Bayesian geophysical inversion with Gaussian process machine learning and trans-D Markov chain Monte Carlo

Summary

A key aspect of geophysical inversion is the ability to model the earth with a low dimensional representation. There exist various approaches to solve the inverse problem. However, most methods do not automatically adapt inverse model complexity or the number of active model parameters as dictated by data noise and sparse receiver coverage, do not quantify inverse model uncertainty or do not work equally well for 1D, 2D or 3D earth models. Low frequency electromagnetic (EM) inversion for example, can require for 3D problems upward of 10⁶ cells to forward model. Only a small fraction of these cells is effectively resolvable and there are significant trade-offs between them. To address these limitations, we present a novel approach to earth model parametrization by using a Gaussian Processes (GP) machine learning (ML) technique, coupled with a parsimonious Bayesian trans-dimensional (trans-D) Markov chain Monte Carlo (McMC) sampling scheme. One aspect that sets our approach apart from recent spatial dimension agnostic algorithms in the trans-D or ML literature is the ability to specify inversion property priors directly, as opposed to doing so in a transform domain of the property. Finally, we note that our method falls in the category of ML approaches that do not attempt to learn the physics of the process, but instead learn the representation of parameter values through a misfit function. We apply the trans-D-GP method to a 1D controlled source electromagnetic (CSEM) and 2D non-linear regression problem, using actual field data from the Northwest Australian Shelf for the former. The key advantages in using our method are the simplicity of prior specification, parsimonious low dimensional representations, and ease of representing large-scale models in 1D, 2D or even 3D with the same parametrization and computer code.

• inverse theory
• Bayesian probability
• electrical properties
• machine learning