Torleif Dahlin

2D resistivity surveying for environmental and engineering applications

Pressure on natural resources from growing populations, with growing demands for water supply, infrastructure and housing, has increased in the past decades and can be expected to continue to rise. Further stress on the environment due to pollution will increase the need for detailed geological knowledge, for geotechnical, hydrogeological, and environmental protection purposes.

The development of DC resistivity imaging techniques

The development of direct current resistivity imaging techniques has been rapid in the last years. This applies to data acquisition as well as inverse modelling techniques, and has lead to a greatly expanded practical applicability of the method. Resistivity imaging is now becoming widely used in environmental and engineering applications where increased knowledge about the subsurface is sought. The ongoing development can be expected to continue.

A comparison of the Gauss-Newton and quasi-Newton methods in resistivity imaging inversion

The smoothness-constrained least-squares method is widely used for two-dimensional (2D) and three-dimensional (3D) inversion of apparent resistivity data sets. The Gauss-Newton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the least-squares equation. The quasi-Newton method has also been used to reduce the computer time. In this method. the Jacobian matrix for a homogeneous earth model is used for the first iteration, and the Jacobian matrices for subsequent iterations are estimated by an updating technique. Since the Gauss-Newton method uses the exact partial derivatives, it should require fewer iterations to converge. However, for many data sets, the quasi-Newton method can be significantly faster than the Gauss-Newton method. The effectiveness of a third method that is a combination of the Gauss-Newton and quasi-Newton methods is also examined. In this combined inversion method, the partial derivatives are directly recalculated for the first two or three iterations, and then estimated by a quasi-Newton updating technique for the later iterations. The three different inversion methods are tested with a number of synthetic and field data sets. In areas with moderate (less than 10:1) subsurface resistivity contrasts, the inversion models obtained by the three methods are similar. In areas with large resistivity contrasts, the Gauss-Newton method gives significantly more accurate results than the quasi-Newton method. However, even for large resistivity contrasts, the differences in the models obtained by the Gauss-New-ton method and the combined inversion method are small. As the combined inversion method is faster than the Gauss-Newton method, it represents a satisfactory compromise between speed and accuracy for many data sets. (Less)

Resolution of 2D Wenner resistivity imaging as assessed by numerical modelling

Modelling of 2D resistivity imaging was done in order to understand the principle resolution of the technique in different geological situations, and for assessing the behaviour of the interpretation methods under controlled circumstances. The Wenner array was used throughout. The results show that the 1D approximation only provides reasonable results in environments with very gradual lateral resistivity changes, otherwise the result may be strongly misleading. Inversion using the 2D quasi-Newton technique results in adequate resolution of the structures in moderately complex environments, but the Gauss–Newton method holds a significant advantage in some complicated cases. The data density can also be of crucial importance for the resolution capability, notably of narrow structures.

A 3‐D resistivity investigation of a contaminated site at Lernacken, Sweden

A contaminated site at Lernacken in southern Sweden, formerly used for sludge disposal, was investigated using a 3-D resistivity imaging technique. The data acquisition was carried out using a roll-along technique for 3-D data acquisition that allows using standard multielectrode equipment designed for engineering and environmental applications. The technique allows for the measurement of large true 3-D resistivity data sets, and data were measured using two perpendicular electrode-orientation directions with only one layout of the cables. The data were plotted as two sets of pseudo depth slices using the two electrode orientation directions, which resulted in markedly different plots. The complete data set was inverted to form a resistivity-depth model of the ground using a 3-D least-squares smoothness constrained inversion technique. The results obtained were compared to other geophysical and background data, and a good agreement was found. The results show that the 3-D roll-along technique in combination with 3-D inversion can be highly useful for engineering and environmental applications. However, multichannel measurement equipment is necessary to speed up the data acquisition process for routine application.

Properties and Effects of Measurement Errors on 2D Resistivity Imaging Surveying

Electrode spacing errors and errors correlated with the magnitude of the observed potential are two key factors that affect the data quality for DC resistivity imaging measurements. This paper investigates the properties and effects of these two kinds of error on 2D resistivity imaging or inversion for practical applications. By analytic analysis and numerical simulations, the off-line and in-line electrode spacing errors were quantitatively estimated for all common electrode arrays (pole-pole, pole-dipole, pole-bipole, Wenner, Schlumberger, dipole-dipole, γ-array, Wenner-β) in 2D resistivity imaging surveys. Meanwhile, the spreading patterns of the spacing errors in the pseudosection and the possible artefacts in the imaging (inverted model) are evaluated. We show that the magnitude of the spacing errors are quite different with these arrays, being largest for dipole-dipole, Wenner-β and γ-array surveys, for which a 10% in-line spacing error may cause twice as large an error (>20%) in the observed resistance or apparent resistivity, which in turn will produce some artefacts in the inverted model. The observed potential errors obtained with the reciprocity principle and collected from different sites and with different electrode arrays, were analysed to show the properties of the potential error caused by many aspects in the field. Using logarithmic plots and error pseudosections, we found that with different electrode arrays and at different sites the potential errors demonstrate a general property, which may be regarded as a negative-power function of potential reading. Power net transients, background telluric variation and instrument malfunction are possible sources that may cause the large errors present as outliers deviating from this function. We reaffirm the fact that the outliers are often correlated with high contact resistances for some of the electrodes used in a measurement, but this may also be caused by an unsatisfactory connection between the electrode and the cable due to, for example, dirt or oxide on the connectors. These outliers are often the main part of the errors affecting the imaging results. Furthermore, a robust inversion and a smoothness-constrained inversion were applied to the investigation of the effects of the measurement errors. Using two real data sets, we show that the smoothness-constrained least-squares inversion is much more sensitive to the potential errors than the robust inversion, but the two inversion schemes produce very similar models with a high data quality. Artefacts or indefinite parts in the inverted models correlate with the distribution zones of the outliers in the potential error pseudosection.

Multiple-gradient array measurements for multichannel 2D resistivity imaging

Two-dimensional resistivity imaging using multiple gradient, Wenner and dipole-dipole electrode arrays was carried out at two field sites in Sweden and one in Nicaragua, with the objective of confirming the practical applicability of results obtained with numerical modelling. The results support earlier numerical modelling studies that concluded that the gradient array, using multiple current electrode combinations, has resolution as good as or better than the commonly used Wenner array. The array behaved well in terms of sensitivity to noise at the test sites, and the results obtained generally agree with dipole-dipole array results, although the latter at two of the sites gave resistivities that differed significantly from the other arrays in the deeper parts of the inverted models. A formula proposed for pseudosection plotting works well for data quality assessment, where it can be an advantage to make separate plots for each m-factor (the distance between the midpoints of the current and potential electrode pairs) or for each a-spacing. The gradient array is well suited for multichannel data acquisition, and can significantly increase the speed of data acquisition in the field and at the same time give higher data density, but it is also an attractive option for single-channel data acquisition. The Wenner array, on the other hand, is not suitable for measuring in more than one channel. Compared to the dipole-dipole array, it offers lower sensitivity to noise which may be a major advantage in real data acquisition, and the remote electrode needed for the pole-dipole array is avoided, which is often a significant advantage for field logistics.

Measuring techniques in induced polarisation imaging

Multi-electrode geoelectrical imaging has become very popular and is used for many different purposes. For some of these, the inclusion of IP data would be desirable as it would allow the interpreter to distinguish between, e.g. sand formations with saltwater infiltration and clay formations or help delineate landfills. However, present-day IP measuring techniques require the use of nonpolarisable potential electrodes and special wire layout and are thus cumbersome and expensive. In this paper, we suggest making IP measurements with multi-electrode cables and just one set of steel electrodes. The polarisation potentials on the potential electrodes are corrected for by subtracting the polarisation potential measured when no primary current and no IP signal are present. Test measurements indicate that the polarisation potentials vary slowly and that the correction procedure is feasible. At two sites in southern Sweden, we have compared measurements with only stainless steel electrodes and measurements with both stainless steel and Pb-PbCl nonpolarisable electrodes using one or two sets of multicore cables, respectively. Almost no difference between the two data sets was observed. At one site, the charge-up effect on the potential electrodes was not important, while at the other site, the correction procedure was crucial. Though only two sites have been studied so far, it seems that time-domain IP imaging measurements can be taken with only steel electrodes and ordinary multicore cables. Coupling in the multicore cables has not presented any problems at the investigated sites where grounding resistances were moderate, making the coupling effect small. High grounding resistance sites have not yet been investigated

2.5D resistivity modeling of embankment dams to assess influence from geometry and material properties

Repeated resistivity measurement is a potentially powerful method for monitoring development of internal erosion and anomalous seepage in earth embankment dams. This study is part of a project to improve current longterm monitoring routines and data interpretation and increasing the understanding when interpreting existing data. This is accomplished by modeling various occurrences typical of embankment structures using properties from two rockfill embankment dams with central till cores in the north of Sweden. The study evaluates the influence from 3D effects created by specific dam geometry and effects of water level fluctuations in the reservoir. Moreover, a comparison between different layout locations is carried out, and detectability of internal erosion scenarios is estimated through modeling of simulated damage situations. Software was especially developed to model apparent resistivity for geometries and material distributions for embankment dams. The model shows that the 3D effect from the embankment geometry is clearly significant when measuring along dam crests. For dams constructed with a conductive core of fine-grained soil and high-resistive rockfill, the effect becomes greatly enhanced. Also, water level fluctuations have a clear effect on apparent resistivities. Only small differences were found between the investigated arrays. A layout along the top of the crest is optimal for monitoring on existing dams, where intrusive investigations are normally avoided, because it is important to pass the current through the conductive core, which is often the main target of investigation. The investigation technique has proven beneficial for improving monitoring routines and increasing the understanding of results from the ongoing monitoring programs. Although the technique and software are developed for dam modeling, it could be used for estimation of 3D influence on any elongated structure with a 2D cross section.

Treatment of landfill leachate by irrigation of willow coppice – Plant response and treatment efficiency

Landfill leachates usually need to be treated before discharged, and using soil-plant systems for this has gained substantial interest in Sweden and in the UK. A three-year field study was conducted in central Sweden to quantify plant response, treatment efficiency and impact on groundwater quality of landfill leachate irrigation of short-rotation willow coppice (Salix). Two willow varieties were tested and four irrigation regimes in sixteen 400-m2 plots. The willow plants did not react negatively, despite very high annual loads of nitrogen (<or=2160 kg N/ha), chloride (<or=8600 kg Cl/ha) and other elements. Mean annual growth was 1.5, 9.8 and 12.6 tonnes DM/ha during years 1-3. For one of two willow varieties tested, relative leaf length accurately predicted growth rate. Irrigation resulted in elevated groundwater concentrations of all elements applied. Treatment efficiency varied considerably for different elements, but was adequate when moderate loads were applied.