| Abstract: | A fundamental theory of stationary, homogeneous stochastic waves is developed 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 technique is demonstrated with the aid of a numerical example in which a sample of a stationary, homogeneous, two-dimensional, dispersive Rayleigh wave consistent, in its analytical form of spatial variability, with Lotung, Taiwan dense-array data is digitally generated. Although the stochastic wave model considered in this work is stationary and homogeneous, it is a straightforward task to extend the methodology introduced to nonstationary and / or non-homogeneous stochastic waves characterized by an evolutionary power spectrum. |
