A Sensitivity Analysis of Electrical Resistivity Tomography Array Types Using Analytical Element Modeling

electrode arrays allows for the interpretation of the twodimensional distribution of electrical conductivity in the The analytic element method is used to investigate the spatial subsurface. The electrical conductivity distribution can sensitivity of different electrical resistivity tomography (ERT) arrays. By defining the sensitivity of an array to a subsurface location we then be related to the volumetric water content, concenwere able to generate maps showing the distribution of the sensitivity tration of electrolytic solutes in the pore water, and the throughout the subsurface. This allows us to define regions of the surface conductivity of the subsurface materials. subsurface where different ERT arrays are most and least sensitive. Each ERT measurement represents some average of We compared the different arrays using the absolute value of the the heterogeneous subsurface electrical conductivities sensitivity and using its spatial distribution. Comparison is presented in the shallow subsurface. Given that the current is apfor three commonly used arrays (Wenner, Schlumberger, and double plied and the potential is measured at the surface, all dipole) and for one atypical array (partially overlapping). Most comERT arrays are more sensitive to the properties of shalmon monitoring techniques use a single measurement to measure a low subsurface materials than to deeper material propproperty at a single location. The spatial distribution of the property erties. In general, arrays with larger electrode separations is determined by interpolation of these measurements. In contrast, ERT is unique in that multiple measurements are interpreted simultaare assumed to have sample areas that extend deeper neously to create maps of spatially distributed soil properties. We beneath the ground surface, while the sample areas of define the spatial sensitivity of an ERT survey to each location on smaller arrays are limited to the shallow subsurface. To the basis of the sum of the sensitivities of the single arrays composing form a more unique image of the subsurface electrical the survey to that location. With the goal of applying ERT for timeconductivity distribution, the apparent resistivity is mealapse measurements, we compared the spatial sensitivities of different sured through many electrode combinations and intersurveys on a per measurement basis. Compared are three surveys preted simultaneously. In general, it is felt that the use based on the typical Wenner, Schlumberger, and double dipole arrays, of a large number of arrays with different array sizes one atypical survey based on the partially overlapping array, and one will lead to a more accurate representation of the spatial mixed survey built of arrays that have been shown to be optimal for structure of the subsurface electrical conductivity. a series of single perturbations. Results show the inferiority of the double dipole survey compared with other surveys. On a per measureWith modern field equipment, many electrodes can ment basis, there was almost no difference between the Wenner and be installed and measurements can be made automatithe Schlumberger surveys. The atypical partially overlapping survey cally using multiple electrode arrays. As a result, many is superior to the typical arrays. Finally, we show that a survey comthousands of combinations of electrodes can be formed posed of a mixture of array types is superior to all of the single array using a standard set of 21 electrodes. However, caution type surveys. By analyzing the spatial sensitivity of the single array, should be used in choosing the arrays comprising a surand most significantly the sensitivity of the ERT survey, we set the vey to minimize soil charge time (Dahlin, 2000). The basis for quantitative measurement of subsurface properties using ERT, total time required to collect stacked measurements for with applications to both static and transient hydrologic processes. each array is typically only about 15 s. However, the total measurement time can become impractical if too many arrays are used. Therefore, more efficient applicaE resistivity tomography is widely used for tion of the ERT method requires the development of mapping shallow subsurface geological structure a quantitative method to define the most useful subset (Storz et al., 2000), solute distribution (Binley et al., of ERT arrays to form an ERT survey. 1996), water content (Zhou et al., 2001), and other enviThe identification of an optimal ERT array set is even ronmental, hydrological, and engineering features (Dahmore critical when monitoring transient processes. The lin, 2000). The method is based on the introduction of simultaneous inversion of multiple measurements is electrical current into the soil through two surface elecbased on the underlying assumption that all measuretrodes and the simultaneous measurement of the inments were made on an identical subsurface conductivduced potential gradient with other surface electrodes. ity field. However, for many transient processes, such Each potential measurement gives insight into the elecas water infiltration or solute transport, the subsurface trical properties of the subsurface materials. The inverelectrical conductivity distribution can change rapidly sion of multiple measurements made with overlapping with time. To use ERT to monitor these processes it is critical that all electrode arrays are measured within a A. Furman and T.P.A. Ferré, Hydrology and Water Resources Detime frame during which it is reasonable to assume that partment, University of Arizona, Tucson, AZ 85721; A.W. Warrick, the conductivity field is unchanging. In practice, this Soil, Water, and Environmental Sciences Department, University of time frame will be defined based on the expected rate Arizona, Tucson, AZ 85721. Received 23 Sept. 2002. Original Research Paper. *Corresponding author ([email protected]). of change of the subsurface electrical conductivity Published in Vadose Zone Journal 2:416–423 (2003).  Soil Science Society of America Abbreviations: ERT, electrical resistivity tomography; TDR, time domain reflectometry. 677 S. Segoe Rd., Madison, WI 53711 USA