New Model for Multivariate Non-Gaussian Random Fields Involving between-Variable Nonlinear Correlation

Abstract

Quantifying and simulating multivariate non-Gaussian random fields with nonlinear between-variable dependence is a critical yet still challenging task in various scientific and engineering applications. It is still hard for existing multivariate random field models, combining marginal distributions with the linear correlations of the variables, to simultaneously capture the three essential characteristics: the randomness of individual variables (i.e., marginal distributions), the spatial correlation of the field, and the between-variable nonlinear probabilistic correlation. In this paper, a novel multivariate non-Gaussian random field model based on the transformed correlation function and the bridge function is proposed. In this study, to avoid the incompleteness of quantifying the probabilistic dependence of non-Gaussian variables by the linear correlation function, the transformed correlation function as the correlation function of the marginally transformed random variables is introduced to characterize spatial variability at the second-order statistical level while preserving marginal distributions of variables. The bridge function, which has been established for Gaussian multivariate fields to bridge the correlation coefficient of two different Gaussian fields and that of the auxiliary standard Gaussian fields, is then extended to establish a flexible probabilistic transformation to ensure consistency with given spatial correlation and nonlinear dependence structures. Further, a corresponding simulation method is developed, enabling efficient multiple field sample generation. Numerical examples validate the effectiveness of the proposed approach, demonstrating its capability to accurately quantify and simulate complex multivariate non-Gaussian fields with nonlinear intervariable correlations.