3 D resistivity inversion with electrodes displacements
3 D resistivity monitoring surveys are used to detect temporal changes in the subsurface using the measurements repeated over the same site. The positions of the electrodes are measured at the start of the survey program and perhaps at occasional intervals. In areas with unstable ground, the positions of the electrodes can be displaced by ground movements. If this occurs at times when the positions of the electrodes are not measured, they have to be estimated from the resistivity data. The smoothness constrained least squares optimisation method can be modified to include the electrodes positions as additional unknown parameters. 3 D resistivity surveys present a special challenge due to the greater computational requirements for the forward modelling routine and the possible movements of the electrodes in three directions. To reduce the calculation time, a fast adjoint equation method is used to calculate the Jacobian matrices required by the least squares method. It is several orders of magnitude faster than the simpler perturbation method previously used for 2 D problems. In areas with large near surface resistivity contrasts, the inversion routine sometimes cannot accurately distinguish between electrodes displacements and subsurface resistivity variations. To overcome this problem, the model for the initial time lapse data set (with accurately known electrodes positions) is used as the starting model for the inversion of the later time data set. This greatly improves the accuracy of the estimated electrode positions compared to the use of a homogeneous half space starting model.