Volume 20, Issue 2
Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media

Jie Yao, Anne-Cécile Lesage, Fazle Hussain & Donald J. Kouri

Commun. Comput. Phys., 20 (2016), pp. 353-373.

Published online: 2018-04

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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 non-iteratively. 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.

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@Article{CiCP-20-353, author = {Jie Yao , and Anne-Cécile Lesage , and Fazle Hussain , and Donald J. Kouri , }, title = {Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {2}, pages = {353--373}, 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 non-iteratively. 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.050515.210116a}, url = {http://global-sci.org/intro/article_detail/cicp/11156.html} }
TY - JOUR T1 - Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media AU - Jie Yao , AU - Anne-Cécile Lesage , AU - Fazle Hussain , AU - Donald J. Kouri , JO - Communications in Computational Physics VL - 2 SP - 353 EP - 373 PY - 2018 DA - 2018/04 SN - 20 DO - http://doi.org/10.4208/cicp.050515.210116a UR - https://global-sci.org/intro/article_detail/cicp/11156.html KW - AB -

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 non-iteratively. 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.

Jie Yao, Anne-Cécile Lesage, Fazle Hussain & Donald J. Kouri. (2020). Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media. Communications in Computational Physics. 20 (2). 353-373. doi:10.4208/cicp.050515.210116a
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