Multi-dimensional Inverse acoustic scattering series using the Volterra renormalization of the Lippmann-Schwinger equation

We report the extension of the Volterra inverse acoustic scattering series (VISS) approach presented in (Lesage et al., 2013) using reflection data (R_k) to multi-dimensions. The approach consists in combining two ideas: the renormalization of the Lippmann-Schwinger equation to obtain a Volterra equation framework (Kouri and Vijay, 2003) and the formal series expansion using reflection coefficients (Moses, 1956). The benefit of formulating acoustic scattering in terms of a Volterra kernel is substantial. Indeed the corresponding Born-Neumann series solution is absolutely convergent independent of the strength of the coupling characterizing the interaction. While treating the depth variation in the same manner as in the one-dimensional case, additional lateral and longitudinal variations are addressed through Fourier expansions of the pressure wave, the reflection data and the velocity perturbation. We derive new multi-dimensional inverse acoustic scattering series for reflection data which we evaluate numerically for 2-dimensional velocity models presenting depth and lateral variations. Our results compare well to results obtained by (Liu et al., 2005).