Theory for Magnetotelluric Observations on the Surface of a Layered Anisotropic Half Spaces†

Summary A magnetotelluric model is considered which consists of a vertical cylinder comprised of horizontal layers, each having a conductivity that is homogeneous both laterally and vertically. There are thus no lateral variations in the magnetic, electric, and current vector fields within the vertical cylinder centered about the observation site. The layer conductivities may be either isotropic, symmetrically anisotropic, or asymmetrically anisotropic in arbitrary vertical sequence, with the horizontal anisotropies oriented at any azimuth about the vertical axis. The intrinsic properties of the impedance tensor in the layered half space permit the tensor to be propagated through the layers without resort to the calculation of the associated electric and magnetic field vectors, as in previous works. The resulting new algorithm permits the calculation to be performed with second rank matrices instead of fourth rank as previously required, with a considerable improvement in speed and accuracy. The calculation of a number of these models illustrates the need for observations that span a sufficiently broad range of periods. Computed results, when considered over a narrow bandwidth, are shown to greatly resemble those for completely dis‐similar models. The new algorithm is also used for downward propagation of the impedance tensor at the observational surface, so that it is possible to recover the vertical distribution of conductivity under favourable circumstances.