Geoscience Reference
In-Depth Information
For simplicity we ignore this difference and set the magnetic permeability is equal
to unity everywhere. The induction of remanent magnetic field,
B
, within the zone
R
c
<r<R
e
is described by the following Maxwell equation:
r
B
D
0
r
J
:
(11.23)
The detonation point is chosen to be the origin of coordinate system with
z
-axis
parallel to the vector
J
. Spherical coordinates, i.e. the radius r and the polar angle
measured from
z
-axis are used. For the region r>R
e
the solution of Eq. (
11.23
)
isgivenbyEq.(
7.5
) which describes the field of magnetic dipole. Taking Eq. (
9.29
)
for
J
the effective magnetic moment of the magnetized rock can be written as
follows:
Z
R
e
r
02
s
rr
r
0
dr
0
;
M
D
4C
m
J
(11.24)
R
c
where C
m
denotes the piezomagnetic coefficient.
According to this model, far away from the detonation point the residual
magnetic field decreases with distance as B
r
3
. However, this dependence con-
tradicts the data obtained during the experiment referred to as MASSA (Erzhanov
et al.
1985
). The detonation of chemical high explosive (HE) with mass of 251 t was
made on the sandstone surface. Survey of the changes of the geomagnetic field for
this detonation was made at the different points in the distance range from 0.5 to
10 km. It was found that the decrease of the residual magnetic field is closer to the
dependence B
r
1
in character.
This discrepancy between the theory and experiment can be due to the fact that
the observation point was located at the distances within R
c
<r<R
e
where
the remanent rock magnetization should occur (Surkov
1989
). The solution of this
problem is found in Appendix I. Since the elastic strain and stress are predominant
in this region, the magnitude of the normal stress in the seismic wave satisfies the
following law: s
rr
.r/
D
P
c
R
c
=r, where the parameter P
c
is of the order of the
crushing strength or of tensile one. Substituting this expression into Eqs. (
11.90
)
and (
11.91
) and performing integration, we obtain the solution of the problem
.R
c
<r<R
e
/
1
;
R
c
r
2
0
C
m
JP
c
R
c
cos
r
B
r
D
(11.25)
1
C
r
2
:
R
c
0
C
m
JP
c
R
c
sin
2r
B
D
(11.26)
As is seen from Eqs. (
11.25
) and (
11.26
), the magnetic field components decrease
with distance slower than the rate expected from the dipole law. When r
2
R
c
,
they decrease with distance approximately as r
1
. However, this solution provides
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