Bayesian inversion of joint SH seismic and seismoelectric data to infer glacier system properties

International audienceIn glacial studies, properties such as glacier thickness and the basement permeabilityand porosity are key to understand the hydrological and mechanical behaviour ofthe system. The seismoelectric method could potentially be used to determine keyproperties of glacial environments. Here we analytically model the generation of seis-mic and seismoelectric signals by means of a shear horizontal seismic wave sourceon top of a glacier overlying a porous basement. Considering a one-dimensionalsetting, we compute the seismic waves and the electrokinetically induced electricfield. 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, westudy the possibility of inferring these key parameters from a set of very low noisesynthetic data, adopting a Bayesian framework to pay particular attention to theuncertainty of the model parameters mentioned above. We tackle the resolution ofthe probabilistic inverse problem with two strategies: (1) we compute the marginalposterior distributions of each model parameter solving multidimensional integralsnumerically and (2) we use a Markov chain Monte Carlo algorithm to retrieve acollection of model parameters that follows the posterior probability density func-tion of the model parameters, given the synthetic data set. Both methodologies areable to obtain the marginal distributions of the parameters and estimate their meanand standard deviation. The Markov chain Monte Carlo algorithm performs betterin terms of numerical stability and number of iterations needed to characterize thedistributions. The inversion of seismic data alone is not able to constrain the values ofporosity and permeability further than the prior distribution. In turn, the inversion ofthe electric data alone, and the joint inversion of seismic and electric data are usefulto constrain these parameters as well as other glacial system properties. Furthermore,the joint inversion reduces the uncertainty of the model parameters estimates andprovides more accurate results