In this paper, the coefficient inverse problem for the elasticity system for horizontally stratified media is considered. The different numerical experiments for solving this problem are presented. The numerical experiments with the residual functional allow us to formulate the minimization strategy for solving the inverse problem in the frequency domain. The pressure and shear velocities in the member of thin layers are numerically reconstructed by means of this strategy.
IntroductionAt present there are many theoretical works devoted to one-dimensional and multidimensional inverse problems for the elasticity system, for example, [1][2][3][4][5]. We refer the reader to the theoretical results in these works and the references therein: the existence, uniqueness and conditional stability for solutions of inverse problems for the elasticity system were proved. These works are known to use combined sources together, such as combinations of the vertical impact together with an instantaneous centre of rotation [1], slopping impacts [2-4] and directed explosion [5]. This choice of sources makes it possible to decompose the elasticity system and hence the original inverse problems may be reduced to a sequence of simple inverse problems for scalar hyperbolic equations. Numerical solutions of inverse problems for scalar equations are well investigated.The reconstruction inverse problem of the medium parameters with sources which can excite different types of waves in the medium is considered in applied geophysics now. Multiwave methods in geophysics were first proposed in Russia [6-12] and now have world wide application, for example, [13][14][15][16][17]. Many papers on multiwave methods are reported in the EAGE Conference and Exhibition, for example, [18][19][20] and others.A usual source in seismic practice is explosion. This source is described mathematically as the centre of compression. This mathematical model for the source gives no decomposition