Forward Scattering and Volterra Renormalization for Acoustic Wavefield Propagation in Vertically Varying Media (Communications in Computational Physics, 2018)
We extend the full wavefield modeling with forward scattering theory andVolterra Renormalization to a vertically varying two-parameter (velocity and density)acoustic medium. The forward scattering series, derived by applying Born-Neumanniterative procedure to the Lippmann-Schwinger equation (LSE), is a well known toolfor modeling and imaging. However, it has limited convergence properties dependingon the strength of contrast between the actual and reference medium or the angleof incidence of a plane wave component. Here, we introduce the Volterra renormalizationtechnique to the LSE. The renormalized LSE and related Neumann series areabsolutely convergent for any strength of perturbation and any incidence angle. Therenormalized 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 thisVolterra Renormalization modeling is a promising and efficient method. In addition,it can also provide insight for developing a scattering theory-based direct inversionmethod.