Polar and azimuthal geometrical divergences in two-dimensional media with a blockwise constant gradient

The ray method has long been used to solve numerically various problems of mathematical seismics. Many papers were devoted to questions of calculation of geometrical divergence in combined two- and three-dimensional media with curvilinear interfaces. For layered and blockwise gradient media (in this paper, no distinction is made between these media), explicit expressions for ray, eikonal, and geometrical divergence have been widely used in computer realizations of the ray method. For instance, explicit expressions used in the calculation of geometrical divergence for a three-dimensional blockwise linear medium written in a special curvilinear system of coordinates and not yet adapted to the two-dimensional case are also known.

In this paper, the authors present their long experience of work with computational schemes of the ray method for the calculation of geometrical divergence in two-dimensional blockwise linear media.