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Direct and inverse problems of wave propagation through a one-dimensional inhomogeneous medium

Published online by Cambridge University Press:  01 February 1999

A. S. ALEKSEEV  and
V. S. BELONOSOV
A. S. ALEKSEEV
Affiliation:
Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk 630090, Russia
V. S. BELONOSOV
Affiliation:
Sobolev Institute of Mathematics, Novosibirsk 630090, Russia
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Abstract

This paper deals with a wave process induced by an acoustic impulse in a vertically inhomogeneous half-space. The solvability of the corresponding direct initial boundary value problem is proved. We also consider a class of one-dimensional inverse problems including, in particular, the classical inverse problem of the scattering theory, the transmission and reflection problems of seismology, etc. It is shown that all these inverse problems are equivalent in a certain sense, and therefore can be solved by identical methods. Theoretical results are illustrated by numerical examples.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 10 , Issue 1 , February 1999 , pp. 79 - 96
Copyright
1999 Cambridge University Press

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Footnotes

This work has received financial support from the Russian Fundamental Research Foundation, Grant Nos. 97-01-00508, 96-05-66058, 96-15-98542.