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arXiv · 2205.08861

An introduction to variational inference in Geophysical inverse problems

Xin Zhang·Muhammad Atif Nawaz·Xuebin Zhao·Andrew Curtis
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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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Xin Zhang, Muhammad Atif Nawaz, Xuebin Zhao, Andrew Curtis. 2022-05-18. An introduction to variational inference in Geophysical inverse problems. https://doi.org/10.1016/bs.agph.2021.06.003

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