Stochastic anisotropic aquifer characterization: a poroelastic finite element model and the potential of using InSAR data

Effective aquifer management depends on predictive models calibrated with diverse data sources. Surface deformation measurements from Interferometric Synthetic Aperture Radar (InSAR) provide valuable insights into subsurface hydraulic properties by leveraging the poroelastic coupling between fluid flow and ground deformation. However, most Bayesian frameworks assume isotropic priors, limiting their capacity to represent complex anisotropic behavior in real aquifers. To address this, we introduce a Bayesian model for anisotropic hydraulic conductivity based on a Lie group framework for constructing symmetric positive definite (SPD) tensors. The hydraulic conductivity tensor is represented via spectral decomposition, separating uncertainties in magnitude and orientation. Directional uncertainty is modeled using a Bayesian mixture of von Mises distributions, calibrated against fracture outcrop data. We apply this approach to the Anderson Junction aquifer in Utah, a site characterized by strong anisotropy. Two modeling scenarios are explored: one incorporating pumping test data, and another relying solely on geological observations. Forward uncertainty propagation reveals that directional uncertainty significantly influences predicted InSAR line-of-sight (LOS) displacements. Our results highlight the importance of incorporating stochastic anisotropy for robust and flexible characterization of aquifer systems.