The continuous redistribution of water involved in the hydrologic cycle leads to deformation of the solid Earth. On a global scale, this deformation is well explained by the loading imposed by hydrological mass variations and can be quantified to first order with space-based gravimetric and geodetic measurements. At the regional scale, however, aquifer systems also undergo poroelastic deformation in response to groundwater fluctuations. Disentangling these related but distinct 3D deformation fields from geodetic time series is essential to accurately invert for changes in continental water mass, to understand the mechanical response of aquifers to internal pressure changes as well as to correct time series for these known effects. Here, we demonstrate a methodology to accomplish this task by considering the example of the well-instrumented Ozark Plateaus Aquifer System (OPAS) in the central United States. We begin by characterizing the most important sources of groundwater level variations in the spatially heterogeneous piezometer dataset using an Independent Component Analysis. Then, to estimate the associated poroelastic displacements, we project geodetic time series corrected for hydrological loading effects onto the dominant groundwater temporal functions. We interpret the extracted displacements in light of analytical solutions and a 2D model relating groundwater level variations to surface displacements. In particular, the relatively low estimates of elastic moduli inferred from the poroelastic displacements and groundwater fluctuations may be indicative of aquifer layers with a high fracture density. Our findings suggest that OPAS undergoes significant poroelastic deformation, including highly heterogeneous horizontal poroelastic displacements.