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Accurate estimation of the hydrological properties of nearsurface aquifers is important because these properties strongly influence groundwater flow and solute transport. Laboratorybased investigations have indicated that induced polarization (IP) properties of porous media may be linked, through either semiempirical or fully mechanistic models, to hydrological properties including hydraulic conductivity. Therefore, there is a need for field assessments of the value of IP measurements in providing insights into the hydrological properties of aquifers. A cross-borehole IP survey was carried out at the Boise Hydrogeophysical Research Site (BHRS), an unconsolidated fluvial aquifer that has previously been well-studied with a variety of geophysical and hydrogeologic techniques. High-quality IP measurements were inverted, with careful consideration of the data error structure, to provide a 3D distribution of complex electrical conductivity values. The inverted distribution was further simplified using k-means cluster analysis to divide the inverted volume into discrete zones with horizontal layering. Identified layers based on complex electrical conductivity inversions are in broad agreement with stratigraphic units identified in previous studies at the site. Although mostly subtle variations in the phase angle are recovered through inversion of field data, greater contrasts in the IP data are evident at some unit boundaries. However, in coarse-grained aquifers, such as the BHRS, the discrimination of mildly contrasting lithologic units and associated changes in hydraulic conductivity of one or two orders of magnitude are unlikely to be achieved through field IP surveys. Despite the difficulty of differentiating subtle differences between all units, overall estimates of hydraulic conductivity purely from our field IP data are typically within an order of magnitude of independently measured values.

There is growing interest in the link between electrical polarization and physical properties of geologic porous media. In particular, spectral characteristics may be controlled by the same pore geometric properties that influence fluid permeability of such media. Various models have been proposed to describe the spectral-induced-polarization (SIP) response of permeable rocks, and the links between these models and hydraulic properties have been explored, albeit empirically. Computation of the uncertainties in the parameters of such electrical models is essential for effective use of these relationships. The formulation of an electrical dispersion model in terms of a distribution of relaxation times and associated chargeabilities has been demonstrated to be an effective generalized approach; however, thus far, such an approach has only been considered in a deterministic framework. Here, we formulate a spectral model based on a distribution of polarizations. By using a simple polynomial descriptor of such a distribution, we are able to cast the model in a stochastic manner and solve it using a Markov-chain Monte Carlo (McMC) sampler, thus allowing the computation of model-parameter uncertainties. We apply the model to synthetic data and demonstrate that the stochastic method can provide posterior distributions of model parameters with narrow bounds around the true values when little or no noise is added to the synthetic data, with posterior distributions that broaden with increasing noise. We also apply our model to experimental measurements of six sandstone samples and compare physical properties of a number of samples of porous media with stochastic estimates of characteristic relaxation times. We demonstrate the utility of our method on electrical spectra with different response characteristics and show that a single metric of relaxation time for the SIP response is not sufficient to provide clear insight into the physical characteristics of a sample.

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