Information Technology Reference
In-Depth Information
Functions
Q
1
,
Q
2
,
Q
3
,
Q
4
are defined by
∞
1
2
Q
l
(
r
)
=
q
l
(
m
)
J
1
(
mr
)
dm
,
l
=
1
,
2
,
3
,
4
,
(7
.
103)
π
0
where
J
1
is the first order Bessel function, and
1
−
1
Z
TE
m Z
TE
Z
TE
q
1
(
m
)
=
−
i
o
S
1
,
q
2
(
m
)
=
S
1
Z
TE
)
,
m Z
TE
−
o
−
o
(1
+
i
i
m Z
TE
1
q
3
(
m
)
=
S
1
Z
TE
)
,
q
4
(
m
)
=
S
1
Z
TM
.
m Z
TE
−
i
o
(1
+
1
+
104)
The spectral TE- and TM-impedances
Z
TE
and
Z
TM
of the two-layered horizontally
homogeneous medium underlying the inhomogeneous
S
1
−
(7
.
plane are computed as
m
2
i
o
2
Z
TE
Z
TM
=−
tanh
2
h
2
,
=
2
2
tanh
2
h
2
,
2
=
−
i
o
/
2
.
(7
105)
They relate to the TE- and TM-modes which reflect the induction and galvanic
effects respectively.
As is seen from (7.102), (7.103) and (7.104), the Green tensor [
G
E
] governing
the anomaly of the electric field involves both impedances, “inductive”
Z
TE
and
“galvanic”
Z
TM
, while the Green tensor [
G
H
] governing the anomaly of the mag-
netic field involves only the “inductive” impedance
Z
TE
. This defines essentially
different character of electric and magnetic anomalies. With lowering frequency the
inductive impedance
Z
TE
tends to zero:
.
Z
TE
→
→
0
,
(7
.
106)
0
Z
TM
takes on a static value:
whereas the galvanic impedance
Z
TM
→
→
m
2
tanh
mh
2
.
(7
.
107)
0
Substituting (7.106), (7.107) into (7.102), (7.103) and (7.104), we have
⎧
⎨
⎫
⎬
∞
E
r
P
r
1
1
r
2
+
d
dr
J
1
(
mr
)
→
0
→
dm
2
π
S
1
⎩
1
+
mS
1
2
tanh
mh
2
⎭
0
⎧
⎨
⎩
−
⎫
⎬
∞
E
A
P
→
1
1
r
2
+
1
r
J
1
(
mr
)
(7
.
108)
→
mS
1
2
tanh
mh
2
dm
⎭
2
π
S
1
1
+
0
0
H
r
→
H
A
H
z
0
→
0
,
→
0
→
0
,
→
0
→
0
.
