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Z
int
xx
H
int
Z
int
xy
H
int
E
x
=
+
x
y
Z
int
yx
H
int
Z
int
yy
H
int
E
y
=
+
,
x
y
where
5
J
E2
x
Z
N
J
H2
y
(
J
E2
x
J
H1
y
J
E1
x
J
H2
y
0
.
−
+
−
)
Z
int
xx
=
0
.
25
+
0
.
5(
J
H2
x
+
J
H1
y
)
+
(
J
H2
x
J
H1
y
−
J
H1
x
J
H2
y
)
Z
N
(0
.
5
+
J
H2
x
)
+
0
.
5
J
E1
x
+
(
J
E1
x
J
H2
x
−
J
E2
x
J
H1
x
)
Z
int
xy
=
.
+
.
5(
J
H2
x
+
J
H1
y
+
(
J
H2
x
J
H1
y
−
J
H1
x
J
H2
y
0
25
0
)
)
5
J
E2
y
J
H1
y
(
J
E2
y
J
H1
y
J
E1
y
J
H2
y
0
.
−
Z
N
(0
.
5
+
)
+
−
)
Z
int
yx
=
0
.
25
+
0
.
5(
J
H2
x
+
J
H1
y
)
+
(
J
H2
x
J
H1
y
−
J
H1
x
J
H2
y
)
5
J
E1
y
Z
N
J
H1
x
(
J
E1
y
J
H2
x
J
E2
y
J
H1
x
0
.
+
+
−
)
Z
int
yy
=
)
.
0
.
25
+
0
.
5(
J
H2
x
+
J
H1
y
)
+
(
J
H2
x
J
H1
y
−
J
H1
x
J
H2
y
Thus, we have the complex-valued tensor
Z
int
that transforms the horizontal
internal magnetic field
H
int
τ
into the horizontal electric field
E
τ
:
E
τ
=
Z
int
H
int
τ
.
(11
.
43)
With a knowledge of magnetic tensor [
M
], it is possible to establish relations
between the impedance tensors
Z
int
and [
Z
]. Let us menage to locate the base site
within an undistorbed area where
H
(
x
B
,
=
H
N
=
2
H
ext
τ
.
y
B
)
Then at any observation
site
H
int
τ
(
x
,
y
)
=
H
τ
(
x
,
y
)
−
0
.
5 [
M
(
x
B
,
y
B
|
x
,
y
) ]
H
τ
(
x
,
y
)
.
(11
44)
=
([
I
]
−
0
.
5 [
M
(
x
B
,
y
B
|
x
,
y
) ])
H
τ
(
x
,
y
)
.
So, in view of (11.43)
=
Z
int
(
x
y
)
H
int
τ
E
τ
(
x
,
y
)
,
(
x
,
y
)
=
Z
int
(
x
y
)
([
I
]
|
,
−
0
.
5 [
M
(
x
B
,
y
B
x
,
y
) ])
H
τ
(
x
,
y
)
=
,
,
,
[
Z
(
x
y
)]
H
τ
(
x
y
)
(11
.
45)
whence
=
Z
int
(
x
y
)
([
I
]
[
Z
(
x
,
y
)]
,
−
0
.
5 [
M
(
x
B
,
y
B
|
x
,
y
) ])
(11
.
46)
and
Z
int
(
x
y
)
=
y
) ])
−
1
,
,
−
.
,
y
B
|
x
,
.
.
[
Z
(
x
y
)] ([
I
]
0
5 [
M
(
x
B
(11
47)
