<p>Sustainable aquifer management depends on reliable predictive models calibrated against diverse sources of data. Poroelastic coupling between fluid flow and surface displacement in an aquifer indicates that precise Interferometric Synthetic Aperture Radar (InSAR) displacement observation can be used to calibrate lateral hydraulic conductivity values. While previous Bayesian inference approaches to this problem have assumed isotropic random models for the hydraulic conductivity, many aquifers are characterized by strong anisotropic hydraulic conductivity (AHC). Consequently, isotropic models are in many cases inadequate. Leveraging a recently proposed Lie group approach for constructing random symmetric positive definite matrices, we propose a new random model for describing AHC in aquifer systems that can incorporate directional information from complex and potentially multi-modal structural geological data. We apply this methodology to describing two conceptual states of uncertainty at the 1996 Anderson Junction aquifer pump test where both multi-modal circular fracture outcrop and AHC principal magnitude data is available. After calibration against this data, the induced uncertainty in AHC is propagated through a partial differential equation-based conceptual model of the test. Our results show that the proposed methodology provides a flexible tool for modeling the effect of uncertain anisotropic hydraulic conductivity on InSAR-measurable surface displacements. Complete open source scripts using the DOLFINx finite element solver and numpyro/JAX are given as supplementary material.</p>