Numerical solution to the inverse problem for a system of elasticity for vertically inhomogeneous medium
The article is devoted to studying a multidimensional inverse problem of seismics for the system of elasticity theory with a source given by the function \(\pi\nabla_{x,y,z}\delta(x,y,z-z_*)f(t)\), where \(f(t) = \rho Ae^{-bt}\cos(\omega_0t + \psi)\). In the framework of the theory of explosion, the source can be interpreted as the center of compression. Here \(\rho\) is the density of the medium in which the explosion takes place, \(A\), \(b\), \(\omega_0\), \(\psi\) are the values characterizing the explosion, \(z_*\) is the coordinate (depth) of the explosion (\(z_* \neq 0\)). It is assumed that the medium has \(n\)-layered structure and each layer is characterized by the longitudinal velocity \(v_{\rho}\) and the transverse velocity \(v_s\). The author finds the longitudinal velocity \(v_{\rho}\) and the transverse velocity \(v_s\) in each layer when longitudinal and transverse displacements are known on the surface.NEWLINENEWLINE The author first solves the direct problem and then formulates and studies numerically the inverse problem using the additional informational obtained with help of the solution to the direct problem. The results of reconstructing the velocities of the medium for Western Siberia are presented. It is shown that satisfactory reconstruction is possible if the inverse problem data have error about 5-40 percents.
scientific article; zbMATH DE number 1622426