Understanding telluric distortion matrices

Abstract

Telluric distortion occurs when electric charges accumulate along near‐surface inhomogeneities. Practical parametrizations of a telluric distortion matrix separate it into recoverable and non‐recoverable parameters. A very simple parametrization used by Bahr (1988) does this, and is easily interpreted in terms of rotations and amplifications of the regional electric field components aligned with the regional strike directions. Groom & Bailey's (1989) parametrization is equivalent, but more complicated. Optimal estimates of the electric field rotations, the regional strike, and scaled regional impedances are made easily using the simple parametrization advocated here. The regional impedance estimates have a variance that is modestly improved over those obtained by simply rotating the measured impedance matrix. Optimal esitmates of Groom & Bailey's parameters are obtained easily from the parametrization used here. The recoverable 3‐D distortion parameters do not characterize distorting bodies very well as their values depend to varying degree on the orientation of the regional strike. Owing to inherent non‐uniqueness, any measured impedance matrix that can be represented as a 3‐D distortion of a regional 2‐D impedance can equally well be represented as a 2‐D distortion of a regional 2‐D impedance in the form given by Zhang, Roberts & Pedersen (1987). The superficial 2‐D strike and anisotropy are easily recovered from the parametrization used here, and characterize 2‐D distortion well, as they are coordinate‐independent for 2‐D distortions. The optimal estimates are straightforward even for the realistic case of measurement errors that are correlated between elements of a measured impedance matrix. Copyright © 1995, Wiley Blackwell. All rights reserved