Practical aspects of applied optimized survey design for electrical resistivity tomography

Abstract

SUMMARY The use of optimized resistivity tomography surveys to acquire field data imposes extra constraints on the design strategy beyond maximizing the quality of the resulting tomographic image. In this paper, methods are presented to (1) minimize electrode polarization effects (2) make efficient use of parallel measurement channels and (3) incorporate data noise estimates in the optimization process. (1) A simulated annealing algorithm is used to rearrange the optimized measurement sequences to minimize polarization errors. The method is developed using random survey designs and is demonstrated to be effective for use with single and multichannel optimized surveys. (2) An optimization algorithm is developed to design surveys by successive addition of multichannel groups of measurements rather than individual electrode configurations. The multichannel surveys are shown to produce results nearly as close to optimal as equivalent single channel surveys, while reducing data collection times by an order of magnitude. (3) Random errors in the data are accounted for by weighting the electrode configurations in the optimization process according to a simple error model incorporating background and voltage‐dependent noise. The use of data weighting produces optimized surveys that are more robust in the presence of noise, while maintaining as much of the image resolution of the noise‐free designs as possible. All the new methods described in this paper are demonstrated using both synthetic and real data, the latter having been measured on an active landslide using a permanently installed geoelectrical monitoring system.

Computation of optimized arrays for 3-D electrical imaging surveys

“…This is expected as the optimization procedure tends to choose arrays with higher geometric factors (Wilkinson et al 2012). However, despite the higher data misfits, the optimized data sets have better resolution, particularly at the deepest block.…”

“…This number is reduced by excluding the gamma type arrays with crossed current and potential electrodes (Carpenter & Habberjam 1956) and those with large geometric factors (Stummer et al 2004;Loke et al 2010a). A maximum geometric factor limit is set according to the expected noise level in a field survey (Wilkinson et al 2012). A local optimization procedure is used to select a subset of the viable configurations (the comprehensive data set) that will maximize the model resolution.…”

“…A selected number of configurations that have the largest F CR values are added to the base set after each iteration until the target number of optimized array configurations is selected. We note that both the least-squares and array optimization methods can be modified to include the L1 and L2 norms for the model roughness and data misfit, as well as the effect of known data errors (Farquharson & Oldenburg 1998;Loke et al 2010b;Wilkinson et al 2012).…”

“…The vector g contains the sensitivity values of the model cells for the new test configuration. The following function F CR (Wilkinson et al 2012) is used to the rank the improvement in the resolution of a model with m cells due to an add-on array.…”

“…The main effect of increasing the number of data points in the optimized data set to 2500 and 5001 data points is an increase in the model resistivity at the locations of the three blocks (Figs 13c and d, Table 2). The region with resistivity values above 17.8 m also covers the entire volume of block C. Pearson correlation coefficients between the inverted images and the model were also calculated to quantify image quality (Wilkinson et al 2012). Since the model targets are infinitely resistive, the resistivities ρ, of the model and images were transformed into a coefficient given by…”