Geoscience Reference
In-Depth Information
the Br¯unt-Vaisala period is 300 s
.
The frequencies of the acoustic branch
are more than
ω
a
=(
γg/
4
H
)
1
/
2
corresponding to periods of less than 300 s.
The maximal signal amplitude is to be on the front of the pulse formed by
high-frequency components. However, atmospheric thermal conductivity and
viscosity cause the initial pulse to broaden. The damping factor
α
of sound is
defined as [22]
4
3
η
+
ζ
+
κ
(
γ
,
ω
2
2
ρ
0
c
s
−
1)
α
=
c
p
where
η
and
ζ
are coecients of the dynamic and the second viscosity, re-
spectively,
κ
is the thermal conductivity coecient. Hence, one can find the
pulse duration:
R
4
3
η
+
ζ
+
κ
(
γ
.
dr
2
ρ
0
c
s
−
1)
τ
p
=
(15.25)
c
p
0
If the viscosity is taken into account, then the expressions for the spectral
harmonics of velocity and pressure should be multiplied by
ω
2
τ
p
.
Then, for instance, the vertical velocity of the neutral gas in the wave can be
presented as follows ([9], [11])
exp
−
R
t
exp
z
.
c
s
+
2
c
s
τ
p
R/c
s
)
2
4
τ
p
H
3
z
8
π
3
/
2
γc
s
τ
p
R
2
(
t
−
w
=
−
2
H
−
(15.26)
R
For distances larger than the length of the pulse
R
c
s
τ
p
, we get from (15.26)
that, at
t
=
R/c
s
+2
1
/
2
τ
p
, the velocity reaches the maximal value
γ
√
32
π
3
e
exp
z
z
R
2
H
3
τ
p
c
s
.
1
w
m
=
(15.27)
2
H
From (15.25) the duration of the initial 1 s-pulse at the heights of 120
,
150
and 200 km is 1
,
1
.
5
,
3 and 6 s respectively. Below 100 km, 1 s-pulse is virtually
constant. Relation (15.27) allows us to estimate the value of the maximal
velocity in the sound pulse. For blast energy of 100 t TNT and
z
= 120 km
the maximal velocity
w
m
≈
10
2
cm/s. Then the maximal magnetic field
induced produced by such local source is of
4
×
0
.
1nT.
Internal gravity waves (IGW) are other possible transmission channels of
the explosion effects over long distances. Behind the front, the acoustic mode
is damped much more sharply than the IGW-mode which can excite low-
frequency geomagnetic disturbances through dynamo action. The numerical
computations show that 10 min after the explosion, the IGW-front reaches a
height of
∼
170 km. About 1 h after the explosion, the wave field fills the space
with a radius of about 1000 km.
≈
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