Inverse scattering as nonlinear tomography

V. P. Palamodov

doi:10.1016/j.wavemoti.2010.05.003

Inverse scattering as nonlinear tomography

V. P. Palamodov^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The reconstruction problem for the acoustic tomography with non-homogeneous background is discussed. We develop a method of beam-like solutions of a Helmholtz equation which is not sensitive to caustics. For small perturbations of the speed the inverse scattering problem is reduced to inversion of a ray integral transform. An explicit formula is given for beam-like solutions in a homogeneous medium.

Original language	English
Pages (from-to)	635-640
Number of pages	6
Journal	Wave Motion
Volume	47
Issue number	8
DOIs	https://doi.org/10.1016/j.wavemoti.2010.05.003
State	Published - Dec 2010

Keywords

Beam-like solution
Debye's method
Geodesic
Helmholtz equation
Plane wave solution

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10.1016/j.wavemoti.2010.05.003

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title = "Inverse scattering as nonlinear tomography",

abstract = "The reconstruction problem for the acoustic tomography with non-homogeneous background is discussed. We develop a method of beam-like solutions of a Helmholtz equation which is not sensitive to caustics. For small perturbations of the speed the inverse scattering problem is reduced to inversion of a ray integral transform. An explicit formula is given for beam-like solutions in a homogeneous medium.",

keywords = "Beam-like solution, Debye's method, Geodesic, Helmholtz equation, Plane wave solution",

author = "Palamodov, {V. P.}",

year = "2010",

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AB - The reconstruction problem for the acoustic tomography with non-homogeneous background is discussed. We develop a method of beam-like solutions of a Helmholtz equation which is not sensitive to caustics. For small perturbations of the speed the inverse scattering problem is reduced to inversion of a ray integral transform. An explicit formula is given for beam-like solutions in a homogeneous medium.

KW - Beam-like solution

KW - Debye's method

KW - Geodesic

KW - Helmholtz equation

KW - Plane wave solution

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VL - 47

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JO - Wave Motion

JF - Wave Motion

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ER -

Inverse scattering as nonlinear tomography

Abstract

Keywords

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