Efficient Simulation of Stationary Multivariate Gaussian Random Fields with Given Cross-Covariance

Abstract

The present paper introduces a new approach to simulate any stationary multivariate Gaussian random field whose cross-covariances are predefined continuous and integrable functions. Such a field is given by convolution of a vector of univariate random fields and a functional matrix which is derived by Cholesky decomposition of the Fourier transform of the predefined cross-covariance matrix. In contrast to common methods, no restrictive model for the cross-covariance is needed. It is stationary and can also be reduced to the isotropic case. The computational effort is very low since fast Fourier transform can be used for simulation. As will be shown the algorithm is computationally faster than a recently published spectral turning bands model. The applicability is demonstrated using a common numerical example with varied spatial correlation structure. The model was developed to support simulation algorithms for mineral microstructures in geoscience.

Numerical studies of earth structure assessment via the theory of porous media using fuzzy probability based random field material descriptions

“…For example, in regions of aged material of a dam structure the hydraulic permeability might be increased while the mechanical stiffness is reduced. These cross‐correlated heterogeneous material properties can be modeled using cross‐correlated random fields . Since auto‐correlation lengths in soil not only vary spatially and temporally, but can also not be determined holistically by experiments, due to the fractal behavior of the soil, alternative approaches are required to properly capture their influence.…”