Increased interest in realistic modeling of natural phenomena leads naturally to their description as random processes in space and time. Methods of generating realizations of multi-dimensional random processes, specifically the Fast Fourier Transform, Turning Bands, and Moving Average algorithms, are critically evaluated and means of improving accuracy and computational efficiency are suggested. As an alternative and complement to these methods, a technique called Local Average Subdivision (LAS) is introduced which producesrealizations of locally averaged random processesin one, two, or three dimensions. The main advantage of the LAS method is that it can be easily conditioned on known data and that changes in resolution of the field are properly represented statistically.

The LAS method is employed in a simulation-based study of the statistics of excursions and extrema of two-dimensional Gauss-Markov processes. Empirical relationships for the average number of isolated excursions and their areas are presented and compared with existing theories. A measure related to the degree of clustering of the excursionsis also proposed. Some common extreme value cumulative distribution functions are compared to the simulation-based distributions.

Best linear estimation techniques in the frequency domain are incorporated in a new approach to the simulation of optionally conditioned stationary or non-stationary space-time processes and applied to earthquake ground motion simulation. This method is used along with the Local Average Subdivision algorithmin a liquefaction risk case study where the soil is modeled as a three-dimensional stochastic medium and input ground motions come from a space-time random field. The liquefaction analysis is performed by a non-linear multiphase finite element model for which the LAS realizations are ideally suited as they give random properties representing the average over each element.