Stochastic Wave Representation of Seismic Ground Motion. II: Simulation

In this paper, the seismic ground motion is simulated as a stochastic wave according to its analytically derived frequency‐wave number spectra. The simulation is performed using an extension of the spectral representation method, which considers that the simulated wave consists of the superposition of a number of plane waves having amplitudes consistent with the frequency‐wave number spectra. On the other hand, the frequency‐wave number spectra provide all the information concerning the correlational characteristics of ground motion. Therefore, the main characteristics of both the coherent component of ground motion (representation by plane waves) and the incoherent component of ground motion (representation by its cross‐correlational characteristics) are described in the simulated wave. At this stage, the model used to obtain analytically the frequency‐wave number spectra is relatively simple, considering the seismic source as a double couple (point source) located in an elastic half‐space. In addition, the model considers the propagation of three‐dimensional waves in the elastic half‐space that are generated at the seismic source and their eventual reflection at the ground surface.