M.H. Loke

Noninvasive monitoring of DNAPL migration through a saturated porous medium using electrical impedance tomography.

Electrical impedance tomography (EIT) was used to monitor the movement of a fluorinated hydrocarbon dense nonaqueous phase liquid (DNAPL) through a saturated porous medium within a laboratory column. Impedance measurements were made using a horizontal plane of 12 electrodes positioned at regular intervals around the centre of the column. A 2D inversion algorithm, which incorporated the cylindrical geometry of the column, was used to reconstruct resistivity and phase images from the measured data. Differential time-lapse images of DNAPL movement past the plane of electrodes were generated by the cell-by-cell subtraction of resistivity and phase baseline models from those associated with the DNAPL release stage of the experiment. The DNAPL pulse was clearly delineated as resistive anomalies in the differential time-lapse resistivity images. The spatial extent of the resistive anomalies indicated that in addition to vertical migration, some lateral spreading of the DNAPL had occurred. Residual contamination could be detected after quasi-static conditions were reestablished. Residual DNAPL saturation was estimated from the resistivity model data by applying Archies second equation.Despite significant measured phase changes due to DNAPL contamination, the differential phase images revealed only weak anomalies associated with DNAPL flow; these anomalies could be seen only in the initial stages of the experiment during peak flow through the plane of electrodes.

Optimized arrays for 2D cross-borehole electrical tomography surveys

The use of optimized arrays generated using the ‘Compare R’ method for cross-borehole resistivity measurements is examined in this paper. We compare the performances of two array optimization algorithms, one that maximizes the model resolution and another that minimizes the point spread value. Although both algorithms give similar results, the model resolution maximization algorithm is several times faster. A study of the point spread function plots for a cross-borehole survey shows that the model resolution within the central zone surrounded by the borehole electrodes is much higher than near the bottom end of the boreholes. Tests with synthetic and experimental data show that the optimized arrays generated by the ‘Compare R’ method have significantly better resolution than a ‘standard’ measurement sequence used in previous surveys. The resolution of the optimized arrays is less if arrays with both current (or both potential) electrodes in the same borehole are excluded. However, they are still better than the ‘standard’ arrays.

Reconstruction of landslide movements by inversion of 4‐D electrical resistivity tomography monitoring data

Reliable tomographic inversion of geoelectrical monitoring data from unstable slopes relies critically on knowing the electrode positions, which may move over time. We develop and present an innovative inverse method to recover movements in both surface directions from geoelectrical measurements made on a grid of monitoring electrodes. For the first time, we demonstrate this method using field data from an active landslide to recover sequences of movement over timescales of days to years. Comparison with GPS measurements demonstrated an accuracy of within 10 % of the electrode spacing, sufficient to correct the majority of artefacts that would occur in subsequent image reconstructions if incorrect positions are used. Over short timescales where the corresponding subsurface resistivity changes were smaller, the constraints could be relaxed and an order-of-magnitude better accuracy was achievable. This enabled the onset and acceleration of landslide activity to be detected with a temporal resolution of a few days.

Optimized arrays for 2D resistivity surveys with combined surface and buried arrays

The ‘Compare R’ method is used to automatically generate optimized arrays for two-dimensional resistivity surveys with electrodes arranged along parallel lines on the surface and the subsurface. The resolution at depth is greatly improved by carrying out measurements with at least one line of electrodes below the surface using a direct push installation technique. The performance of the optimized arrays is compared with a standard measurement sequence created manually that was used for previous surveys. Tests were conducted using a synthetic model and a field survey in an area with karst geology that has some ground truth. Both tests show that the optimized arrays have significantly better resolution compared with a standard measurement sequence. We also show that artefacts in the inversion model can be reduced by using higher damping factors near the positions of the subsurface electrodes.

Rapid Inversion of Data from 2-D and from 3-D Resistivity Surveys with Shifted Electrodes

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.

Rapid Parallel Computation of Optimised Arrays for Electrical Imaging Surveys

Modern automatic multi-electrode survey instruments have made it possible to use non-traditional arrays to maximise the subsurface resolution from electrical imaging surveys. One of the best methods for generating optimised arrays is to select the array configurations that maximises the model resolution for a homogeneous earth model. The Sherman-Morrison Rank-1 update is used to calculate the change in the model resolution when a new array is added to a selected set of array configurations. This method had the disadvantage that it required several hours of computer time. The algorithm was modified to calculate the change in the model resolution rather than the entire resolution matrix. This reduces the computer time and memory required and also the round-off errors. The matrix-vector multiplications for a single add-on array were replaced with parallel matrix-matrix multiplications for 512 add-on arrays using the computer GPU for the calculations. These changes reduced the computer time by more than two orders of magnitude. The damped and smoothness-constrained least-squares formulations were used in the array optimisation model resolution equation. The smoothness-constrained method can improve the model resolution for deep extended structures where the resolution is poor.

Rapid inversion of data from 2D resistivity surveys with electrode displacements

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 half-space 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.