Geoscience Reference
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r 2 ….r;t t a / and f .r/ under the integral sign can be considered as constant
values. Taking these function at r D R f and performing integrations yields
3.1 C t= s / n2 1 exp
1 exp
4ǛLJP R 0 r
t
r
t
r
d .t/ D
(11.21)
Here we have introduced the auxiliary function
f R f
r C f R f D
0 .1 C t= s / n
r C 0 .1 C t= s / n ;
.t/ D
(11.22)
where s D R 0 =U. We notice that the spherically symmetric portion of Eq. ( 11.19 )
which is independent of does not contribute to the dipole moment in Eq. ( 11.21 )
at all. This obvious result follows the fact that the spherically symmetric charge
distribution confined by two concentric spheres does not create the electromagnetic
field in the outer space.
The dipole moment given by Eq. ( 11.21 ) determines the electromagnetic field
of SW far away from the explosion point. The analysis of the near field spectrum
caused by the SW has shown that the spectral intensity is enhanced in the vicinity
of typical frequencies ! r , ! s and ! 1
where D 0 r =. 0 C r /
(Surkov 1986 ). This frequency range lies within an interval from several Hz to one
kHz that is in a reasonable agreement with typical spectra of the EMP observed
during large-scale underground explosions.
In Sect. 3.1.4 we have noted that in the atmosphere the vertical dipole antenna
is a more effective radiator of electromagnetic waves than the horizontal one
(see Fig. 3.5 ). By contrast, it follows from the theory that the horizontal component
of the underground dipole antenna plays more significant role than the vertical
component (Wait 1961 , 1970 ). To clarify this statement we note that the vertical
dipole generates a symmetrical distribution of electric current in the surrounding
conductive space as shown in Fig. 11.6 a. On the ground surface these currents flow
in the radial directions from the point O. The effective electric dipole d of such a
system of surface radial currents is equal to zero, which means that the effective
antenna produced by these surface currents does not radiate. On the other hand in
the case of the horizontal dipole, shown in Fig. 11.6 b, the surface electric currents
flow approximately along the direction of dipole vector d . These current systems
are equivalent to the nonzero electric dipole turned to the same direction.
Thus, as a first approximation, the electromagnetic field generated by the SW of
underground explosion is equivalent to that of horizontal component of the effective
current dipole, which is usually assumed to be located in a homogeneous conducting
half-space. The shape of the signals detected on the ground surface depends on both
the function d.t/ given by Eq. ( 11.21 ) and the conductivity of the half-space. A
theoretical analysis of this problem has shown that the EMP has a bipolar shape
similar to that shown with lines 2 in Fig. 11.3 (Surkov 1986 ). In this model the
first narrow spike is due to the fast variation of the shock-induced dipole moment
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