Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

Details Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

Jun 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010geoji.181.1441f&link_type=abstract

Geophysical Journal International, Volume 181, Issue 3, pp. 1441-1458.

Mathematics

Probability

2

Inverse Theory, Probability Distributions, Seismic Cycle

Scientific paper

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework.
In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

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