MOVING AVERAGES FOR GAUSSIAN SIMULATION IN 2 AND 3 DIMENSIONS

The square-root method provides a simple and computationally inexpensi ve way to generate multidimensional Gaussian random fields. It is appl ied by factoring the multidimensional covariance operator analytically , then sampling the factorization at discrete points to compute an arr ay of weighted averages that can be convolved with an array of random normal deviates to generate a correlated random field. In many respect s this is similar to the LU decomposition method and to the one-dimens ional method of moving averages. However it has been assumed that the method of moving averages could not be used in higher dimensions, wher eas direct application of the matrix decomposition approach is too exp ensive to be practical on large grids. In this paper, I show that it i s possible to calculate the square root of many two- and three-dimensi onal covariance operators analytically so that the method of moving av erages can be applied directly to the problem of multidimensional simu lation. A few numerical examples of nonconditional simulation on a 256 x 256 grid that show the simplicity of the method are included. the m ethod is fast and can be applied easily to nested and anisotropic vari ograms.