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In-Depth Information
1
+
P
q
H
1
+
P
q
H
2
2
2Im
P
qt
H
2Im
P
qt
H
b
qt
H
a
qt
H
=
+
−
−
qt
H
qt
H
=
1
1
=
tan
,
P
q
H
P
q
H
2
2
2Im
P
qt
H
2Im
P
qt
H
+
+
+
+
−
(4
.
28)
where
1
2
arcsin(sin 2
qt
H
qt
H
sin
qt
H
)
=
.
(4
.
29)
It is notable that
Re
W
zx
Im
W
zy
−
Re
W
zy
Im
W
zx
P
1
Im
P
qt
H
=−
=−
2
,
(4
.
30)
2
|
W
zx
|
|
W
zx
|
where
P
1
is the rotational invariant defined by (4.9). In the two-dimensional
and axisymmetric three-dimensional models,
P
1
0 and hence Im
P
qt
H
=
=
0
qt
H
=0.
Now introduce the tipper phase
and
V
. We can derive
V
directly from the quasi-
transverse field
H
qt
:
τ
H
qt
z
V
=
arg
(
H
q
x
)
2
(
H
q
y
)
2
,
(4
.
31)
+
where
H
qt
W
zx
H
qt
W
zy
H
qt
=
+
.
In view of (4.9) and (4.22)
z
x
y
W
zy
H
qt
W
zy
W
zx
y
H
qt
W
zx
+
W
zx
+
W
zy
H
qt
2
2
=
W
=
W
z
x
(
H
q
x
)
2
(
H
q
y
)
2
=
1
=
W
,
H
qt
2
W
zy
W
zx
2
W
2
|
W
|
+
y
H
qt
1
+
+
x
whence
arg
W
zx
+
V
=
arg
W
=
W
zy
.
.
(4
.
32)
as argument of the rotational invariant
W
.
It indicates the relations between the phase of excess electric currents generating the
vertical magnetic field and the phase of the horizontal magnetic field. If
Here the phase
V
is defined modulo
V
is close
to0or
/2
the reactive currents prevail. This information could be helpful in geoelectric zoning
and structural classification.
Note that with lowering frequency the Vozoff tipper
V
attenuates slower than
the Wiese-Parkinson tipper Re
W
. It seems that it provides the larger investigation
depth.
, the in-phase (or anti-phase) active currents prevail. If
V
is close to
±
