Random wave propagation in a viscoelastic layered half space

An extremely efficient and accurate solution method is presented for the propagation of stationary random waves in a viscoelastic, transversely isotropic and stratified half space. The efficiency and accuracy are obtained by using the pseudo excitation method (PEM) with the precise integration method (PIM). The solid is multi-layered and located above a semiinfinite space. The excitation sources form a random field which is stationary in the time domain. PEM is used to transform the random wave equation into deterministic equations. In the frequency-wavenumber domain, these equations are ordinary differential equations which can be solved precisely by using PIM. The power spectral densities (PSDs) and the variances of the ground responses can then be computed. The paper presents the full theory and gives results for instructive examples. The comparison between the analytical solutions and the numerical results confirms that the algorithm presented in this paper has exceptionally high precision. In addition, the numerical results presented show that: surface waves are very important for the wave propagation problem discussed; the ground displacement PSDs and variances are significant over bigger regions in the spatial domain when surface waves exist; and as the depth of the source increases the ground displacement PSDs decrease and the regions over which they have significant effect become progressively more restricted to low frequencies while becoming more widely distributed in the spatial domain.