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

In seismic numerical modelling, it is readily to simulate the wave field of the cavities with simple and regular geometric boundaries. however, the real cavities are always complex or irregular, such as general quadrilateral or horny 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, we transform the original cavity model in the physical domain into a certain simple regular model in the computational domain and, accordingly, transform the boundary condition in the physical domain into that in the computational domain. then, the wave field on the boundary in the computational domain is calculated. finally, we generate the wave field on the boundary in the physical domain by using the inverse conformal mapping, when the conformal mapping function is invertible. two experiments by adopting either a displacement boundary condition or a stress boundary condition illustrate that the wave fields for the three different kinds of cavities mainly concentrate on the boundary of the corresponding cavity.