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SUMMARYSteady state scattering of incident P, SV, SH and Rayleigh waves by general non-axisymmetric three dimensional dipping layers is investigated by using an indirect boundary integral equation method. Material of the half-space and the layer is assumed to be linear, weakly anelastic, homogeneous and isotropic.Systematic comparisons between three dimensional and two dimensional models demonstrate that the validity of a two dimensional approximation for a given basin shape may be affected strongly by changes in azimuthal angle of incidence, type of incident wave and frequency. The discrepancies of two dimensional modelling appear to be much more pronounced for the case of an incident SH wave. Another important feature of the results is the existence of strong coupling between P/SV and SH modes, which has no correspondence in two dimensional models. Such off-azimuthal mode conversions are particularly strong for an incident SB wave.

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SUMMARYComparison of different quadratures for evaluation of the improper wavenumber integrals which arise in evaluation of the Green functions for a viscoelastic half space and harmonic line loadings is investigated. The model is assumed to be of the plane strain type. Extensive testing of the numerical accuracy for various quadratures is performed. A measure of numerical efficiency of the quadratures is proposed and compared for different integration formulae. It was determined that among the procedures tested the Clenshaw-Curtis quadrature offers the most efficient way of evaluating the wavenumber integrals numerically.

SUMMARYTransient response of three dimensional dipping layers of different shapes subjected to incident P, SV, SH and Rayleigh waves is investigated. The time domain response is constructed from steady state solutions through the Fourier synthesis. An indirect boundary integral equation method is applied to calculate the required steady state solutions. The material of the half-space and the layer is assumed to be linear, weakly inelastic, homogeneous and isotropic.Numerical results show that the maximum amplification of motion is strongly dependent upon the type of incident wave, the shape of the basin and signal frequency. The change in the shape of the valley from hemispherical to semiprolate causes a significant increase in the amplitude of surface waves near the edges; however, the maximum amplification of motion near the centre of the valley decreases. This phenomenon is especially apparent for the case of an incident P wave. In comparison to the corresponding two dimensional responses, the amplitude of motion near the centre of the valley is in general higher for three dimensional models.