161
This procedure needs modeling the full matrix of cross-covariance functions. In second
step, only the direct variograms of secondary variable is enough for accomplishing this step.
The simple cokriging systems also can be substituted for ordinary cokriging systems in the
case that the mean values for both variables are perfectly known in the study area. This
algorithm is implemented in a copper deposit as a case study, aiming at estimation of gold
grade taking into account the copper grade as secondary variable which is more available.
The results are then compared with traditional ordinary cokriging approaches, considering
the isotopic searching strategy.
3 ACTUAL CASE STUDY
The case study belongs to a copper deposit obtained from borehole campaign. Two variables are available at sample locations, Copper (Cu) and Gold (Au). Au is undersampled in
relation to Cu, indicating the partially heterotopic sampling pattern. In order to preserve the
confidentiality of data set, the name and location of deposit are not disclosed. Following the
proposed algorithm, the copper grade can be considered as secondary variable due to more
availability and gold grade can be taken into account as primary variable or target variable
to be estimated in the region. Since the sampling pattern is irregular, it is required that the
dataset is declustered to provide more representative statistical parameters. To do so, cell
declustering is chosen based on dimension of 50 m*50 m*12 m. The declustered statistical
parameters are illustrated in Table 1. Figure 1 also shows the declustered histogram distribution. Shape of distribution in copper grades approximately follow the log-normal distribution and in gold grades follow exponential distribution, respectively.
In order to check the bivariate relation between the underlying variables, correlation coefficient is computed through the isotopic locations, wherever both information are accessible as
ρ = 0 76
. .
76 Scatter plot, showing interrelationship of gold grade versus copper grade, accompanying with relatively high correlation coefficient (Fig. 2), shows that there exist a satisfying
Table 1. Declustered statistical parameters for
copper and gold grades.
Parameter
Au (ppm)
Cu (%)
Number of data
902
2376
Mean
2.79
0.90
Variance
34.95
0.342
Minimum
0
0.12
Maximum
68.82
7.24
Figure 1. Diclustered histogram of copper and gold grades.
250
Histogram for Cu
1 -
Global l
~ 200
"0
'o
~ 150
"
"
"0
a 100
.!l
~
~
Q 50
Value
700
~ 600
""' 'o 500
~ 400
"
"
] 300
*
..3 200
8 100
0
0
Histogram for Au
10
20
30
40
50
60
70
Value
This procedure needs modeling the full matrix of cross-covariance functions. In second
step, only the direct variograms of secondary variable is enough for accomplishing this step.
The simple cokriging systems also can be substituted for ordinary cokriging systems in the
case that the mean values for both variables are perfectly known in the study area. This
algorithm is implemented in a copper deposit as a case study, aiming at estimation of gold
grade taking into account the copper grade as secondary variable which is more available.
The results are then compared with traditional ordinary cokriging approaches, considering
the isotopic searching strategy.
3 ACTUAL CASE STUDY
The case study belongs to a copper deposit obtained from borehole campaign. Two variables are available at sample locations, Copper (Cu) and Gold (Au). Au is undersampled in
relation to Cu, indicating the partially heterotopic sampling pattern. In order to preserve the
confidentiality of data set, the name and location of deposit are not disclosed. Following the
proposed algorithm, the copper grade can be considered as secondary variable due to more
availability and gold grade can be taken into account as primary variable or target variable
to be estimated in the region. Since the sampling pattern is irregular, it is required that the
dataset is declustered to provide more representative statistical parameters. To do so, cell
declustering is chosen based on dimension of 50 m*50 m*12 m. The declustered statistical
parameters are illustrated in Table 1. Figure 1 also shows the declustered histogram distribution. Shape of distribution in copper grades approximately follow the log-normal distribution and in gold grades follow exponential distribution, respectively.
In order to check the bivariate relation between the underlying variables, correlation coefficient is computed through the isotopic locations, wherever both information are accessible as
ρ = 0 76
. .
76 Scatter plot, showing interrelationship of gold grade versus copper grade, accompanying with relatively high correlation coefficient (Fig. 2), shows that there exist a satisfying
Table 1. Declustered statistical parameters for
copper and gold grades.
Parameter
Au (ppm)
Cu (%)
Number of data
902
2376
Mean
2.79
0.90
Variance
34.95
0.342
Minimum
0
0.12
Maximum
68.82
7.24
Figure 1. Diclustered histogram of copper and gold grades.
250
Histogram for Cu
1 -
Global l
~ 200
"0
'o
~ 150
"
"
"0
a 100
.!l
~
~
Q 50
Value
700
~ 600
""' 'o 500
~ 400
"
"
] 300
*
..3 200
8 100
0
0
Histogram for Au
10
20
30
40
50
60
70
Value