A Simulation Method for Stationary Gaussian Random Functions Based on the Sampling Theorem
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A unified method is developed for simulating realizations of real-valued stationary Gaussian processes, vector processes, fields, and vector fields. The method has direct applications to earthquake engineering. Realizations of Gaussian processes and vector processes can be used to model seismic ground accelerations at single and multiple sites. Gaussian random fields can provide representations of the spatial variation of soil properties that need to be considered in earthquake engineering when dealing with systems extending over large areas such as pipeline systems. The proposed method involves parametric random models consisting of superpositions of deterministic functions of time or space with random fields. The proposed simulation method is efficient and uses algorithms for generating realizations of random processes and fields that are similar to simulation techniques based on ARMA models. Several examples are presented to demonstrate the proposed simulation method and evaluate its efficiency and accuracy.