Anisotropy is widespread in the Earth's interior. However, there is a number of models where anisotropic formations comprise as few as 10-20┬а% of the volume, and this includes fractured reservoirs, thin-layered packs, etc. while the major part of the medium is isotropic. In this situation, the use of computationally intense anisotropy-oriented approaches throughout the computational domain is prodigal. So this paper presents an original advanced finite-difference algorithm based on the domain decomposition technique with individual scheme used inside subdomains. It means that the standard staggered grid scheme or the Virieux scheme is used in the main part of the model which is isotropic, while the anisotropy-oriented Lebedev scheme is utilized inside domains with anisotropic formations. Finite-difference consistency conditions at the artificial interface where the schemes are coupled are designed to make the artificial reflections as low as possible, namely, for the second-order scheme, the third order of convergence of the reflection coefficients is proved
