Definitions for MT Transfer Functions and Derived Quantities

MT Tipper Strike: TSTRIKE

The tipper principal direction or "strike" can be defined as the angle which:

\\ \text{1) Minimizes }|T'_{x}|^2,\\ \text{2) Maximizes }|T'_{y}|^2,\text{ or}\\ \text{3) Maximizes }|T'_{x}|^2+|T'_{y}|^2\\

where T 'x and T 'y are the tipper components rotated to the tipper strike angle. However, this method has the same 90 degree ambiguity as the impedance principal direction. An alternative, preferred method for defining the tipper principal direction, B, is given by Jupp and Vozoff, 1976:

B=\frac{(TxR^2 + TyR^2)*tan^{-1} \bigg( \frac{TyR}{TxR} \bigg) + (TxI^2 + TyI^2)*tan^{-1} \bigg( \frac{TyI}{TxI} \bigg)+90^o} {|Tx|^2+|Ty|^2}\\

where TxR, TxI, TyR, and TyI represent the real and imaginary parts of Tx and Ty respectively, and B is measured clockwise from true north in the defined azimuthal coordinate system. This is the angle which maximizes the coherency between the vertical and horizontal magnetic field. It has an inherent ambiguity of plus or minus 180 degrees. However, one can choose the principal direction for which the phase of COH(H'z,H'x) (the coherency between the vertical magnetic field, Hz, and the horizontal field component, Hx, rotated to the chosen principal direction) falls between +90 degrees and -90 degrees from the real axis in the complex plane.

References

Chave, A.D. and Jones, A.G. eds., 2012. The magnetotelluric method: Theory and practice. Cambridge University Press.
Wight, D.E., 1987. Society of Exploration Geophysicists MT/EMAP Data Interchange Standard.