Pseudo trans-dimensional 3-D geometrical inversion: a proof of concept using gravity data

SUMMARY We present and apply a pseudo trans-dimensional inversion method for 3-D geometrical gravity inversion, in which the number of rock units, their geometry and their density can vary during sampling. The method is designed for efficient exploration of the model space and to infer the presence and properties of units not directly observable but detectable with geophysical data. Sampling relies on a non-reversible Metropolis-Hastings algorithm, during which rock units can be added or removed from the model, interface geometries are perturbed using random fields, and densities are sampled from distributions informed by prior information. To visualize the space of sampled models and to aid interpretation, a workflow is proposed that combines dimensionality reduction with the clustering of models in families. The capabilities of the inversion method are evaluated using two synthetic cases. The first is a motivating example aimed at recovering an intrusion missing from the prior model. It features a layer-cake where fixed-dimensional inversion fails to adequately fit the data and sample models close to the true model, while the proposed pseudo trans-dimensional approach is much more successful. The second case investigates the recovery of two missing units and the capability to overcome prior model biases. Results show the potential of our method to infer the presence of unseen geological features such as intrusions. However, they suggest that with biased prior geological modelling, it may be challenging to infer with certainty the presence of more than two previously unknown rock units at depth.