Abstract
The development of three-dimensional seismic models for the crust
and upper mantle has traditionally focused on finding one model that
provides the best fit to the data while observing some regularization
constraints. In contrast to this, the inversion employed here fits
the data in a probabilistic sense and thus provides a quantitative
measure of model uncertainty. Our probabilistic model is based on
two sources of information: (1) prior information, which is independent
from the data, and (2) different geophysical data sets, including
thickness constraints, velocity profiles, gravity data, surface wave
group velocities, and regional body wave traveltimes. We use a Markov
chain Monte Carlo (MCMC) algorithm to sample models from the prior
distribution, the set of plausible models, and test them against
the data to generate the posterior distribution, the ensemble of
models that fit the data with assigned uncertainties. While being
computationally more expensive, such a probabilistic inversion provides
a more complete picture of solution space and allows us to combine
various data sets. The complex geology of the European Arctic, encompassing
oceanic crust, continental shelf regions, rift basins and old cratonic
crust, as well as the nonuniform coverage of the region by data with
varying degrees of uncertainty, makes it a challenging setting for
any imaging technique and, therefore, an ideal environment for demonstrating
the practical advantages of a probabilistic approach. Maps of depth
to basement and depth to Moho derived from the posterior distribution
are in good agreement with previously published maps and interpretations
of the regional tectonic setting. The predicted uncertainties, which
are as important as the absolute values, correlate well with the
variations in data coverage and quality in the region. A practical
advantage of our probabilistic model is that it can provide estimates
for the uncertainties of observables due to model uncertainties.
We will demonstrate how this can be used for the formulation of earthquake
location algorithms that take model uncertainties into account when
estimating location uncertainties.
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