TITLE:
Efficient Simulation of Stationary Multivariate Gaussian Random Fields with Given Cross-Covariance
AUTHORS:
Jakob Teichmann, Karl-Gerald van den Boogaart
KEYWORDS:
Image Processing, Convolution, Cross-Covariance, Cholesky Decomposition, Fourier Transformation
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.17,
November
22,
2016
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.