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+
W
zy
2
2
W
=
|
W
zx
|
Fig. 4.9
Decomposit
ion of the 3D tip
per invariant
into the 2D tipper
W
zx
W
zx
invariants
W
=
W
zy
and
W
=
W
zy
2
2
2
2
+
+
reflecting partial effects of
the crustal prism CP and mantle prism MP
4.6 Magnetic Perturbation Ellipses
The Schmucker perturbation vectors
p
and
q
are defined by (4.69) and (4.70) as
transforms of the unit normal magnetic fields
1
x
and
1
y
polarized at the base site
in the
x
- and
y
-directions. Now we will show that vectors
p
and
q
can be incorpo-
rated into ellipses, which give better image of geoelectric structures perturbing the
magnetic field.
Let us begin with real vectors Re
p
and Re
q
. Turn to (4.66) and introduce the
following notations:
H
x
(
r
)
H
y
(
r
)
=
U
,
=
V
,
H
x
H
y
(
r
B
)
=
X
,
(
r
B
)
=
Y
,
(4
.
104)
|
|
a
=
Re
S
xx
(
r
r
B
)
,
b
=
Re
S
xy
(
r
r
B
)
,
=
|
,
=
|
,
c
Re
S
yx
(
r
r
B
)
d
Re
S
yy
(
r
r
B
)
