Mathematical Modeling of Wave Fields in Media with Curvilinear Boundaries

摘要

The choice of tests, which allow us to control the accuracy of the algorithms used in modeling, plays a crucial role in the modeling of wave fields, in particular, geophysical fields. At present, there are very few exact solutions to this problem, especially for multidimensional media. In the limited cases in which an exact solution to the problem is known, it usually appears in a cumbersome form consisting of a series, each term of which is presented in integral form. In the present work, an analytical method is suggested for calculating wave fields in media with arbitrary curvilinear boundaries. This problem acquires special importance, for example, in petroleum seismic prospecting. The analytical form of the suggested method is characterized by relative simplicity. The solution to this problem is based on the introduction of a complex generalized thickness of the layer. This renders the presence of diffraction components in the wave field physically clear.