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

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 pos...

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Bibliographic Details
Published in:Geoscientific Model Development Vol. 12; no. 7; pp. 2941 - 2960
Main Authors: Scalzo, Richard, Kohn, David, Olierook, Hugo, Houseman, Gregory, Chandra, Rohitash, Girolami, Mark, Cripps, Sally
Format: Journal Article
Language:English
Published: Katlenburg-Lindau Copernicus GmbH 15.07.2019
Copernicus Publications
Subjects:
Adaptive sampling
Bayesian analysis
Covariance
Efficiency
Geochemical cycles
Geological structures
Geophysical methods
Geophysics
Ill posed problems
Inversions
Markov analysis
Markov chains
Markov processes
Measurement methods
Monte Carlo methods
Monte Carlo simulation
Noise levels
Obsidian
Probability theory
Random walk
Sampling
Sampling methods
Sensors
Statistical methods
Uncertainty
Australia
ISSN:1991-9603, 1991-959X, 1991-962X, 1991-9603, 1991-962X
Online Access:Get full text
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Summary: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.
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ISSN:1991-9603
1991-959X
1991-962X
1991-9603
1991-962X
DOI:10.5194/gmd-12-2941-2019