Hydraulic tomography (i.e., a sequential aquifer test) has recently been proposed as a method for characterizing aquifer heterogeneity. During a hydraulic tomography experiment, water is sequentially pumped from or injected into an aquifer at different vertical portions or intervals of the aquifer. During each pumping or injection, hydraulic head responses of the aquifer at other intervals are monitored, yielding a set of head/discharge (or recharge) data. By sequentially pumping (or injecting) water at one interval and monitoring the steady state head responses at others, many head/discharge (recharge) data sets are obtained. In this study a sequential inverse approach is developed to interpret results of hydraulic tomography. The approach uses an iterative geostatistical inverse method to yield the effective hydraulic conductivity of an aquifer, conditioned on each set of head/discharge data. To efficiently include all the head/discharge data sets, a sequential conditioning method is employed. It uses the estimated hydraulic conductivity field and covariances, conditioned on the previous head/discharge data set, as prior information for next estimations using a new set of pumping data. This inverse approach was first applied to hypothetical, two-dimensional, heterogeneous aquifers to investigate the optimal sampling scheme for the hydraulic tomography, i.e., the design of well spacing, pumping, and monitoring locations. The effects of measurement errors and uncertainties in statistical parameters required by the inverse model were also investigated. Finally, the robustness of this inverse approach was demonstrated through its application to a hypothetical, three-dimensional, heterogeneous aquifer.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000WR900114

Hydraulic tomography: Development of a new aquifer test method

This paper reviews the recent geophysical literature addressing the estimation of saturated hydraulic conductivity (K) from static low frequency electrical measurements (electrical resistivity, induced polarization (IP) and spectral induced polarization (SIP)). In the first part of this paper, research describing how petrophysical relations between electrical properties and effective (i.e. controlling fluid transport) properties of (a) the interconnected pore volumes and interconnected pore surfaces, have been exploited to estimate K at both the core and field scale is reviewed. We start with electrical resistivity measurements, which are shown to be inherently limited in K estimation as, although resistivity is sensitive to both pore volume and pore surface area properties, the two contributions cannot be separated. Efforts to utilize the unique sensitivity of IP and SIP measurements to physical parameters that describe the interconnected pore surface area are subsequently introduced and the incorporation of such data into electrical based Kozeny–Carman type models of K estimation is reviewed. In the second part of this review, efforts to invert geophysical datasets for spatial patterns of K variability (e.g. aquifer geometries) at the field-scale are considered. Inversions, based on the conversion of an image of a geophysical property to a hydrological property assuming a valid petrophysical relationship, as well as joint/constrained inversion methods, whereby multiple geophysical and hydrological data are inverted simultaneously, are briefly covered. This review demonstrates that there currently exists an opportunity to link, (1) the petrophysics relating low frequency electrical measurements to effective hydraulic properties, with (2) the joint inversion strategies developed in recent years, in order to obtain more meaningful estimates of spatial patterns of K variability than previously reported.

Near Surface Electrical Characterization of Hydraulic Conductivity: From Petrophysical Properties to Aquifer Geometries—A Review

[1] Hydraulic tomography is a cost-effective technique for characterizing the heterogeneity of hydraulic parameters in the subsurface. During hydraulic tomography surveys a large number of hydraulic heads (i.e., aquifer responses) are collected from a series of pumping or injection tests in an aquifer. These responses are then used to interpret the spatial distribution of hydraulic parameters of the aquifer using inverse modeling. In this study, we developed an efficient sequential successive linear estimator (SSLE) for interpreting data from transient hydraulic tomography to estimate three-dimensional hydraulic conductivity and specific storage fields of aquifers. We first explored this estimator for transient hydraulic tomography in a hypothetical one-dimensional aquifer. Results show that during a pumping test, transient heads are highly correlated with specific storage at early time but with hydraulic conductivity at late time. Therefore reliable estimates of both hydraulic conductivity and specific storage must exploit the head data at both early and late times. Our study also shows that the transient heads are highly correlated over time, implying only infrequent head measurements are needed during the estimation. Applying this sampling strategy to a well-posed problem, we show that our SSLE can produce accurate estimates of both hydraulic conductivity and specific storage fields. The benefit of hydraulic tomography for ill-posed problems is then demonstrated. Finally, to affirm the robustness of our SSLE approach, we apply the SSLE approach to a hypothetical three-dimensional heterogeneous aquifer.

/pdf/characterization-of-aquifer-heterogeneity-using-transient-438p0vk3oc.pdf

Characterization of aquifer heterogeneity using transient hydraulic tomography

[1] Hydraulic tomography is a method to identify the three-dimensional spatial distribution of hydraulic properties in the subsurface. We propose a tomographic approach providing the inversion of travel times of hydraulic or pneumatic tests conducted in a tomographic array. The inversion is based on the relation between the peak time of a recorded transient pressure curve and the diffusivity of the investigated system. The development of a transformation factor enables the inversion of further travel times besides the peak time of a transient curve. As the early travel times of the curve are mainly related to preferential flow features while the inversion based on late travel times are reflecting an integral behavior, it can be assumed that the different inversion results reflect the properties of the overall system. By comparing the different reconstructions the system interpretation therefore becomes more comprehensive and reliable. Furthermore, the similarity of the proposed hydraulic tomographic approach to seismic travel time tomography allows us to apply the inversion algorithms which are used for seismic tomography. We therefore apply the method of staggered grids, which enables to refine the grid resulting in a higher nominal resolution, to data from a set of interference tests arranged in a tomographic array. The tests were conducted in an unsaturated fractured sandstone cylinder in the laboratory. The three-dimensional reconstructions of the diffusivity distribution are found to be highly reliable and robust. In particular, the mapped fracture of the sandstone cylinder coincides with our reconstructed diffusivity distribution.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2003WR002262

A travel time based hydraulic tomographic approach

[1] Traditional analysis of aquifer tests uses the observed drawdown at one well, induced by pumping at another well, for estimating the transmissivity (T) and storage coefficient (S) of an aquifer. The analysis relies on Theis' solution or Jacob's approximate solution, which assumes aquifer homogeneity. Aquifers are inherently heterogeneous at different scales. If the observation well is screened in a low-permeability zone while the pumping well is located in a high-permeability zone, the resulting situation contradicts the homogeneity assumption in the traditional analysis. As a result, what does the traditional interpretation of the aquifer test tell us? Using numerical experiments and a first-order correlation analysis, we investigate this question. Results of the investigation suggest that the effective T and S for an equivalent homogeneous aquifer of Gaussian random T and S fields vary with time as well as the principal directions of the effective T. The effective T and S converge to the geometric and arithmetic means, respectively, at large times. Analysis of the estimated T and S, using drawdown from a single observation well, shows that at early time both estimates vary with time. The estimated S stabilizes rapidly to the value dominated by the storage coefficient heterogeneity in between the pumping and the observation wells. At late time the estimated T approaches but does not equal the effective T. It represents an average value over the cone of depression but influenced by the location, size, and degree of heterogeneity as the cone of depression evolves.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2004WR003717

Traditional analysis of aquifer tests: Comparing apples to oranges?

A tomographical method is presented that allows the reconstruction of the structure of soil layers between two boreholes. If the soil is water saturated, the transient field equation for pore water pressure S(x) delta tu(x,t)- Del .(k(x) Del u(x,t))=Q can be used to reconstruct the soil structure from its permeability k(x). The transient potential field u(x, t) is controlled by hydraulic dipoles (point source and point sink). The positions of source and sink are varied over both boreholes. Pore water pressure observations are used as data for the inverse problem. Uniqueness problems are discussed. The forward problem is discretized in a FE algorithm, the inverse problem solved by a standard output least-squares method.

https://iopscience.iop.org/article/10.1088/0266-5611/11/2/005/pdf

Identification of the permeability distribution in soil by hydraulic tomography

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Identification of the permeability distribution in soil by hydraulic tomography