[1] An algorithm is developed to interpret self-potential (SP) data in terms of distribution of Darcy velocity of the ground water. The model is based on the proportionality existing between the streaming current density and the Darcy velocity. Because the inverse problem of current density determination from SP data is underdetermined, we use Tikhonov regularization with a smoothness constraint based on the differential Laplacian operator and a prior model. The regularization parameter is determined by the L-shape method. The distribution of the Darcy velocity depends on the localization and number of non-polarizing electrodes and information relative to the distribution of the electrical resistivity of the ground. A priori hydraulic information can be introduced in the inverse problem. This approach is tested on two synthetic cases and on real SP data resulting from infiltration of water from a ditch.

The geostatistical structure of a heterogeneous coarse fluvial aquifer is investigated with porosity data derived from neutron logs at a research well field (Boise Hydrogeophysical Research Site, or BHRS) that was designed, in part, to support three‐dimensional geostatistical analysis of hydrologic and geophysical parameters. Recognizing that the coarse fluvial deposits include subdivisions (units between bounding surfaces), we adopt a hierarchical approach and examine the porosity geostatistics of the aquifer at three scales. At the BHRS, the saturated fluvial deposits as a whole (maximum interwell spacing ∼80 m, thickness ∼16–18 m) are at hierarchical level 1; five subhorizontal units within these deposits (four cobble‐dominated units and a channel sand) can be traced across the central area of the BHRS and are at hierarchical level 2; and subunits (patches or lenses) in one of the level 2 units (Unit 4), are at hierarchical level 3. We use variography and porosity statistics to recognize nonstationarity at hierarchical level 1 and in one of the level 2 units (Unit 4) where the means and variances of porosity differences as a function of lag are not constant between distinct units and subunits, respectively. The geostatistical structure at level 1 is modeled with different horizontal and vertical structures that have different sills (vertical sill greater than horizontal sill). The difference in sills can be explained quantitatively by the summing of weighted sills from all individual units and combined units (i.e., a given pair of different units), where the weights are the proportions of data pairs contributing to the sills at each lag from the individual and combined units. Extension of this analysis leads to a weighted, multistructure form of the variogram function whereby a global experimental variogram in a hierarchical system can be decomposed quantitatively into weighted component individual‐ and combined‐unit (or facies) structures for any number of units or hierarchical levels. Such decomposition of the global horizontal variogram from the BHRS indicates that short‐range periodicity in that structure is due to both (1) combined‐unit structures associated with patches or lenses at hierarchical level 3 in Unit 4 and (2) variations in thickness of Unit 2. For hierarchical multifacies systems, structure models fit to global horizontal and vertical experimental variograms may not be useful for subsequent stochastic modeling if the system on which the structure models are based is nonstationary.

[1] 3-D Hydraulic tomography (3-D HT) is a method for aquifer characterization whereby the 3-D spatial distribution of aquifer flow parameters (primarily hydraulic conductivity, K) is estimated by joint inversion of head change data from multiple partially penetrating pumping tests. While performance of 3-D HT has been studied extensively in numerical experiments, few field studies have demonstrated the real-world performance of 3-D HT.Here we report on a 3-D transient hydraulic tomography (3-D THT) field experiment at the Boise Hydrogeophysical Research Site which is different from prior approaches in that it represents a ''baseline'' analysis of 3-D THT performance using only a single arrangement of a central pumping well and five observation wells with nearly complete pumping and observation coverage at 1 m intervals. We jointly analyze all pumping tests using a geostatistical approach based on the quasi-linear estimator of Kitanidis (1995). We reanalyze the system after progressively removing pumping and/or observation intervals; significant progressive loss of information about heterogeneity is quantified as reduced variance of the K field overall, reduced correlation with slug test K estimates at wells, and reduced ability to accurately predict independent pumping tests. We verify that imaging accuracy is strongly improved by pumping and observational densities comparable to the aquifer heterogeneity geostatistical correlation lengths. Discrepancies between K profiles at wells, as obtained from HT and slug tests, are greatest at the tops and bottoms of wells where HT observation coverage was lacking.Citation: Cardiff, M., W. Barrash, and P. K. Kitanidis (2013), Hydraulic conductivity imaging from 3-D transient hydraulic tomography at several pumping/observation densities, Water Resour. Res., 49,[7311][7312][7313][7314][7315][7316][7317][7318][7319][7320][7321][7322][7323][7324][7325][7326]

[1] Periodic pumping tests, in which a fluid is extracted during half a period, then reinjected, have been used historically to estimate effective aquifer properties. In this work, we suggest a modified approach to periodic pumping test analysis in which one uses several periodic pumping signals of different frequencies as stimulation, and responses are analyzed through inverse modeling using a ''steady-periodic'' model formulation. We refer to this strategy as multifrequency oscillatory hydraulic imaging. Oscillating pumping tests have several advantages that have been noted, including no net water extraction during testing and robust signal measurement through signal processing. Through numerical experiments, we demonstrate additional distinct advantages that multifrequency stimulations have, including: (1) drastically reduced computational cost through use of a steady-periodic numerical model and (2) full utilization of the aquifer heterogeneity information provided by responses at different frequencies. We first perform fully transient numerical modeling for heterogeneous aquifers and show that equivalent results are obtained using a faster steady-periodic heterogeneous numerical model of the wave phasor. The sensitivities of observed signal response to aquifer heterogeneities are derived using an adjoint state-based approach, which shows that different frequency stimulations provide complementary information. Finally, we present an example 2-D application in which sinusoidal signals at multiple frequencies are used as a data source and are inverted to obtain estimates of aquifer heterogeneity. These analyses show the different heterogeneity information that can be obtained from different stimulation frequencies, and that data from several sinusoidal pumping tests can be rapidly inverted using the steady-periodic framework.

[1] Hydraulic tomography is a field scale aquifer characterization method capable of estimating 3-D heterogeneous parameter distributions, and is directly sensitive to hydraulic conductivity (K), thus providing a useful data source for improving flow and transport models. We present results from a proof-of-concept field and modeling study in which we apply 3-D transient hydraulic tomography (3DTHT) to the relatively high-K and moderately heterogeneous unconfined aquifer at the Boise Hydrogeophysical Research Site. Short-duration (20 min) partially penetrating pumping tests, for which observed responses do not reach steady state, are used as the aquifer stimulation. To collect field data, we utilize a system of temporarily emplaced packer equipment to isolate multiple discrete intervals in boreholes. To analyze the data, we utilize MODFLOW combined with geostatistical inversion code based on the quasilinear approach of Kitanidis (1995). This combination of practical software allows inversion of large datasets (>250 drawdown curves, and almost 1000 individual data points) and estimation of K at >100,000 locations; reasonable runtimes are obtained using a single multicore computer with 12 GB of RAM. The K heterogeneity results from 3DTHT are cross-validated against K characterization from a large set of partially penetrating slug tests, and found to be quite consistent. The use of portable, modular equipment for field implementation means that 3DTHT data collection can be performed (including mobilization/demobilization) within a matter of days. Likewise, use of a practical, efficient and scalable numerical modeling and inversion strategy means that computational effort is drastically reduced, such that 3-D aquifer property distributions can be estimated quickly.Citation: Cardiff, M., W. Barrash, and P. K. Kitanidis (2012), A field proof-of-concept of aquifer imaging using 3-D transient hydraulic tomography with modular, temporarily-emplaced equipment, Water Resour. Res., 48, W05531,