Efficient scattering approach to seismic full-waveform inversion in anisotropic elastic media with variable density

Abstract: This paper introduces a novel matrix-free approach for full waveform inversion in anisotropic elastic media, incorporating density variation through the utilization of the distorted Born iterative method. This study aims to overcome the computational and storage challenges associated with the conventional matrix-based distorted Born iterative inversion method while accurately capturing the subsurface's anisotropic properties and density variations. An elastic integral equation is utilized to account for the anisotropic nature of elastic wave propagation, enabling more precise modeling of subsurface complexities. This integral equation is efficiently solved by a fast Fourier transform accelerated Krylov subspace method. Leveraging the integral equation with the distorted Born approximation, a linear relationship between the scattered wavefield and the model parameter perturbation is formulated for an integrated inversion scheme. To address the inherent ill-posedness of each linear inversion step, we formulate the normal equation with a regularization term. This is achieved by minimizing an objective function using the generalized Tikhonov method. Therefore, we can find an adequate solution for the inverse scattering problem by solving the normal equation. Following the physical interpretation of Green's function, the Fr{\'e}chet and adjoint operators within the normal equation can be employed in a matrix-free manner, allowing for significant improvement of the computational efficiency and memory demand without compromising accuracy. The proposed matrix-free full waveform inversion framework is thoroughly validated through extensive numerical experiments on synthetic datasets, showcasing its ability to reconstruct complex anisotropic structures and accurately recover stiffness parameters and density.