Институт вычислительной математики
и математической геофизики

Abstracts

Numerical solution of differential and integral equations

The most appropriate description of the field continuation process from an observation surface inside a medium under investigation and back in time to solve the inverse problem of reconstruction of field sources (the medium’s inhomogeneities that play the role of secondary sources) can be obtained on the basis of the Green identity in which the fundamental solution of advanced type is used.

In this paper, the solutions of inverse problems in a spectral (omega – k) space for various configurations of the observation system are presented, namely, for a system with a fixed primary field source, for a system in which the source coincides with the receiver, and for a system with multiple overlaps, in which both the receivers and sources fill the observation surface. Common elements present in these solutions are established, and differences typical for each of them are analyzed.

It should be noted that the solution for the observation system with a fixed source that leads to the integral Radon transform has not been described in the literature up to now.

The work was supported by the Russian Foundation for the Basic Research under Grant 03-05-64081.

Note. Abstracts are published in author's edition

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