Scattering of plane P- and SV-waves by periodic topography: Modeled by a PIBEM

Abstract

For model of periodic topography subjected to plane waves, the wave fields have feature of repeating themselves with a certain shift of phase in the frequency domain. By fully exploring this particular feature, a periodic indirect boundary element method (PIBEM) is proposed to study the scattering of plane P- and SV-waves by periodic topography. The discretization effort of the PIBEM is reduced to a single topography using Green's functions of equivalent distributed loads acting on an inclined line as fundamental solutions. Compared to the traditional way of choosing a certain number of topographies to solve the problem with boundary conditions of other topographies being relaxed, the new method has the merits of higher precision and lower memory requirement. By taking periodic hill and canyon as examples, parametric studies are conducted to investigate the complex effects due to the periodic irregularity. Numerical results show that responses of periodic topography are quite different from those of a single and multiple topographies, demonstrating that it is very difficult to obtain the accurate results by choosing a certain number of topographies. In addition, periodic canyon has a stronger shielding effect on P-waves, while periodic hill has a stronger shielding effect on SV-waves.