Spectral Theory and Wave Processes pp 23-33 | Cite as

# The Inverse Problem for the Wave Equation with an Unknown Source

Chapter

## Abstract

In this paper† we consider the problem of deducing the properties of a medium from data on the behavior of the wave field at the boundary of the medium. Such problems commonly arise in seismology. As a rule, difficulties of an experimental nature make it impossible to assume that the form of the signal sent out by the wave source (for example, an explosion or an earthquake) is completely known. Therefore, in formulating the problem we will assume that only certain properties of the function describing the source are known. The problem considered below is a model from the point of view of seismology.

## Keywords

Integral Equation Inverse Problem Wave Equation Direct Problem Consultant Bureau## Preview

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## Literature Cited

- 1.A. S. Blagoveshchenskii, “Some inverse boundary value problems for hyperbolic equations,” in: Proceedings of the International Congress of Mathematicians, Moscow (1966).Google Scholar
- 2.A. S. Blagoveshchenskii, “Some inverse problems in the theory of wave propagation,” in Reports from the IV All-Union Symposium on the Diffraction and Propagation of Waves, Kharkov (1967).Google Scholar
- 3.M. Riesz, “L’intégrale de Riemann-Liouville et le problême de Cauchy,” Acta. Math., 81: 1–223 (1949).MathSciNetMATHCrossRefGoogle Scholar
- 4.L M. Gel’fand and G. E. Shilov, Generalized Functions, Fizmatgiz, Moscow (1958).Google Scholar
- 5.A. S. Blagoveshchenskii, “On the inverse problem in the theory of propagation of seismic waves,” in: Topics in Mathematical Physics, Vol. 1, Consultants Bureau, New York (1967).Google Scholar

## Copyright information

© Consultants Bureau, New York 1971