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Bayesian spatial modelling for high-dimensional seismic inverse problems

Zhang, Ran, Claudia Czado, and Karin Sigloch (2013), Bayesian spatial modelling for high-dimensional seismic inverse problems, Journal of the Royal Statistical Society, Series C, submitted.

Abstract
We study high-dimensional linearised inverse problems in seismic tomography by
means of Bayesian spatial modelling. Seismic tomography is an imaging technique in geo-
physics used to infer the three-dimensional seismic velocity structure of the earth’s interior by
assimilating data measured at the surface. Main novelties are that we develop a spatial depen-
dency model of the earth’s three-dimensional velocity structure based on a Gaussian Mat´ ern
field approximation using the theory of stochastic partial differential equations (SPDEs), and we
carry out the uncertainty quantification of the high-dimensional parameter space by means of
the integrated nested Laplace approximation (INLA) techniques. We provide an application us-
ing seismological data from the continental-scale USArray experiment, thereby revealing major
structures of the mantle beneath the western USA with uncertainty assessments, while provid-
ing correlation estimation of the parameters. We simultaneously model the spatial correlation
of the data errors on a single- and multi-regions basis, which captures spatial dependency
caused by different regions. We demonstrate that our model substantially improves previous
work relying on common deterministic optimisation or MCMC sampling methods in terms of
statistical misfits and computing time with a speedup of about 1.5 to 2 times.
BibTeX
@article{id1900,
  author = {Ran Zhang and Claudia Czado and Karin Sigloch},
  journal = {Journal of the Royal Statistical Society, Series C},
  note = {submitted},
  title = {{Bayesian spatial modelling for high-dimensional seismic inverse problems}},
  year = {2013},
}
EndNote
%0 Journal Article
%A Zhang, Ran
%A Czado, Claudia
%A Sigloch, Karin
%D 2013
%J Journal of the Royal Statistical Society, Series C
%T Bayesian spatial modelling for high-dimensional seismic inverse problems
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Printed 20. Mar 2019 04:45