Mathematical modeling to reconstruct Elastic and geoelectrical parameters

Abstract

The monitoring of the underground medium requires estimation of accuracy of the methods used. Numerical simulation of the solution of 2D inverse problem on the reconstruction of seismic and electrical parameters of local (comparable in size with the wavelength) inhomogeneities by the diffraction tomography method based upon the first order Born approximation is considered. The direct problems for the Lame and Maxwell equations are solved by the finite difference method that allows us to take correctly into account the diffraction phenomenon produced by the target inhomogeneities with simple and complex geometry. For reconstruction of the local inhomogeneities the algebraic methods and the optimizing procedures are used. The investigation includes a parametric representation of inhomogeneities by the simple and complex functions. The results of estimation of the accuracy of the reconstruction of elastic inhomogeneities and inhomogeneities of electrical conductivity by the diffraction tomography method are represented.

Keywords

• diffraction tomography
• mathematical modeling
• seismic tomography
• electromagnetic tomography