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Loke M.H.,Geotomo Software | Wilkinson P.B.,British Geological Survey | Chambers J.E.,British Geological Survey | Strutt M.,British Geological Survey
Geophysical Prospecting | Year: 2014

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. © 2013 European Association of Geoscientists & Engineers.

Wilkinson P.B.,British Geological Survey | Loke M.H.,Geotomo Software | Meldrum P.I.,British Geological Survey | Chambers J.E.,British Geological Survey | And 3 more authors.
Geophysical Journal International | Year: 2012

The use of optimized resistivity tomography surveys to acquire field data imposes extra constraints on the design strategy beyond maximizing the quality of the resulting tomographic image. In this paper, methods are presented to (1) minimize electrode polarization effects (2) make efficient use of parallel measurement channels and (3) incorporate data noise estimates in the optimization process. (1) A simulated annealing algorithm is used to rearrange the optimized measurement sequences to minimize polarization errors. The method is developed using random survey designs and is demonstrated to be effective for use with single and multichannel optimized surveys. (2) An optimization algorithm is developed to design surveys by successive addition of multichannel groups of measurements rather than individual electrode configurations. The multichannel surveys are shown to produce results nearly as close to optimal as equivalent single channel surveys, while reducing data collection times by an order of magnitude. (3) Random errors in the data are accounted for by weighting the electrode configurations in the optimization process according to a simple error model incorporating background and voltage-dependent noise. The use of data weighting produces optimized surveys that are more robust in the presence of noise, while maintaining as much of the image resolution of the noise-free designs as possible. All the new methods described in this paper are demonstrated using both synthetic and real data, the latter having been measured on an active landslide using a permanently installed geoelectrical monitoring system. © 2012 British Geological Survey/NERC Geophysical Journal International © 2012 RAS.

Loke M.H.,Geotomo Software | Wilkinson P.B.,British Geological Survey | Chambers J.E.,British Geological Survey | Uhlemann S.S.,British Geological Survey | Sorensen J.P.R.,British Geological Survey
Journal of Applied Geophysics | Year: 2015

Previous studies show that optimized arrays generated using the 'Compare R' method have significantly better resolution than conventional arrays. This method determines the optimum set of arrays by selecting those that give the maximum model resolution. The number of possible arrays (the comprehensive data set) increases with the fourth power of the number of electrodes. The optimization method faces practical limitations for 2-D survey lines with more than 60 electrodes where the number of possible arrays exceeds a million. Several techniques are proposed to reduce the calculation time for such survey lines. A single-precision version of the 'Compare R' algorithm using a new ranking function reduces the calculation time by two to eight times while providing results similar to the double-precision version. Recent improvements in computer GPU technology can reduce the calculation time by about seven times. The calculation time is reduced by half by using the fact that arrays that are symmetrical about the center of the line produce identical changes in the model resolution values. It is further reduced by more than thirty times by calculating the Sherman-Morrison update for all the possible two-electrode combinations, which are then used to calculate the model resolution values for the four-electrode arrays. The calculation time is reduced by more then ten times by using a subset of the comprehensive data set consisting of only symmetrical arrays. Tests with a synthetic model and field data set show that optimized arrays derived from this subset produce inversion models with differences of less than 10% from those derived using the full comprehensive data set. The optimized data sets produced models that are more accurate than the Wenner-Schlumberger array data sets in all the tests. © 2014 Elsevier B.V.

Loke M.H.,Geotomo Software | Wilkinson P.B.,British Geological Survey | Chambers J.E.,British Geological Survey
Computers and Geosciences | Year: 2010

Four different methods to automatically select an optimal set of array configurations that gives the maximum subsurface resolution with a limited number of measurements for 2D electrical imaging surveys were tested. The first (CR) method directly calculates the change in the model resolution for each new array added to the base data set, and uses this to select array configurations that gave the maximum model resolution. However this method is the slowest. The algorithm used by the CR method for calculating rank-one updates was optimized to reduce computational time by a factor of eighty. The sequence of calculations was modified to reduce the traffic between the computer main memory and the CPU registers. Further code optimizations were made to take advantage of the parallel processing capabilities of modern CPUs. The second (ETH) and third (BGS) methods use approximations based on the sensitivity values to estimate the change in the model resolution matrix. The ETH and BGS methods, respectively, use the first and second power of the sensitivity values to calculate approximations of the model resolution. Both methods are about an order of magnitude faster than the CR method. The results obtained by the BGS method are significantly better than the ETH method, and it approaches that of the CR method. The fourth method (BGS-CR) uses a combination of the BGS and CR methods. It produces results that are almost identical to the CR method but is several times faster. The different methods were tested using data from synthetic models and field surveys. The models obtained from the inversion of the data sets generated by the four different methods confirm that the models generated by the CR method have the best resolution, followed by the BGS-CR, BGS and ETH methods. © 2010 Elsevier Ltd.

Rucker D.F.,HydroGEOPHYSICS Inc. | Loke M.H.,Geotomo Software | Levitt M.T.,HydroGEOPHYSICS Inc. | Noonan G.E.,HydroGEOPHYSICS Inc.
Geophysics | Year: 2010

An electrical-resistivity survey was completed at the T tank farm at the Hanford nuclear site in Washington State, U.S.A. The purpose of the survey was to define the lateral extent of waste plumes in the vadose zone in and around the tank farm. The T tank farm consists of single-shell tanks that historically have leaked and many liquid-waste-disposal facilities that provide a good target for resistivity mapping. Given that the site is highly industrialized with near-surface metallic infrastructure that potentially could mask any interpretable waste plume, it was necessary to use the many wells around the site as long electrodes. To accommodate the long electrodes and to simulate the effects of a linear conductor, the resistivity inversion code was modified to assign low-resistivity values to the well's location. The forward model within the resistivity code was benchmarked for accuracy against an analytic solution, and the inverse model was tested for its ability to recreate images of a hypothetical target. The results of the tank-farm field survey showed large, low-resistivity targets beneath the disposal areas that coincided with the conceptual hydrogeologic models developed regarding the releases. Additionally, in areas of minimal infrastructure, the long-electrode method matched the lateral footprint of a 3D surface-resistivity survey with reasonable fidelity. Based on these results, the long-electrode resistivity method may provide a new strategy for environmental characterization at highly industrialized sites, provided a sufficient number and density of wells exist. © 2010 Society of Exploration Geophysicists.

Loke M.H.,Geotomo Software | Chambers J.E.,Natural Environment Research Council | Rucker D.F.,HydroGEOPHYSICS Inc. | Kuras O.,Natural Environment Research Council | Wilkinson P.B.,Natural Environment Research Council
Journal of Applied Geophysics | Year: 2013

There have been major improvements in instrumentation, field survey design and data inversion techniques for the geoelectrical method over the past 25. years. Multi-electrode and multi-channel systems have made it possible to conduct large 2-D, 3-D and even 4-D surveys efficiently to resolve complex geological structures that were not possible with traditional 1-D surveys. Continued developments in computer technology, as well as fast data inversion techniques and software, have made it possible to carry out the interpretation on commonly available microcomputers. Multi-dimensional geoelectrical surveys are now widely used in environmental, engineering, hydrological and mining applications. 3-D surveys play an increasingly important role in very complex areas where 2-D models suffer from artifacts due to off-line structures. Large areas on land and water can be surveyed rapidly with computerized dynamic towed resistivity acquisition systems. The use of existing metallic wells as long electrodes has improved the detection of targets in areas where they are masked by subsurface infrastructure. A number of PC controlled monitoring systems are also available to measure and detect temporal changes in the subsurface. There have been significant advancements in techniques to automatically generate optimized electrodes array configurations that have better resolution and depth of investigation than traditional arrays. Other areas of active development include the translation of electrical values into geological parameters such as clay and moisture content, new types of sensors, estimation of fluid or ground movement from time-lapse images and joint inversion techniques. In this paper, we investigate the recent developments in geoelectrical imaging and provide a brief look into the future of where the science may be heading. © 2013 Elsevier B.V.

Loke M.H.,Geotomo Software | Dahlin T.,Lund University | Rucker D.F.,HydroGEOPHYSICS Inc.
Near Surface Geophysics | Year: 2014

Three-dimensional resistivity surveys and their associated inversion models are required to accurately resolve structures exhibiting very complex geology. In the same light, 3D resistivity surveys collected at multiple times are required to resolve temporally varying conditions. In this work we present 3D data sets, both synthetic and real, collected at different times. The large spatiooral data sets are then inverted simultaneously using a least-squares methodology that incorporates roughness filters in both the space and time domains. The spatial roughness filter constrains the model resistivity to vary smoothly in the x-, y- and z-directions. A temporal roughness filter is also applied that minimizes changes in the resistivity between successive temporal inversion models and the L-curve method is used to determine the optimum weights for both spatial and temporal roughness filters. We show that the use of the temporal roughness filter can accurately resolve changes in the resistivity even in the presence of noise. The L1- and L2-norm constraints for the temporal roughness filter are first examined using a synthetic model. The synthetic data test shows that the L1-norm temporal constraint produces significantly more accurate results when the resistivity changes abruptly with time. The model obtained with the L1-norm temporal constraint is also less sensitive to random noise compared with independent inversions (i.e., without any temporal constraint) and the L2-norm temporal constraint. Anomalies that are common in models using independent inversions and the L2-norm and L1-norm temporal constraints are likely to be real. In contrast, anomalies present in a model using independent inversions but that are significantly reduced with the L2-norm and L1-norm constraints are likely artefacts. For field data sets, the method successfully recovered temporal changes in the subsurface resistivity from a landfill monitoring survey due to rainwater infiltration, as well as from an experiment to map the migration of sodium cyanide solution from an injection well using surface and borehole electrodes in an area with significant topography. © 2014 European Association of Geoscientists & Engineers.

Rucker D.F.,HydroGEOPHYSICS Inc. | Fink J.B.,HydroGEOPHYSICS Inc. | Loke M.H.,Geotomo Software
Journal of Applied Geophysics | Year: 2011

Highly industrialized areas pose challenges for surface electrical resistivity characterization due to metallic infrastructure. The infrastructure is typically more conductive than the desired targets and will mask the deeper subsurface information. The risk of this occurring may be minimized if steel-cased wells are used as long electrodes in the area near the target. We demonstrate a method of using long electrodes to electrically monitor a simulated leak from an underground storage tank with both synthetic examples and a field demonstration. Although the method of using long electrodes has been proposed by others, no time-lapse resistivity data have been collected, modeled, and analyzed within a nuclear waste tank farm environment. Therefore, the main objective of this work was to test whether the long electrode method using steel-cased wells can be employed to spatially and temporally track simulated leaks in a highly industrialized setting. A secondary objective was to apply a time-lapse regularization procedure in the inverse modeling code, similar to the 4D tomography approach by Kim et al. (2009), and to test the procedure's effect on the quality of the outcome regarding plume intensity and position.For the synthetic examples, a simple target of varying electrical properties was placed beneath different types of layers of low resistivity to simulate the effects of the infrastructure. Both surface and long electrodes were tested on the synthetic domain, and the test cases covered a variety of survey parameters including low and high electrode density, noise, array type, and the explicit location of the wells relative to the target. All data were processed in four dimensions, where the regularization procedure was applied in both the time and space domains. The synthetic test case showed that the long electrode resistivity method could detect relative changes in resistivity that was commensurate with the differing target properties. The surface electrodes, on the other hand, had a more difficult time matching the original target's footprint unless the electrodes were distributed at a greater density on the surface. The simulated tank leak in the field experiment was conducted by injecting a high conductivity fluid in a perforated well within the S tank farm at the Hanford Site, and the resistivity measurements were made before and after the leak test. The field results showed a lowered resistivity feature develops south of the injection site after cessation of the injections. The parameter used in the time-lapsed inversion had a strong influence on the differences in inverted resistivity between the pre- and post-injection datasets, but the interpretation of the target was consistent across all values of the parameter. The long electrode electrical resistivity monitoring (ERM) method may provide a tool for near real-time monitoring of leaking underground storage tanks given a sufficient density of wells. © 2011 Elsevier B.V.

Rucker D.F.,HydroGEOPHYSICS Inc. | Crook N.,HydroGEOPHYSICS Inc. | Glaser D.,Washington River Protection Services LLC | Loke M.H.,Geotomo Software
Geophysical Prospecting | Year: 2012

A validation experiment, carried out in a scaled field setting, was attempted for the long electrode electrical resistivity tomography method in order to demonstrate the performance of the technique in imaging a simple buried target. The experiment was an approximately 1/17 scale mock-up of a region encompassing a buried nuclear waste tank on the Hanford site. The target of focus was constructed by manually forming a simulated plume within the vadose zone using a tank waste simulant. The long electrode results were compared to results from conventional point electrodes on the surface and buried within the survey domain. Using a pole-pole array, both point and long electrode imaging techniques identified the lateral extents of the pre-formed plume with reasonable fidelity but the long electrode method was handicapped in reconstructing vertical boundaries. The pole-dipole and dipole-dipole arrays were also tested with the long electrode method and were shown to have the least favourable target properties, including the position of the reconstructed plume relative to the known plume and the intensity of false positive targets. The poor performance of the pole-dipole and dipole-dipole arrays was attributed to an inexhaustive and non-optimal coverage of data at key electrodes, as well as an increased noise for electrode combinations with high geometric factors. However, when comparing the model resolution matrix among the different acquisition strategies, the pole-dipole and dipole-dipole arrays using long electrodes were shown to have significantly higher average and maximum values within the matrix than any pole-pole array. The model resolution describes how well the inversion model resolves the subsurface. Given the model resolution performance of the pole-dipole and dipole-dipole arrays, it may be worth investing in tools to understand the optimum subset of randomly distributed electrode pairs to produce maximum performance from the inversion model. © 2012 European Association of Geoscientists & Engineers.

Loke M.H.,Geotomo Software | Wilkinson P.B.,Natural Environment Research Council | Chambers J.E.,Natural Environment Research Council
Geophysical Journal International | Year: 2010

Modern automatic multi-electrode survey instruments have made it possible to use non-traditional arrays to maximize the subsurface resolution from electrical imaging surveys. Previous studies have shown that one of the best methods for generating optimized arrays is to select the set of array configurations that maximizes 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 even for short 2-D survey lines. 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 as well as the computational round-off errors. The matrix-vector multiplications for a single add-on array were replaced with matrix-matrix multiplications for 28 add-on arrays to further reduce the computer time. The temporary variables were stored in the double-precision Single Instruction Multiple Data (SIMD) registers within the CPU to minimize computer memory access. A further reduction in the computer time is achieved by using the computer graphics card Graphics Processor Unit (GPU) as a highly parallel mathematical coprocessor. This makes it possible to carry out the calculations for 512 add-on arrays in parallel using the GPU. The changes reduce the computer time by more than two orders of magnitude. The algorithm used to generate an optimized data set adds a specified number of new array configurations after each iteration to the existing set. The resolution of the optimized data set can be increased by adding a smaller number of new array configurations after each iteration. Although this increases the computer time required to generate an optimized data set with the same number of data points, the new fast numerical routines has made this practical on commonly available microcomputers. © 2010 The Authors Geophysical Journal International © 2010 RAS.

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