Electromagnetic Effects Resulted from Natural Disasters - Ultra and Extremely Low Frequency Electromagnetic Fields - page 380

electromagnetic noise. This rough estimate does not depend on the damping
constant Ǜ since it holds as the ground-recording station is located not far from
the cracked zone.
For the numerical estimation of the magnetic effect caused by rock fracture we
take typical parameters of regional seismicity LJ D 2 10 3 m 2b =s and b D 1:11
(Turcotte 1997 ) and the following constants k D 0:01, l max D 1 km, D 10 2 S=m,
B 0 D 5 10 5 T, C t =C l D 0:5 and D =4. Suppose also that the magnetometer
is situated at the distance r 1 km from the cracked zone. Substituting these
parameters into Eq. ( 10.28 ) gives the rough assessment of the mean level of the ULF
electromagnetic noise jh ı B t ij 0:3 pT. It should be noted that we have considered
the case of equal probability for the crack orientation. A certain order of the
crack orientation may enhance our estimate of the mean noise level. Likewise, due
to the fluctuations the noise magnitude is rather large as compared to the mean
value jh ı B t ij .
The ULF magnetic noise occasionally observed prior to the strong crust EQs
(e.g., see Fraser-Smith et al. 1990 ; Kopytenko et al. 1990 ; Hayakawa et al. 1996 ,
2000 ) lies in the frequency range of 0.01-1 Hz. The average level jh ı B t ij related
to the square root of these characteristic frequencies gives the value of about
0.3-3 pT/Hz 1=2 that can serve as a rough estimate of the power spectral intensity.
This assessment is consistent in magnitude with the observation considering the
uncertainties in the parameters. Moreover, it is worth mentioning that the seismic
activity before and after the EQ occurrence may be greatly enhanced that leads to
an increase in the actual value of regional seismicity parameter, LJ, and eventually to
an increase in the ULF electromagnetic noise level.
In this study we have dealt only with the tension cracks since the consideration of
the shear cracks requires very complicated expressions. Actually all types of cracks
including the tension and shear cracks are formed during rock fracture and probably
the majority will tend to be shear ones (Scholz 1990 ). As alluded earlier in Sect. 7.3 ,
the shear crack can radiate the acoustic waves in such a way that the effective
magnetic moment induced in the conductive medium is non-parallel to the vector
B 0 depending on the crack orientation. If there is an equal probability for the shear
crack orientation, then the mean magnetic moment of the crack ensemble is equal to
zero. At the same time one may expect that the shear cracks will predominantly grow
along the axis of maximal shear stresses or, more precisely, along the directions that
make the angle 0:5 arctan k f with this axis (Scholz 1990 ). Here k f denotes the
coefficient of internal friction of the rock. Likewise, most of the shear cracks will
possibly tend to be parallel to the fault plane. Taken together, this means that the
mean magnetic moment of the shear crack ensemble can be nonzero. On account
of the fact that the displacement discontinuity Πu along the shear crack surface is
proportional to the crack surface, we come to an estimate similar to that given by
Eq. ( 10.28 ).
In summary, we describe two aspects of the problem.
(1) It follows from our calculations that the large cracks make a main contribution
to the ULF electromagnetic noise. The small cracks appear to have no effect