Pol D. Spanos Simulation of Homogeneous Two- Dimensional Random Fields: Part 11-MA and ARMA Models

Alternatively to the autoregressive (AR) models examined in Introduction In the first part of this series, an autoregressive (AR) linear system is introduced for the accurate representation of random fields with a given (target) power spectrum. It is demonstrated in that part that this first approximation can be used in a twostage format to derive efficiently reliable autoregressive moving average (ARMA) algorithms for the simulation of a target random field. The purpose of this part of the series is to investigate the applicability of moving average (MA) models for the simulation of random fields. Furthermore, the feasibility of a twostep determination of ARMA simulation algorithms from this prior MA approximation is addressed. For clarity, the present discussion will be restricted to the case of scalar two-dimensional fields. However, the techniques and results can readily be extended to the multidimensional case. Further, as in Part I, it is assumed that the first of the two coordinates is a spatial location while the second one represents time. This convention has no bearing, indeed, on the validity of the results and techniques derived which are also applicable when both dimensions represent space