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ske
w B =
0, we can rotate the reference frame counterclockwise through the strike
angle
determined by (1.58) and rearrange the tensor [ Z ] to the anti-diagonal tensor
(1.54) with the longitudinal and transverse components on the secondary diagonal.
What is more, following (1.16), we can rearrange the anti-diagonal tensor [ Z ]tothe
diagonal tensor [ Z ] with the longitudinal and transverse components on the principal
diagonal.
Generally such a simple solution to the magnetotelluric eigenstate problem is
unworkable. When it comes to the complex-valued impedance tensor [ Z ] character-
istic of three-dimensional media, the conditions ske
0 are violated
and there is no real rotation angle that enables us to reduce the impedance tensor to
the anti-diagonal (or diagonal) form. Clearly, in magnetotellurics we have to look
for more general approaches that would be applicable in the case of asymmetric
media. Swift (1967) was likely the first to suggest some basic ideas in this field.
Statement of the impedance eigenstate problem needs some extensions asso-
ciated with the elliptic polarization of the magnetotelluric field. For the sake of
integrity, it would be useful to give a brief review of the polarization definitions
(Yee and Paulson, 1987).
w S =
0, ske
w B =
2.2 Polarization of the Magnetotelluric Field
Following Yee and Paulson (1987), we consider the complex electric and magnetic
fields
E x
E y
H x
H y
e i
x
e i
x
| E x |
| H x |
E τ =
=
,
H τ =
=
.
(2
.
8)
e i
y
e i
y
| E y |
| H y |
Their polarization ratios are :
E x = | E y |
E y
E
y
E
x )
e i (
E e i
E
P E =
=
tan
,
| E x |
(2
.
9)
H x = | H y |
H y
e i (
y
x )
H
H e i
=
=
tan
,
P H
| H x |
where
|= | E y |
E
E
tan
=| P E
| E x | ,
[0
,π/
2]
,
=| P H |= | H y |
H
H
tan
| H x | ,
[0
,π/
2]
,
and
E
E
y
E
x
=
=
arg P E ,
 
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