Images of the magnetotelluric apparent resistivity tensor

We present a method for converting the magnetotelluric (MT) impedance tensor into an apparent resistivity tensor. The inclusion of anisotropic permittivity and conductivity into Maxwell's equations leads to a tensor expression for the propagation constant. To solve Maxwell's equations we assume exponentially decreasing electric fields in the vertical direction, which implies that the subsurface is regarded as homogeneous but anisotropic. This approach effectively makes use of an anisotropic substitute model, in which contrasts and strike directions of conductivity anomalies are transformed into equivalent amounts and directions of anisotropy. We call this method propagation number analysis (PNA). Rotationally invariant parameters calculated from the resistivity tensor are physically meaningful quantities that are directly applicable to imaging methods. Imaging results of PNA are compared with Egger's eigenstate analysis and LaTorraca's singular-value decomposition method using synthetic data from 3-D MT modelling. With PNA, we obtain a comprehensive image of the subsurface that uniquely images structural details of the anomalies. Contrary to other methods, the results of PNA are stable and significant under extreme 3-D conditions. Application of PNA to MT data from the Waterberg Fault in Namibia unravels a complicated 3-D impedance and reveals a clear correlation between the resistivity tensor and the surface geology.