Finite Difference Analysis of Rayleigh Wave Scattering at Vertical Discontinuities

The finite difference iterative method yields the full wave solution to problems without exact solution that involve the scattering of elastic surface waves at vertical discontinuities in homogeneous media. The technique successfully predicts the results for a problem for which an analytical solution does exist, that of a Rayleigh wavelet propagating on a homogeneous, isotropic, semi-infinite half space. For a Rayleigh wave of unit amplitude incident normally at a 90° corner in a homogeneous medium of Poisson's ratio σ = 0.245, the amplitude coefficients for transmission and reflection were found to be 0.64 ± 0.02 and 0.36 ± 0.02, respectively, whereas the corresponding phase shifts were −79 ± 5° and 38 ± 5°. About 45% of the incident energy is converted into body waves at the corner, and more than 90% of this energy is radiated back into a sector of the plane included between lines making angles of 15° with the two free surfaces. All these results, which are independent of wavelength, agree well with other published data. In the related problem of Rayleigh wave scattering at a downward step discontinuity, the dependence on step height of the transmission and reflection coefficients and of the phase shifts for a given wavelength component has also been investigated. Results show good agreement with both experimental curves and earlier theoretical work. This type of numerical simulation may be applied to other two-dimensional geometries, including layered media problems.