Two algorithms for the numerical modeling of the elastic wave propagation in non-homogeneous anisotropic media are proposed. A common feature of both algorithms is the reduction of the 3D problem of elastic wave propagation to a series of 1D problems, by means of the finite integral Fourier transform with respect to the horizontal coordinate x and y.

Algorithm I is based on the explicit finite difference method with the second order approximation with respect to time and with the fourth order approximation with respect to the spatial variable. Algorithm II is based on employing the Laguerre transformation with respect to the time coordinate and the finite difference approximation with respect to the spatial variable z.

Both the proposed algorithms can be effectively implemented on massively-parallel computer architectures.