Improved strategies for the automatic selection of optimized sets of electrical resistivity tomography measurement configurations

Abstract

S U M M A R YTwo strategies are presented for obtaining the maximum spatial resolution in electrical resistivity tomography surveys using a limited number of four-electrode measurement configurations. Both methods use a linearized estimate of the model resolution matrix to assess the effects of including a given electrode configuration in the measurement set. The algorithms are described in detail, and their execution times are analysed in terms of the number of cells in the inverse model. One strategy directly compares the model resolution matrices to optimize the spatial resolution. The other uses approximations based on the distribution and linear independence of the Jacobian matrix elements. The first strategy produces results that are nearer to optimal, however the second is several orders of magnitude faster. Significantly however, both offer better optimization performance than a similar, previously published, method. Realistic examples are used to compare the results of each algorithm. Synthetic data are generated for each optimized set of electrodes using simple forward models containing resistive and/or conductive prisms. By inverting the data, it is demonstrated that the linearized model resolution matrix yields a good estimate of the actual resolution obtained in the inverted image. Furthermore, comparison of the inversion results confirms that the spatial distribution of the estimated model resolution is a reliable indicator of tomographic image quality.

Optimized arrays for 2D cross‐borehole electrical tomography surveys

“…The 'Compare R' method (Wilkinson et al 2006b) attempts to determine the set of array configurations that will maximize the average resolution value for a homogeneous earth Wenner- type configuration as well as those large geometric factors that exceed a set limit are also excluded (Stummer et al 2004). The remaining configurations form the 'comprehensive' data set.…”

“…There have been many significant developments in algorithms to automatically select arrays to maximize the resolution of the inversion model for linear surface arrays and cross-borehole surveys (Stummer et al 2004;Wilkinson et al 2006aWilkinson et al , 2006bLoke et al 2010a;Nenna et al 2011;Hagrey 2012). A non-linear method that calculates the model resolution (the 'Compare R' method) by Wilkinson et al (2006b) proved to be the best method (Loke et al 2010a). …”

Internal structure of two alpine rock glaciers investigated by quasi-3-D electrical resistivity imaging

“…The inversion continues until acceptable convergence between the calculated and the measured data is reached (see Rödder and Kneisel, 2012, for more details on inversion settings). To investigate model reliability, a resolution matrix approach (Hilbich et al, 2009;Wilkinson et al, 2006;Stummer et al, 2004) was performed on all data sets. This approach provides a measure of the information content of the model cells.…”

Surface Geophysical Exploration - Compendium Document

“…Stummer et al, 2004;Wilkinson et al, 2006; used the model resolution to derive the best combination of surface measurements to obtain improved representation of subsurface targets for 2D problems. Applying a hybrid of these approaches, we investigated the consequence of typical decisions made for inverting resistivity data to resolve a target, including model parameters (inverse model cell size) and electrode density.…”