Diffraction of Rayleigh wave by simple surface irregularity using boundary element method

The topographic amplification effect is studied in this paper in the case of a semi-circular canyon under incident Rayleigh wave. Time-frequency domain boundary element method has been applied to investigate the wave diffraction phenomena. The model consists of a semi-circular canyon cut from an isotropic elastic half plane. The total response is decomposed into free field motion and scattered wave field. The former can be constructed analytically by superposing on incident and reflected Rayleigh waves in the half plane and the later by using boundary element method with linear elements. The analyses are performed in the frequency domain and then converted into time domain using fast Fourier transform (FFT) algorithm. It is shown that the weak and strong singularities in the governing integral equations for linear elements can be removed by analytical approaches. Different ranges of Rayleigh wavelengths from low to high are considered. The results are presented versus dimensionless frequency and distance. A limiting value for Rayleigh wavelength can be recognized beyond which the canyon has no important effects on scattering of harmonic incident waves. Furthermore, a parametric study has been performed for different values of Poisson's ratios. The published works in the effects of this parameter are somewhat few and limited to specific values of Poisson's ratio. Finally, the spatial variations of surface displacements for the Rayleigh wave impulse of Ricker wavelet type are obtained. The spatial distribution shows the generation of backward-scattered Rayleigh wave which its intensity depends on predominant frequency of the input impulse as well as Poisson's ratio of the medium. Dynamic responses of the points just located at the edges of the semi-circular canyon are compared to each other which accounts for the isolation efficiency of the canyon. (paper)