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- Title
Rapid Discriminative Variational Bayesian Inversion of Geophysical Data for the Spatial Distribution of Geological Properties.
- Authors
Nawaz, M. A.; Curtis, A.
- Abstract
We present a new, fully probabilistic and nonlinear inversion method to estimate the spatial distribution of geological properties (depositional facies, diagenetic rock types, or other rock properties) from geophysical data (e.g., seismic data). Contrary to the conventional generative approach that models solution probabilities via the likelihood of observed data, our method uses a discriminative approach that directly models the posterior distribution of the geological properties given the data. This reduces the modeling effort significantly and allows machine learning algorithms such as neural networks to be deployed to solve large geophysical inference problems. We show that our method honors spatial distributions of geological parameters supplied as prior information about local geology and can be trained using supervised learning to be robust against noise present in the data as long as we can provide statistical characteristics of the noise. Exact Bayesian inference is almost always infeasible in practice because it requires normalization of the posterior distribution; this is intractable for large models and must therefore be approximated. Most existing probabilistic inversion methods use stochastic sampling (e.g., Markov chain Monte Carlo, McMC) for approximate inference. However, McMC involves the use of subjective criteria to detect convergence. We use the variational Bayes method to transform probabilistic inference into numerical optimization. This is a more efficient, deterministic alternative to McMC‐based inference for suitably structured problems. Our method thus avoids extensive sampling during inference, yet provides fully probabilistic Bayesian results, and is therefore scalable to higher dimensional problems. Plain Language Summary: We present a new method for the estimation of geological properties such as type and physical properties of rocks, from geophysical measurements such as seismic data. Most existing methods assume that the geophysical data have been perfectly localized to produce data at each point in space (e.g., through tomography or imaging) and that the data are free of correlated noise or errors. Although neither requirement is met in reality, existing methods use these assumptions to make solutions computationally tractable. Our method removes both of these assumptions and is still computationally tractable for suitably structured problems (a class of problems that can be decomposed into interlinked subproblems). We achieve this by abandoning the usual approach of modeling the likelihood—a measure of how probable it is that the observed data were generated by any given geological model. Instead, our method models the geological parameters from the observed data directly, using examples of the direct data‐model relationship. This reduces the required computational resources significantly for large‐scale problems. To further improve computational efficiency, our method avoids extensive use of Monte Carlo sampling, and instead uses numerical optimization to estimate the desired geological properties and their fully probabilistic uncertainties. Key Points: Our fully nonlinear Bayesian inversion method requires no assumptions of localization or conditional independence of dataThe discriminative approach ensures that the method can be applied using supervised machine learningThe method performs fully nonlinear probabilistic inference while avoiding Markov chain Monte Carlo sampling
- Subjects
GEOPHYSICS research; SEISMOLOGICAL research; COMPUTERS in geophysics; GEOPHYSICS methodology; BAYESIAN analysis; EARTH sciences
- Publication
Journal of Geophysical Research. Solid Earth, 2019, Vol 124, Issue 6, p5867
- ISSN
2169-9313
- Publication type
Article
- DOI
10.1029/2018JB016652