Bayesian joint inversion of surface deformation and hydraulic data for aquifer characterization

Remote sensing and geodetic measurements are providing a wealth of new, spatially-distributed, time-series data that promise to improve the characterization of regional aquifers. The integration of these geodetic measurements with other hydrological observations has the potential to aid the sustainable management of groundwater resources through improved characterization of the spatial variation of aquifer properties. The joint inversion of geomechanical and hydrological data is challenging, because it requires fully-coupled hydrogeophysical inversion for the aquifer parameters, based on a coupled geomechanical and hydrological process model. We formulate a Bayesian inverse problem to infer the lateral permeability variation in an aquifer from geodetic and hydraulic data, and from prior information. We compute the maximum a posteriori (MAP) estimate of the posterior permeability distribution, and use a local Gaussian approximation around the MAP point to characterize the uncertainty. For two-dimensional test cases we also explore the full posterior permeability distribution through Markov-Chain Monte Carlo (MCMC) sampling. To cope with the large parameter space dimension, we use local Gaussian approximations as proposal densities in the MCMC algorithm. Using increasingly complex model problems, based on the work of Mandel (1953) and Segall (1985), we find the following general properties of poroelastic inversions: (1) Augmenting standard hydraulic well data by surface deformation data improves the aquifer characterization. (2) Surface deformation contributes the most in shallow aquifers, but provides useful information even for the characterization of aquifers down to 1 km. (3) In general, it is more difficult to infer high permeability regions, and their characterization requires frequent measurement to resolve the associated short response time scales. (4) In horizontal aquifers, the vertical component of the surface deformation provides a smoothed image of the pressure distribution in the aquifer. The coupled inversion is therefore a promising approach to detect flow barriers and to monitor pore pressure evolution. Model problemd for poroelastic inversion.