Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized Radon transform

Journal of Mathematical Physics - Tập 26 Số 1 - Trang 99-108 - 1985
Gregory Beylkin1
1Schlumberger–Doll Research, Old Quarry Road, Ridgefield, Connecticut 06877-4108

Tóm tắt

This paper treats the linearized inverse scattering problem for the case of variable background velocity and for an arbitrary configuration of sources and receivers. The linearized inverse scattering problem is formulated in terms of an integral equation in a form which covers wave propagation in fluids with constant and variable densities and in elastic solids. This integral equation is connected with the causal generalized Radon transform (GRT), and an asymptotic expansion of the solution of the integral equation is obtained using an inversion procedure for the GRT. The first term of this asymptotic expansion is interpreted as a migration algorithm. As a result, this paper contains a rigorous derivation of migration as a technique for imaging discontinuities of parameters describing a medium. Also, a partial reconstruction operator is explicitly derived for a limited aperture. When specialized to a constant background velocity and specific source–receiver geometries our results are directly related to some known migration algorithms.

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Tài liệu tham khảo

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Thông tin xuất bản

Journal of Mathematical Physics

Tập 26 Số 1

99-108

Thông tin tác giả