Anisotropic resistivity tomography

Abstract

Geophysical tomographic techniques have the potential to remotely detect and characterize geological features, such as fractures and spatially varying lithologies, by their response to signals passed through these features. Anisotropic behaviour in many geological materials necessitates the generalization of tomographic methods to include anisotropic material properties in order to attain high-quality images of the subsurface. In this paper, we present a finite element (FE) based direct-current electrical inversion method to reconstruct the conductivity tensor at each node point of a FE mesh from electrical resistance measurements. The inverse problem is formulated as a functional optimization and the non-uniqueness of the electrical inverse problem is overcome by adding penalty terms for structure and anisotropy. We use a modified Levenberg-Marquardt method for the functional optimization and the resulting set of linear equation is solved using pre-conditioned conjugate gradients. The method is tested using both synthetic and field experiments in cross-well geometry. The acquisition geometry for both experiments uses a cross-well experiment at a hard-rock test site in Cornwall, southwest England. Two wells, spaced at 25.7 m, were equipped with electrodes at a 1 m spacing at depths from 21-108 m and data were gathered in pole-pole geometry. The test synthetic model consists of a strongly anisotropic and conductive body underlain by an isotropic resistive formation. Beneath the resistive formation, the model comprises a moderately anisotropic and moderately conductive half-space, intersected by an isotropic conductive layer. This model geometry was derived from the interpretation of a seismic tomogram and available geological logs and the conductivity values are based on observed conductivities. We use the test model to confirm the ability of the inversion scheme to recover the (known) true model. We find that all key features of the model are recovered. However, the inversion model is smoother than the true model and the difference in absolute value of anisotropy and conductivity between features is slightly underestimated. Using an anisotropic conductivity distribution aggravates the problem of non-uniqueness of the solution of the inverse electrical problem. This problem can be overcome by applying appropriate structural and anisotropy constraints. We find that running a suite of inversions with varying constraint levels and subsequent examination of the results (including the inspection of residual maps) offers a viable method for choosing appropriate numerical values for the imposed constraints. Inversion of field data reveals a strongly anisotropic subsurface with marked spatial variations of both magnitude of anisotropy and conductivity. Average conductivities range from 0.001 S m-1 (= 1000 Ω m) to 0.003 S m-1 (= 333 Ω m) and anisotropy values range from 0 per cent to more than 300 per cent. As an independent test of the reliability of the structures revealed by anisotropic electric tomography, anisotropic seismic traveltime tomograms were calculated. We find a convincing structural agreement between the two independently derived images. Areas of high electric anisotropy coincide with seismically anisotropic areas and we observe an anticorrelation between electric conductivity and seismic velocity. Both observations are consistent with anisotropy anomalies caused by fracturing or layering. © 2004 RAS.