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Parametric geological models such as implicit or kinematic models provide low-dimensional, interpretable representations of 3-D geological structures. Combining these models with geophysical data in a probabilistic joint inversion framework provides an opportunity to directly quantify uncertainty in geological interpretations. For best results, care must be taken with the intermediate step of rendering parametric geology in a finite-resolution discrete basis for the geophysical calculation. Calculating geophysics from naively voxelized geology, as exported from commonly used geological modeling tools, can produce a poor approximation to the true likelihood, degrading posterior inference for structural parameters. We develop a simple integrated Bayesian inversion code, called Blockworlds, showcasing a numerical scheme to calculate anti-aliased rock properties over regular meshes for use with gravity and magnetic sensors. We use Blockworlds to demonstrate anti-aliasing in the context of an implicit model with kinematic action for simple tectonic histories, showing its impact on the structure of the likelihood for gravity anomaly.

Unlike some other well-known challenges such as facial recognition, where machine learning and inversion algorithms are widely developed, the geosciences suffer from a lack of large, labelled data sets that can be used to validate or train robust machine learning and inversion schemes. Publicly available 3D geological models are far too restricted in both number and the range of geological scenarios to serve these purposes. With reference to inverting geophysical data this problem is further exacerbated as in most cases real geophysical observations result from unknown 3D geology, and synthetic test data sets are often not particularly geological or geologically diverse. To overcome these limitations, we have used the Noddy modelling platform to generate 1 million models, which represent the first publicly accessible massive training set for 3D geology and resulting gravity and magnetic data sets (https://doi.org/10.5281/zenodo.4589883, Jessell, 2021). This model suite can be used to train machine learning systems and to provide comprehensive test suites for geophysical inversion. We describe the methodology for producing the model suite and discuss the opportunities such a model suite affords, as well as its limitations, and how we can grow and access this resource.

The rigorous quantification of uncertainty in geophysical inversions is a challenging problem. Inversions are often ill-posed and the likelihood surface may be multi-modal; properties of any single mode become inadequate uncertainty measures, and sampling methods become inefficient for irregular posteriors or high-dimensional parameter spaces. We explore the influences of different choices made by the practitioner on the efficiency and accuracy of Bayesian geophysical inversion methods that rely on Markov chain Monte Carlo sampling to assess uncertainty using a multi-sensor inversion of the three-dimensional structure and composition of a region in the Cooper Basin of South Australia as a case study. The inversion is performed using an updated version of the Obsidian distributed inversion software. We find that the posterior for this inversion has a complex local covariance structure, hindering the efficiency of adaptive sampling methods that adjust the proposal based on the chain history. Within the context of a parallel-tempered Markov chain Monte Carlo scheme for exploring high-dimensional multi-modal posteriors, a preconditioned Crank–Nicolson proposal outperforms more conventional forms of random walk. Aspects of the problem setup, such as priors on petrophysics and on 3-D geological structure, affect the shape and separation of posterior modes, influencing sampling performance as well as the inversion results. The use of uninformative priors on sensor noise enables optimal weighting among multiple sensors even if noise levels are uncertain.