Modeling of two-dimensional random fields

This paper presents a method of conditional stochastic modeling of two-dimensional fields which can be used to predict values at certain field points at a given time, based on field values at other locations at the same time and on data about second order field moments at given points. For computer simulations, the Gaussian truncated distributions are used. The aim of this work is also to present a derivation of a formula for the probability density of an n-dimensional random variable with the Gaussian conditional truncated distribution. As a numerical example, a soil contamination field described by correlation functions corresponding to the white noise field, the Shinozuka field and the Markov field is analyzed. The acceptance-rejection method is applied to generate covariance matrices and vectors of field values. Then, conditional expected field values for adequate correlation functions are calculated.