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Understanding the detailed spatial variation of hydraulic properties in the subsurface has been the subject of intensive research over the past three decades. A recently developed approach to characterize subsurface properties is hydraulic tomography, in which a series of pumping tests are jointly inverted using a heterogeneous numerical model. Recently, Cardiff et al. (2013) proposed a modified tomography approach named Oscillatory Hydraulic Tomography (OHT), in which periodic pumping signals of different frequencies serve as the aquifer stimulation, and pressure responses are recorded at observation locations for tomographic analysis. Its key advantages over traditional hydraulic tomography are that: (1) there is no net injection or extraction of water, and (2) the impulse (an oscillatory signal of known frequency) is easily extracted from noisy data. However, OHT has only been evaluated through numerical experiments to date. In this work, we evaluate OHT performance by attempting to image known heterogeneities in a synthetic aquifer. An instrumented laboratory sandbox is filled with material of known hydraulic properties, and we measure aquifer responses due to oscillatory pumping stimulations at periods of 2, 5, 10, and 20 s. Pressure oscillation time series are processed through Fourier Transforms and inverted tomographically to obtain estimates of aquifer heterogeneity, using a fast, steady‐periodic groundwater flow model. We show that OHT is able to provide robust estimates of aquifer hydraulic conductivity even in cases where relatively few pumping tests and observation locations are available. The use of multiple stimulation frequencies is also shown to improve imaging results.

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The minimum relative entropy (MRE) method has been applied in a wide variety of fields since it was first introduced. Woodbury and Ulrych (Water Resour Res 29(8): 2847–2860, 1993, Water Resour Res 32(9): 2671–2681, 1996) adopted and improved this method to solve linear inverse problems in aquifers. In this work, the MRE method was improved to detect the source release history in 2-D aquifer characterized by a non-uniform flow-field. The approach was tested on two cases: a 2-D homogeneous conductivity field and a heterogeneous one (the hydraulic conductivity presents three orders of magnitude in terms of variability). In the latter case the transfer function cannot be described with an analytical formulation, thus, the transfer functions were estimated by means of a numerical procedure. In order to analyze the method performance in different conditions, two datasets have been used: observations collected at the same time at 20 different monitoring points, and observations collected at 2 monitoring points at several times. The observed data have been processed with and without a random error and the Boxcar and Gaussian probability distribution functions were considered as a priori information. The agreement between the true and the estimated data has been evaluated through the calculation of the normalized Root Mean Square error. The approach was able to recover the release history even in the most difficult case.

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