Sensitivity of electrical resistivity tomography data to electrode position errors

Limitations of imaging using electrical resistivity tomography (ERT) arise because of the difficulty of quantifying the reliability of tomographic images. A major source of uncertainty in tomographic inversion is data error. Data error due to electrode mislocations is characterized by the sensitivity of electrical potential to both source and receiver positions. This sensitivity is described by a scattering-type equation and, therefore, depends not only on source-receiver separation, but also on the location and magnitude of contrasts in electrical conductivity. At the overlapping scales of near-surface environmental and engineering geophysical surveys, for which electrodes may be close to the target and experiment dimensions may be on the same order as those of the target, errors associated with electrode mislocations can significantly contaminate the ERT data and the reconstructed electrical conductivity. For synthetic experiments, variations in the data due to electrode mislocation are comparable in magnitude to typical experimental noise levels and, in some cases, may overwhelm variations in the data due to changes in material properties. Furthermore, the statistical distribution of electrode mislocation errors can be complicated and multimodal such that bias may be introduced into the ERT data. The resulting perturbations of the reconstructed electrical conductivity field due to electrode mislocations can be significant in magnitude with complex spatial distributions that are dependent both on the model and the experiment.