Fully Non-linear Seismic Tomography using Normalizing Flows
Abstract
We propose a fully non-linear method to solve seismic tomography using the observed travel time data. Unlike previous approaches that are mainly based on Markov chain Monte Carlo (McMC), which is computational expensive for high dimensional model space due to the curse of dimensionality, we use variational inference to calculate the posterior distribution for Bayesian inversion. The variational method is an efficient alternate to McMC, which seeks the best approximation to the posterior, such that the original inference problem is solved under an optimization framework while still providing fully probabilistic results. We apply a new variational method -- normalizing flows -- to solve probabilistic travel time tomography. The method models the posterior distribution by employing a series of invertible and differentiable transforms - the flows. By optimizing the parameters of these transforms the flows are designed to convert a simple and analytically known distribution into a good approximation of the posterior. Numerical examples show that normalizing flows can provide an accurate tomographic result including full uncertainty information while significantly decreasing the computational cost compared to McMC and other variational methods. More attractively, this method could potentially provide an analytic solution to the posterior distribution other than just an ensemble of posterior samples.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2020
- Bibcode:
- 2020AGUFMS053.0004Z
- Keywords:
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- 0555 Neural networks;
- fuzzy logic;
- machine learning;
- COMPUTATIONAL GEOPHYSICS;
- 1910 Data assimilation;
- integration and fusion;
- INFORMATICS;
- 1914 Data mining;
- INFORMATICS;
- 1942 Machine learning;
- INFORMATICS