Modification to the matrix method for the direct and inverse problems of
seismology

Anastasiia Pavlova
Page No. 1-10

The modification of 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.
The theory of the matrix propagator in a homogeneous anisotropic medium by introducing a "wave
propagator" is presented. It is shown that for anisotropic layered medium the matrix propagator
can be represented by a "wave propagator" in each layer. The matrix propagator P(z,z0=0) 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
approbation of the modification of the matrix method for isotropic and anisotropic media with TI
symmetry is done. A comparative analysis of our results with the synthetic seismic records
obtained by other methods and published in foreign papers is executed.
Keywords: matrix method, seismic tensor, synthetic seismograms