extended phase tensor, wavenumber tensor, apparent resistivity tensor, extended Born

This paper describes how subsurface resistivity distributions can be estimated directly from
the magnetotelluric (MT) tensor relationship between electric and magnetic fields observed on a
three-dimensional (3-D) half-space. It presents an inhomogeneous plane wave analogy where relationships
between horizontal electric and magnetic fields, and an apparent current density define an apparent
resistivity tensor constructed from a quadratic function of the MT tensor. An extended-Born relationship
allows the electric field to be normalized with respect to an apparent background current density. The model
is generalized by including the vertical magnetic field in a 3 by 3 MT response tensor. A complex apparent
wave number tensor, constructed from this tensor, has eigenvalues which, using the plane wave analogy,
are the vertical wave numbers associated with the eigenpolarizations of propagating waves in the model half
space. The elements associated with the vertical magnetic field transfer function define the horizontal wave
numbers. An extended 3 by 3 phase tensor contains four elements of the conventional 2 by 2 phase tensor
and two elements associated with the vertical magnetic transfer function. The extended phase tensor and a
single real distortion tensor with six independent elements can be used to quantify static electric and
magnetic field distortions. The approach provides a theoretical basis for visualization and migration of MT
data, in comparison with results from other electrical and EM techniques, a starting point for constrained 3-D
inversions, and an assessment of results with other geophysical and geological data.