WaRIance: wavefield reconstruction inversion with stochastic variable projection

TL;DR

WaRIance introduces a stochastic variable projection method for wavefield reconstruction inversion, enhancing robustness and scalability for large 3D seismic problems by leveraging randomized linear algebra techniques.

Contribution

It presents a novel stochastic approximation approach to wavefield reconstruction inversion, enabling improved convergence and applicability to large-scale 3D seismic inversion.

Findings

Enhanced robustness against convergence issues

Applicable to large 3D seismic inversion problems

Demonstrated effectiveness through numerical experiments

Abstract

We propose a variation on wavefield reconstruction inversion for seismic inversion, which takes advantage of randomized linear algebra as a way to overcome the typical limitations of conventional inversion techniques. Consequently, we can aim both to robustness towards convergence stagnation and large-sized 3D applications. The central idea hinges on approximating the optimal slack variables involved in wavefield reconstruction inversion via a low-rank stochastic approximation of the wave-equation error covariance. As a result, we obtain a family of inversion methods parameterized by a given model covariance (suited for the problem at hand) and the rank of the related stochastic approximation sketch. The challenges and advantages of our proposal are demonstrated with some numerical experiments.