A geostatistically based inverse model for electrical resistivity surveys and its applications to vadose zone hydrology

Abstract

[1] A sequential, geostatistical inverse approach was developed for electrical resistivity tomography (ERT). Unlike most ERT inverse approaches, this new approach allows inclusion of our prior knowledge of general geological structures of an area and point electrical resistivity measurements to constrain the estimate of the electrical resistivity field. This approach also permits sequential inclusion of different data sets, mimicking the ERT data collection scheme commonly employed in the field survey. Furthermore, using the conditional variance concept, the inverse model quantifies uncertainty of the estimate caused by spatial variability and measurement errors. Using this approach, numerical experiments were conducted to demonstrate the effects of bedding orientation on ERT surveys and to show both the usefulness and uncertainty associated with the inverse approach for delineating the electrical resistivity distribution using down-hole ERT arrays. A statistical analysis was subsequently undertaken to explore the effects of spatial variability of the electrical resistivity-moisture relation on the interpretation of the change in water content in the vadose zone, using the change in electrical resistivity. Core samples were collected from a field site to investigate the spatial variability of the electrical resistivity-moisture relation. Numerical experiments were subsequently conducted to illustrate how the spatially varying relations affect the level of uncertainty in the interpretation of change of moisture content based on the estimated change in electrical resistivity. Other possible complications are also discussed.

Improved hydrogeophysical characterization using joint inversion of cross‐hole electrical resistance and ground‐penetrating radar traveltime data

“…Weakly nonlinear problems can be solved with an iterative procedure that solves the cokriging equations at each iteration [Yeh et al, 1996] and applications to geophysics have been reported [Yeh et al, 2002].…”

Stochastic Fusion of Information for Characterizing and Monitoring the Vadose Zone

“…The relative inexpensiveness of the sensor makes such a deployment feasible, thus making ERT a highly desirable monitor tool for vadose zone investigations. Nonetheless, a recent field study (Baker, 2001 andYeh et al, 2002) indicated that the parameters of Arche's law (i.e., the resistivity/moisture content relation) exhibit profound spatial variability. This variability compounds the difficulty in translating resistivity to moisture content.…”

“…For large -scale investigations, recently developed geophysical methods (such as electrical resistivity tomography, ERT; ground penetrating radars, GPR; Binley et al, 2001. Daily et al, 1992 for characterizing and monitoring the vadose zone, coupled with geostatistically based inverse methods Yeh et al, 2002) appear to be promising.…”

Modeling 3-D permeability distribution in alluvial fans using facies architecture and geophysical acquisitions

“…Recently, data fusion techniques have been developed for coupled inversion of multiplesource data to estimate K distributions for groundwater numerical modeling. Geophysical data (such as surface electric resistivity and various logging data) are relatively inexpensive and can provide considerable information for characterizing subsurface heterogeneous properties (Hubbard et al, 2001;Yeh et al, 2002;Dai et al, 2004a;Morin, 2006;Sikandar et al, 2010;Bevington et al, 2016). Electric resistivity data have been proven useful to derive sediment porosity distributions (Niwas and Singhal, 1985;Niwas et al, 2011;Niwas and Celik, 2012;Zhu et al, 2016b).…”