Fast computation of optimized electrode arrays for 2D resistivity surveys

Four different methods to automatically select an optimal set of array configurations that gives the maximum subsurface resolution with a limited number of measurements for 2D electrical imaging surveys were tested. The first (CR) method directly calculates the change in the model resolution for each new array added to the base data set, and uses this to select array configurations that gave the maximum model resolution. However this method is the slowest. The algorithm used by the CR method for calculating rank-one updates was optimized to reduce computational time by a factor of eighty. The sequence of calculations was modified to reduce the traffic between the computer main memory and the CPU registers. Further code optimizations were made to take advantage of the parallel processing capabilities of modern CPUs. The second (ETH) and third (BGS) methods use approximations based on the sensitivity values to estimate the change in the model resolution matrix. The ETH and BGS methods, respectively, use the first and second power of the sensitivity values to calculate approximations of the model resolution. Both methods are about an order of magnitude faster than the CR method. The results obtained by the BGS method are significantly better than the ETH method, and it approaches that of the CR method. The fourth method (BGS–CR) uses a combination of the BGS and CR methods. It produces results that are almost identical to the CR method but is several times faster. The different methods were tested using data from synthetic models and field surveys. The models obtained from the inversion of the data sets generated by the four different methods confirm that the models generated by the CR method have the best resolution, followed by the BGS–CR, BGS and ETH methods