ik_17 17307 -0.04 0.26 0.02 0.03 0 0.26 0.02 0.03

ik_20 17307 -0.34 0.46 0.03 0.06 0 0.46 0.03 0.05

ik_25 17307 -0.02 0.27 0.02 0.03 0 0.27 0.02 0.03

ik_30 17307 -0.03 0.21 0.01 0.02 0 0.21 0.01 0.02

ik_35 17307 -0.03 0.12 0.01 0.01 0 0.12 0.01 0.01

ik_40 17307 -0.02 0.19 0.01 0.02 0 0.19 0.01 0.02

ik_50 17307 -0.09 0.27 0 0.02 0 0.27 0.01 0.02

ik_60 17307 -0.01 0.12 0 0.01 0 0.12 0 0.01

ik_70 17307 -0.01 0.11 0 0.01 0 0.11 0 0.01

ik_80 17307 -0.11 0.26 0 0.01 0 0.26 0 0.01

ik_100 17307 -0.01 0.08 0 0 0 0.08 0 0

ik_120 17307 0 0.16 0 0.01 0 0.16 0 0.01

ind_150 17307 0 0.41 0 0.01 0 0.41 0 0.01

90

Figure 108 Diagram of all post processing indicator, the indicator (x=cut-off) has minimum=0,

Maximum =1 and probability >= 0. (Adapted of Rivoirard 2011, CFSG 2010-2011 Courses)

Finally, in order to obtain the Estimation result by Indicator, we use the

formula:

Where: Y (x) k (is the estimated value), i (different cutoff), [1 Y(x)=i]

k (Indicator Kriging of class value)

In the Figure 109 we can see the final result of Indicator Kriging that looks similar to previous results.

Figure 109 Block Model of estimated gold by Indicator kriging (25 cutoff) bench (left) and section

YoZ (right), the blocks with gold value.

Table 38 Comparison declustered gold and estimation results


Au Data Declus 10875 0.0025 145.1557 0.7562 1.8482

Au OK 17481 0.02 10.47 0.78 0.79

Au OK (ln) 17481 0.08 9.50 0.76 0.72

Au OK (gaus) 17481 0.11 11.22 0.77 0.69

Au IK 17481 0.05 9.33 0.75 0.71

91

5.5.3 AuCN by Cokriging (AuFA and AuCN)

We use the last parameters (Crossvariography between gold cyanide and gold, and choice

Neighbourhood in both oxide and sulphide zones) for running the Ordinary Cokriging (Figure 110) and

Standard Deviation Cokriging (Figure 111) for gold cyanide in goldshape (oxide and sulphide together).

Figure 110 Block Model of estimated gold cyanide by ordinary Cokriging, bench (left) and section

YoZ (right), the blocks with gold value and drillholes in black points.

Figure 111 Block Model of Standard deviation of gold by ordinary Cokriging, bench (left) and

section YoZ (right), the blocks with standard deviation kriging value and drillholes in black points

92

5.5.4 AuFA by Turning Band Conditional Simulation

We use the last parameters (Variography of Gaussian declustered gold and choice Neighbourhood) for

running the 100 Conditional Simulations by turning bands (Figure 112 and Figure 113). The parameters

are: variography and neighbourhood of Gaussian declustered gold and 400 bands.


Simulation (left) and bench with 25th

Simulation (right), the blocks with simulated gold value.



Simulation (right), the blocks with simulated gold value.

In order to use the result of gold Simulation, we will do the mean of the 100 simulation (Figure 114) for

each block; and we will make the standard deviation of the 100 simulation (Figure 119). The unique

validation of these simulation is the comparison of statistics of declustered gold and the mean of

simulated gold (Table 39) where the values of mean is closer in both cases.

93

Figure 114 Block Model of mean gold of 100 Simulations; bench (left) and section YoZ (right), the

blocks with gold value (Mean of 100 Simulations) and drillholes in black points.

Figure 115 Block Model of Standard deviation gold of 100 Simulations; bench (left) and section

YoZ (right), the blocks with standard deviation simulated value and drillholes in black points

Table 39 Comparison of Statistics between declustered gold and Mean of Simulated Gold


Au Data Declus 10875 0.0025 145.1557 0.7562 1.8482

Au Mean Sim 17475 0.02 19.18 0.77 0.78

94

5.5.5 Residual by Turning Band Conditional Simulation

We use the last parameters (Variography of Gaussian declustered residual and choice Neighbourhood in

both oxide and sulphide domain) for running the 100 Conditional Simulations by turning bands (Figure

116 and Figure 117).

The parameters are: variography and neighbourhood of Gaussian declustered gold and 400 bands.



Simulation (right), the blocks with simulated residual value.



Simulation (right), the blocks with simulated residual value.

95

In order to use the result of Residual Simulation, we will do the mean of the 100 simulation (Figure 118)

for each block; and we will make the standard deviation of the 100 simulation (Figure 119).

Figure 118 Block Model of mean residual of 100 Simulations; bench (left) and section YoZ (right),

the blocks with residual value (Mean of 100 Simulations) and drillholes in black points.

Figure 119 Block Model of Standard deviation residual of 100 Simulations; bench (left) and section

YoZ (right), the blocks with standard deviation simulated value and drillholes in black points.

96

5.5.6 AuCN by Simulation of Residual and Simulation of AuFA

In order to find the Gold Cyanide value by simulation of residual and simulation of gold, first we will

need get the mean of 100 simulations of gold (AuFA by Turning Band Conditional Simulation) for each

block model, after that the same sense we will find the mean of 100 simulation of residual. Finally, we

will use the residual equations (for different zone: oxide and sulphide) and will get the final gold cyanide

result by both simulations.

AuCN = Residual (simulated mean) + 0.91Au (simulated mean) -0.01 (in Oxide Zone)

AuCN = Residual (simulated mean) +0.38 Au (simulated mean) + 0.04 (in Sulphide Zone)

Figure 120 Block Model of gold cyanide value by simulation of gold and residual (combined

zones: oxide and sulphide), bench (left) and section YoZ (right), the blocks with gold value and

drillholes in black points.

Table 40 Comparison of Statistics between declustered gold and Mean of Simulated Gold


AuCN Declus 7180 0.0025 20.00 0.605 1.222

AuCN CoKrig 17475 0.02 19.18 0.5024 0.765

AuCN Sim 17358 0.0001 17.284 0.5454 0.72098

97

5.5.7 Comparison Different Gold block model results

Finally, the different gold block model values by different method are shown in Table 41 (All values are

inside of optimization pit) where the first gold model has the higher mean value and the indicator

method is the lower.

Table 41 Comparison between different gold block model value by different method inside of

optimize pit, [Ordinary kriging with different variogram (Au_OK is normal, Au_OK_var_ln is variogram from

logarithm, Au_OH_var_gauss is variogram from Gaussian); Indicator Kriging (Au_Ind) and Conditional

Simulation (Au_sim)]

VARIABLE Count Min. Max. Mean Std. Dev Variance

Au_OK 5019 0.02 10.47 1.22 1.15 1.33

Au_OK_var_ln 5019 0.08 9.5 1.2 1.02 1.04

Au_OK_var_gauss 5019 0.12 11.22 1.2 0.96 0.93

Au_Ind 5019 0.08 9.33 1.15 0.99 0.97

Au_sim 5019 0.02 19.18 1.21 1.15 1.32

We will use the tonnage - cut-off curves and grade – cut-off curves (Figure 121), where the first gold

model has overestimated values (lower tonnage and higher grade) respect to the other models; the gold

(variogram from Gaussian) has more tonnage with low grade between cut-off from 0.7 to 1.3 gpt (60%

of the total tonnage); the indicator model has lower values in higher cut-off. The gold values by

simulation has higher grade (since 2.7 gpt value).

Figure 121 Comparison between different gold block models in Tonnage and Cutoff curve (left)

and Mean Grade and Cutoff curve (right), Gold = First model of gold, Gold (vario lnAu) = gold model

with variogram from logarithm gold, Gold (vario gauss) = gold model with variogram from gaussian gold,

gold (by indicator) = gold model by indicator kriging and gold (mean sim) = gold value by mean of

simulated gold; these block model are inside the production pit.

98

5.5.8 Comparison Different Gold Cyanide block model results

Finally, the different gold cyanide block model values by different method are shown in Table 42 (All

values are inside of optimization pit) where the gold cyanide model by simulation (residual and gold) has

the higher mean value and the Cokriging method is the lower.

Table 42 Comparison between different gold cyanide block model value by different method inside

of optimize pit, [Ordinary Cokriging (AUCN_cokrig) and Conditional Simulation of two variables

(AuCN_sim_res_au)]

VARIABLE Count Min. Max. Mean Std. Dev Variance

AUCN_cokrig 5019 0 10.37 1.02 1.16 1.34

AuCN_sim_res_au 5014 0 17.28 1.07 1.05 1.11

We will use the tonnage - cut-off curves and grade – cut-off curves (Figure 122), where the gold cyanide

model by Cokriging has lower tonnage and higher grade than the gold cyanide model by two

Simulations.

Figure 122 Comparison between different gold cyanide block models in Tonnage and Cutoff curve

(left) and Mean Grade and Cutoff curve (right), Gold Cya (coKrig) = estimated by Cokriging and Gold

Cya (by 2 Sim) = gold cyanide value by simulated gold and simulated residual; these block model are

inside the production pit.

99

6. CONCLUSION AND RECOMMENDATION

- The metallurgical process (leaching by cyanide) has made it necessary to define the oxide and

sulphide domains.

- The higher estimation result is when using Gold Domain (Goldshape)

- The gold cyanide estimation has been divided in two estimation domain (oxide and sulphide),

because these have different behaviour.

- The gold and gold cyanide have been top cut to 20 gpt, in order to reduce the high variability

without reducing too much the mean.

- The first gold model (raw gold variogram) has less anisotropy than the other models, therefore

the estimation result shows higher mean value (over estimated).

- The gold (variogram from Gaussian) model has more tonnage with low grade between cut-off

from 0.7 to 1.3 gpt (60% of the total tonnage);

- The estimation result value of the preliminary study of indicators is lower than the ordinary

kriging results.

- When we use indicator kriging with different variogram models for different cut-off, there is a

possibility that we will produce a negative estimate or an estimate above 1; in these situations,

it is proper to adjust these estimates to appropriate lower or upper bound, negative estimates

should be set to 0 and estimates greater than 1 should be set to 1.

- The indicators give nested sets, therefore the choice estimation is indicator Cokriging.

- The indicator model has lower values in higher cut-off (from 2 gpt value).

- The simulated gold values have higher grades (from 2.7 gpt value).

- The gold cyanide has been estimated by Cokriging because of the high correlation with gold in

both domains (oxide and sulphide).

- In order to make a comparison with the Cokriging of gold cyanide, the relation between gold

cyanide, gold and residual has been studied in both domains (oxide and sulphide), where the

regression line formula for residual in oxide is: Residual = AuCN -0.91Au +0.01; and the

regression line formula in sulphide is: Residual = AuCN -0.38 Au - 0.04.

- The simulated gold cyanide result seems to be over estimated, more than the cokriged gold

cyanide.

- The same way, the simulated gold over estimates high values, more than the previous kriged

result.

- It is recommendable to use blasthole data in order to improve reconciliation between

exploration model (with drillhole) and production model (with blasthole), and obtain better

comparisons.

100

7. REFERENCE

Amstrong, M, 1998. Basic Linear Geostatistics, Springer-Verlag Berlin Heidelberg 1998.

Bell, P. Gomez, J. Loayza, C. Pinto, R 2005. Geology of the gold deposits of the Yanacocha District, Northerh Peru. In

PACRIM 2004, XXVII Convencion Minera 2005. 17 p.

Chile, J.P. Delfiner P., 1999. Geostatistics Modeling Spatial Uncertainty, Wiley-Interscience Publication, 695 p.

Dimitrakopoulos, R, 1994. Geostatistics for the next century, Kluwer Academic Press, 497pp.

Harvey, B, Myers, S and Klein, T, 1999. Yanacocha Gold District, Northern Peru, in PACRIM ’99 Conference

Guidebook, Bali, Indonesia, pp 445-459.

Isaaks, E.H., Srivastava, R.M., 1989. An introduction to Applied Geostatistics, Oxford University Press, New York

561 pp.

Journel, A.G. and Huijbregts, C.J. 1978. Mining Geostatisttics. Academic Press 600 pp.

Loayza, C, 2002. Geologic study of Cerro Yanacocha gold-silver deposit, Yanacocha district, northern Peru, Master

Thesis, University of Nevada, Reno, USA, 94 p.

Longo, T, in press. Volcanic stratigraphy and the temporal relationship of volcanism to gold and copper

mineralization, Yanacocha Mining district, Peru. Unpublished PhD thesis, Oregon State University.

Matheron, G, 1963. Principles of geostatistics, Economic Geology, Vol 58, pp 1246-66.

Matheron, G, 1965. Les variables régionalisées et leur estimation. Paris, Masson. 306pp.

Noble, D C, Mckee, E H, Mourier, T, and Megard, F, 1990. Cenozoic stratigraphy, magmatic activity, compressive

deformation and uplift in northern Peru: Geological Society of America Bulletin, 102: pp 1105-1113.

Pinto, R, 2002. Transición de un sistema de alta sulfuración a un sistema porfirítico de alto nivel en Kupfertal,

distrito minero de Yanacocha, Cajamarca, Perú: Tesis para título profesional de Ingeniero Geólogo, Universidad

Nacional Mayor de San Marcos, Lima, Perú, 96 p.

Quiroz, A, 1997. El corredor estructural Chicama Yanacocha y su importancia en la metalogenia en el norte del

Perú; in Resúmenes extendidos IX Congreso Peruano de Geología, pp 149-154, (Sociedad Geológica del Perú:

Lima).

Rivera, L, 1980. Mapa geológico del cuadrángulo de Cajamarca. Sector Energía y Minas, Instituto Geológico

Minero y Metalúrgico, República del Perú, Boletín Nº 31, 67 p.

Rivoirard, J, 2003. Course on Multivariate Geostatistics, Ecole des Mines de Paris, 67 p.

Rivoirard, J, 2011, No linear Course, in CFSG 2010-2011 Courses.

101

Teal, L, Harvey, B, Williams, C and Goldie, M, 2002. Geologic overview of the Yanacocha district gold deposits,

northern, Peru. Society of Economic Geologists; Global Exploration 2002, Integrated methods for discovery, 2002,

Abstracts pp 43-44.

Turner, S, 1997. The Yanacocha epithermal gold deposits, northern Peru: high sulfidation mineralization in a flow

dome setting. PhD Thesis, Colorado School of Mines, Colorado, USA, 342 p.

Wilson, J, 1985. Mapa geológico del cuadrángulo de Cajamarca. Sector Energía y Minas, Instituto Geológico Minero

y Metalúrgico, República del Perú. Boletín Nº 38, 104 p.

102

8. ANNEX

8.1 GOLD STATISTICS

Histogram of Gold FireAssay Total [Green=Sulfide(40%), Red=Oxide(60%)].

Histogram of Gold FireAssay in Oxide Zone and Histogram of Gold FireAssay (Total) in Sulfide

Zone

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au

Au

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

Frequencies

Frequencies

Nb Samples: 22202

Minimum: 0.0025

Maximum: 145.1557

Mean: 0.5495

Std. Dev.: 1.8195

Histogram (Au)

Isatis

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au

Au

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

0.25 0.25

Frequencies

Frequencies

Nb Samples: 8193

Minimum: 0.00

Maximum: 145.16

Mean: 1.14

Std. Dev.: 2.76

Histogram (Au)

Isatis

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au

Au

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

Frequencies

Frequencies

Nb Samples: 2682

Minimum: 0.00

Maximum: 18.26

Mean: 0.86

Std. Dev.: 1.34

Histogram (Au)

Isatis

103

Histogram of Declustered Gold FireAssay (Total) in Oxide Zone (Goldshape Domain) and

Histogram of Declustered Gold FireAssay (Total) in Sulfide Zone (Goldshape Domain)

Histogram of Capped and declustered Gold Fire Assay (capped to 20 gpt) in Gold

Shape[Green=Sulphide(25%), Blue=Oxide(75%)].

The Measurement of gold fire assay have been capping because this have high variability and have a

economical risk. Then it is capped to 20 gpt and have 2% less grade than the previous one, but the

standard deviation have been reducing in 25% less.


Oxide AuFA 8193 0.0025 20.000 0.83 1.53

Sulphide AuFA 2682 0.0033 18.2601 0.6267 1.1633

AuFA Total 10875 0.0025 20.000 0.74 1.39

Statistics Summary of Capped and declustered Gold Fire Assay: Oxide and Sulphide Zones in

Goldshape Domain (Oxide and Sulphide Statistics Graphics are in the Index).

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au

Au

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

Frequencies

Frequencies

Nb Samples: 8193

Minimum: 0.0025

Maximum: 145.1557

Mean: 0.8508

Std. Dev.: 2.2137

Histogram (Au)

Isatis

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au_cap

Au_cap

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

Frequencies

Frequencies

Nb Samples: 10875

Minimum: 0.00

Maximum: 20.00

Mean: 0.74

Std. Dev.: 1.39

Histogram (Au_cap)

Isatis

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au

Au

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

Frequencies

Frequencies

Nb Samples: 2682

Minimum: 0.0033

Maximum: 18.2601

Mean: 0.6267

Std. Dev.: 1.1633

Histogram (Au)

Isatis

104

Histogram of Capped and declustered Gold FireAssay (Total) in Oxide Zone and Histogram of

Capped and declustered Gold FireAssay (Total) in Sulfide Zone

ScatterPlot between Easting and Gold and ScatterPlot between Northing and Gold in GoldShape

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au_cap

Au_cap

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

Frequencies

Frequencies

Nb Samples: 8193

Minimum: 0.00

Maximum: 20.00

Mean: 0.83

Std. Dev.: 1.53

Histogram (Au_cap)

Isatis

12000

12000

12250

12250

12500

12500

12750

12750

13000

13000

13250

13250

Easting

Easting

0 0

50 50

100 100

150 150

Au

Au

rho=0.056

Scatter Diagram (Au, Easting)

Isatis

DATA/TOTAL(Gold)

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au_cap

Au_cap

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

Frequencies

Frequencies

Nb Samples: 2682

Minimum: 0.00

Maximum: 18.26

Mean: 0.63

Std. Dev.: 1.16

Histogram (Au_cap)

Isatis

25250

25250

25500

25500

25750

25750

26000

26000

26250

26250

26500

26500

Northing

Northing

0 0

50 50

100 100

150 150

Au

Au

rho=0.060

Scatter Diagram (Au, Northing)

Isatis

DATA/TOTAL(Gold)

105

High Grade and Low Grade in OXIDE ZONE (GOLDSHAPE)

Comparison between Histograms of Gold of High and Low grade in Oxide Zone

Comparison between Histograms of Gold Cyanide of High and Low grade in Oxide Zone

0

0

5

5

10

10

15

15

Au

Au

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

Frequencies

Frequencies

Nb Samples: 2985

Minimum: 0.00

Maximum: 145.16

Mean: 2.41

Std. Dev.: 4.25

Histogram (Au)

Isatis

DATA/GOLD(oxide_hg)

0

0

1

1

2

2

3

3

4

4

5

5

Au

Au

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

0.25 0.25

Frequencies

Frequencies

Nb Samples: 5208

Minimum: 0.00

Maximum: 6.24

Mean: 0.42

Std. Dev.: 0.42

Histogram (Au)

Isatis

0

0

5

5

10

10

15

15

Au_CN

Au_CN

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

Frequencies

Frequencies

Nb Samples: 2601

Minimum: 0.03

Maximum: 132.94

Mean: 2.28

Std. Dev.: 3.89

Histogram (Au_CN)

Isatis

DATA/GOLD(oxide_hg)

0

0

1

1

2

2

3

3

4

4

5

5

Au_CN

Au_CN

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

0.25 0.25

Frequencies

Frequencies

Nb Samples: 2852

Minimum: 0.03

Maximum: 5.86

Mean: 0.51

Std. Dev.: 0.39

Histogram (Au_CN)

Isatis

106

0

0

1

1

2

2

3

3

4

4

5

5

Au

Au

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

0.25 0.25

Frequencies

Frequencies

Nb Samples: 1974

Minimum: 0.00

Maximum: 3.46

Mean: 0.37

Std. Dev.: 0.35

Histogram (Au)

Isatis

High Grade and Low Grade in SULFIDE ZONE (GOLDSHAPE)

Comparison between Histograms of Gold of High and Low grade in Sulfide Zone

Comparison between Histograms of Gold Cyanide of High and Low grade in Sulfide Zone

0

0

5

5

10

10

15

15

Au

Au

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

Frequencies

Frequencies

Nb Samples: 708

Minimum: 0.01

Maximum: 18.26

Mean: 2.21

Std. Dev.: 1.99

Histogram (Au)

Isatis

0

0

5

5

10

10

15

15

Au_CN

Au_CN

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

Frequencies

Frequencies

Nb Samples: 651

Minimum: 0.03

Maximum: 8.13

Mean: 0.95

Std. Dev.: 1.15

Histogram (Au_CN)

Isatis

0

0

1

1

2

2

3

3

4

4

5

5

Au_CN

Au_CN

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

0.6 0.6

Frequencies

Frequencies

Nb Samples: 1076

Minimum: 0.03

Maximum: 1.69

Mean: 0.22

Std. Dev.: 0.25

Histogram (Au_CN)

Isatis

107

BoxPlot of Gold by Domains: HG_ox (High Grade and Oxide Domain), LG_ox (Low Grade and

Oxide Domain), HG_su (High Grade and Sulfide Domain), LG_su (Low Grade and Sulfide Domain).

BoxPlot of Gold Cyanide by Domains: HG_ox (High Grade and Oxide Domain), LG_ox (Low Grade

and Oxide Domain), HG_su (High Grade and Sulfide Domain), LG_su (Low Grade and Sulfide

Domain).

108

Cross validation of Gold (variogram of gold)

12000

12000

12250

12250

12500

12500

12750

12750

13000

13000

13250

13250

X (m)

X (m)

25250 25250

25500 25500

25750 25750

26000 26000

26250 26250

26500 26500

Y (m)

Y (m)

0

0

10

10

20

20

Z* : Au (Estimates)

Z* : Au (Estimates)

0 0

10 10

20 20

Z : Au (True value)

Z : Au (True value)

rho = 0.870

0

0

10

10

20

20

Z* : Au (Estimates)

Z* : Au (Estimates)

-20 -20

-10 -10

0 0

10 10

20 20

(Z*-Z)/S*

(Z*-Z)/S*

rho = -0.042

-20

-20

-10

-10

0

0

10

10

20

20

(Z*-Z)/S*

(Z*-Z)/S*

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

0.6 0.6

0.7 0.7

0.8 0.8

0.9 0.9

Frequencies

Frequencies

Nb Samples: 10875

Minimum: -16.7608

Maximum: 10.7687

Mean: 0.00218306

Std. Dev.: 0.859746

Cross Validation of Au [Gold]

Isatis

109

8.2 AUCN STATISTICS

Histogram of Gold Cyanide in Oxide Zone and Histogram of Gold Cyanide in Sulfide Zone

ScatterPlot between Gold FireAssay and Gold Cyanide in Oxide Zone and ScatterPlot between

Gold FireAssay and Gold Cyanide in Sulfide Zone

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au_CN

Au_CN

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

0.25 0.25

Frequencies

Frequencies

Nb Samples: 5453

Minimum: 0.03

Maximum: 132.94

Mean: 1.36

Std. Dev.: 2.85

Histogram (Au_CN)

Isatis

0

0

50

50

100

100

150

150

Au

Au

0 0

50 50

100 100

150 150

Au_CN

Au_CN

rho=0.991


Isatis

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

Au_CN

Au_CN

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

Frequencies

Frequencies

Nb Samples: 1727

Minimum: 0.03

Maximum: 8.13

Mean: 0.50

Std. Dev.: 0.82

Histogram (Au_CN)

Isatis

DATA/GOLD(sulfide)

0

0

10

10

20

20

Au

Au

0 0

10 10

20 20

Au_CN

Au_CN

rho=0.704


Isatis

110

Scatterplot between Gold Cyanide and Elevation. (Red: Oxide Zone, Blue: Sulphide Zone, cor coef

= 0.299); and Scatterplot between Logarithm Gold Cyanide and Elevation. (Red: Oxide Zone, Blue:

Sulphide Zone)

Dowhole Cross Variogram between Gold Fire Assay and Gold Cyanide in Oxide Domain.

3100

3100

3200

3200

3300

3300

3400

3400

3500

3500

3600

3600

Elevation

Elevation

-4 -4

-3 -3

-2 -2

-1 -1

0 0

1 1

2 2

3 3

4 4

5 5

LnAuCN

LnAuCN

rho=0.345

Isatis

0

0

10

10

20

20

30

30

40

40

50

50

60

60

70

70

80

80

90

90

Distance (m)

Distance (m)

0 0

1 1

2 2

3 3

Variogram : Au

Variogram : Au

0

0

10

10

20

20

30

30

40

40

50

50

60

60

70

70

80

80

90

90

Distance (m)

Distance (m)

0 0

1 1

2 2

3 3



0

0

10

10

20

20

30

30

40

40

50

50

60

60

70

70

80

80

90

90

Distance (m)

Distance (m)

0 0

1 1

2 2

3 3

Variogram : Au_CN

Variogram : Au_CN

Variogram (Au, Au_CN)

Isatis

3100

3100

3200

3200

3300

3300

3400

3400

3500

3500

3600

3600

Elevation

Elevation

0 0

10 10

20 20

Au_CN

Au_CN

rho=0.219

Isatis

111

Dowhole Cross Variogram between Gold Fire Assay and Gold Cyanide in Sulphide Domain.

0

0

10

10

20

20

30

30

40

40

50

50

60

60

70

70

80

80

90

90

Distance (m)

Distance (m)

0.00 0.00

0.25 0.25

0.50 0.50

0.75 0.75

1.00 1.00

1.25 1.25

Variogram : Au

Variogram : Au

0

0

10

10

20

20

30

30

40

40

50

50

60

60

70

70

80

80

90

90

Distance (m)

Distance (m)

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

0.6 0.6



0

0

10

10

20

20

30

30

40

40

50

50

60

60

70

70

80

80

90

90

Distance (m)

Distance (m)

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

Variogram : Au_CN

Variogram : Au_CN

Variogram (Au, Au_CN)

Isatis

112

8.3 SILVER STATISTICS

This measurement will be evaluated in two different domains: Oxide and Sulphide. We will use the

correlation with gold fire assay in sulphide domain.

Histogram and Cumulative plot (logarithm scale) of Silver [Green=Sulfide(28%), Red=Oxide(72%)].

ScatterPlot between Gold and Silver in GoldShape and ScatterPlot between Ln(Gold) and

Ln(Silver)

0

0

50

50

100

100

150

150

Au

Au

0 0

100 100

200 200

300 300

Ag

Ag

rho=0.085

Scatter Diagram (Au, Ag)

Isatis

0

0

10

10

20

20

Ag

Ag

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

Frequencies

Frequencies

Nb Samples: 9187

Minimum: 0.10

Maximum: 278.27

Mean: 3.04

Std. Dev.: 7.22

Histogram (Ag)

Isatis

-5

-5

0

0

5

5

LnAu

LnAu

-5 -5

0 0

5 5

LnAg

LnAg

rho=0.304

Scatter Diagram (LnAu, LnAg)

Isatis

DATA/TOTAL(Gold)

113

Histogram of Silver in Oxide Zone and in Sulphide Zone

ScatterPlot between Ln(Gold) and Ln(Silver) in Oxide Zone and ScatterPlot between Ln(Gold) and

Ln(Silver) in Sulfide Zone

0

0

10

10

20

20

30

30

Ag

Ag

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

Frequencies

Frequencies

Nb Samples: 6595

Minimum: 0.10

Maximum: 155.51

Mean: 2.88

Std. Dev.: 5.58

Histogram (Ag)

Isatis

DATA/GOLD(oxide)

-5

-5

0

0

5

5

LnAu

LnAu

-5 -5

0 0

5 5

LnAg

LnAg

rho=0.651

Scatter Diagram (LnAu, LnAg)

Isatis

-5

-5

0

0

5

5

logAu

logAu

-3 -3

-2 -2

-1 -1

0 0

1 1

2 2

3 3

4 4

5 5

logAg

logAg

rho=0.218

Scatter Diagram (logAu, logAg)

Isatis

114

8.4 Copper Cyanide STATISTICS

Histogram of Copper Cyanide [Green=Sulfide(35%), Red=Oxide(65%)].

Histogram of Copper Cyanide in Oxide Zone and Histogram of Copper Cyanide in Sulfide Zone

0

0

100

100

200

200

300

300

400

400

500

500

CuCN_FULL

CuCN_FULL

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

Frequencies

Frequencies

Nb Samples: 13266

Minimum: 1.00

Maximum: 32230.00

Mean: 212.29

Std. Dev.: 839.86

Histogram (CuCN_FULL)

Isatis

0

0

100

100

200

200

300

300

400

400

500

500

CuCN_FULL

CuCN_FULL

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

0.6 0.6

0.7 0.7

Frequencies

Frequencies

Nb Samples: 8754

Minimum: 1.00

Maximum: 32230.00

Mean: 73.64

Std. Dev.: 521.15


Isatis

DATA/TOTAL(Oxide)

0

0

100

100

200

200

300

300

400

400

500

500

CuCN_FULL

CuCN_FULL

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

Frequencies

Frequencies

Nb Samples: 4512

Minimum: 1.00

Maximum: 21693.00

Mean: 481.30

Std. Dev.: 1198.86


Isatis

DATA/TOTAL(Sulfide)

115

8.5 SULPHIDE SULPHUR STATISTICS

Histogram of Sulfide Sulphur [Green=Sulfide(55%), Red=Oxide(45%)].

Histogram of Sulfide Sulphur in Oxide Zone and Histogram of Sulfide Sulphur in Sulfide Zone

0

0

10000

10000

20000

20000

30000

30000

40000

40000

50000

50000

60000

60000

S_SS_PREF

S_SS_PREF

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4 Frequencies

FrequenciesNb Samples: 2681

Minimum: 50.00

Maximum: 221133.33

Mean: 15458.28

Std. Dev.: 18115.71

Histogram (S_SS_PREF)

Isatis

0

0

50000

50000

100000

100000

S_SS_PREF

S_SS_PREF

0.0 0.0

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4

0.5 0.5

0.6 0.6

0.7 0.7

0.8 0.8

Frequencies

Frequencies

Nb Samples: 1215

Minimum: 50.00

Maximum: 99500.00

Mean: 4485.71

Std. Dev.: 10219.35


Isatis

0

0

50000

50000

100000

100000

S_SS_PREF

S_SS_PREF

0.00 0.00

0.05 0.05

0.10 0.10

0.15 0.15

0.20 0.20

0.25 0.25

Frequencies

Frequencies

Nb Samples: 1466

Minimum: 50.00

Maximum: 221133.33

Mean: 24552.19

Std. Dev.: 18197.03


Isatis

DATA/TOTAL(Sulfide)

116

ScatterPlot between Copper Cyanide and Sulfide Sulphur (red=Oxide Blue=sulphide) and

ScatterPlot between Ln(Copper Cyanide) and Ln(Sulfide Sulphur) and (red=Oxide Blue=sulphide)

ScatterPlot between Copper Cyanide and Sulfide Sulphur in Oxide Zone and ScatterPlot between

Ln(Copper Cyanide) and Ln(Sulfide Sulphur) in Oxide

0

0

10000

10000

20000

20000

30000

30000

CuCN_FULL

CuCN_FULL

0 0

100000 100000

200000 200000

S_SS_PREF

S_SS_PREF

rho=0.239

Scatter Diagram (CuCN_FULL, S_SS_PREF)

Isatis

0

0

10000

10000

20000

20000

30000

30000

CuCN_FULL

CuCN_FULL

0 0

50000 50000

100000 100000

S_SS_PREF

S_SS_PREF

rho=0.054


Isatis

DATA/TOTAL(Oxide)

0

0

5

5

10

10

LnCuCN

LnCuCN

0 0

5 5

10 10

LnSS

LnSS

rho=0.458

Scatter Diagram (LnCuCN, LnSS)

Isatis

0

0

5

5

10

10

LnCuCN

LnCuCN

0 0

5 5

10 10

LnSS

LnSS

rho=0.427


Isatis

DATA/TOTAL(Oxide)

117

ScatterPlot between Copper Cyanide and Sulfide Sulphur in Sulfide Zone ScatterPlot between

Ln(Copper Cyanide) and Ln(Sulfide Sulphur) in Sulfide

0

0

5000

5000

10000

10000

15000

15000

CuCN_FULL

CuCN_FULL

0 0

100000 100000

200000 200000

S_SS_PREF

S_SS_PREF

rho=0.332


Isatis

DATA/TOTAL(Sulfide)

0

0

5

5

10

10

LnCuCN

LnCuCN

0 0

5 5

10 10

LnSS

LnSS

rho=0.421


Isatis

DATA/TOTAL(Sulfide)

118

8.6 RECONCILIATION APPROACH

Each month during the year, month-end reconciliations are performed between ore control

of metal, tonnage and grades during the month (BlastHole) and the current model’s of metal,

tonnage and grade estimates (Drillholes). This reconciliation is done using the model and

cut-off grades being used during the month.

Reconciliation Process

Exploration Model (Estimated Value): This has made with grade value of sampled drillhole, it

has a spacing of 25 meters and Quality Control for all samples; the parameters of estimated

blocks are 25x25x12, the density varies according to type of alteration, metallurgical zone

and type of rock. Each block has been estimated by Ordinary Kriging (using capping

parameters, variography, neighborhood and change support).

Ore Control Model (True Value): It has been done using the grade value of sampled

blasthole, it has a spacing of 25 meters and Quality Control for all samples; the parameter of

blocks are 5x5x12, the density is the same that the current model one. Each block has been

estimated by Ordinary Kriging (using capping parameters, variography, neighborhood and

change support).

Classified True Value with Mined Polygons: For each mined polygon has been obtained the

tonnage, metal and grade with:

Tonnages = Σ[percentage of block x Volumen(5 x 5 x 12) m3 x density of block(Tons/m3) ]

ex: Tonnage = (0.43 x (5 x 5 x 12) x 2.7) + (1 x (5 x 5 x 12) x 2.7) = 1158.3 Ton

Metal = Σ[grade of block (grams / Tons) x (percentage of block x volume x density)]

ex: Metal =(0.1(g/tonnes)x0.43x(5x5x12)x2.7)+(0.3(g/tones)x1x(5x5x12)x2.7)=277.83 g

Grade = Metal (grams) / Tonnages (Tons)

ex: Grade = Metal / Tonnages = 277.83 g / 1158.3 Tons = 0.24 g/Tons

In order to define ore or waste polygon is necessary to evaluate the cost parameters

(different monthly) and the characteristics of each mined polygon (oxide, sulphide, etc.)

Classified Estimated Value with mined Polygons: For each mined polygon has been gotten

the tonnage, metal and grade with:

Tonnages = Σ [percentage of block x (25 x 25 x 12) m3 x density of block (Tons/m3) ]

Metal = Σ[grade of block (grams / Tons) x percentage of block x Tonnage of block]

Grade = Metal (grams) / Tonnages (Tons)

In order to classified ore or waste polygon is necessary to evaluate the cost parameters and

the characteristics of each mined polygon (oxide, sulphide, etc.)

119

Therefore, the true value of ore (tonnage, metal and grade) monthly is the sum of ore mined

polygons (by blasthole model), and the true value of waste (tonnage, metal and grade) is the

sum of waste mined polygons (blasthole model). The estimed value of ore (tonnage, metal

and grade) is the sum of ore mined polygons (by drillhole model), and the estimated value of

waste (tonnage, metal and grade) is the sum of waste mined polygons (drillhole model).

Finally, there are four zones: Ore Polygons classified Ore, Waste Polygons Classified Waste

(both the best results), Ore Polygons Classified Waste (Underestimated), and Waste

polygons Classified Ore (Overestimated) in the figure 5.

Figure 05: True Value vs Estimated Value

a.1 Presentation of the problem:

The grade Reconciliation of estimated model (by drillhole) against ore control model (true

value) for three years is 8% less tonnages, 5% higher grade and 2% less metal than predicted

by the deposit model. Otherwise, the reconciliation by year increase the uncertainty, it is

+- 10% in tonnage, +- 15% in grade, and +- 15% in metal.

a.2 Difficulties: The last Drillhole Model is available, but the Blasthole Data and Model is not

available

a.3 Conclusions:

- Use Cokriging for True Model, and for Short Term Planing Model.

- Improve the reconciliation results with the use of other estimation methods.

120

8.7 Table of Statistics of Gold block model by Conditional Simulation

with turning bands

VARIABLE Count Minimum Maximum Mean

Std.

Dev

Au_gaussian[00001] 17475 0.01 33.66 0.8 1.13

Au_gaussian[00002] 17475 0 29.06 0.77 1.06

Au_gaussian[00003] 17475 0 22.08 0.77 0.97

Au_gaussian[00004] 17475 0 17.17 0.75 1.01

Au_gaussian[00005] 17475 0 39.01 0.76 1.05

Au_gaussian[00006] 17475 0 26.55 0.82 1.15

Au_gaussian[00007] 17475 0.01 31.09 0.78 1.12

Au_gaussian[00008] 17475 0.01 26.13 0.79 1.02

Au_gaussian[00009] 17475 0.01 21.51 0.76 1.02

Au_gaussian[00010] 17475 0.01 36.24 0.77 1.04

Au_gaussian[00011] 17475 0 29.92 0.75 1.02

Au_gaussian[00012] 17475 0.01 22.27 0.77 0.96

Au_gaussian[00013] 17475 0 41.74 0.77 1.05

Au_gaussian[00014] 17475 0.01 25.17 0.75 0.99

Au_gaussian[00015] 17475 0.01 31.54 0.74 0.97

Au_gaussian[00016] 17475 0.01 39.48 0.79 1.05

Au_gaussian[00017] 17475 0.01 38.53 0.79 1.07

Au_gaussian[00018] 17475 0 30.52 0.75 1.04

Au_gaussian[00019] 17475 0 34.04 0.75 1.03

Au_gaussian[00020] 17475 0.01 38.81 0.79 1.1

Au_gaussian[00021] 17475 0 28.46 0.75 0.99

Au_gaussian[00022] 17475 0.01 32.3 0.8 1.05

Au_gaussian[00023] 17475 0 35.47 0.76 1.07

Au_gaussian[00024] 17475 0.01 21.35 0.74 0.98

Au_gaussian[00025] 17475 0 18.06 0.73 0.9

Au_gaussian[00026] 17475 0 23.17 0.75 1.02

Au_gaussian[00027] 17475 0 39.18 0.74 0.97

Au_gaussian[00028] 17475 0 30.87 0.8 1.08

Au_gaussian[00029] 17475 0 28.89 0.78 1.08

Au_gaussian[00030] 17475 0 23.35 0.76 1.07

Au_gaussian[00031] 17475 0 21.88 0.76 1.03

Au_gaussian[00032] 17475 0.01 45.42 0.78 1.17

Au_gaussian[00033] 17475 0 20.71 0.77 1.01

Au_gaussian[00034] 17475 0.01 25.43 0.78 1.04

Au_gaussian[00035] 17475 0 26.53 0.74 1.04

Au_gaussian[00036] 17475 0.01 16.6 0.79 0.99

121


Std.

Dev

Au_gaussian[00037] 17475 0.01 29.93 0.79 1.07

Au_gaussian[00038] 17475 0.01 38.05 0.79 1.03

Au_gaussian[00039] 17475 0 31.79 0.75 1.02

Au_gaussian[00040] 17475 0 41.21 0.75 1.02

Au_gaussian[00041] 17475 0 28.6 0.75 1.02

Au_gaussian[00042] 17475 0.01 23.49 0.74 0.97

Au_gaussian[00043] 17475 0 31.11 0.77 1.02

Au_gaussian[00044] 17475 0.01 32.35 0.76 1.07

Au_gaussian[00045] 17475 0 39.01 0.76 1.08

Au_gaussian[00046] 17475 0.01 35.36 0.76 1.08

Au_gaussian[00047] 17475 0.01 30.09 0.75 1.1

Au_gaussian[00048] 17475 0.01 29.49 0.77 0.99

Au_gaussian[00049] 17475 0.01 33.74 0.8 1.1

Au_gaussian[00050] 17475 0 21.71 0.8 1.09

Au_gaussian[00051] 17475 0 15.49 0.78 0.97

Au_gaussian[00052] 17475 0.01 30.76 0.79 1.04

Au_gaussian[00053] 17475 0.01 44.3 0.75 0.98

Au_gaussian[00054] 17475 0 20.68 0.76 1.03

Au_gaussian[00055] 17475 0.01 30.84 0.75 1.03

Au_gaussian[00056] 17475 0 18.31 0.77 1

Au_gaussian[00057] 17475 0.01 15.84 0.75 0.96

Au_gaussian[00058] 17475 0.01 19.48 0.75 0.98

Au_gaussian[00059] 17475 0.01 27.87 0.76 1.06

Au_gaussian[00060] 17475 0 23.55 0.76 1.05

Au_gaussian[00061] 17475 0 20.24 0.75 1.01

Au_gaussian[00062] 17475 0.01 19.06 0.75 0.95

Au_gaussian[00063] 17475 0 28.19 0.78 1.01

Au_gaussian[00064] 17475 0 19.66 0.78 1.02

Au_gaussian[00065] 17475 0.01 36.18 0.8 1.12

Au_gaussian[00066] 17475 0 19.26 0.79 1.02

Au_gaussian[00067] 17475 0 44.98 0.78 1.12

Au_gaussian[00068] 17475 0 30.19 0.76 1.08

Au_gaussian[00069] 17475 0.01 26.18 0.76 1

Au_gaussian[00070] 17475 0 19.07 0.78 1.05

Au_gaussian[00071] 17475 0 30.16 0.79 1.1

Au_gaussian[00072] 17475 0 20.2 0.74 0.94

Au_gaussian[00073] 17475 0.01 31.08 0.76 1.04

Au_gaussian[00074] 17475 0.01 21.8 0.78 1.04

Au_gaussian[00075] 17475 0 24.67 0.79 1.05

Au_gaussian[00076] 17475 0 44.51 0.75 1.04

122


Std.

Dev

Au_gaussian[00077] 17475 0.01 38.09 0.76 1.08

Au_gaussian[00078] 17475 0.01 18.1 0.76 0.96

Au_gaussian[00079] 17475 0.01 39.19 0.76 1.19

Au_gaussian[00080] 17475 0 32.1 0.75 1.03

Au_gaussian[00081] 17475 0.01 27.31 0.77 1.03

Au_gaussian[00082] 17475 0.01 29.82 0.76 0.98

Au_gaussian[00083] 17475 0 23.44 0.78 1.01

Au_gaussian[00084] 17475 0 33.72 0.76 1.04

Au_gaussian[00085] 17475 0 18.94 0.78 0.97

Au_gaussian[00086] 17475 0 62.92 0.78 1.1

Au_gaussian[00087] 17475 0.01 36.33 0.76 1.13

Au_gaussian[00088] 17475 0.01 20.72 0.75 0.96

Au_gaussian[00089] 17475 0.01 26.7 0.77 1.01

Au_gaussian[00090] 17475 0.01 37.6 0.8 1.17

Au_gaussian[00091] 17475 0 20.9 0.78 1.03

Au_gaussian[00092] 17475 0.01 23.9 0.8 1.02

Au_gaussian[00093] 17475 0.01 57.48 0.76 1.25

Au_gaussian[00094] 17475 0 37.62 0.74 1.09

Au_gaussian[00095] 17475 0.01 19.45 0.76 0.95

Au_gaussian[00096] 17475 0.01 17.54 0.76 0.94

Au_gaussian[00097] 17475 0.01 21.36 0.77 1.02

Au_gaussian[00098] 17475 0 35.29 0.75 1.03

Au_gaussian[00099] 17475 0.01 25.14 0.77 1.03

Au_gaussian[00100] 17475 0 24.72 0.75 1

Documents

Report project fernando saez cfsg