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A Bayesian linear model for the high-dimensional inverse problem of seismic tomography

Zhang, Ran, Claudia Czado, and Karin Sigloch (2013), A Bayesian linear model for the high-dimensional inverse problem of seismic tomography, Annals of Applied Statistics, 7(2), 1111-11138, doi:10.1214/12-AOAS623.

Abstract
We apply a linear Bayesian model to seismic tomography, a high-dimensional inverse problem in geophysics. The objective is to estimate the three-dimensional structure of the earth's interior from data measured at its surface. Since this typically involves estimating thousands of unknowns or more, it has always been treated as a linear(ized) optimization problem. Here we present a Bayesian hierarchical model to estimate the joint distribution of earth structural and earthquake source parameters. An ellipsoidal spatial prior allows to accommodate the layered nature of the earth's mantle. With our efficient algorithm we can sample the posterior distributions for large-scale linear inverse problems, and provide precise uncertainty quanti cation in terms of parameter distributions and credible intervals given the data. We apply the method to a full-edged tomography problem, an inversion for upper-mantle structure under western North America that involves more than 11,000 parameters. In studies on simulated and real data, we show that our approach retrieves the major structures of the earth's interior similarly well as classical least-squares minimization, while additionally providing uncertainty assessments.
Further information
BibTeX
@article{id1803,
  author = {Ran Zhang and Claudia Czado and Karin Sigloch},
  journal = {Annals of Applied Statistics},
  month = {mar},
  number = {2},
  pages = {1111-11138},
  title = {{A Bayesian linear model for the high-dimensional inverse problem of seismic tomography}},
  volume = {7},
  year = {2013},
  url = {http://projecteuclid.org/euclid.aoas/1372338481},
  doi = {10.1214/12-AOAS623},
}
EndNote
%0 Journal Article
%A Zhang, Ran
%A Czado, Claudia
%A Sigloch, Karin
%D 2013
%N 2
%V 7
%J Annals of Applied Statistics
%P 1111-11138
%T A Bayesian linear model for the high-dimensional inverse problem of seismic tomography
%U http://projecteuclid.org/euclid.aoas/1372338481
%8 mar
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