caused by the stimulating electrodes with the electrical field that would result if the recording pair was stimulated.
δ : The elements of this vector represent the conductivity perturbation (with respect to the σ uniform conductivity, semi-infinite model) over a regular grid covering the region of interest.
This is the solution that is referred to as the “conductivity distribution reconstruction”.
The solution of the problem requires the inverse of S. The matrix is ill-conditioned and requires a regularization procedure in order to calculate its inverse. The mine detection algorithm is based on a matched filter approach. It consists of calculating the detector response for a replica of the size and shape of the object of interest for a number of grid locations underneath the detector. The detector response for a given replica is calculated by assigning zero conductivity to the nodes of the calculation grid that represent the size and shape of the replica. A correlation is then performed between the detector response for the replica and the actual detector response obtained from the measurements for all the replica positions considered. The position that yields the largest correlation value is identified as the most likely position for the mine. A grid with a resolution of 15x15x3 nodes is used for the calculations. This resolution is equivalent to a 0.5 electrode spacing (7 cm), in x, y and z. For every node i of that grid, the correlation operation is defined. An example of a reconstruction is shown in Figure 60.
Figure 60. Detector response for a mine-like object buried at a depth of 7 cm (source: Church P., et al, 2001, Performance Assessment of an Electrical Impedance Tomography Detector for Mine-Like Objects, Proc. SPIE Conference on Detection and Remediation Technologies for Mines and Mine-like Targets VI. Vol. 4394, Orlando, FL, USA, 16-20 April)
The authors conclude that when using mine-like objects with a size of the order of two electrode-spacings (ES), reliable detections were obtained down to a range of 1.0-1.5 ES. For an AT mine with a diameter of 28 cm this results in a detection range of about 15-20 cm in
strength of the detection varies for targets buried at depths of 21 cm (1.5 ES). This performance is consistent with the whole set of experiments that have been performed in various soils, either with the small scale lab model used in the initial phase of investigation [3] or with the current 64 electrode instrument.
The detector was found to be capable of resolving very well two mine-like objects buried at 1 ES and separated by 0.5 ES. For two AT mines with a 28 cm diameter and buried at a depth of 14 cm, this corresponds to a distance of 7 cm separating the edges of the two objects (35 cm centre-to-centre). The resolution of two mine-like objects buried at 1.5 ES and separated by 1 ES was not successful, indicating that the resolution power of the detector decreases rapidly with the depth of burial. The EIT detector performed unexpectedly well in the DRES Mine Pen facility. The hard soil crust, covered with small pebbles was thought to be too difficult to achieve a good electrode-soil contact. AT mines (TMA3, M15, PTMiBAIII) were clearly detected down to depth of 16 cm. The detector’s response for the TMA4 buried at 19 cm was not as clear as for the other mines, the detector being at the limit of its detection capability for that depth level. The metal AT mine M16 was detected as a non-conductive object, presumably because of its coat of paint. The same behaviour had been observed for the metal mine TM46 during the trials at CDC.
Another set of experiments was conducted along an alley of surrogate AT mines set up at DRES. The results presented unexpected anomalies. The signal from the surrogate AT mine was weaker than expected and the detector often showed a strong broad signal at the lower layers. These anomalies may actually be related in the sense that the broad signal masks the features we were trying to detect. It appears that the ground environment is likely to be responsible for the problems encountered. The results from experiments point to the presence of a double layer of soil with different electrical conductivities. The current conductivity reconstruction algorithm assumes a conductivity perturbation in a semi-infinite homogeneous medium. The algorithm requires revision in order to work properly in environments that present multi-layers of soils of very different conductivities.
This work concludes a two-phase study on the suitability of using EIT technology as the basis of a confirmatory detector for AT mines. As a very general conclusion, EIT technology has proved to be useful in the role of a confirmatory detector for AT mines. This has been demonstrated through the experiments in the DRES Mine Pen facility. Results from the trials at CDC and DRES have also indicated that the detector is capable of reliably detecting AT type mines at depths of 15 to 20 cm. The detector is also capable of resolving a typical AT size mine buried at depths of up to 16 cm and separated by distances as small as 7 cm. A detection algorithm based on a replica of the object of interest has also proved to be efficient in reducing the false alarm rate of the detector. The trials performed at DRES have also shown that the soil environment may have a significant impact on the detector’s performance if this is not accounted for in the reconstruction model. However, in order to provide a balanced evaluation of the EIT detection technology, it should be pointed out that the detector also faces limitations because an electrode-soil contact is required. Electrical contact cannot be assured in all types of environment and the deployment of electrodes in the close proximity of explosives is a potential operational issue, although no large force is required to achieve contact. EIT technology, as a mine detection application, appears to have a special niche in environments such as beaches, ocean littorals and other wet areas where EIT works at its best.
The detector has been shown to be unexpectedly efficient in sand, even if it is poorly conductive, as long as the sand holds some moisture. The fluidity of the sand also provides an easy reliable contact with the electrodes. EIT may also have an application in locating intact
mines in the berms formed when mine clearing equipment neutralizes and removes mines.
Most mines in such berms are already inert, reducing the likelihood of initiation when inserting the sensor head. Further, the EIT sensor head could be made cheaply enough to be disposable and inserted remotely to improve safety.
The following paper does not touch directly on the problem of demining, although the issues discussed are very similar and are important in demining. Candansayar and Basokur (Candansayar M. E. and A. T. Basokur, 2001) discuss the problem of detecting small archaeological targets. Achievements in this area, however, may also be of use in demining.
The detecting capabilities of some electrical arrays for the estimation of position, size and depth of small-scale targets are examined in the light of the results obtained from 2-D inversions of apparent-resistivity data. The two-sided three-electrode apparent resistivity data are obtained by the application of left and right-hand pole-dipole arrays that also permit the computation of four-electrode and dipole-dipole apparent-resistivity values without actually measuring them. Synthetic apparent-resistivity data sets of the dipole-dipole, four-electrode and two-sided three-electrode arrays are calculated for models that simulate buried tombs.
The results of 2-D inversions are compared with regard resolution in detecting the exact location, size and depth of the target, showing some advantage of the two-sided three-electrode array. A field application was carried out in the archaeological site known as Alaca Hoyuk, a religious temple area of the Hittite period. The 2-D inversion of the two-sided three-electrode apparent-resistivity data led to the location of part of the city wall and a buried small room. The validity of the interpretation has been checked against the results of subsequent archaeological excavations.
Figure 61. (a) A view of the exposed city wall from the southern side (area EA1); (b) a view of the exposed room and kiln (area EA2). (source: Candansayar M. E. and A. T.
Basokur, 2001, Detecting small-scale targets by the 2-D inversion of two-sided three-electrode data: application to an archaeological survey, Geophysical Prospecting, 49, 13 – 25)
A comparison test has been applied to examine the resolution obtained with earth models derived from the 2-D inversions of three and four-electrode synthetic data. Furthermore, a computer program that handles two types of electrode array has been developed as an adaptation of the algorithm published by Uchida and Murakami (1990) and this includes the
modelling of topography. The forward and inversion schemes utilize, respectively, the finite-element and damped least-square methods.
Figure 62. Plan views of the final model inverted from the two-sided three-electrode apparent-resistivity data measured at the Alaca Hoyuk archaeological site. The figure shows the variation of the intrinsic resistivity values inside the blocks within the same depth range. The resistivity maps correspond to the depth ranges (a) 0.41±1.83, (b) 1.83±3.11 and (c) 3.11±5.20, respectively. The excavation areas are outlined by black rectangles (EA1 and EA2). Yellow dashed lines indicate the exposed wall and room. The green lines mark the geophysical interpretation.
(source: Candansayar M. E. and A. T. Basokur, 2001, Detecting small-scale targets by the 2-D inversion of two-sided three-electrode data: application to an archaeological survey, Geophysical Prospecting, 49, 13 – 25)
The problem of water content variation in soil considered by Panissod (Panissod C. et al, 2001) is also important from the perspective of demining. Firstly, the visualized geometries are relatively small, although they are still larger than mines. Secondly, the variation in water content in the soil associated with vegetation is examined. This problem is significant when electromagnetic methods used for mine detection are considered as a whole.
Figure 63. Location of the electrodes in relation to the corn plant rows (7, 8, 9... for the smaller pseudo-section and 7’, 8’, 9’... for the larger pseudo-section) and model
scheme used for 3-D modellings. (source: Panissod C., D. Michot, Y. Benderitter and A. Tabbagh, 2001, On the effectiveness of 2-D electrical inversion results: an agricultural case study, Geophysical Prospecting, 49, 570-576)
The authors used electrical resistivity tomography in Beauce (France) to assess the water extraction by corn plants (evapotranspiration). The acquired pseudo-sections show conductive anomalies under the plants. A 2-D inversion of measurements led us to identify clear resistive features associated with the water losses under the corn plant rows. New models have been calculated with two different 3-D algorithms (finite difference and moment method) to take into account the 3-D structure of the ground and to confirm that periodic resistive features may generate shifted apparent-resistivity anomalies. The effectiveness of 2-D inversion results is demonstrated with a field example showing the evapotranspiration effect in relation to corn plant rows. The increase in the electrical resistivity due to the water extraction corresponds to a typical 2-D structure of the ground with resistive features under the corn rows.
Figure 64. 2-D inversion of calculated data (pseudo-section with a=0.2 m for short length L=0.25 m (perpendicular to the pseudo-section plane) of the corn plant rows).
(source: Panissod C., D. Michot, Y. Benderitter and A. Tabbagh, 2001, On the effectiveness of 2-D electrical inversion results: an agricultural case study, Geophysical Prospecting, 49, 570-576)
The 3-D modellings (using both finite difference and moment method) confirm the reality of 2-D artefacts, show that 3-D effects are not significant and allow numerical artefacts to be excluded. The boundary between the 2-D and the 3-D cases can be defined by combining the use of 3-D modelling and 2-D inversion algorithms. In the present example, the 2-D inversion of pseudo-sections is very efficient and demonstrates well the effects of evapotranspiration.
The transport of water in soil plays an important role in modifying the electrical properties of the soil. Thus the phenomena involved may also be examined accurately using impedance techniques. This problem has been studied by Slater et al (Slater L., et al, 2000) and presented in their paper entitled “Cross-hole electrical imaging of a controlled saline tracer injection”.
Electrical imaging of tracer tests can provide valuable information on the spatial variability of solute transport processes. This concept was investigated by cross-borehole electrical imaging of a controlled release in an experimental tank. A saline tracer of conductivity 8=103 mS/m
and volume 270 l was injected into a tank facility with dimensions 10×10×3 m and consisting of alternating sand and clay layers. Injection was from 0.3 m below the surface at a point where maximum interaction was expected between the tank structure and the tracer transport. Repeated imaging over a two-week period detected non-uniform tracer transport, partly caused by the sand/clay sequence. Tracer accumulation on two clay layers was observed and a density-driven spill of the tracer over a clay shelf was imaged. An additional unexpected flow pathway, probably caused by complications during array installation, was identified close to the electrode array.
Figure 65. Circulating measurement configurations used in electrical imaging, The ‘‘normal’’
transfer resistance measurement and its reciprocal. (source: Slater L., A.M.
Binley, W. Daily, R. Johnson, 2000, Cross-hole electrical imaging of a controlled saline tracer injection, Journal of Applied Geophysics, 44, 85–102)
Pore water samples obtained following termination of electrical imaging generally supported the observed electrical response, although discrepancies arose when the response of individual pixels was analysed. The pixels that make up the electrical images were interpreted as a large number of breakthrough curves. The shape of the pixel breakthrough-recession curve allowed some quantitative interpretation of solute traveltime, as well as a qualitative assessment of spatial variability in advective-dispersive transport characteristics across the image plane.
Although surface conduction effects associated with the clay layers complicated interpretation, the plotting of pixel breakthroughs was considered a useful step in the hydrological interpretation of the tracer test. The spatial coverage provided by the high density of pixels is the most encouraging factor in the approach.
Figure 66. Images of the conductivity ratio obtained at nine intervals during tracer injection.
a) Between 8 and 47 h after the start of the tracer injection. b) Between 71 and 264 h after the start of the tracer injection. (source: Slater L., A.M. Binley, W.
Daily, R. Johnson, 2000, Cross-hole electrical imaging of a controlled saline tracer injection, Journal of Applied Geophysics, 44, 85–102)
Appendices
A. Linear least squares inversion