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

Abstract

The analytic element method is used to investigate the spatial sensitivity of different electrical resistivity tomography (ERT) arrays. By defining the sensitivity of an array to a subsurface location we were able to generate maps showing the distribution of the sensitivity throughout the subsurface. This allows us to define regions of the subsurface where different ERT arrays are most and least sensitive. We compared the different arrays using the absolute value of the sensitivity and using its spatial distribution. Comparison is presented for three commonly used arrays (Wenner, Schlumberger, and double dipole) and for one atypical array (partially overlapping). Most common monitoring techniques use a single measurement to measure a property at a single location. The spatial distribution of the property is determined by interpolation of these measurements. In contrast, ERT is unique in that multiple measurements are interpreted simultaneously to create maps of spatially distributed soil properties. We define the spatial sensitivity of an ERT survey to each location on the basis of the sum of the sensitivities of the single arrays composing the survey to that location. With the goal of applying ERT for time-lapse measurements, we compared the spatial sensitivities of different surveys on a per measurement basis. Compared are three surveys based on the typical Wenner, Schlumberger, and double dipole arrays, one atypical survey based on the partially overlapping array, and one mixed survey built of arrays that have been shown to be optimal for a series of single perturbations. Results show the inferiority of the double dipole survey compared with other surveys. On a per measurement basis, there was almost no difference between the Wenner and the Schlumberger surveys. The atypical partially overlapping survey is superior to the typical arrays. Finally, we show that a survey composed of a mixture of array types is superior to all of the single array type surveys. By analyzing the spatial sensitivity of the single array, and most significantly the sensitivity of the ERT survey, we set the basis for quantitative measurement of subsurface properties using ERT, with applications to both static and transient hydrologic processes.