General Optimization Framework for Robust and Regularized 3D Full Waveform Inversion

TL;DR

This paper introduces a versatile optimization framework for 3D full waveform inversion that can incorporate various noise models, regularizers, and constraints, improving robustness and flexibility in seismic imaging.

Contribution

A generic, expandable optimization framework for seismic inversion that integrates robust noise models, regularizers, and reparametrizations, enhancing flexibility over traditional methods.

Findings

Framework effectively incorporates robust noise models like Huber and Student's t

Supports sparse regularizers, projected constraints, and Total Variation regularization

Numerical examples demonstrate its versatility and robustness

Abstract

Scarcity of hydrocarbon resources and high exploration risks motivate the development of high fidelity algorithms and computationally viable approaches to exploratory geophysics. Whereas early approaches considered least-squares minimization, recent developments have emphasized the importance of robust formulations, as well as formulations that allow disciplined encoding of prior information into the inverse problem formulation. The cost of a more flexible optimization framework is a greater computational complexity, as least-squares optimization can be performed using straightforward methods (e.g., steepest descent, Gauss-Newton, L-BFGS), whilst incorporation of robust (non-smooth) penalties requires custom changes that may be difficult to implement in the context of a general seismic inversion workflow. In this study, we propose a generic, flexible optimization framework capable of incorporating a broad range of noise models, forward models, regularizers, and reparametrization transforms. This framework covers seamlessly robust noise models (such as Huber and Student's $t$), as well as sparse regularizers, projected constraints, and Total Variation regularization. The proposed framework is also expandable --- we explain the adjustments that are required for any new formulation to be included. Lastly, we conclude with few numerical examples demonstrating the versatility of the formulation.