Simulation of one-dimensional correlated fields using a matrix-factorization moving average approach

The simulation of one-dimensional stationary correlated fields is of increasing importance in the earth sciences. A new method for repeated generation of independent realizations, which are long and dense relative to the correlation scale of the underlying stochastic process, is examined here. This method is conceptually simple and easy to apply. It consists of a matrix-factorization technique for derivation of moving average coefficients which are used as weights in the construction of successive observations from linear combinations of random normal deviates. The matrix-factorization procedure is fast and need be performed only once for a given correlation function and density of observations. This technique can be used to generate evenly spaced observations in time or a single space dimension for any prescribed correlation function and marginal distribution which is Gaussian with arbitrary mean and variance. Tests of ensemble properties of generation procedures have been developed and results for this method compared with those for a popular generation technique. For correlation functions and generation conditions examined, the matrix-factorization moving average approach more accurately produces ensemble characteristics of the prescribed underlying process. For repeated generation of 2001 observations spaced evenly over realizations with length equal to 100 times the correlation scale, the moving average approach requires only about one fifth the CPU time used by the Shinozuka and Jan method to obtain similar accuracy.