Numerical investigation of a multi-step one-shot method for frequency domain acoustic full waveform inversion

Full waveform inversion is an imaging method consisting in the spatial reconstruction of the parameter field of a wave propagation problem through the optimization of a misfit functional between the synthetic solution of the problem and the observed solution. Full waveform inversion is typically articulated in two distinct layers: the inner layer consisting in solving the forward and adjoint problems for the calculation of the misfit gradient, and the outer layer performing the optimization.

For large scale problems, the forward and adjoint problems need to be solved using an iterative domain decomposition method. The one-shot paradigm couples these iterative solutions with the optimization steps by limiting the number of forward and adjoint solver iterations to a small number, thus producing an inexact gradient.

In this talk, we investigate the practical feasibility and performance of the one-shot paradigm in the context of full waveform inversion in the frequency domain. We apply the one-shot algorithm proposed in [1] with gradient descent for minimization and an Optimized Restricted Additive Schwartz-preconditioned stationary iterative solver for the forward and adjoint problems. The computational cost is investigated in terms of the number of forward and adjoint iterations, the gradient descent step and the number of subdomains.

Joint work with C. Guezaine and B. Martin.

[1] M. Bonazzoli, H. Haddar, and T.A. Vu. On the convergence analysis of one-shot inversion
methods. SIAM J. Appl. Math. (2024).