Multi-Frequency Oscillatory Hydraulic Tomography Improves Heterogeneity Imaging and Resolution and Reduces Uncertainty

Understanding subsurface heterogeneity is crucial to predicting groundwater flow pathways, mixing, and other processes in aquifers and other fluid reservoirs. Despite significant effort developing geophysical tools to understand this heterogeneity, geophysical mapping of aquifer flow parameters—transmissivity $(T)$, and storativity $(S)$—remains challenging due to both uncertainty in petrophysical relationships and resolution/data coverage issues. A more direct approach to mapping heterogeneity over a range of scales is by inducing aquifer flow at various scales and analyzing spatially distributed pressure responses, so-called Hydraulic Tomography (HT). Oscillatory Hydraulic Tomography (OHT) is a recently-developed variant of HT that takes advantage of signal processing routines and fast computational models to reduce data noise impacts and enable high-performance tomography workflows. Laboratory and field studies have demonstrated that OHT tests performed at multiple frequencies appear to improve aquifer imaging results; however, a rigorous analysis of data content, resolution and uncertainty in OHT workflows has not been performed to-date. This work assesses the resolution and uncertainty in single- and multi-frequency OHT testing through numerical experiments and three separate approaches to assessing tomographic resolution: singular value decomposition, geophysical “checkerboard” tests, and stochastic imaging experiments. Contrary to results in some prior published work, all three approaches verify the ability of OHT to image aquifer parameters at resolutions of roughly $\frac{1}{2}$ inter-well spacing distances, and similarly demonstrate the added information provided by multi-frequency data.