An Introduction to Variational Inference in Geophysical Inverse Problems

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 nonunique 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.