A turning bands program for conditional co-simulation of cross-correlated Gaussian random fields

Abstract

A Matlab program (TBCOSIM) is provided for co-simulating a set of stationary or intrinsic Gaussian random fields in R-3, whose simple and cross-covariance functions are fitted by a linear model of coregionalization. It relies oil the turning bands method, which performs three-dimensional Simulation via a series of one-dimensional simulations along lines that span R-3. There is no restriction on the number of random fields to simulate, on the number of basic structures used in the coregionalization model, and on the number and configuration of the locations where simulation has to be performed. Additionally, the realizations can be made conditional to data, back-transformed and averaged over a block support. TBCOSIM uses parallel simulation algorithms: at each location, the random fields are simulated simultaneously and a single co-kriging is needed for conditioning all the realizations. The capabilities of the program are illustrated with the analysis of a set of non-conditional realizations and with an application to a soil contamination dataset.