Joint inversion of steady-state hydrologic and self-potential data for 3D hydraulic conductivity distribution at the Boise Hydrogeophysical Research Site

We combine sedimentological, hydraulic and geophysical information to characterize the 3D distribution of transport properties of an heterogeneous aquifer. We focus on the joint inversion of hydraulic head and self-potential measurements collected during an extensive experimental campaign performed at the Boise Hydrogeophysical Research Site (BHRS), Boise, Idaho, and involving a series of dipole tests. While hydraulic head data obtained from piezometric readings in open wells represent a depth-averaged value, self-potential signals provide an estimate of the water table location. The aquifer is conceptualized as a multiple-continuum, where the volumetric fraction of a geo-material within a cell of the numerical flow model is calculated by Multiple Indicator Kriging. The latter is implemented on the basis of available sedimentological information. The functional format of the indicator variograms and associated parameters are estimated on the basis of formal model identification criteria. Self-potential and hydraulic head data have been embedded jointly within a three-dimensional inverse model of groundwater flow at the site. Each identified geo-material (category) is assumed to be characterized by a constant hydraulic conductivity. The latter constitute the set of model parameters. The hydraulic conductivity associated with a numerical block is then calculated as a weighted average of the conductivities of the geo-materials which are collocated in the block by means of Multiple Indicator Kriging. Model parameters are estimated by a Maximum Likelihood fit between measured and modeled state variables, resulting in a spatially heterogeneous distribution of hydraulic conductivity. The latter is effectively constrained on the sedimentological data and conditioned on both self-potential and borehole hydraulic head readings. Minimization of the Maximum Likelihood objective function allows estimating the relative weight of measurement errors associated with self-potential and borehole-based head data. The procedure adopted allowed a reconstruction of the heterogeneity of the site with a level of details, which was not obtained in previous studies and with relatively modest computational efforts. Further validation against dipole tests which were not used in the inversion procedure supports the robustness of the results.