Normalising Flows for Bayesian Gravity Inversion

TL;DR

This paper introduces a Bayesian gravity inversion method using Normalising Flows, providing probabilistic source estimates efficiently and robustly, outperforming traditional methods in speed and scalability for high-dimensional data.

Contribution

The paper presents a novel application of Normalising Flows for Bayesian gravity inversion, enabling fast, scalable, and probabilistic source parameter estimation.

Findings

Achieves comparable accuracy to Nested Sampling

200 times faster than standard Bayesian methods

Remains tractable at 512 dimensions

Abstract

Gravity inversion is a commonly applied data analysis technique in the field of geophysics. While machine learning methods have previously been explored for the problem of gravity inversion, these are deterministic approaches returning a single solution deemed most appropriate by the algorithm. The method presented here takes a different approach, where gravity inversion is reformulated as a Bayesian parameter inference problem. Samples from the posterior probability distribution of source model parameters are obtained via the implementation of a generative neural network architecture known as Normalising Flows. Due to its probabilistic nature, this framework provides the user with a range of source parameters and uncertainties instead of a single solution, and is inherently robust against instrumental noise. The performance of the Normalising Flow is compared to that of an established Bayesian method called Nested Sampling. It is shown that the new method returns results with comparable accuracy 200 times faster than standard sampling methods, which makes Normalising Flows a suitable method for real-time inversion in the field. When applied to data sets with high dimensionality, standard sampling methods can become impractical due to long computation times. It is shown that inversion using Normalising Flows remains tractable even at 512 dimensions and once the network is trained, the results can be obtained in $O(10)$ seconds.