Resistivity inversion in 2-D anisotropic media: numerical experiments

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 description

Modélisation directe et inverse en prospection électrique sur les structures 3D complexes par la méthode des éléments finis

This work presents the adaptation and the use of the CESAR-LCPC finite element code for the forward and inverse modelling of 3D resistivity data. These codes are better suited for imaging structures with complex geometries.The forward modelling code uses an electrode-independent mesh that allows to place the electrodes at their exact locations and to use a coarse mesh at the same time. In this approach, the choice for the mesh size is solely governed by the need for accurate results. It is also possible to calculate apparent resistivities, without the use of the geometrical factor (that can be evaluated only for simple structures). To calculate apparent resistivity values, a normalisation approach is used that gives significantly better results than the use of the geometrical factor and allows the modelling of any kind of complex 3D structure. As a singularity removal technique cannot be used on complex 3D models, a minimum of 5 to 6 nodes between two current transmitting electrodes should be considered to guarantee the quality of the results. Synthetic results are presented to illustrate the efficiency of the forward modelling technique.An inversion code was also presented for the processing of resistivity tomographies on complex 3D structures using any electrode arrangement. This algorithm is well suited for the processing of large data sets with a lot of unknown model parameters. The inversion code uses an original strategy to avoid the explicit calculation of a sensitivity matrix. The adjoint-state of the potential field is used to minimize an objective function for the electrical inverse problem. Then, a steepest descent formulation can be used for the first iteration. Further iterations are carried out using a conjugate gradient approach to improve the convergence. As can be seen on synthetic data, a satisfactory reconstruction of the models can be achieved with a minor computational cost. This kind of inverse problem would have been very difficult to solve using a more traditional Gauss-Newton approach. Strategies are nevertheless needed to improve the stabilisation of the inverse process and to include a priori information in the problem.Finally, a ROI (Region Of Investigation) index method is used to assess whether features in the model are caused by the data or are artefacts of the inversion process. This method carries out two inversions of the same data set using different values of the reference resistivity model. The two inversions reproduce the same resistivity values in areas where the data contain information about the resistivity of the subsurface whereas the final result depends on the reference resistivity in areas where the data do not constrain the model.Ce travail a pour objectif la mise au point d'un ensemble d'outils de modélisation directe et inverse en utilisant le code d'éléments finis CESAR-LCPC. Ces outils sont adaptés aux données électriques collectées sur des structures 3D à géométrie complexe. Pour le problème direct, un programme utilitaire servant d'interface avec le solveur CESAR a été créé afin de modéliser des séquences de mesures électriques (tomographies). Afin de pouvoir inverser un nombre important de données sur des modèles de grandes dimensions, une fonction objectif est minimisée en utilisant la technique de l'état adjoint. Cette approche est originale car elle vise le calcul direct de la variation à apporter aux paramètres du modèle, sans évaluation explicite de la matrice de sensibilité. Des données synthétiques ont été utilisées pour valider cet algorithme d'inversion. La fiabilité des modèles inversés est testée en utilisant une méthode de calcul de l'indice ROI (Region of Investigation)

Internal structure and permafrost distribution in two alpine periglacial talus slopes, Valais, Swiss Alps

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 35 kΩm is present. In the uppermost part of the profiles, the resistivities are lower than 10–15 kΩm. 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