Polynomial surrogates for Bayesian traveltime tomography
| Autor: | Pierre Sochala, Olivier Le Maitre, Alexandrine Gesret |
|---|---|
| Přispěvatelé: | Uncertainty Quantification in Scientific Computing and Engineering (PLATON), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Bureau de Recherches Géologiques et Minières (BRGM) (BRGM), Centre de Géosciences (GEOSCIENCES), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Polynomial
Polynomial chaos Seismic tomography 010504 meteorology & atmospheric sciences Statistical methods Computer science Eikonal equation [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph] Bayesian probability Posterior probability Inference Sampling (statistics) 010502 geochemistry & geophysics Bayesian inference 01 natural sciences Physics::Geophysics [SPI.MECA.GEME]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanical engineering [physics.class-ph] Surrogate models [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Modeling and Simulation Inverse problem General Earth and Planetary Sciences Algorithm 0105 earth and related environmental sciences |
| Zdroj: | GEM-International Journal on Geomathematics GEM-International Journal on Geomathematics, Springer, 2021, 12 (1), ⟨10.1007/s13137-021-00184-0⟩ GEM-International Journal on Geomathematics, 2021, 12 (1), ⟨10.1007/s13137-021-00184-0⟩ |
| ISSN: | 1869-2672 1869-2680 |
| Popis: | International audience; This paper tackles the issue of the computational load encountered in seismic imaging by Bayesian traveltime inversion. In Bayesian inference, the exploration of the posterior distribution of the velocity model parameters requires extensive sampling. The computational cost of this sampling step can be prohibitive when the first arrival traveltime prediction involves the resolution of an expensive number of forward models based on the eikonal equation. We propose to rely on polynomial chaos surrogates of the traveltimes between sources and receivers to alleviate the computational burden of solving the eikonal equation during the sampling stage. In an offline stage, the approach builds a functional approximation of the traveltimes from a set of solutions of the eikonal equation corresponding to a few values of the velocity model parameters selected in their prior range. These surrogates then substitute the eikonal-based predictions in the posterior evaluation, enabling very efficient extensive sampling of Bayesian posterior, for instance, by a Markov Chain Monte Carlo (MCMC) algorithm. We demonstrate the potential of the approach using numerical experiments on the inference of two-dimensional domains with layered velocity models and different acquisition geometries (microseismic and seismic refraction contexts). The results show that, in our experiments, the number of eikonal model evaluations required to construct accurate surrogates of the traveltimes is low. Further, an accurate and complete characterization of the posterior distribution of the velocity model is possible, thanks to the generation of large sample sets at a low cost. Finally, we discuss the extension of the current approach to more realistic velocity models and operational situations. |
| Databáze: | OpenAIRE |
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