Towards assimilating InSAR data into a model of a highly anisotropic aquifer system

The flow of water in many aquifers is driven by strong anisotropy created by preferential flow features such as cracks and faults. This anisotropy can be modeled by introducing the anisotropic hydraulic conductivity (AHC) tensor into the equations of poroelasticity. Our overall goal is to assimilate Interferometric Synthetic Aperture Radar (InSAR) remote sensing data into a model of an aquifer system in order to infer information about AHC. In this work we develop a flexible stochastic prior model of the AHC tensor that respects its underlying symmetry and positive definiteness. Our method for calibrating and constructing a random AHC tensor involves three steps: 1) fitting a Bayesian model with circular von Mises distributions to fracture outcrop data, 2) fitting a Bayesian model of two independent log-normal distributions to hydraulic conductivity estimates, and 3) feeding these stochastic models into an extended version of [1] model to construct random symmetric positive definite tensors using spectral decomposition to encode size and orientation separately.