Numerical solution to the inverse problem for a system of elasticity for vertically inhomogeneous medium
type: Item
instance of: scholarly article
zbMATH Open document ID: 1050.86519
author: A. L. Karchevsky
publication date: 2001-07-22T00:00:00Z
Mathematics Subject Classification ID: 86A15
Mathematics Subject Classification ID: 86A22
Mathematics Subject Classification ID: 74B05
Mathematics Subject Classification ID: 86-08
zbMATH DE Number: 1622426
zbMATH Keywords: inverse problem of seismics
zbMATH Keywords: system of elasticity equations
zbMATH Keywords: numerical solution
zbMATH Keywords: variational method
MaRDI profile type: Publication
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title: Numerical solution to the inverse problem for a system of elasticity for vertically inhomogeneous medium
published in: Bulletin of the Novosibirsk Computing Center. Series: Mathematical Modeling in Geophysics
review text: 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.
reviewed by: Vladimir N. Grebenev
description: scientific article; zbMATH DE number 1622426