Information Technology Reference
In-Depth Information
In this notation,
O
i
o
V
y
(0)
1
h
y
(
y
,
M
o
)
=
y
o
)
2
+
(
y
−
(
y
−
y
o
)
4
O
(10
.
41)
2
i
o
V
z
(0)
1
h
z
(
y
,
M
o
)
=
y
o
)
3
+
.
(
y
−
(
y
−
y
o
)
5
Now return to (10.35) and determine the anomalous magnetic field at the great
distances from the inhomogeneity. Let
|
y
−
y
o
|
>>
d
. Then,
o
V
y
(0)
S
(
y
−
y
S
)
2
S
i
j
x
(
M
o
)
(
y
−
y
o
)
2
i
o
V
y
(0)
i
o
V
y
(0)
(
y
−
y
S
)
2
H
o
y
(
y
)
=
dS
=
j
x
(
M
o
)
dS
=
J
x
o
V
z
(0)
S
y
S
)
3
S
2
i
j
x
(
M
o
)
(
y
2
i
o
V
z
(0)
2
i
o
V
z
(0)
H
A
o
z
(
y
)
=
dS
=
j
x
(
M
o
)
dS
=
J
x
,
−
y
o
)
3
(
y
−
(
y
−
y
S
)
3
(10
.
42)
where
J
x
=
j
x
(
M
o
)
dS
S
is the total excess current in the inhomogeneity and
y
S
is the coordinate of the central
point of its cross-section
S
. Thus, with regard for (10.40), we have
H
A
o
z
(
y
)
2
V
z
(0)
V
y
(0)
=−
2
V
z
(0)
dV
z
(
z
)
dz
z
=
0
o
y
(
y
)
=
(10
.
43)
H
A
(
y
−
y
S
)
(
y
−
y
S
)
H
A
H
A
0
y
can be expressed through the normal
impedance of the Earth. Let us introduce the function
It is easy to show that the ratio
0
z
/
V
z
(
z
)
dV
z
(
z
)
dz
Z
(
z
)
=
i
o
.
(10
.
44)
It is seen from (10.40) that
Z
(
z
) satisfies the Riccati equation
dZ
(
z
)
dz
N
(
z
)
Z
2
(
z
)
−
=
i
o
(10
.
45)
with the boundary condition
−
i
o
D
Z
(
D
)
=
.
