# Computation of Optimized Electrode Arrays for 3-D Electrical Resistivity Tomography Surveys
## 6 Conclusions  
The work describes an experimental method to select electrode configurations that carry the maximum resolving capability in order to reconstruct the subsurface resistivity distribution. The technique is based on the sensitivity and the examination of Jacobian matrix entries. The basic differences of the specific method in relation to approaches utilizing the model resolution matrix to select the optimum array protocols have already been stressed for the 2-D resistivity problem. The main one is attributed to the fact that the optimum data set is created solely depending on each individual array. On the contrary, the initiation of any algorithm based on resolution matrix approaches needs the compilation of an initial base data set and the enrichment of this base set with added configurations coming from a comprehensive data set having every possible electrode combination based on the update of the resolution matrix. Thus, the sensitivity approach can be faster since the calculation of the Jacobian is part of the forward resistivity problem and there is no need to perform any inversion, as is the case for the resolution matrix approaches. The comparative tests performed in this work showed that the Jacobian method is about 20% faster than previous approaches using the resolution matrix. Furthermore, the Jacobian matrix method avoids the evaluation of the goodness function since the algorithm picks the most sensitive measurements. Therefore, the extra time gained in selecting optimum measurements is increased, which is amplified in cases of large 3-D resistivity tomographic problems and data. The 3-D optimum protocols are produced from 3-D data sets compiled by the merging of multiple equally spaced parallel 2-D profiles assuming traditional arrays: dipole-dipole, pole-dipole, pole-tripole and gradient. The two different approaches involved the application of 2-D and 3-D optimization algorithms to select the optimum protocols ranged from 14% (synthetic data set) and ~50% (field data set) of the original full data sets. The cumulative Jacobian matrix (normalized sensitivity value of each parameter) showed that the optimum protocols have the same sensitivity values with the full data set, although fewer measurements are used than the traditional protocols. The algorithms were validated with a synthetic model where the inversion results verified the comparable similarity of the reconstructed models between the comprehensive  
Figure 19: Inversion results from the Optimum Elounda field data set. and the optimum (from 2-D or 3-D) data sets. The efficiency of optimization procedure was validated with field data from completely different environments using a comprehensive data set which is comprised of different traditional arrays (dipole-dipole and gradient, pole-dipole forward and reverse), where the inversion models of the optimum protocols showed similar results, although half of the initial complete data set was used for the inversion. In general, the specific work shows the flexibility and effectiveness of an experimental procedure based on the sensitivity matrix in selecting optimum resistivity protocols in a 3-D context. The two different approaches in compiling the optimum 3-D tomographic protocols show comparable results in terms of the inverted resistivity models. In relatively more complicated subsurface geometry and resistivity distribution, the full 3-D optimization method can give slightly superior results in relation to the 2-D approach with minimum extra time. Finally, the optimized data sets can also be used as a basis for 3-D monitoring experiments to experience enhanced resolving capabilities of the time-lapse resistivity images for monitoring the subsurface contamination in environmental applications [32]. K.S. : Software development, methodology, data processing/analysis/interpretation, writing--original draft preparation; N.P. : conceptualization, review and editing, funding acquisition; D.O. : data acquisition/interpretation, visualization, validation.