P. Schmoldt, PhD - MTNet - DIAS

3.2. Deriving magnetotelluric parameters
and the resistivity ρ can be calculated from the norm of the EM field ratio, i.e.
2
Ex0
⇔
= ıω
By0
e
µσxy
−ıφxy
2
=
ω
µ ρxy
(3.27)
⇔ ρxy = µ
2
Ex0
ω
. (3.28)
By0
Equivalently, the resistivity can be expressed using the magnetising field H instead of
the magnetic field B, related via the magnetic permeability as described in Equation 3.8,
yielding
ρxy = 1
2
Ex0
µω
. (3.29)
The resistivity for the orthogonal case ρyx can be solved in the same manner, using the
terms of Equation 3.23 that have an êx component, resulting in
and
ρyx = µ
ω
ρyx = 1
µω
Hy0
Ey0
Bx0
Ey0
Hx0
2
(3.30)
2
. (3.31)
Phase relationships between orthogonal horizontal electric and magnetic fields can be
derived from Equation 3.26, i.e.
⎛
Im
φxy = arctan ⎜⎝
Ex/Hy
Re ⎞
⎟⎠
, (3.32)
Ex/Hy
and, for the orthogonal case,
⎛
Im
φyx = arctan ⎜⎝
Ey/Hx
Re ⎞
⎟⎠
. (3.33)
Ey/Hx
3.2.1. Common notation for magnetotelluric relations
It is common practise to describe the relationship between all horizontal electric and magnetic
fields relevant for MT by using the electric impedance Z, which can be written in
compact form as
Ex
=
Ey
Zxx Zxy
Zyx Zyy
Hx
Hy
. (3.34)
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