Optimised sequential experimental design for Geoelectrical Resistivity Monitoring Surveys

Sequential experimental design methods use previous data and results to guide the choice and design of future experiments. This paper describes the application of a sequential design technique to produce optimal resistivity imaging surveys for time-lapse geoelectrical monitoring experiments. These survey designs are time-dependent, and are optimised to focus a greater degree of the image resolution on the regions of the subsurface that are actively changing than static optimised surveys that do not change over time. The sequential design method is applied to a synthetic 2.5D monitoring experiment comprising a well-defined cylindrical target moving along a trajectory that changes its depth and lateral position. The data are simulated to be as realistic as possible, incorporating survey design constraints for a real resistivity monitoring system and realistic levels and distributions of random noise, in order to match a forthcoming experimental test of the method. The results of the simulations indicate that sequentially designed optimal surveys yield an increase in image quality over and above that produced by using a static (time-independent) optimised survey

Computation of optimized arrays for 3-D electrical imaging surveys

3-D electrical resistivity surveys and inversion models are required to accurately resolve structures in areas with very complex geology where 2-D models might suffer from artefacts. Many 3-D surveys use a grid where the number of electrodes along one direction (x) is much greater than in the perpendicular direction (y). Frequently, due to limitations in the number of independent electrodes in the multi-electrode system, the surveys use a roll-along system with a small number of parallel survey lines aligned along the x-direction. The ‘Compare R’ array optimization method previously used for 2-D surveys is adapted for such 3-D surveys. Offset versions of the inline arrays used in 2-D surveys are included in the number of possible arrays (the comprehensive data set) to improve the sensitivity to structures in between the lines. The array geometric factor and its relative error are used to filter out potentially unstable arrays in the construction of the comprehensive data set. Comparisons of the conventional (consisting of dipole-dipole and Wenner–Schlumberger arrays) and optimized arrays are made using a synthetic model and experimental measurements in a tank. The tests show that structures located between the lines are better resolved with the optimized arrays. The optimized arrays also have significantly better depth resolution compared to the conventional arrays

Distribution-based fuzzy clustering of electrical resistivity tomography images for interface detection

A novel method for the effective identification of bedrock subsurface elevation from electrical resistivity tomography images is described. Identifying subsurface boundaries in the topographic data can be difficult due to smoothness constraints used in inversion, so a statistical population-based approach is used that extends previous work in calculating isoresistivity surfaces. The analysis framework involves a procedure for guiding a clustering approach based on the fuzzy c-means algorithm. An approximation of resistivity distributions, found using kernel density estimation, was utilized as a means of guiding the cluster centroids used to classify data. A fuzzy method was chosen over hard clustering due to uncertainty in hard edges in the topography data, and a measure of clustering uncertainty was identified based on the reciprocal of cluster membership. The algorithm was validated using a direct comparison of known observed bedrock depths at two 3-D survey sites, using real-time GPS information of exposed bedrock by quarrying on one site, and borehole logs at the other. Results show similarly accurate detection as a leading isosurface estimation method, and the proposed algorithm requires significantly less user input and prior site knowledge. Furthermore, the method is effectively dimension-independent and will scale to data of increased spatial dimensions without a significant effect on the runtime. A discussion on the results by automated versus supervised analysis is also presented