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.
Highlights
Diffraction tomography is an imaging technique that makes use of a large volume of input data to produce the image of underground medium parameters with high spatial resolution
In contrast to ray tomography, for which the resolution is connected with the Fresnel zone and the large number of the source-receiver pairs is required, diffraction tomography
In our study (a complete review of development of the diffraction tomography is introduced in (Devaney and Zhang, 1991)) most attention is given to an estimation of the accuracy of multiparametric reconstruction of elastic parameters and reconstruction of an electrical conductivity with the use of sounding by elastic wave and electromagnetic wave correspondingly
Summary
1984; Devaney and Zhang, 1991; Zhou et al, 1993; Ryzhikov and Troyan, 1994; Alumbaugh and Morrison, 1995; Kiselev and Troyan, 1997) provides information on the medium parameters with subwavelength resolution. Beylkin and Burridge (1990) describe the multiparametric inversion in the time domain in the cases of acoustic and elasticity on the basis of the generalized Radon transform. This approach requires a large number of the sourcereceiver pairs. The multiparametric reconstruction makes use of amplitude information connected to the scattering characteristic (Wu and Aki, 1985; Beylkin and Burridge, 1990) of the elementary disturbances of the reconstructed parameters. Under tomography experiment, these scattering characteristics should be taken into account by the use of the relevant observation schemes. Scattering by the elementary disturbances of the parameters can be described with the use of tomography functionals (Ryzhikov and Troyan, 1994; Troyan and Ryzhikov, 1994), which in a form of the ray series are represented for elastic and electromagnetic cases
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