A Bayesian linear model for the highdimensional inverse problem of seismic tomography
Zhang, Ran, Claudia Czado, and Karin Sigloch (2013),
A Bayesian linear model for the highdimensional inverse problem of seismic tomography,
Annals of Applied Statistics, 7(2), 111111138, doi:10.1214/12AOAS623.
 Abstract
 We apply a linear Bayesian model to seismic tomography, a highdimensional inverse problem in geophysics. The objective is to estimate the threedimensional 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 largescale linear inverse problems, and provide precise uncertainty quantication in terms of parameter distributions and credible intervals given the data. We apply the method to a fulledged tomography problem, an inversion for uppermantle 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 leastsquares 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 = {111111138},
title = {{A Bayesian linear model for the highdimensional inverse problem of seismic tomography}},
volume = {7},
year = {2013},
url = {http://projecteuclid.org/euclid.aoas/1372338481},
doi = {10.1214/12AOAS623},
}
 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 111111138
%T A Bayesian linear model for the highdimensional inverse problem of seismic tomography
%U http://projecteuclid.org/euclid.aoas/1372338481
%8 mar