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.
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Literature Cited
A. S. Blagoveshchenskii, “Some inverse boundary value problems for hyperbolic equations,” in: Proceedings of the International Congress of Mathematicians, Moscow (1966).
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).
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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).
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© 1971 Consultants Bureau, New York
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Blagoveshchenskii, A.S. (1971). The Inverse Problem for the Wave Equation with an Unknown Source. In: Birman, M.S. (eds) Spectral Theory and Wave Processes. Topics in Mathematical Physics, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8926-2_3
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DOI: https://doi.org/10.1007/978-1-4684-8926-2_3
Publisher Name: Springer, Boston, MA
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