GeoPVI: a Python package for geoscientific inversion using parametric variational inference

SUMMARY In many fields of geoscience, researchers study the Earth’s properties by solving inverse or inference problems. Probabilistic approaches have gained increased attention over the past decade because they address the nonlinearity and non-uniqueness properties of many naturally-inspired inverse problems and allow uncertainties in the solutions to be estimated. However, implementing such methods is computationally expensive and requires expertise in inverse and inference theory, high performance computing and the geoscientific theory to be inverted. This makes the methods inaccessible to many geoscientists. In this paper, we first review the theoretical background of a particular suite of probabilistic algorithms referred to as parametric variational inference (PVI), and introduce GeoPVI, an open-source Python package designed to facilitate the implementation of these methods. With GeoPVI, users can model uncertainties in their geophysical parameter estimates efficiently given their expertise in inverse theory. It differs from sampling-based, non-parametric variational methods in that the probabilistic solution—the posterior or post-inversion probability distribution function that describes uncertainty in the model parameters of interest—is parametrized by explicit mathematical expressions. These expressions allow for the efficient storage and transfer, and for the evaluation of the posterior probability density for any set of parameter values. We demonstrate how to use the package to solve a set of problems, including tomographic imaging using traveltime data, full waveform inversion, surface wave dispersion inversion and vertical electrical sounding. We provide built-in forward functions to simulate first arrival traveltimes and full acoustic waveform data (in two spatial dimensions), and external forward functions can be incorporated into the package easily. We also demonstrate how to change prior information efficiently post-inversion, using the method of variational prior replacement. Contributions from the community are welcome, to make the package more broadly applicable.