Bayesian Travel Time Inversion adopting Gaussian Process Regression
Abstract
A major application in seismology is the determination of seismic velocity models. Travel time measurements are putting an integral constraint on the velocity between source and receiver. We provide insight into travel time inversion from a correlation-based Bayesian point of view. Therefore, the concept of Gaussian process regression is adopted to estimate a velocity model. The non-linear travel time integral is approximated by a 1st order Taylor expansion. A heuristic covariance describes correlations amongst observations and a priori model. That approach enables us to assess a proxy of the Bayesian posterior distribution at ordinary computational costs. No multi dimensional numeric integration nor excessive sampling is necessary. Instead of stacking the data, we suggest to progressively build the posterior distribution. Incorporating only a single evidence at a time accounts for the deficit of linearization. As a result, the most probable model is given by the posterior mean whereas uncertainties are described by the posterior covariance.As a proof of concept, a synthetic purely 1d model is addressed. Therefore a single source accompanied by multiple receivers is considered on top of a model comprising a discontinuity. We consider travel times of both phases - direct and reflected wave - corrupted by noise. Left and right of the interface are assumed independent where the squared exponential kernel serves as covariance.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2017
- Bibcode:
- 2017AGUFM.S31E..04M
- Keywords:
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- 1873 Uncertainty assessment;
- HYDROLOGY;
- 3260 Inverse theory;
- MATHEMATICAL GEOPHYSICS;
- 3275 Uncertainty quantification;
- MATHEMATICAL GEOPHYSICS;
- 7290 Computational seismology;
- SEISMOLOGY