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. The rigorous quantification of uncertainty in geophysical inversions is achallenging problem. Inversions are often ill-posed and the likelihood surfacemay be multi-modal; properties of any single mode become inadequate uncertaintymeasures, and sampling methods become inefficient for irregular posteriorsor high-dimensional parameter spaces. We explore theinfluences 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 inversionof the three-dimensional structure and composition of a region in theCooper Basin of South Australia as a case study. The inversion is performedusing an updated version of the Obsidian distributed inversion software.We find that the posterior for thisinversion has a complex local covariance structure, hindering the efficiency ofadaptive sampling methods that adjust the proposal based on the chain history.Within the context of a parallel-tempered Markov chain Monte Carlo scheme forexploring high-dimensional multi-modal posteriors, a preconditionedCrank–Nicolson proposal outperforms more conventional forms of random walk.Aspects of the problem setup, such as priors on petrophysics and on 3-Dgeological structure, affect the shape and separation of posterior modes,influencing sampling performance as well as the inversion results. The use ofuninformative priors on sensor noise enablesoptimal weighting among multiple sensors even if noise levels are uncertain.

Efficiency and robustness in Monte Carlo sampling for 3-D geophysical inversions with Obsidian v0.1.2: setting up for success