Numerical solution to combined one-dimensional inverse problems for Maxwell's equation and equations of porous media
type: Item
instance of: scholarly article
zbMATH Open document ID: 1051.78515
author: È. V. Goryunov
author: Kholmatzhon Imomnazarov
publication date: 2001-07-22T00:00:00Z
Mathematics Subject Classification ID: 78M25
Mathematics Subject Classification ID: 78A46
Mathematics Subject Classification ID: 78M50
Mathematics Subject Classification ID: 65M32
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65M70
zbMATH DE Number: 1622422
zbMATH Keywords: Maxwell equation
zbMATH Keywords: porous media equations
zbMATH Keywords: inverse problem
zbMATH Keywords: numerical solution
zbMATH Keywords: optimization approach
MaRDI profile type: Publication
title: Numerical solution to combined one-dimensional inverse problems for Maxwell's equation and equations of porous media
published in: Bulletin of the Novosibirsk Computing Center. Series: Mathematical Modeling in Geophysics
review text: In the first part of the article, the authors formulate the inverse problem for determining the conductivity of porous body, liquid, and friction coefficients for the process of propagation of SH-waves in the case of the energy dissipation caused by the friction coefficient in a one-dimensional inhomogeneous medium. The authors find a solution to this combined inverse problem as a minimum point of the so-called misfit functionals. To organize the iterative process for finding the minimum points of the misfit functionals, the authors use a special modification of the conjugate gradients method. The authors present calculation results and supply the results obtained by physical explanations. It is indicated that the allowance for the friction coefficient causes the amplitude decay of the incoming signal (energy dissipation).NEWLINENEWLINE The second part is devoted to numerical determining the conductivity of a porous elastic body, liquid, and second longitudinal wave velocity for the process of propagation of seismic waves. The numerical solution of the inverse problem for the seismic waves equations in conducting porous media is found by the optimization approach using misfit functionals. Representative series of numerical calculations are given for various models of media.
reviewed by: Vladimir N. Grebenev
description: scientific article; zbMATH DE number 1622422