P. Schmoldt, PhD - MTNet - DIAS

4. Distortion of magnetotelluric data
use the phase information of the impedance tensor elements. The approach aims to recover
the regional geoelectric strike direction by determining a rotation angle, that, when
applied to the impedance tensor, causing the two elements belonging to the same telluric
vector ei (i ∈ [x, y]) to have the same phase. Accordingly
Im(Zxi/Zyi) = 0, (4.32)
which is equally to Re(Zxi/Zyi) = 0 [Bahr, 1985]. Furthermore, the author introduces the
phase information of the impedance tensor elements to distinguish between local telluric
distortion and regional induction. For that reason, he introduces the complex variables
S 1 = Zxx + Zyy : sum of diag. elements (trace) (4.33)
S 2 = Zxy + Zyx : sum of off-diag. elements (4.34)
D1 = Zxx − Zyy : difference of diag. elements (4.35)
D2 = Zxy − Zyx : difference of off-diag. elements (anti-trace) (4.36)
with S 1 and D2 are invariant under rotation of the coordinate system around its vertical
axis. From these variables, the commutators [Bahr, 1988] are calculated:
[Ψ1, Υ2] = Im(Ψ1 · Υ ∗
2 ) (4.37)
with Ψ and Υ ∈ [S, D], and ∗ denoting complex conjugate. The commutators are used
to define the parameters
allowing to rewrite Equation 4.32 as
A = [S 1, D1] + [S 2, D2],
B = [S 1, S 2] − [D1, D2],
C = [D1, S 2] − [S 1, D2],
− A sin(2α) + B cos(2α) + C = 0 (4.38)
where α is the angle that rotates the distorted impedance tensor into direction of the regional
strike.
As a measure of subsurface dimensionality the parameters given in table 4.2 were introduced
by Bahr [1988], and the strike direction can be calculated by finding the angle
Θ that forces one the phases φei to be 0 and the other one to be π
(Im[Zxi(Θ)])
φei (Θ) = arctan
2 + (Im[Zyi(Θ)]) 2
(Re[Zxi(Θ)]) 2 + (Re[Zyi(Θ)]) 2
with i representing the direction of the telluric vectors ex and ey.
70
1/2
(4.39)