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Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media

Part of: Inverse problems Geophysics Nonlinear integral equations Integral equations, integral transforms Miscellaneous topics - Partial differential equations Volterra integral equations Geophysics (general) General mathematical topics and methods in quantum theory Scattering theory

Published online by Cambridge University Press:  21 July 2016

Jie Yao ,
Anne-Cécile Lesage ,
Fazle Hussain  and
Donald J. Kouri
Jie Yao*
Affiliation:
Department of Mechanical Engineering, Physics, Mathematics, University of Houston, Houston, Texas 77204, USA
Anne-Cécile Lesage*
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, Texas 79409, USA
Fazle Hussain*
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, Texas 79409, USA
Donald J. Kouri*
Affiliation:
Department of Mechanical Engineering, Physics, Mathematics, University of Houston, Houston, Texas 77204, USA
*
*Corresponding author. Email addresses:yjie2@uh.edu (J. Yao), anne-cecile.lesage@ttu.edu (A.-C. Lesage), fazle.hussain@ttu.edu (F. Hussain), kouri@central.uh.edu (D. Kouri)
*Corresponding author. Email addresses:yjie2@uh.edu (J. Yao), anne-cecile.lesage@ttu.edu (A.-C. Lesage), fazle.hussain@ttu.edu (F. Hussain), kouri@central.uh.edu (D. Kouri)
*Corresponding author. Email addresses:yjie2@uh.edu (J. Yao), anne-cecile.lesage@ttu.edu (A.-C. Lesage), fazle.hussain@ttu.edu (F. Hussain), kouri@central.uh.edu (D. Kouri)
*Corresponding author. Email addresses:yjie2@uh.edu (J. Yao), anne-cecile.lesage@ttu.edu (A.-C. Lesage), fazle.hussain@ttu.edu (F. Hussain), kouri@central.uh.edu (D. Kouri)
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Abstract

We extend the full wavefield modeling with forward scattering theory and Volterra Renormalization to a vertically varying two-parameter (velocity and density) acoustic medium. The forward scattering series, derived by applying Born-Neumann iterative procedure to the Lippmann-Schwinger equation (LSE), is a well known tool for modeling and imaging. However, it has limited convergence properties depending on the strength of contrast between the actual and reference medium or the angle of incidence of a plane wave component. Here, we introduce the Volterra renormalization technique to the LSE. The renormalized LSE and related Neumann series are absolutely convergent for any strength of perturbation and any incidence angle. The renormalized LSE can further be separated into two sub-Volterra type integral equations, which are then solved noniteratively. We apply the approach to velocity-only, density-only, and both velocity and density perturbations. We demonstrate that this Volterra Renormalization modeling is a promising and efficient method. In addition, it can also provide insight for developing a scattering theory-based direct inversion method.

Keywords

Acoustic modelingscattering theoryVolterra renormalizationvelocity and density variation

MSC classification

Secondary: 35R30: Inverse problems 45D05: Volterra integral equations 45G10: Other nonlinear integral equations 45Q05: Inverse problems 65R20: Integral equations 81Q15: Perturbation theories for operators and differential equations 81U40: Inverse scattering problems 86A15: Seismology
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 2 , August 2016 , pp. 353 - 373
Copyright
Copyright © Global-Science Press 2016 

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