Transient scattering of elastic waves by three dimensional non‐axisymmetric dipping layers

Scattering of elastic plane waves by three dimensional non‐axisymmetric multiple dipping layers embedded in an elastic half‐space is investigated by using a boundary method. The dipping layer is subjected to incident Rayleigh waves and oblique incident SH, SV and P waves. For the steady state problem, spherical wave functions are used to express the unkown scattered field. These functions satisfy the equation of motion and radiation conditions at infinity but they do not satisfy the stress free boundary conditions on the surface of the half‐space. The boundary and continuity conditions are imposed locally in the least‐square sense at points on the layer interfaces and on the surface of the half‐space. The transient response is constructed from the steady state solution by using Fourier synthesis. Numerical results are presented for both steady state and transient problems. Steady state problems include solutions for two non‐axisymmetric dipping layers in the form of a prolate. Transient responses are presented for one and two dipping layer models subjected to incident wave signals in the shape of a Ricker wavelet. It is shown that change in azimuthal orientation of the incident wave may significantly change the surface response of the dipping layer. For the transient problem, response comparison of one and two dipping layers indicates that the addition of an extra layer may also completely change the response characteristics of the alluvium. In particular, the delay in arrival of much larger amplitude surface waves by two dipping layers in comparison with other geometrically compatible models demonstrates the importance of the detailed three dimensional modelling of layered irregularities.