An analysis of the magnetotelluric impedance for three‐dimensional conductivity structures

Abstract

The eigenstate analysis of Lanczos, also known as singular value decomposition (SVD), is used to define eight parameters which uniquely describe the magnetotelluric impedance Z. These parameters are independent of a priori assumptions about Z and can be interpreted in terms of three‐dimensional conductivity structures. Through SVD, the impedance is represented by two characteristic states. These states consist of two pairs (E and H) of complex vectors and two corresponding, real, singular values which together describe the extremal properties of Z. The singular values are the maximum and minimum |E|/|H| ratios possible at the observation site and therefore yield the true maximum and minimum apparent resistivities. We use a variation of SVD analysis by incorporating phases in the singular values, which are then called characteristic values. These phases reflect the delay (caused by the earth’s conductivity) of the electric fields relative to their associated magnetic fields. In this analysis of Z, the characteristic values contain four parameters, two singular values and two phases. The characteristic vectors contain the remaining four parameters, two principal axis directions and two ellipticities. The principal axis directions for the E and H vectors need not be at right angles as in biorthogonal analysis. The deviation of these axes from orthogonality is called the “skew angle” S. From a model by Park, we have found S to be closely related to distortions in the telluric current system caused by current gathering due to a good conductor. From the same model, we have found the ellipticity parameters to be the largest in regions of high current distortion and at the shorter periods. Consequently, we speculate that the ellipticity parameters are associated with local induction.