Numerical solution to combined one-dimensional inverse problems for Maxwell's equation and equations of porous media (Q2729319)

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.