Bayesian inversion of joint SH seismic and seismoelectric data to infer glacier system properties
Résumé
In glacial studies, properties such as glacier thickness and the basement permeability
and porosity are key to understand the hydrological and mechanical behaviour of
the system. The seismoelectric method could potentially be used to determine key
properties of glacial environments. Here we analytically model the generation of seis-
mic and seismoelectric signals by means of a shear horizontal seismic wave source
on top of a glacier overlying a porous basement. Considering a one-dimensional
setting, we compute the seismic waves and the electrokinetically induced electric
field. We then analyse the sensitivity of the seismic and electromagnetic data to rele-
vant model parameters, namely depth of the glacier bottom, porosity, permeability,
shear modulus and saturating water salinity of the glacier basement. Moreover, we
study the possibility of inferring these key parameters from a set of very low noise
synthetic data, adopting a Bayesian framework to pay particular attention to the
uncertainty of the model parameters mentioned above. We tackle the resolution of
the probabilistic inverse problem with two strategies: (1) we compute the marginal
posterior distributions of each model parameter solving multidimensional integrals
numerically and (2) we use a Markov chain Monte Carlo algorithm to retrieve a
collection of model parameters that follows the posterior probability density func-
tion of the model parameters, given the synthetic data set. Both methodologies are
able to obtain the marginal distributions of the parameters and estimate their mean
and standard deviation. The Markov chain Monte Carlo algorithm performs better
in terms of numerical stability and number of iterations needed to characterize the
distributions. The inversion of seismic data alone is not able to constrain the values of
porosity and permeability further than the prior distribution. In turn, the inversion of
the electric data alone, and the joint inversion of seismic and electric data are useful
to constrain these parameters as well as other glacial system properties. Furthermore,
the joint inversion reduces the uncertainty of the model parameters estimates and
provides more accurate results.
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