Abstract <p>The paper is devoted to the numerical simulation of the acoustic wave propagation. A two-dimensional problem, typical for the seismic exploration process with the linear profiling is considered. A novel numerical algorithm is developed. It uses the operator splitting method to reduce an original multi-dimensional system of equations to the series of one-dimensional systems. Further, the grid-characteristic method is used to construct solutions of each one-dimensional hyperbolic problems. A distinctive feature of the developed algorithm is an application of a seven-point spatial stencil, which allows us to construct a fifth order one-dimensional scheme. The special multi-step operator splitting method is presented, that preserves an achieved approximation order in the final multi-dimensional scheme. The procedure of constructing consistent boundary and contact condition approximations is presented. Multiple test problems were successfully solved.</p>