Three-dimensional grid-characteristic schemes of high order of approximation

This paper examines seismic wave propagation in a full three-dimensional case. In practice, the stress-strain state of a geological medium during seismic exploration is frequently described using acoustic and linear elastic models. The governing systems of partial differential equations of both models are linear hyperbolic. A computational algorithm for them can be constructed by applying a grid-characteristic approach. In the case of multidimensional problems, an important role is played by dimensional splitting. However, the final three-dimensional scheme fails to preserve the achieved high order even in the case of extended spatial stencils used to solve the resulting one-dimensional problems. In this paper, we propose an approach based on multistage operator splitting schemes, which made it possible to construct a three-dimensional grid-characteristic scheme of the third order. Several test problems are solved numerically.