Rapid Inversion of Data from 2-D and from 3-D Resistivity Surveys with Shifted Electrodes
M.H. Loke, P.B. Wilkinson and J.E. Chambers
Event name: Near Surface Geoscience 2015 - 21st European Meeting of Environmental and Engineering Geophysics
Session: ERT I
Publication date: 06 September 2015
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Geoelectrical monitoring surveys are used to detect temporal changes in the subsurface below unstable slopes with the measurements repeated over an extended period. The positions of the electrodes are measured at the start of the campaign and possibly at regular intervals. However, ground movements sometimes occur between the times of the electrode positions measurements. For some data sets the precise positions of the electrodes are not accurately known and have to be estimated from the resistivity data. The smoothness-constrained least-squares optimization method is modified to include the electrode positions as unknown parameters to be determined. The Jacobian matrices with the sensitivity of the apparent resistivity measurements to changes in the electrode positions are required by the optimization method. A fast adjoint-equation method to calculate the required Jacobian matrices is described. It is one to two orders of magnitude faster than the perturbation method previously used. We also modify the inversion routine by using the inversion model for the initial time-lapse data set (with known electrode positions) as the starting model for the inversion of the later-time data sets. This greatly improves the accuracy of the recovered electrode positions compared to the use of a homogeneous earth starting model.