An ellipticity criterion in magnetotelluric tensor analysis

We examine the magnetotelluric (MT) impedance tensor from the viewpoint of polarization states of the electric and magnetic field. In the presence of a regional 2-D conductivity anomaly, a linearly polarized homogeneous external magnetic field will generally produce secondary electromagnetic fields, which are elliptically polarized. If and only if the primary magnetic field vector oscillates parallel or perpendicular to the 2-D structure, will the horizontal components of the secondary fields at any point of the surface also be linearly polarized. When small-scale inhomogeneities galvanically distort the electric field at the surface, only field rotations and amplifications are observed, while the ellipticity remains unchanged. Thus, the regional strike direction can be identified from vanishing ellipticities of electric and magnetic fields even in presence of distortion. In practice, the MT impedance tensor is analysed rather than the fields themselves. It turns out, that a pair of linearly polarized magnetic and electric fields produces linearly polarized columns of the impedance tensor. As the linearly polarized electric field components generally do not constitute an orthogonal basis, the telluric vectors, i.e. the columns of the impedance tensor, will be non-orthogonal. Their linear polarization, however, is manifested in a common phase for the elements of each column of the tensor and is a well-known indication of galvanic distortion. In order to solve the distortion problem, the telluric vectors are fully parametrized in terms of ellipses and subsequently rotated to the coordinate system in which their ellipticities are minimized. If the minimal ellipticities are close to zero, the existence of a (locally distorted) regional 2-D conductivity anomaly may be assumed. Otherwise, the tensor suggests the presence of a strong 3-D conductivity distribution. In the latter case, a coordinate system is often found, in which three elements have a strong amplitude, while the amplitude of the forth, which is one of the main-diagonal elements, is small. In terms of our ellipse parametrization, this means, that one of the ellipticities of the two telluric vectors approximately vanishes, while the other one may not be neglected as a result of the 3-D response. The reason for this particular characteristic is found in an approximate relation between the polarization state of the telluric vector with vanishing ellipticity and the corresponding horizontal electric field vector in the presence of a shallow conductive structure, across which the perpendicular and tangential components of the electric field obey different boundary conditions.