Mathematical simulation of wave fields in media with arbitrary curvilinear boundaries

The method of calculation of wave fields in media with curvilinear interfaces is proposed. After integral transformations, the solution in the explicit form is obtained. For solving the problem, we introduce the notion of the generalized thickness of a layer. This value becomes real in the case of a plane boundary and coincides with an “ordinary” thickness of a layer. If the boundary is curvilinear, the generalized thickness of a layer becomes a complex value. The use of the generalized thickness of a layer brings about the fact that conditions on infinity (Sommerfeld's conditions) are automatically fulfilled. The conditions of appearance of loops on the travel-time curves for different boundaries have been elucidated. Some examples of calculations are given.