An All‐At‐Once Solver for Visco‐Acoustic Full Waveform Inversion in the Time‐Domain

Full waveform inversion (FWI) is the cutting-edge seismic imaging technique used to reconstruct subsurface material properties such as wave velocities, mass density, and attenuation from measurements of reflected wavefields. In this article, we present the first implementation of FWI in the visco-acoustic regime, based on a new time-domain all-at-once (AAO) formulation of the seismic inverse problem [Math. Meth. Appl. Sci. 2021; 44: 6376-6388]. The AAO approach solves for the material properties and the wavefield simultaneously. This offers advantages over classical methods, particularly in mitigating cycle-skipping by reducing dependency on initial models. Our algorithm combines an inexact Newton-type method, a problem-specific line search, and preconditioning to address the ill-posed nature of seismic imaging. Numerical experiments demonstrate the algorithm's robustness against noise and its increased domain of convergence compared to classical methods. Our study suggests combining the AAO algorithm with classical FWI algorithms to leverage the former's larger domain of convergence and the latter's higher accuracy when it converges. In conclusion, our AAO-FWI algorithm is a viable tool for seismic imaging, offering flexibility and robustness, with potential for further advancements and extensions to practical field data applications.