Transformation of VLF anomaly maps into apparent resistivity and phase

Abstract

We investigate a transformation of magnetic transfer functions into the tangential‐electric mode part of the impedance tensor in the scope of the plane‐wave electromagnetic tensor–VLF method. The transformation, which is applicable to any 2D data representing the response of arbitrary 3D geoelectric structures, overcomes the difficulties of quantitative interpretation of magnetic transfer functions, which predominantly provide a measure of the lateral changes of the electrical conductivity in the earth. We require densely sampled magnetic transfer functions of one frequency as input data. These may be decomposed into their normal and anomalous parts (deviation from the response of a layered earth) for a unit external plane‐wave source field using the Hilbert transform relationship between the magnetic field components. Faraday's law then directly provides the anomalous toroidal electric field. Unfortunately, there is no chance to estimate the normal electric field from magnetic data, since the magnetic field is not sensitive to a layered earth. This constant must be provided as a boundary condition, e.g., from one ground measurement, to derive an impedance tensor and related apparent resistivities and phases.