Geoscience Reference
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Fig. 11.11
A coordinate
system and effective point
charges which model the
actual charge distribution
z
- q
2
q
1
l/
2
l/
2
y
q
2
q
r
x
- q
1
electric variations decreases with distance, r, approximately as r
4
,atleastatthe
initial stage of the surface explosion. This is indicative of high symmetry of the
electric charge distribution which results in a quadrupole character of the electric
field in the initial stages of the explosion. In order to interpret the experimental data,
the actual charge distribution was modeled by two effective point charges q
1
and
q
2
and their mirror images in the conducting ground. The origin of coordinate
system is placed at the detonation site while the point charges are located on x;
z
plane as shown in Fig.
11.11
. Far away from the charges the electric field might be
expanded in a series of a small parameter l=r where l denotes the distance between
the charges. The vertical electric field on the ground surface is given by
d
z
.t/
4"
0
r
3
Q
x
z
.t/
4"
0
r
4
C
:::
E
z
.r;;t/
D
(11.32)
Here, d
z
D
2.q
1
h
1
q
2
h
2
/ is the projection of the dipole moment onto the
z
-axis,
and Q
x
z
D
3l .q
1
h
1
C
q
2
h
2
/ cos is the single nonzero component of the tensor of
quadrupole moment of the charge system.
The experimental data suggest that the second term on the right-hand side of
Eq. (
11.32
) is greater than the first one during the initial stage. For the detonation of
HE with mass of 5 kg the numerical value Q
x
z
D
.0:4-1:3/
10
4
C
m
2
brings
the closest fit with experimental data. Taking the notice of empirical dependence,
according to which the electric charge of products of the surface explosion varies
as the 0:65
˙
0:05 power of the explosive mass (Adushkin and Soloviev
1996
),
the effective charges and the characteristic horizontal distance between them were
estimated as q
1
q
2
2C and 2-7 mm, respectively (Soloviev et al.
2002
). It is
plausible that the horizontal separation of positive and negative charges in space will
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