Abstract:In the case of two-dimensional elliptic anisotropic medium, an anisotropic wave equation can be decomposed into a SH wave equation and a P-SV wave equation system. Common-shot SH wave records in two-dimensional elliptic anisotropic medium may be modelled by using the finite difference method which differentiates through convolution. Whether the modeling is successful or not depends on boundary condition treatment in solving SH wave equation. Given in the paper are absorption formulae of inner boundary and boundary end points, various common shot records and wave field snapshots in isotropic and elliptic anisotropic media, some showing SH wave field property in elliptic anisotropic medium. From these figures we can see the following points: (1)time-distance curve of reflected SH wave is not hyperbolic, (2)reflected and transmitted waves at an interface in anisotropic medium still satisfy Snell's law, and(3)SH waves in anisotropic medium and isotropic medium have homologous wave modes but their corresponding waves in the two different media are different in travel time, velocity, event shape and energy distribution.