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The mayor axes of their polarization ellipses are oriented in the directions that
can be regarded as quasi-longitudinal and quasi-transverse directions of the three-
dimensional structure. The orthogonal quasi-longitudinal and quasi-transverse mag-
netic fields
H
ql
and
H
qt
are
tipper eigenfields
.
To determine the quasi-transverse direction, we find the clockwise angle
τ
τ
qt
H
between the
x
-axis and the major axis of the polarization ellipse of the quasi-
transverse field
H
qt
. By virtue of (2.18)
τ
2Re
P
qt
H
qt
H
q
H
cos
qt
H
=
=
,
.
tan 2
tan 2
(4
25)
P
q
H
2
1
−
P
q
H
,
qt
H
qt
H
arg
P
q
H
. Equation (4.25) defines
qt
H
=
=
where tan
modulo
.
qt
H
qt
H
qt
H
The angle
is taken within quadrant I (0
≤
≤
/
2)orIII(
≤
≤
3
/
2)
qt
H
qt
H
qt
H
if cos
≥
0 and within quadrant II (
/
2
>
≥
)orIV(3
/
2
>
≥
q
H
<
0. For the definiteness sake, we introduce the complementary
2
) if cos
condition
arctg
Re
W
zy
Re
W
zx
<
2
,
qt
H
−
(4
.
26)
qt
H
which brings
closer to direction of the real Wiese-Parkinson tipper Re
W
.
q
H
, we obtain the
Vozoff tipper
W
By plotting
in the direction
V
=
V
x
1
x
+
V
y
1
y
,
(4
.
27)
where
qt
H
qt
H
V
x
=
V
y
=
W
cos
W
sin
.
The magnitude and direction of the Vozoff tipper fill two of four degrees of
freedom for the complex-valued components
W
zx
and
W
zy
of the matrix [
W
].The
tipper magnitude
characterizes the intensity of a magnetovariational anomaly,
while the tipper direction
W
q
H
helps in locating and identifying conductive and non-
conductive structures. Over a wide range of sufficiently low frequencies the Vozoff
tippers, similar to the real Wiese-Parkinson tippers, are directed away from the
zones of higher conductivity and towards the zones of lower conductivity.
Two more parameters are the
tipper ellipticity,
qt
H
, and the
tipper phase,
V
. With
these parameters we fill all the four degrees of freedom of the Wiese-Parkinson
matrix.
The ellipticity
qt
H
is estimated as a ratio between semi-axes of the polarization
ellipse of the quasi-transverse magnetic field
H
qt
. According to (2.19)
τ
