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.

SUMMARYScattering of elastic waves by two dimensional multilayered dipping sediments of arbitrary shape embedded in an elastic half-space is investigated by using a boundary method. The displacement field is evaluated throughout the elastic media for both steady state and transient incident SH waves. The unknown scattered field is expressed in terms of wave fiinctions which satisfy the equation of motion, traction-free boundary condition and appropriate radiation conditions. The transient response is constructed from the steady state solution by using the fast Fourier transform technique.The numerical results presented demonstrate that scattering of waves by subsurface irregularities may cause locally very large amplification of surface ground motion. The motion can be affected greatly by the scattered surface waves in the sediments. The results clearly indicate that the surface ground motion depends upon a number of parameters present in the problem, such as frequency and the angle of incidence of the incoming wave, impedance contrast between the layers and location of the observation point.

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.

SUMMARYScattering 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 unknown 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.

No abstract