Geoscience Reference
In-Depth Information
This solution corresponds to a wave propagating with very weak damping at
large distances with phase velocity
c
2
k
0
h X,
ω
Re
k
(0)
≈
V
ph
=
(8.57)
and linear polarization
b
x
b
y
αY
sin
I
=
Y
sin
I
X
.
=
(8.58)
= 0 no waves with purely transverse
magnetic polarization exist, i.e. in the general case the magnetic component
in the direction of propagation is finite.
Comparison of amplitudes of TEM-mode and the integral part in the
ground magnetic field in components
T
AS
and
T
AA
shows that the ground
magnetic field in the electric mode is determined basically by the TEM-mode.
The validity of this assertion follows both from consideration of diverse lim-
iting cases and from the results of numerical computation.
One can see from (8.58) that at
Y
Fields in a Far Zone
Obtain asymptotic expressions for fields on the ground at distances much
more than the value of the skin depth
d
g
in the ground (
x
d
g
). It enables
us to neglect the integral term
G
g
(see (8.53)) in (8.43), since (8.48) gives
exp (
−
x/d
g
)
x
|
G
g
|∝
.
In order to calculate
∆
T
m
,
one can use approximate (7.120), because (7.
119
)
is true on the integration contour
Γ
2
m
. Indeed, on
Γ
2
m
we get Re
k
=
k
0
√
ε
m
,
therefore, the applicability condition for (7.120) can be written in the form
sin
2
I
ε
m
Xh
k
0
|
ε
a
|
,
which holds for periods
10
4
s
T
day,
night.
10
3
s
T
2
×
In order to obtain
∆
T
m
,
we choose the branches of the root at the sides of
the branch cut according to the rule
⎧
⎨
+
k
A
−
k
2
left-hand cut
k
A
−
κ
S
=
,
(8.59)
⎩
k
2
−
right-hand cut
where assuming that Re
k
A
−
k
2
>
0.
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