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where
S
xx
=
M
xx
−
1
S
xy
=
M
xy
S
yx
=
M
yx
S
yy
=
M
yy
−
1
S
zx
=
W
zx
M
xx
+
W
zy
M
yx
S
zy
=
W
zx
M
xy
+
W
zy
M
yy
.
Using the horizontal Schmucker tensor [
S
τ
], we can define the anomalous mag-
netic fields
p
and
q
that correspond to the unit normal magnetic fields
1
x
and
1
y
linearly polarized in the
x
- and
y
-directions. According to (4.66),
p
=
S
xx
1
x
+
S
yx
1
y
,
q
=
S
xy
1
x
+
S
yy
1
y
(4
.
69)
and
Re
p
=
Re
S
xx
1
x
+
Re
S
yx
1
y
Re
q
=
Re
S
xy
1
x
+
Re
S
yy
1
y
(4
.
70)
Im
p
=
Im
S
xx
1
x
+
Im
S
yx
1
y
Im
q
=
Im
S
xy
1
x
+
Im
S
yy
1
y
.
The vectors Re
p
Im
q
are given the name real and imaginary
per-
turbation vectors
(
perturbation arrows
). They indicate intensity, phase and direction
of the anomalous magnetic fields depending on polarization of the normal magnetic
field. When rotated counterclockwise by
,
Im
p
and Re
q
,
2, they give an idea of the excess cur-
rents, which concentrate in zones of higher conductivity and flow around zones of
lower conductivity.
Using the matrix [
S
z
], we can construct the real and imaginary
Schmucker tippers
(
Schmucker induction arrows
):
/
=
Re
S
zx
1
x
+
Re
S
zy
1
y
,
=
Im
S
zx
1
x
+
Im
S
zy
1
y
.
.
Re
S
Im
S
(4
71)
A distinguishing feature of the Schmucker tippers is that they eliminate considera-
tion of the horizontal components of the anomalous magnetic field and expose the
pure effect of its vertical component.
Figure 4.8 shows, as an example, a map of the real Schmucker tippers Re
S
for
the Pacific coast of USA (Schmucker, 1970). All the arrows point away from the
ocean and their magnitude decreases toward the continent. We observe here a typical
coastal effect caused by the influence of oceanic currents flowing along the coast.
4.5 Magnetovariational Response Functions
in the Superimposition Model
Let us consider the Wiese-Parkinson relation in the superimposition model contain-
ing local near-surface inhomogeneities against deep regional background.
Following Zhang et al. (1987, 1993), we assume that the vertical component of
the anomalous magnetic field,
H
z
,
observed in the superimposition model can be
written as the sum
