An introduction to variational inference in Geophysical inverse problems

Abstract

In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be quantified in order to define the family of all possible solutions. Bayesian inference provides a powerful theoretical framework which defines the set of solutions to inverse problems, and variational inference is a method to solve Bayesian inference problems using optimization while still producing fully probabilistic solutions. This chapter provides an introduction to variational inference, and reviews its applications to a range of geophysical problems, including petrophysical inversion, travel time tomography and full-waveform inversion. We demonstrate that variational inference is an efficient and scalable method which can be deployed in many practical scenarios.

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Cited by in corpus (5)

• 3D Bayesian Variational Full Waveform Inversion
• WISE: full-Waveform variational Inference via Subsurface Extensions
• Variational Prior Replacement in Bayesian Inference and Inversion
• WISER: multimodal variational inference for full-waveform inversion without dimensionality reduction
• Interrogating probabilistic inversion results for subsurface structural information