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

Scattering of elastic waves by three‐dimensional canyons embedded within an elastic half‐space is investigated by using a wave function expansion technique. The geometry of the canyon is assumed to be non‐axisymmetric. The canyon is subjected to incident plane Rayleigh waves and oblique incident SH, SV and P waves. The unknown scattered wavefield is expressed in terms of spherical wave functions which satisfy the equations of motion and radiation conditions at infinity, but they do not satisfy stress‐free boundary conditions at the half‐space surface. The boundary conditions are imposed locally in the least‐squares sense at several points on the surface of the canyon and the half‐space. Through a comparative study the validity and limitations of two‐dimensional approximations (antiplane strain and plane strain models) have been examined. It is shown that scattering of waves by three‐dimensional canyons may cause substantial change in the surface displacement patterns in comparison to the two‐dimensional models. These results emphasize the need for three‐dimensional modelling of realistic problems of interest in strong ground motion seismology and earthquake engineering.