Minson, S. E. and Simons, M. and Beck, J. L.
Bayesian inversion for finite fault earthquake source models
I—theory and algorithm.
Geophysical Journal International
- Published Version
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The estimation of finite fault earthquake source models is an inherently underdetermined
problem: there is no unique solution to the inverse problem of determining the rupture history
at depth as a function of time and space when our data are limited to observations at
the Earth’s surface. Bayesian methods allow us to determine the set of all plausible source
model parameters that are consistent with the observations, our a priori assumptions about the
physics of the earthquake source and wave propagation, and models for the observation errors
and the errors due to the limitations in our forward model. Because our inversion approach
does not require inverting any matrices other than covariance matrices, we can restrict our
ensemble of solutions to only those models that are physically defensible while avoiding the
need to restrict our class of models based on considerations of numerical invertibility. We
only use prior information that is consistent with the physics of the problem rather than some
artefice (such as smoothing) needed to produce a unique optimal model estimate. Bayesian inference
can also be used to estimate model-dependent and internally consistent effective errors
due to shortcomings in the forward model or data interpretation, such as poor Green’s functions
or extraneous signals recorded by our instruments. Until recently, Bayesian techniques
have been of limited utility for earthquake source inversions because they are computationally
intractable for problems with as many free parameters as typically used in kinematic
finite fault models. Our algorithm, called cascading adaptive transitional metropolis in parallel
(CATMIP), allows sampling of high-dimensional problems in a parallel computing framework.
CATMIP combines the Metropolis algorithm with elements of simulated annealing and
genetic algorithms to dynamically optimize the algorithm’s efficiency as it runs. The algorithm
is a generic Bayesian Markov Chain Monte Carlo sampler; it works independently of the
model design, a priori constraints and data under consideration, and so can be used for a wide
variety of scientific problems. We compare CATMIP’s efficiency relative to several existing
sampling algorithms and then present synthetic performance tests of finite fault earthquake
rupture models computed using CATMIP.
|Additional Information:||© The Authors 2013. Published by Oxford University Press on behalf of The Royal Astronomical Society.
Accepted 2013 May 2. Received 2013 May 1; in original form 2012 October 15.
First published online: June 19, 2013.
The authors would like to thank Michael Aivazis for helpful discussions.
This work is supported by the National Science Foundation
through grant number EAR-0941374 and is Caltech Seismological
Laboratory contribution 10086.|
|Funding Agency||Grant Number|
|Subject Keywords:||Inverse theory; Probability distributions; Computational seismology|
|Other Numbering System:|
|Other Numbering System Name||Other Numbering System ID|
|Caltech Seismological Laboratory||10086|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited On:||01 Aug 2013 20:04|
|Last Modified:||04 Oct 2016 22:20|
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