Abstract
An effective method of the elastic modeling for thin-layered media is presented. The solution of the elasticity system is obtained in the spectral domain and after that the synthetic seismograms are built. In order to solve the elasticity system in the spectral domain we reduce the system to matrix differential Riccati equation (MDRE). The MDRE has the analytic solution in each layer that does not give accumulation of errors and provides fast calculation. This algorithm is general and differs from previous analogues. It can be used efficiently both in mathematical modeling and for the solution of an inverse problem for the elasticity medium parameters reconstruction.
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