Many rocks and layered/fractured sequences have a clearly expressed electrical anisotropy although it is rare in practice to incorporate anisotropy into resistivity inversion. In this contribution, we present a series of 2.5-D synthetic inversion experiments for various electrode configurations and 2-D anisotropic models. We examine and compare the image reconstructions obtained using the correct anisotropic inversion code with those obtained using the false but widely used isotropic assumption. Superior reconstruction in terms of reduced data misfit, true anomaly shape and position, and anisotropic background parameters were obtained when the correct anisotropic assumption was employed for medium to high coefficients of anisotropy. However, for low coefficient values the isotropic assumption produced better-quality results. When an erroneous isotropic inversion is performed on medium to high level anisotropic data, the images are dominated by patterns of banded artefacts and high data misfits. Various pole–pole, pole–dipole and dipole–dipole data sets were investigated and evaluated for the accuracy of the inversion result. The eigenvalue spectra of the pseudo-Hessian matrix and the formal resolution matrix were also computed to determine the information content and goodness of the results. We also present a data selection strategy based on high sensitivity measurements which drastically reduces the number of data to be inverted but still produces comparable results to that of the comprehensive data set. Inversion was carried out using transversely isotropic model parameters described in two different co-ordinate frames for the conductivity tensor, namely Cartesian versus natural or eigenframe. The Cartesian frame provided a more stable inversion product. This can be simply explained from inspection of the eigenspectra of the pseudo-Hessian matrix for the two model descriptions.

Abstract We present a set of 2.5D synthetic inversion experiments for a model comprising an isotropic block embedded within an anisotropic background. We examine and compare the image reconstructions obtained using the correct anisotropic code and those obtained using code based on the inappropriate but widely adopted isotropic assumption. Superior reconstruction in terms of reduced data misfit, true anomaly shape and position, and anisotropic background parameters were obtained when the correct anisotropic code was employed for media characterized by moderate to high coefficients of anisotropy. However, for low coefficient values, the isotropic inversion produced slightly better results because there are fewer parameters to determine. When an erroneous isotropic inversion is performed on medium to high level anisotropic data, the images are dominated by patterns of banded artefacts and high data misfits.

The hydrogeological properties and responses of a productive aquifer in northeastern Switzerland are investigated. For this purpose, 3D crosshole electrical resistivity tomography (ERT) is used to define the main lithological structures within the aquifer (through static inversion) and to monitor the water infiltration from an adjacent river. During precipitation events and subsequent river flooding, the river water resistivity increases. As a consequence, the electrical characteristics of the infiltrating water can be used as a natural tracer to delineate preferential flow paths and flow velocities. The focus is primarily on the experiment installation, data collection strategy, and the structural characterization of the site and a brief overview of the ERT monitoring results. The monitoring system comprises 18 boreholes each equipped with 10 electrodes straddling the entire thickness of the gravel aquifer. A multichannel resistivity system programmed to cycle through various four-point electrode configurations of the 180 electrodes in a rolling sequence allows for the measurement of approximately 15,500 apparent resistivity values every 7 h on a continuous basis. The 3D static ERT inversion of data acquired under stable hydrological conditions provides a base model for future time-lapse inversion studies and the means to investigate the resolving capability of our acquisition scheme. In particular, it enables definition of the main lithological structures within the aquifer. The final ERT static model delineates a relatively high-resistivity, low-porosity, intermediate-depth layer throughout the investigated aquifer volume that is consistent with results from well logging and seismic and radar tomography models. The next step will be to define and implement an appropriate time-lapse ERT inversion scheme using the river water as a natural tracer. The main challenge will be to separate the superposed time-varying effects of water table height, temperature, and salinity variations associated with the infiltrating water.

In order to determine the spatial extension and the characteristics of permafrost within alpine talus slopes, two sites located in the western part of the Swiss Alps were studied using borehole drilling and electrical resistivity tomography (ERT) profiles. Three boreholes were drilled along an upslope–downslope transect in both talus slopes. In both sites, frozen sediments are present only in the two lowest boreholes, whereas the upper borehole does not present ice. This stratigraphy is confirmed by ground temperatures registered in the boreholes. In each site, three upslope–downslope ERT profiles were crossed with five, respectively four horizontal ERT profiles. All the upslope–downslope profiles show a difference in resistivities between the upper and lower parts of the slope, where a large resistive body with values higher than 35kΩm is present. In the uppermost part of the profiles, the resistivities are lower than 10–15kΩm. The borehole data allowed the stratigraphy obtained from the ERT inverted profiles to be validated, with regards to the distribution of frozen sediments as well as the depth of the detected structures. The results confirm that, in the two studied sites, permafrost is present in the lower sections of the talus slopes, whereas it is absent in the upper parts. Finally, the analysis of the talus structure showed that the permafrost stratigraphy, and in particular the ice content, may be an important element of interpretation of the palaeoclimatic significance of an alpine talus slope.

In this paper we develop analytic solutions for the electric potential, current density and Fréchet derivatives at any interior point within a 3-D transversely isotropic medium having a tilted axis of symmetry. The current electrode is assumed to be on the surface of the Earth and the plane of stratification given arbitrary strike and dip. Profiles can be computed for any azimuth. The equipotentials exhibit an elliptical pattern and are not orthogonal to the current density vectors, which are strongly angle dependent. Current density reaches its maximum value in a direction parallel to the longitudinal conductivity direction. Illustrative examples of the Fréchet derivatives are given for the 2.5-D problem, in which the profile is taken perpendicular to strike. All three derivatives of the Green’s function with respect to longitudinal conductivity, transverse resistivity and dip angle of the symmetry axis (dG/dσ l , dG/dσ t , dG/dθ0) show a strongly asymmetric pattern compared to the isotropic case. The patterns are aligned in the direction of the tilt angle. Such sensitivity patterns are useful in real-time experimental design as well as in the fast inversion of resistivity data collected over an anisotropic earth.

In order to determine the spatial extension and the characteristics of the permafrost within alpine talus slopes, thermal and geoelectrical measurements were carried out in several sites of the Swiss Alps (Lambiel 2006, Pieracci et al. 2008). The observations and the measurements carried out at the study sites allowed proposing a model of the permafrost distribution in talus slopes located within the Alpine periglacial belt (Lambiel & Pieracci 2008). According to this model, permafrost appears likely in the lower part of the slope, whereas it is generally improbable upslope. In order to validate the model, in the Attelas talus slope (Verbier area, Valais Alps, 2600-2800 m a.s.l., west-facing flank of the Mont Gele) a fix Electrical Resistivity Tomography (ERT) profile along an upslopedownslope transect composed by 48 electrodes (4 meters interval) was installed in summer 2007, and three boreholes were drilled along the ERT profile in autumn 2008.

The inversion and interpretation of electrical resistivity tomography (ERT) data from coarse blocky and ice-rich permafrost sites are challenging due to strong resistivity contrasts and high contact resistances. To assess temporal changes during ERT monitoring (ERTM), corresponding inversion artefacts have to be separated from true subsurface changes. Appraisal techniques serve to analyse an ERTM data set from a rockglacier, including synthetic modelling, the depth of investigation index technique and the so-called resolution matrix approach. The application of these methods led step by step to the identification of unreliable model regions and thus to the improvement in interpretation of temporal resistivity changes. An important result is that resistivity values of model regions with strong resistivity contrasts and highly resistive features are generally of critical reliability, and resistivity changes within or below the ice core of a rockglacier should therefore not be interpreted as a permafrost signal. Conversely, long-term degradation phenomena in terms of warming of massive ground ice at the permafrost table are detectable by ERTM. Copyright (C) 2009 John Wiley & Sons, Ltd.

Many rocks possess electrical properties with a clearly expressed anisotropy. The anisotropic character of the rocks is often overlooked in forming the Fréchet derivatives or sensitivity functions for parameter updating during the inversion of DC resistivity data. In this study we have compared the sensitivity patterns for an isotropic, homogeneous model with that for a transversely isotropic (i.e. anisotropic) model having a tilted axis of symmetry using a pole–pole array. The sensitivity functions are expressed in terms of the derivatives of the electric potential U with respect to the average conductivity σm (geometric mean of the longitudinal and transverse conductivities) and the coefficient of anisotropy λ. Results are plotted in both cross-section form and plan view for various dip and strike angles of the axis of symmetry. The derivative dU/dλ decreases more rapidly than the isotropic value dU/dσ, and shows pronounced asymmetry and weakening of magnitude with increasing dip of the plane of symmetry. The derivative dU/dσm also exhibits the asymmetric pattern (except for vertical and horizontal dip cases). The positive region between the electrodes only extends to a small depth compared to the isotropic derivative, even in the case of a vertical axis of symmetry (VTI medium). The ratio of this anisotropic derivative to the isotropic derivative, when plotted as a function of position and depth shows prominent differences in both the sign and the magnitude of the sensitivities, especially for steep dips and for strongly anisotropic rocks. The plot highlights the dangers of an isotropic assumption. Even for mildly anisotropic rocks (λ<1.2) the possibility for error in interpretation is considerable. Combined borehole and surface measurements are needed to diagnose anisotropy. Further work is needed to design optimal electrode configurations in anisotropic situations.

We have developed explicit expressions for the Fréchet derivatives or sensitivity functions in resistivity imaging of a heterogeneous and fully anisotropic earth. The formulation involves the Green’s functions and their gradients, and it is developed from a formal perturbation analysis and by means of a numerical (finite-element) method. A critical factor in the equations is the derivative of the electrical conductivity tensor with respect to the principal conductivity values and the angles defining the axes of symmetry. The Fréchet derivative expressions were derived for the 2.5D and 3D problems using constant-point and constant-block model parameterizations. Special cases such as an isotropic earth and tilted transversely isotropic (TTI) media emerge from the general solutions. Numerical examples were investigated for various sensitivities as functions of dip angle and strike of the plane of stratification in uniform TTI media.

ABSTRACTIn this paper we present and analyse DC resistivity sensitivity patterns for uniform anisotropic media and for various surface electrode arrays. The sensitivity functions (or Fréchet derivatives) give the responsive change in measured electric potential for a perturbation in a model parameter at a particular point in the subsurface for a specific electrode configuration. The anisotropic model investigated is the common tilted transversely isotropic medium, which is defined by four model parameters. We examine the changes in the Fréchet derivatives of the Green’s functions with respect to both the longitudinal and transverse conductivity and the dip and azimuth angle of the symmetry axis for varying model parameters. Anisotropic sensitivities are vastly different in strength and shape compared to the isotropic sensitivity pattern. The various arrays (pole‐pole, dipole‐dipole, Wenner and square array) produce distinctive patterns that are important in assessing resolution. Valuable insights were gained: the anisotropic Fréchet derivatives can vary greatly from the isotropic pattern in both strength and shape depending on the nature of the anisotropy. Also it was found that the relationship between components of current density (parallel and perpendicular to the symmetry axis) and the sensitivity patterns is somewhat akin to the dot product of the true source and adjoint source current density vectors in isotropic media. Understanding of the anisotropic sensitivity pattern variations will enable, through further analysis, computation of model resolution matrices and improvement of experimental design. Appreciation of the significant differences between isotropic and anisotropic sensitivities should help avoid errors in using inappropriate isotropic inversion schemes to interpret measurements made over anisotropic ground.

Introduction In this paper we present and analyse DC resistivity sensitivity patterns for uniform anisotropic media. The sensitivity functions (or Fréchet derivatives) give the responsive change in measured electric potential for a perturbation in a model parameter at a particular point in the subsurface for a specific electrode configuration. The anisotropic model investigated is the common tilted transversely isotropic medium (TTI) which is defined by four model parameters. We examine the changes in the Fréchet derivatives of the Green’s functions with respect to both the longitudinal and transverse conductivity and the dip and azimuth angle of the symmetry axis (dG/dσ1, dG/dσt, dG/dθ0, dG/dϕ0) for varying model parameters. Secondly, we wish to illustrate the differences that exist between the sensitivities calculated using an isotropic assumption and those computed with the correct anisotropic formulation. It is shown that in certain cases gross errors in inversion may occur if isotropic Fréchet derivatives are mistakenly used. Here we work with two special forms of the derivatives -one taken with respect to the mean conductivity and the other with respect to the magnitude of the anisotropy- and investigate a range of possible cases.

This article addresses the comments of Sakamato et al. on Greenhalgh et al.'s "Modeling and migration of 2-D georadar data: A stationary phase approach". Here, Greenhalgh et al. emphasizes the comprehensiveness of their approach over Sakamato et al.'s SEABED algorithm.

Introduction Surface electrical resistivity surveying is based on the principle that the distribution of electrical potential in the ground in the vicinity of an electrode array depends on the electrical resistivity distribution of the surrounding soils and rocks. The usual practice in the field is to inject a direct or slowly alternating electrical current through two electrodes implanted in the ground and to measure the difference in potential between two other electrodes. The current is either direct, commutated direct (i.e. an alternating square-wave) or low frequency (typically below 20 Hz) alternating.

We introduce a new finite-element-based scheme for the fast nonlinear inversion of large 3D geoelectric data sets acquired around isolated objects or across the earth's surface. The principal novelty of this scheme is the combination of a versatile finite-element approach with (1) a method involving minimization of an objective function using a conjugate-gradient algorithm that includes an adjoint-field technique for efficiently establishing the objective-function gradient and (2) parabolic interpolation for estimating suitable inversion step lengths. This scheme is capable of handling large volumes of data acquired using diverse electrode configurations located around or across 3D structures. Only three solutions to the forward problem are required for each iteration. Computation of the Jacobian matrix, which might require computers with a large amount of memory, is not necessary. To minimize artificial irregularities in the inverted models, particularly near the electrodes, we smooth the model parameters after each iteration. By including the influence of a reference model in the objective function, a priori information can be incorporated in the inversion process. Our new scheme is tested successfully on synthetic data generated for current and potential electrodes distributed around the surface of a complex object of finite extent. We also demonstrate the utility of the new scheme on geoelectric data acquired around a laboratory-scale object. Tomographic inversion of the 52,272 simulated voltage values in terms of an 8775-element model requires less than 45 minutes on a relatively slow Sun workstation. For the inversion of the 1016 observed voltage values in terms of an 81,480-element model, approximately 60 minutes of computer time is required. The rapid and flexible inversion scheme opens up new possibilities for resistivity imaging in geology, hydrology, engineering, nondestructive testing, and even biology and medicine, fields of study in which finite-element models are already used to represent complicated targets.

We plan to employ crosshole electrical resistivity tomography for monitoring fast hydrological processes that involve complex interactions between a river that frequently floods and the adjacent groundwater. To obtain as much information as possible over relatively short periods, we need to optimise the electrode configurations that will be used to acquire the resistivity data. For this purpose, we have adapted an experimental design procedure first introduced for the planning of surface electrical resistivity surveys. Our new experimental design algorithm seeks electrode configurations for which the linear dependencies are low, such that each electrode configuration provides information that is largely independent of information supplied by all other electrode configurations. The resultant optimised electrode configurations yield overall resolution values and inter-borehole coverage that are superior to those supplied by a random selection approach.

A geoelectrical investigation has been carried out in the Swiss Alps (near the Dent de Nendaz within the southern part of the Rhone valley in the Swiss Alps) to delineate groundwater circulation within an unstable slope. This unstable zone is characterized by a landslide area with clear scarps and hummocky ground at the bottom of the slope. Large scale apparent resistivity mapping provided information on the main pathways for water transport within the slope. Subsequently, 2D resistivity and induced polarization imaging supplied details on the region of instability located at the bottom of the slope. Polarizable units identified in the region of instability could be linked to a clay-rich unit or to local enrichment of graphite within the bedrock. Our results illustrate how low permeability clay/graphite units and permeable water-bearing units could be distinguished using a combined interpretation of resistivity and IP data in slope instability studies.