Regularized Seismic Full Waveform Inversion Using Inverse Scattering Approach and Preconditioned L-BFGS Optimization

Abstract

Although full waveform inversion (FWI) is widely recognized as one of the state-of-the-art techniques in geophysical exploration, there remain several aspects of FWI that require further improvements, specifically in resolution and modeling efficiency. To address this, we introduce an inverse scattering approach to frequency-domain seismic FWI by utilizing a regularized objective function. Different from traditional adjoint methods, the scattering theory allows us to derive the sensitivity kernel explicitly through two Greens’ functions and transforms the nonlinear inverse scattering problem into a series of linear inverse scattering problems, thereby facilitating the calculation of the gradient and Hessian. To mitigate the computational cost when calculating the background and actual wavefields, the fast Fourier transform (FFT) combined with the Krylov subspace method is used to solve the Lippmann-Schwinger (L-S) integral equation (IE) iteratively. Additionally, we incorporate minimum support (MS) stabilizing functional as an extra model misfit term alongside the traditional data misfit function, for a better recovery of the shape structure within the model. Furthermore, the inversion framework is enhanced by integrating an improved limited memory Broyden-Fletcher–Goldfarb-Shanno algorithm, with the regularized Hessian serving as a preconditioner. To demonstrate the efficacy of our method, numerical tests on Marmousi and BP models are presented to validate the performance and robustness of the proposed approach.