Bayesian geophysical inversion with trans-dimensional Gaussian process machine learning

Abstract

S U M M A R Y 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 1-D, 2-D or 3-D earth models. Low-frequency electromagnetic (EM) inversion, for example, can require for 3-D problems upwards of 106 cells to forward model. Only a small fraction of these cells are effectively resolvable and there are significant trade-offs between them. To address such problems and get around 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 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. We develop the theory, describe the effects of specifying different geological priors and apply the trans-D-GP method to a 1-D controlled source EM and 2-D nonlinear 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 1-D, 2-D or even 3-D with the same parametrization and computer code.