Geoscience Reference
In-Depth Information
where
b
(
i,r
)
=
b
(
i,r
)
,
A
b
(
i,r
)
S
,
2) block matrix
U
(
i,r
)
and
K
(
i,r
)
are:
and the (2
×
τ
=
E
(
i,r
)
,
K
(
i,r
)
=
k
(
i,r
)
.
E
(
i,r
)
S
0
A
A
U
(
i,r
)
τ
b
(
i,r
)
A
b
(
i,r
)
S
k
(
i,r
)
S
0
With(7.75)
E
τ
b
τ
=
U
(
i
τ
exp
i
K
(
i
)
x
3
+
U
(
r
)
exp
i
K
(
r
)
x
3
R
(
k
)
b
(
i
)
.
(7.76)
τ
The problem of finding the electromagnetic fields is thus reduced to de-
termining the reflection coecients matrix
R
(
k
). To find
R
substitute (7.76)
into boundary condition (7.50). After a simple algebra, we get
D
−
r
D
i
,
R
=
−
(7.77)
where the 2
2 matrices
D
i
and
D
r
are
D
α
=
b
(
α
)
×
Y
I
E
(
α
S
,
Y
I
E
(
α
A
,
b
(
α
)
−
−
α
=
i
or
r.
(7.78)
A
S
Equation (7.74) allows the horizontal components of
E
and
b
to be
found for a known incident wave. The component
b
3
=
b
/
sin
I
above the
ionosphere can be found directly from Maxwell's equations. The substitution
of
b
1
=
g
1
n
b
n
=
b
1
/
sin
2
I
−
b
3
cot
I
in
b
3
=
g
3
k
b
k
=
b
1
cot
I
+
b
3
/
sin
2
I
gives
−
b
3
=
b
3
+
b
1
cot
I
On substituting
b
3
=(
k
1
E
2
−
k
2
E
1
)
/k
0
in the last equation we have
b
3
=
k
1
E
2
−
k
2
E
1
+
b
1
cot
I.
(7.79)
k
0
Finally, the longitudinal magnetic component is
sin
I
k
1
E
2
−
+
b
1
cot
I
.
k
2
E
1
b
=
−
b
3
sin
I
=
−
(7.80)
k
0
TMatrix
Fields under the ionosphere are found from (7.47):
E
τ
(0) =
E
τ
(
−
0) =
E
τ
(+0)
,
b
τ
(
−
0) =
b
τ
(+0)
−
GE
τ
(+0)
.
Search WWH ::
Custom Search