HMCtomo: Gradient-based sampling and physical models for large-scale Bayesian geophysical inference

Abstract:

We present a Python and Julia based package to appraise geophysical inference problems using various sampling methods, with a focus on gradient-based sampling. Recently, these gradient-based Monte Carlo sampling methods have increased in popularity for a range of inverse problems across several fields. The capability of performing uncertainty estimation and overcoming nonlinearities is the main driver of increasing popularity. The solution to the inverse problem, in fact, is not a single "optimal" model, but an ensemble of models representing the so-called posterior probability density function, from which potentially different scenarios, all compatible with the observed data, can be inferred.

Many inference problems in geophysics have readily accessible gradient information, through e.g. the adjoint method (which at most requires one additional numerical simulation). This information goes unused in classical appraisals such as Metropolis-Hastings sampling. Using gradient-based sampling helps to accelerate traditional Monte Carlo sampling while increasing the scalability of inference problems, allowing access to uncertainty quantification for problems previously considered too computationally demanding. However, the amount of tuning parameters required by these gradient-based sampling methods, as well as the complexity of existing software and the tuning of the algorithms, limited the geophysical community in adopting a specific tool for performing efficient large-scale Bayesian inference.

This work attempts to make a step towards that gap by providing various gradient-based samplers suited for geophysical inverse problems. Additionally, the package provides a set of different forward models, ranging from elastic and acoustic wave propagation to magnetic anomaly modeling, traveltime-tomography, etc.. To simplify usage, various methods to accelerate burn-in, tuning and sampling are included. The package offers the possibility to the user to appraise their own forward models and priors. With this package and its included tutorials, we hope to illustrate the usefulness and potential of gradient-based sampling in Bayesian inference, but also provide a platform on which users may appraise medium to large scale inference problems.