Extended full waveform inversion in the time domain by the augmented Lagrangian method

TL;DR

This paper introduces a new time-domain extended full waveform inversion algorithm using the augmented Lagrangian method, which efficiently reconstructs wavefields from data, enabling robust and scalable subsurface parameter estimation.

Contribution

The paper proposes a novel time-domain extended FWI algorithm that operates in data space, reducing computational complexity and enabling efficient large-scale inversion.

Findings

Efficient wavefield reconstruction from data using explicit time stepping.

Algorithm achieves comparable cost to standard FWI while enhancing robustness.

Numerical examples demonstrate high performance for large-scale problems.

Abstract

Extended full-waveform inversion (FWI) has shown promising results for accurate estimation of subsurface parameters when the initial models are not sufficiently accurate. Frequency-domain applications have shown that the augmented Lagrangian (AL) method solves the inverse problem accurately with a minimal effect of the penalty parameter choice. Applying this method in the time domain, however, is limited by two main factors: (1) The challenge of data-assimilated wavefield reconstruction due to the lack of an explicit time-stepping and (2) The need to store the Lagrange multipliers, which is not feasible for the field-scale problems. We show that these wavefields are efficiently determined from the associated data (projection of the wavefields onto the receivers space) by using explicit time stepping. Accordingly, based on the augmented Lagrangian, a new algorithm is proposed which performs in "data space" (a lower dimensional subspace of the full space) in which the wavefield reconstruction step is replaced by reconstruction of the associated data, thus requiring optimization in a lower dimensional space (convenient for handling the Lagrange multipliers). We show that this new algorithm can be implemented efficiently in the time domain with existing solvers for the FWI and at a cost comparable to that of the FWI while benefiting from the robustness of the extended FWI formulation. The results obtained by numerical examples show high-performance of the proposed method for large scale time-domain FWI.