Efficient Simulation of Multidimensional Random Fields

Abstract

An efficient stochastic simulation method is presented for generating sample time histories of multidimensional, spatially correlated, stationary Gaussian random fields. A key feature of the method is the use of filtering functions in directly expressing the conditional mean value of any component of the random field. The general formulation and an updating algorithm for determining the required filtering functions for simulation of any general multidimensional random field are established. Also, emphasis is placed on the efficiencies, which can be achieved when relatively simple restrictions are placed on the cross-spectral densities and the incoherence structure of the random field. These restrictions, which are commonly used in modeling seismic ground motion, are shown to allow the computational effort to be reduced by a factor of more than 100 for a three-dimensional random field. Numerical results are presented to illustrate the application of the direct simulation method to the generation of time histories of seismic ground motion. The method is shown to be both efficient and accurate.