Capacity Assessment of Gumbel-Clayton Copula for Geostatistical Estimation

Kriging weights are calculated regarding the sample distances from the estimation point without attention to the sample values. This problem of kriging shows the necessity of developing new methods that consider both distance and sample values for assigning appropriate weights to the samples. In this study, a combination of the Gumbel and Clayton Archimedean copulas is proposed to describe spatial structure of two data sets. One of these sets includes some simulated physico mechanical properties of an andesite quarry and the other one contains borehole data of a porphyry copper deposit. The combined copula was able to describe various kinds of spatial structures with asymmetric upper and lower tails at different lags. The jackknife cross-validation test showed better performance of copula over ordinary kriging such that the mean values of variables were better estimated through the copula method. Correlation coefficients between the estimated and real values were higher for copula than kriging. The copula results had lower mean squared errors and this method better reproduced the data distribution. The kriging performance was severely affected by the variables’ distributions such that for highly skewed variables it showed the worst results. Moreover, accuracy and precision of the kriging results are inversely correlated with the amount of nugget effect. In contrary to kriging, marginal distribution and the nugget effect have far less impact on the copula’s performance. Therefore, this study strongly suggests copula approach for geostatistical estimation due to its flexibility in describing various spatial structures and outperforming ordinary kriging that consequently results in better economic evaluation.