Geoscience Reference
In-Depth Information
Electric and magnetic components in the reflected FMS-wave can be writ-
ten as (see Chapter 7)
=
R
SA
b
(
i
y
exp
k
A
z
,
k
2
b
x
=
b
(
r
)
−
−
x
ik
0
k
2
E
y
=
E
(
r
)
=
b
x
.
y
−
k
A
−
√
ε
m
E
(
i
)
. To find the ground magnetic field, we represent the
current by its spatial Fourier decomposition
where
b
(
i
)
=
y
+
∞
1
√
2
π
I
x
=
I
x
(
k
)exp(
ikx
)
dk,
(9.17)
−∞
where
I
x
(
k
) is the Fourier component of
I
x
(
x
). Let the ratio of the spectral
electric and magnetic components on the ground be
z
=
−h
E
y
b
x
=
Z
(
m
)
g
and
z
=
−
0
E
y
b
x
=
Z
(
m
)
a
(9.18)
is the impedance under the ionosphere. With the impedance
Z
(
m
a
, the electric
and magnetic fields on the ground surface can be obtained from those under
the ionosphere, as it was done in Chapter 7. On the ionosphere, the horizontal
electric field is continuous and discontinuity of the horizontal magnetic field
is proportional to the total electric current, i.e.,
=
4
π
c
E
y
=
E
y
,
b
x
−
b
x
I
y
,
(9.19)
where the plus and minus superscripts denote the components above and
below the ionosphere, respectively. Then from (9.19)
ik
0
k
2
b
x
=
4
π
R
SA
b
(
i
)
=
E
y
,
SA
b
(
i
)
−
I
y
,
y
y
c
k
A
−
E
y
=
Z
(
m
)
b
x
.
(9.20)
a
Hence
1
−
1
=
4
π
c
ik
0
k
2
1
Z
(
m
)
R
SA
b
(
i
)
I
y
−
,
(9.21)
y
k
A
−
a
and the final expressions for the total horizontal magnetic and electric com-
ponents below the ionosphere are
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