Viscoacoustic Gaussian beam inverse scattering imaging method by asymptotic estimation of the single-scattering Hessian operator

Abstract

Attenuation compensation has been introduced in the field of linearized inverse scattering problems for the restoration of geological structures and material properties within viscoacoustic media, which are characterized by P-wave velocity and the quality factor $Q$. It relies on the solution of a true-amplitude asymptotic inversion, incorporating a single-scattering propagation operator. Nonetheless, traditional mathematical treatments of asymptotic inversion often overlook the viscous properties of the medium. In this study, we investigate the application of the Gaussian-beam depth migration technique, which takes into account multiple wave arrivals, to address the complexities associated with true-amplitude viscoacoustic inverse scattering. This method presents a precise and adaptable alternative to conventional single-arrival ray-based migration techniques. Our focus is on viscoacoustic inversion imaging using the single-scattering Hessian operator, deemed essential for full waveform inversion. In this situation, we demonstrate how to derive an appropriate weighting filter that allows the dominant part of the weighted Hessian operator to effectively approximate the identity operator. As a result, we develop a new form of pseudoinverse operator linked to the Born modeling operator for a single-beam-center slowness component of the wavefield. This operator facilitates the implementation of viscoacoustic Gaussian beam prestack depth migration on common-shot gathers, thereby offering a robust solution for imaging complex structures where single-arrival ray-based approaches are insufficient. Numerical results derived from the analysis of 2D realistic synthetic datasets substantiate the effectiveness of the proposed methodology. This work not only advances the understanding of viscoacoustic imaging techniques but also significantly enhances their practical application in challenging geological scenarios.