Multivariate geostatistical simulation by minimising spatial cross-correlation

Joint simulation of attributes in multivariate geostatistics can be achieved by transforming spatially correlated variables into independent factors. In this study, a new approach for this transformation, Minimum Spatial Cross-correlation (MSC) method, is suggested. The method is based on minimising the sum of squares of cross-variograms at different distances. In the approach, the problem in higher space (N × N) is reduced to N × N − 1 / 2 problems in the two-dimensional space and the reduced problem is solved iteratively using Gradient Descent Algorithm. The method is applied to the joint simulation of a set of multivariate data in a marble quarry and the results are compared with Minimum/Maximum Autocorrelation Factors (MAF) method.