Rapid inversion of data from 2D resistivity surveys with electrode displacements
Authors:
M.H. Loke, P.B. Wilkinson, J.E. Chambers and P.I. Meldrum
Journal name: Geophysical Prospecting
Issue: Vol 66, No 3, March 2018 pp. 579 - 594
DOI: 10.1111/1365-2478.12522
Organisations:
Wiley
Language: English
Info: Article, 
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Summary:
Resistivity monitoring surveys are used to detect temporal changes in the subsurface
using repeated measurements over the same site. The positions of the electrodes are
typically measured at the start of the survey program and possibly at occasional later
times. In areas with unstable ground, such as landslide-prone slopes, the positions
of the electrodes can be displaced by ground movements. If this occurs at times
when the positions of the electrodes are not directly measured, they have to be
estimated. This can be done by interpolation or, as in recent developments, from the
resistivity data using new inverse methods. The smoothness-constrained least squares
optimisation method can be modified to include the electrode positions as additional
unknown parameters. The Jacobian matrices with the sensitivity of the apparent
resistivity measurements to changes in the electrode positions are then required by
the optimisation method. In this paper, a fast adjoint-equation method is used to
calculate the Jacobian matrices required by the least squares method to reduce the
calculation time. In areas with large near-surface resistivity contrasts, the inversion
routine sometimes cannot accurately distinguish between electrode displacements and
subsurface resistivity variations. To overcome this problem, the model for the initial
time-lapse dataset (with accurately known electrode positions) is used as the starting
model for the inversion of the later-time dataset. This greatly improves the accuracy
of the estimated electrode positions compared to the use of a homogeneous halfspace
starting model. In areas where the movement of the electrodes is expected to
occur in a fixed direction, the method of transformations can be used to include this
information as an additional constraint in the optimisation routine.
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