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Definitions for MT Transfer Functions and Derived Quantities

MT Impedance Strike: ZSTRIKE

 

The impedance principal direction or "strike" can be defined in many ways. For example it can be defined as the angle which:

\\ \text{1) Maximizes }|Z'_{xy}+Z'_{yx}|^2,\\ \text{2) Maximizes }|Z'_{xy}|^2+|Z'_{yx}|^2,\\ \text{3) Minimizes }|Z'_{xy}|^2+|Z'_{yx}|^2,\text{ or}\\ \text{4) Minimizes }|Z'_{xy}+Z'_{yx}|^2;\\

where Z'xx , Z'xy , Z'yx , and Z'yy are the impedances rotated to the impedance strike angle. The principal direction, A, may be determined by incrementally rotating the impedance tensor, or alternatively it may be calculated analytically from the maximization of (Z'xy+Z'yx)2 (Sims and Bostick, 1969) as:

A=\frac{1}{4}tan^{-1}\bigg( \frac{2R_1*R_2+I_1*I-2}{R_1^2+I_1^2-R_2^2-I_2^2} \bigg)\\ \text{where}\\ R_1 = Re \big( Z_{xx} - Z_{yy} \big),\\ I_1 = Im \big( Z_{xx} - Z_{xy} \big),\\ R_2 = Re \big( Z_{xy} + Z_{yx} \big),\\ I_2 = Im \big( Z_{xy} + Z_{yx} \big).\\

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.