The SIM2D Procedure

Introduction

There are a number of approaches to simulating spatial random fields or, more generally, simulating sets of dependent random variables. These include sequential indicator methods, turning bands, and the Karhunen-Loeve expansion. See Christakos (1992, Chapter 8) and Deutsch and Journel (1992, Chapter V) for details.

A particularly simple method available for Gaussian spatial random fields is the LU decomposition method. This method is computationally efficient. For a given covariance matrix, the $\mr{LU}=\mb{LL}’$ decomposition is computed once, and the simulation proceeds by repeatedly generating a vector of independent $N(0,1)$ random variables and multiplying by the $\mb{L}$ matrix.

One problem with this technique is memory requirements; memory is required to hold the full data and grid covariance matrix in core. While this is especially limiting in the three-dimensional case, you can use PROC SIM2D, which handles only two-dimensional data, for moderately sized simulation problems.