# Computation of Optimized Electrode Arrays for 3-D Electrical Resistivity Tomography Surveys
## 1 Introduction
They compared Compare R, Modified GF, hybrid Modified GF-Compare R and [PERSON]'s method, using synthetic and field tests. The results verified the superiority of Compare R to all the other methods. Their tests outlined that the hybrid Modified GF-Compare R method produced results almost identical to Compare R with the advantage of being several times faster. In another work by [PERSON] et al. [19], it is emphasized that using a smaller step to add optimized measurements to the base data set benefits the final model resolution. Furthermore, the particular study referred to the advantages of replacing matrix-vector with matrix-matrix multiplications, the storing of temporary variables in the double-precision single instruction multiple data (SIMD) registers within the CPU and the use of a computer graphics processor unit (GPU) to decrease the calculation time for selecting the optimum configurations. In a more recent study, [PERSON] et al. [20] presented optimized arrays for 2-D resistivity surveys with buried probes, using implanted electrodes in the subsurface and on the ground surface. This geometry array was able to increase the depth resolution of resistivity surveys at sites where the profile length is limited. Apart from the fact that the resolution is better when optimal arrays are used, the specific study also manifested the increased resolution distances slightly beyond the lateral ends of the arrays and for depths below the buried array. [PERSON] and [PERSON] [21] followed a slightly different path for the sequential experimental design of optimum resistivity data sets by developing a determinant-based objective function that minimizes the posterior model uncertainty. The aspect of computational efficiency was addressed through formulae for updating determinants and matrix inverses without the need for direct calculation. The applicability of the method was demonstrated on single and adaptive borehole ERT surveys. Additionally, [PERSON] et al. [22] applied a new approach based on the resolution matrix to calculate the optimal electrode positions, wherein the results of the study confirmed that a sparse but well-conceived set of electrodes can provide a large part of the information content offered by comparably dense electrode distributions. All the above optimization algorithms rely on the appraisals of the model resolution matrix that is directly related to the calculation of the generalized inverse, which can be extremely time-consuming in large 2-D [23] and 3-D problems [14]. [PERSON] et al. [24] recommended a method to extract the optimal set of ERT arrays using genetic algorithms to identify the array with the optimal cumulative spatial sensitivity. [PERSON] et al. [25] proposed an alternative method to pick the optimal measurements solely on the examination of the sensitivity matrix entries. The extensive testing of the specific algorithm proposed by [PERSON] et al. [25] with surface, cross-hole and surface-to-hole electrode layouts demonstrated comparable results with previously published approaches. The extension of the optimization procedure to generate a set of optimum measurements for 3-D survey grids poses new challenges to balance the time constraints and the need to increase the resolution analysis of the 3-D subsurface inversion images. [PERSON] et al. [26] presented the first effort of computing optimized arrays for 3-D surface electrical surveys. In the specific work, they constructed the comprehensive data set with a mixture of in-line and offset alpha and beta configurations as well as respective equatorial arrays. The unstable measurements were filtered out by setting a maximum limit for the geometric factor and the sensitivity of the array geometric factor in the position of the electrodes. A similar approach was also followed in optimizing resistivity measurements collected from the layout of electrodes placed on nodes of non-regular grids [27]. Recently [PERSON] et al.