  Characterizing the properties of groundwater aquifers is essential for
predicting aquifer response and managing groundwater resources. In this work,
we develop a high-dimensional scalable Bayesian inversion framework governed by
a three-dimensional quasi-static linear poroelastic model to characterize
lateral permeability variations in groundwater aquifers. We determine the
maximum a posteriori (MAP) point of the posterior permeability distribution
from centimeter-level surface deformation measurements obtained from
Interferometric Synthetic Aperture Radar (InSAR). The scalability of our method
to high parameter dimension is achieved through the use of adjoint-based
derivatives, inexact Newton methods to determine the MAP point, and a Mat\'ern
class sparse prior precision operator. Together, these guarantee that the MAP
point is found at a cost, measured in number of forward/adjoint poroelasticity
solves, that is independent of the parameter dimension. We apply our
methodology to a test case for a municipal well in Mesquite, Nevada, in which
InSAR and GPS surface deformation data are available. We solve problems with up
to 320,824 state variable degrees of freedom (DOFs) and 16,896 parameter DOFs.
A consistent treatment of noise level is employed so that the aquifer
characterization result does not depend on the pixel spacing of surface
deformation data. Our results show that the use of InSAR data significantly
improves characterization of lateral aquifer heterogeneity, and the InSAR-based
aquifer characterization recovers complex lateral displacement trends observed
by independent daily GPS measurements.
