Application of conformal mapping to the scattering of plane SH-waves by a cavity

Abstract

In seismic numericalmodelling, it is readilyto simulate the wave field of the cavities with simpleandregular geometric boundaries. However, the real cavities are always complex or irregular, such asgeneral quadrilateral orhorny model. In this paper, conformal mapping is applied to three representative cavity models, including a pentagon model, a generalized quadrangular model and a horny model. First of all, transform the original cavity modelinthephysical domain into certain simple regularmodelin the computational domain and accordingly transform the boundary condition inthephysical domain into that in the computational domain. Thencalculate the wave field on the boundary in the computational domain. Finally, we generate the wave field on the boundary in the physical domain by usingthe inverse conformal mapping,when the conformal mappingfunctionis invertible. Twoexperiments by adoptingeither a displacement boundarycondition or a stress boundary conditionillustratethat the wave fields for three different kinds of cavitiesmainly concentrate on the boundary of the corresponding cavity.