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Fig. 6.8
Thedikemodel
bounded by the infinite vertical interfaces,
y
resistivity
=−
v,
0
≤
z
≤∞
and
y
=
v,
(Fig. 6.8).
Let us begin with solution for the TM-mode. By analogy with (6.1), we write
0
≤
z
≤∞
⎧
⎨
H
x
(
z
)
H
x
(
y
+
,
z
)
|
y
| ≥
v,
z
≥
0
H
x
(
y
,
z
)
=
(6
.
13)
⎩
H
x
(
z
)
H
x
(
y
|
|
≤
v,
+
,
z
)
y
z
≥
0
,
where
H
N
H
A
x
H
N
H
A
x
x
,
and
x
,
are the normal and anomalous magnetic fields outside
and inside the dike.
Solving equations (6.3) and taking into account the symmetry conditions, we get
⎧
⎨
∞
H
A
x
a
m
e
−
|
y
|
sin
mz dm
=
|
y
| ≥
v
0
H
x
=
(6
.
14)
⎩
0
∞
H
x
a
m
cosh
y
sin
mz dm
|
|
≤
v,
=
y
where
m
2
m
2
=
=
−
(
k
)
2
,
−
(
k
)
2
,
>
.
Re
0
The constants
a
m
and
a
m
are defined from the boundary conditions at the vertical
interfaces
y
=±
v
. Similarly to (6.5),
|
y
|=
v
H
N
x
H
N
x
H
A
x
H
A
x
−
=
−
,
(6
.
15)
H
x
=
H
x
y
y
where, according to (6.6) and (6.7),
