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.