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Bayesian spatial modelling for high dimensional seismic inverse problems
Author(s) -
Zhang Ran,
Czado Claudia,
Sigloch Karin
Publication year - 2016
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/rssc.12118
Subject(s) - laplace's method , markov chain monte carlo , inverse problem , bayesian probability , mathematics , covariance , inverse theory , monte carlo method , bayesian inference , laplace transform , gaussian , covariance matrix , computer science , statistical physics , mathematical optimization , algorithm , mathematical analysis , physics , statistics , telecommunications , quantum mechanics , surface wave
Summary We study the application of Bayesian spatial modelling to seismic tomography, a geophysical, high dimensional, linearized inverse problem that infers the three‐dimensional structure of the Earth's interior. We develop a spatial dependence model of seismic wave velocity variations in the Earth's mantle based on a Gaussian Matérn field approximation. Using the theory of stochastic partial differential equations, this model quantifies the uncertainties in the parameter space by means of the integrated nested Laplace approximation. In resolution tests using simulated data and in inversions using real data, our model matches the performance of conventional deterministic optimization approaches in retrieving three‐dimensional structure of the Earth's mantle. In addition it delivers estimates of the full parameter covariance matrix. Our model substantially improves on previous work relying on Markov chain Monte Carlo methods in terms of statistical misfits and computing time.