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Imaging the spatial distribution and variability of the physical properties controlling subsurface fluid flow remains a fundamental geophysical challenge. Oscillatory hydraulic tomography is a minimally invasive hydraulic testing approach to image these hydraulic properties; however, the resolution and uncertainty associated with this tomographic method remains an open question. Using linearized and non-linear approaches, we show that multi-frequency oscillatory hydraulic tomography provides additional information content that improves imaging resolution and reduces estimated parameter uncertainty. 

Abstract Fractured sedimentary bedrock aquifers represent complex flow systems that may contain fast, fracture‐dominated flow paths and slower, porous media‐dominated flow paths. Thus, characterizing the dynamics of flow and transport through these aquifers remains a fundamental hydrogeologic challenge. Recent studies have demonstrated the utility of a novel hydraulic testing approach, oscillatory flow testing, in field settings to characterize single bedrock fractures embedded in low‐porosity sedimentary bedrock. These studies employed an idealized analytical model assuming Darcian flow through a nondeforming, constant‐aperture, nonleaky fracture for data interpretation, and reported period‐dependent effective fracture flow parameters. Here, we present the application of oscillatory flow testing across a range of frequencies and inter‐well spacings on a fracture embedded in poorly cemented sedimentary bedrock with considerable primary porosity at the Field Site for Research in Fractured Sedimentary Rock. Consistent with previous studies, we show an apparent period‐dependence in returned flow parameters, with hydraulic diffusivity decreasing and storativity increasing with increasing oscillation period, when assuming an idealized fracture conceptual model. We present simple analyses that examine non‐Darcian flow and borehole storage effects as potential test design artifacts and a simple analytical model that examines fluid leakage to the surrounding host rock as a potential hydraulic mechanism that might contribute to the period‐dependent flow parameters. These analyses represent a range of conceptual assumptions about fracture behavior during hydraulic testing, none of which account for the measured responses during oscillatory flow testing, leading us to argue that other hydraulic processes (e.g., aperture heterogeneity and/or fracture hydromechanics) are necessary to accurately represent pressure propagation through fractured sedimentary bedrock. 

Abstract Characterizing aquifer properties and their associated uncertainty remains a fundamental challenge in hydrogeology. Recent studies demonstrate the use of oscillatory flow interference testing to characterize effective aquifer flow properties. These characterization efforts relate the relative amplitude and phase of an observation signal with a single frequency component to aquifer diffusivity and transmissivity. Here, we present a generalized workflow that relates extracted Fourier coefficients for observation signals with single and multiple frequency components to aquifer flow properties and their associated uncertainty. Through synthetic analytical modeling we show that multi‐frequency oscillatory flow interference testing adds information that improves inversion performance and decreases parameter uncertainty. We show increased observation signal length, sampling frequency, and pressure sensor accuracy all produce decreased parameter uncertainty. This work represents the first attempt we are aware of to quantify effective aquifer parameters and their associated uncertainty using multi‐frequency oscillatory flow interference testing.