Modeling of wavefields by the modification to the matrix method in anisotropic media

• Methods of mathematical modeling of displacement field of anisotropic medium are developed.
• Two direct problems about determining the displacement field are solved.
• Modification to the matrix method is developed.
• The source of seismic waves is presented by a randomly oriented force and seismic moment tensor.

The modification to the matrix method of construction of wavefield on the free surface of an anisotropic medium is presented. The earthquake source represented by a randomly oriented force or a seismic moment tensor is placed on an arbitrary boundary of a layered anisotropic medium. It is shown that for anisotropic layered medium the matrix propagator can be represented by a “wave propagator” in each layer. The matrix propagator acts on the free surface of the layered medium and generates stress-displacement vector at depth z. The displacement field on the free surface of an anisotropic medium is obtained from the received system of equations considering the radiation condition and that the free surface is stressless. The described theory is the first step of determining of the earthquake parameters. The approbation of the modification to the matrix method for anisotropic media with TI symmetry is done. A comparative analysis of our results with the synthetic seismic records obtained by other methods is shown.