Выпуск: 2 , Том: 4 , Год издания: 2011

This paper presents the Lebedev scheme on staggered grids for the numerical simulation of wave propagation in anisotropic elastic media. Primary attention is given to the approximation of the elastic wave equation by the Lebedev scheme. Based on the differential approach, it is shown that the Lebedev scheme approximates a system of equations, which differs from the original equation. It is proved that the approximated system has a set of 24 characteristics, six of them coincide with those of the elastic wave equation and the rest ones are "artifacts". Requiring the artificial solutions to be equal to zero and the true ones to coincide with those of the elastic wave equation, one comes to the classical definition of the approximation of the initial system on a sufficiently smooth solution. The results obtained and the knowledge of the complete set of characteristics are important for constructing reflectionless boundary conditions during approximation of point sources, etc.