Report project fernando saez cfsg

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
th
Figure 112 Block Model of Conditioning Simulation of gold by Turning Band, bench with 5 Simulation (left) and
th
bench with 25 Simulation (right). ..............................................................................................................................92
th
Figure 113 Block Model of Conditioning Simulation of gold by Turning Band, bench with 50 Simulation (left) and
th
bench with 75 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
th
Figure 116 Block Model of Conditioning Simulation of residual by Turning Band, bench with 5 Simulation (left) and
th
bench with 25 Simulation (right). ..............................................................................................................................94
th
Figure 117 Block Model of Conditioning Simulation of residual by Turning Band, bench with 50 Simulation (left)
th
and bench with 75 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).

11

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

12

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.

13

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).

14

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.

Geology 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

Figure 2 Generalized Stratigraphical Column for the Yanacocha District.

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.

15

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

EL TAPADO

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.

16

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
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

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.

17

Base Map (Au)
X (m)
12000 12500 13000 13500
27000 27000
Au

26500 26500

26000 26000

Y (m)
Y (m)

25500 25500

25000 25000

12000 12500 13000 13500
X (m)
Isatis

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

18

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%)]

OXIDE

SULPHIDE

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

19

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).

20

100

30

20

10

Figure 9 Reduced Histogram and Reduced Cumulative plot (logarithm scale) of Gold fire assay in
Goldshape, ([Green=Sulphide (25%), Red=Oxide(75%)]

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

Top Cutting Top Cut Top Cut
Method value 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)

Domain Samples Minimum Maximum Mean Std. Dev.
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

21

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.

22

Variogram Map - Au

N1

88
N5

7

N2
4.1

9
4.2
N2 N1
89
N2
7 69 14
3.7 N3 3.6

3.1
3.2

2.7 2.6

5
2.2 2.1

1.7 1.6

1.2 N3 1.1
N1 34
07 09 N1
49
N2
0.7 0.6

N3
08

59
N1
N/A N/A

4.8
N2
40 8
N8 4.3
Distance (m)
0.00 0.25 0.50 0.75 1.00 1.25

3.8 3 3

3.3
Variogram : Au

Variogram : Au
2.8 2 2

2.3

1.8 1 1

N6 1.3
68 0
N2
0.8
0 0
N5

0.00 0.25 0.50 0.75 1.00 1.25
N/A
3

Distance (m)
Isatis

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.

23

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 15 Variogram in long range and in perpendicular range of capped gold fire assay in
goldshape. Long range =130m, and perpendicular range = 100m.

Variogram (Au_cap)
Distance (m)
0 25 50 75 100

3 3
Variogram : Au_cap

2 2

1 1

0 0

0 25 50 75 100
Distance (m)

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.

24

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 Rotation Range Minimum Maximum Mean SD. Rho Rho
Model ZR – YR - XR U–V–W (Z-Z*) (Z-Z*) (Z-Z*)/SD (Z-Z*) Cor C. (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

25

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).

0.06

0.05

0.04

0.03

0.02

0.01

0

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.

26

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.

Histogram (LnAu)
LnAu
Nb Samples: 2682
-5 0 5
Minimum: -5.70
Maximum: 2.90
Mean: -0.93
0.20 Std. Dev.:0.20
1.29

0.15 0.15

Frequencies
Frequencies

0.10 0.10

0.05 0.05

0.00 0.00
-5 0 5
LnAu
Isatis

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.

27

Variogram Map - LnAu
V W

3
1.6

N35

N1
N3
1.6

97
09
1.5

13
6
1.5

N3
N1
N2 N1 1.4
84 1.4 75
1.3 1.3
7
N39 1.2 N32 1.2

1.1
1.1
1.0
U V 1.0
0.9

0.8 0.9

0.7 0.8
N91 N34
0.6 8
0.7
07 0.5 41
N2 N1 0.6
N1

N4
0.4
17
84

24
0.3 0.5
N14

N36
N1

N1

N90
N/A N/A
0
0

W
2.0
N28
N2

1.9
50

3

1.8
N5

N2 Distance (m)
1.7
48 0.00 0.25 0.50 0.75 1.00 1.25
1.6

N62 1.5
1.5 1.5
1.4

1.3
Variogram : LnAu

Variogram : LnAu
U 1.2
1.0 1.0
1.1

1.0

N67 0.9

0.8 0.5 0.5
39 0.7
N2
N6

0.6
9
5

0.5
0

N72

0.0 0.0
N2

N80

0.00 0.25 0.50 0.75 1.00 1.25
N/A
Distance (m)
Isatis

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).

28

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.

29

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.

30

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.

31

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.

Variogram Rotation Range Minimum Maximum Mean SD. Rho Rho
Model ZR – YR - XR U–V–W (Z-Z*) (Z-Z*) (Z-Z*)/SD (Z-Z*) Cor C. (Z-Z*)/SD
Model 1 20 -25 -5 170 270 180 -16.2514 10.541 0.002 0.86 0.87 -0.05

3.3.2.4. Neighbourhood Choices:
We will do many comparisons the different neighbourhood parameters in the same block (Table 8); the
best neighbourhood is that have less kriging variance and slope of original data vs estimated data is
close to one.

Table 8 Comparison between different neighbourhood parameters (search and maximum of
samples), the parameters are 170 by 270 by 180 (Mathematical rotation 20 -25 -5) Minimum 2 samples
and Maximum: 4 sector by 40 samples (block = 29i 44j 32k).

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.

32

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).

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.

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.

33

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)

Variogram Map - Gaussian Au

N1

4
1
N2

1.09 0.9

54

N9
N5
9

1.04 N1
N2 9 76 5
2 N6 0.99 N7 0.8

0.94

N11
N57
0.89 0.7

0.84

0.79 0.6
50 0.74
8
0.69 0.5

0.64 N17
0.59 0.4

N2 0.54
N3
49 02 55 56
N2
0.3
0.49
N2
N2
31

0.44

N3
74
N2

09

34
N2

N/A N/A

1.20
N1

31
09

N1

1.10
N9 38 Distance (m)
1 N1 1.00
0.00 0.25 0.50 0.75 1.00 1.25

0.90
N44 1.00 1.00
0.80

Variogram : Gaussian Au
Variogram : Gaussian Au

0.70
0.75 0.75
50
0.60

0.50 0.50 0.50

0.40

N2 0.25 0.25
18 71 0.30
N3
N2
11

0.20
0.00 0.00
0.00 0.25 0.50 0.75 1.00 1.25
89
N3

N/A
Distance (m)
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)
,

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

34

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