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A Uniqueness Theorem for a Lossy Inverse Problem in Reflection Seismology

Bruce J. Chaderjian
SIAM Journal on Applied Mathematics
Vol. 54, No. 5 (Oct., 1994), pp. 1224-1249
Stable URL: http://www.jstor.org/stable/2102466
Page Count: 26
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A Uniqueness Theorem for a Lossy Inverse Problem in Reflection Seismology
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Abstract

A nonlinear inverse problem is studied for recovering a stratified acoustic medium with attenuation (loss) from the medium's response to a point-source input introduced into the pressure field at the medium's surface. The primary focus is on applications in reflection seismology and oil exploration, where the medium is a model of the subsurface of the earth. The point-source response is the vertical component of the particle velocity at the earth's surface. It is shown that in the appropriate function spaces, if the wave speed is fixed, at most one pair of functions for density and attenuation, together with the fixed wave speed, could have produced the observed point-source response. This uniqueness result is based on a contraction mapping fixed-point argument in which the functional operator is derived from an analysis of two plane wave components of solutions to the model equations. The result is established in the time domain. This work also has direct application to some lossy inverse problems in electromagnetics.

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