Transient scattering of elastic waves by dipping layers of arbitrary shape. Part 2: Plane strain model

Abstract

SUMMARYScattering of elastic waves by dipping layers of arbitrary shape embedded within an elastic half-space is investigated for a plane strain model by using a boundary method. Unknown scattered waves are expressed in the frequency domain in terms of wave functions which satisfy the equations of motion and appropriate radiation conditions at infinity. The steady state displacement field is evaluated throughout the elastic medium for different incident waves so that the continuity conditions along the interfaces between the layers and the traction-free conditions along the surface of the half-space are satisfied in the least-squares sense. Transient response is constructed from the steady state one through the Fourier synthesis.The results presented show that scattering of waves by dipping layers may cause locally very large amplification of surface ground motion. This amplification depends upon the type and frequency of the incident wave, impedance contrast between the layers, component of displacement which is being observed, location of the observation station and the geometry of the subsurface irregularity. These results are in agreement with recent experimental observations.

Scattering of plane harmonic SH, SV, P and rayleigh waves by non‐axisymmetric three‐dimensional canyons: A wave function expansion approach

“…This results in a more extensive computation. What makes the computation expensive is the inversion of relatively large matrices in solving the least-squares problem [see equation (8)]. In general, the following criterion has been used to establish the convergence of the results: as the number of expansion terms and collocation points increases, the results are accepted as the final ones if the maximum difference between two successive calculations of the surface displacement field is sufficiently small (less than 4 per cent).…”