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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/gmd-2018-306
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-2018-306
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Development and technical paper 06 Mar 2019

Development and technical paper | 06 Mar 2019

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This discussion paper is a preprint. It is a manuscript under review for the journal Geoscientific Model Development (GMD).

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

Richard Scalzo1, David Kohn2, Hugo Olierook3, Gregory Houseman4, Rohitash Chandra1,5, Mark Girolami6,7, and Sally Cripps1,8 Richard Scalzo et al.
  • 1Centre for Translational Data Science, University of Sydney, Darlington NSW 2008, Australia
  • 2Sydney Informatics Hub, University of Sydney, Darlington NSW 2008, Australia
  • 3School of Earth and Planetary Sciences, Curtin University, Bentley WA 6102, Australia
  • 4School of Earth and Environment, University of Leeds, Leeds, LS2 9JT, UK
  • 5School of Geosciences, University of Sydney, Darlington NSW 2008, Australia
  • 6The Alan Turing Institute for Data Science, British Library, 96 Euston Road, London, NW1 2DB, UK
  • 7Department of Mathematics, Imperial College London, London, SW7 2AZ, UK
  • 8School of Mathematics and Statistics, University of Sydney, Darlington NSW 2008, Australia

Abstract. The rigorous quantification of uncertainty in geophysical inversions is a challenging problem. Inversions are often ill-posed and the likelihood surface may be multimodal; 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 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-Nicholson proposal outperforms more conventional forms of random walk. Aspects of the problem setup, such as priors on petrophysics or on 3-D geological structure, affect the shape and separation of posterior modes, influencing sampling performance as well as the inversion results. Use of uninformative priors on sensor noise can improve inversion results by enabling optimal weighting among multiple sensors even if noise levels are uncertain. Efficiency could be further increased by using posterior gradient information within proposals, which Obsidian does not currently support, but which could be emulated using posterior surrogates.

Richard Scalzo et al.
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Richard Scalzo et al.
Data sets

Supporting data and code for: Efficiency and robustness in Monte Carlo sampling for 3-D geophysical inversions with Obsidian v0.1.2: Setting up for success R. Scalzo, D. Kohn, L. McCalman, S. O'Callaghan, and B. Simpson-Young https://doi.org/10.5281/zenodo.2580422

Model code and software

Supporting data and code for: Efficiency and robustness in Monte Carlo sampling for 3-D geophysical inversions with Obsidian v0.1.2: Setting up for success R. Scalzo, D. Kohn, L. McCalman, S. O'Callaghan, and B. Simpson-Young https://doi.org/10.5281/zenodo.2580422

Richard Scalzo et al.
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Short summary
Producing 3-D models of structures under the Earth's surface based on sensor data is a key problem in geophysics (for example in mining exploration). There may be multiple models that explain the data well. We use the open-source Obsidian software to look at the efficiency of different methods for exploring the model space and attaching probabilities to models, leading to less biased results and a better idea of how sensor data interact with geological assumptions.
Producing 3-D models of structures under the Earth's surface based on sensor data is a key...
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