BRIDGING REMOTE SENSING AND HYDROGEOLOGY: STOCHASTIC MODELING OF ANISOTROPIC HYDRAULIC CONDUCTIVITY FOR AQUIFER CHARACTERIZATION USING INSAR

Managing groundwater resources effectively and sustainably amid growing global demand is a challenging task that requires high-accuracy subsurface models. In many aquifers, preferential flow features such as cracks and fractures introduce anisotropy. This anisotropy can be modeled by incorporating an anisotropic hydraulic conductivity (AHC) tensor into the equations of poroelasticity. This work aims to investigate the potential of interferometric synthetic aperture radar (InSAR) displacement data for inferring information about AHC in an aquifer.
To achieve this, we develop a three-dimensional poroelastic finite element method (FEM) with AHC, replicating key characteristics of the Anderson Junction aquifer in southwestern Utah. Our model implements the essential features of the 1994 Anderson Junction aquifer test, assuming a 24 to 1 hydraulic conductivity ratio along the principal axes, previously estimated using traditional well observation techniques (V. M. Heilweil & Hsieh, 2006).
The results of our FEM poroelastic model demonstrate that anisotropy in the hydraulic conductivity field induces an elliptical surface displacement pattern, which can be detected using InSAR data. However, our simulations indicate that the surface displacement resulting from the original Anderson Junction aquifer test is small to be captured by InSAR. To address this limitation, we propose hypothetical pumping test designs that maximize the utility of InSAR data in characterizing fractured aquifers.
Next, we construct a stochastic prior model of the AHC tensor that respects its symmetry and positive definiteness. This is achieved using a Bayesian model with a mixture of circular von Mises distributions. Finally, we laid the groundwork for Bayesian inversion, and we successfully constructed a NumPyro model that incorporates a Firedrake model and a probabilistic model and derived the corresponding adjoint model.
Furthermore, our stochastic AHC model leverages spectral decomposition to independently encode magnitude and orientation. The results of propagating AHC uncertainty through our aquifer model underscore the critical influence of fracture alignment on aquifer responses, revealing that the model is more stochastically sensitive to directional variations in AHC than to changes in its magnitude.
In the final chapter, we validated the integration between the partial differential equation (PDE) model (Firedrake) and the probabilistic model (JAX/NumPyro) through the Taylor test, which confirmed the correctness of the posterior gradient. In parallel, we solved a non-probabilistic inverse problem using adjoint-based optimization to estimate the AHC tensor from synthetic pressure observations. The results demonstrate that the inverse framework accurately recovers the true AHC tensor, confirming the reliability of our PDE-constrained optimization approach and its potential for future Bayesian inference applications.