Mitigating local minima in full-waveform inversion by expanding the search space

TLDR: In this paper, the objective function consists of a data-misfit term and a penalty term, which measures how accurately the wavefields satisfy the wave-equation, and the solution is forced to solve the waveequation and fit the observed data, which leads to significant computational savings.

Abstract: Wave-equation based inversions, such as full-waveform inversion, are challenging because of their computational costs, memory requirements, and reliance on accurate initial models. To confront these issues, we propose a novel formulation of full-waveform inversion based on a penalty method. In this formulation, the objective function consists of a data-misfit term and a penalty term which measures how accurately the wavefields satisfy the wave-equation. Because we carry out the inversion over a larger search space, including both the model and synthetic wavefields, our approach suffers less from local minima. Our main contribution is the development of an efficient optimization scheme that avoids having to store and update the wavefields by explicit elimination. Compared to existing optimization strategies for full-waveform inversion, our method differers in two main aspects; i) The wavefields are solved from an augmented wave-equation, where the solution is forced to solve the wave-equation and fit the observed data, ii) no adjoint wavefields are required to update the model, which leads to significant computational savings. We demonstrate the validity of our approach by carefully selected examples and discuss possible extensions and future research.