Calculation of the normal scores variogram used for truncated Gaussian lithofacies simulation: theory and FORTRAN code

Abstract

Application of the truncated Gaussian method for categorical variable simulation requires the calculation of an appropriate normal scores variogram for generating the Gaussian random field. In the case of only two categories, the appropriate variogram can be determined by inverting the indicator variogram model from the bivariate Gaussian distribution. Even though no closed-form relation exists for such inversion, the proper normal scores variogram can be obtained through numerical integration via a series approximation. The procedure is illustrated with a small simulation example demonstrating the close reproduction of the variogram of the categorical data.