Simulation of Seismic Ground Motion Using Stochastic Waves

Abstract

A fundamental theory of evolutionary stochastic waves is developed based on Priestley's evolutionary power‐spectrum theory and a technique for digitally generating samples of such waves is introduced as a further extension of the spectral representation method. This is done primarily for the purpose of developing an analytical model for propagating seismic waves that can account for their stochastic characteristics in the time and space domain. From this model, the corresponding‐sample seismic waves can be digitally generated with great computational efficiency. The efficacy of this new technique is demonstrated with the aid of a numerical example in which a sample of a nondispersive Rayleigh wave is digitally generated. This wave is idealized as a nonstationary stochastic wave with two‐dimensional spatial nonhomogeneity consistent with Lotung, Taiwan densearray data. The proposed model is useful for the seismic‐response analysis of such large‐scale structures extending over a wide spatial area such as water‐transmission and gas‐distribution systems and long‐span bridges.