The discovery of oil deposits with complex internal structures requires an improvement of available seismic survey methods. The development of modern high-performance computing systems provides an opportunity to use more sophisticated mathematical models. This paper aims to investigate seismic wave propagation in porous fluid-saturated media. The Dorovsky three velocity model was formulated in the two-dimensional case and its numerical solution was obtained with the grid-characteristic method. The computational domain consisted of three layers with different rheology: a water layer, a porous fluid-saturated layer, and an elastic layer. Explicit contact conditions were derived between them and successfully applied with the help of Riemann invariants. The curvature of geological layers was taken into consideration by means of structured hexahedral grids. The time evolution of the spatial distribution of stress tensors and material velocity vectors were calculated and analyzed. These signals contain a mixture of volume, surface, transmitted and reflected waves.