Electromagnetic Effects Resulted from Natural Disasters - Ultra and Extremely Low Frequency Electromagnetic Fields - page 373

Within a factor of the order of unity this equation coincides with the result obtained
by Tzanis and Vallianatos ( 2002 ).
For the estimate we choose the following values for numerical parameters:
P " D 10 4 s 1 , q d D 10 11 C=m, and b D 0:5 nm (Tzanis and Vallianatos 2002 ).
Substituting Eq. ( 10.7 )forJ D J d into Eq. ( 10.3 ) and taking above values of the
parameters, we obtain the estimates E 0:6V/m and ıB 40 pT. In making this
estimate we have assumed that the dislocation motion occupies the whole volume
V of the EQ focal zone.

10.1.3 Theory of ULF GMPs Due to Acoustic Noise Produced

by Rock Fracture and Crack Formation

In what follows we focus alone on GMPs from the rock fracture and energization
of crack formation in the rock surrounding the fault zone. As we have noted in
Sect. 7.3 , the acoustic emission of the cracks results in the excitation of electric
currents due to the motion of conductive ground in the geomagnetic field. In the
case of tension cracks the effective magnetic moment of the electric currents must be
pointed oppositely to the vector of geomagnetic induction. The magnetic moments
of all the cracks have been shown to be co-directed independently of the crack plane
orientation that gives rise to effective coherent amplification of the ULF GMPs,
whereas the acoustic emission of the cracks is incoherent in nature and thus it cannot
bring the same effect (Surkov 1997 , 1999 , 2000a , b ; Surkov et al. 2003 ). This model
can be extended for the shear cracks (Surkov 2000a , 2001 ; Molchanov et al. 2002 )
but in this case a certain ordering in the crack orientation is required in order to
produce the coherent effect.
We recall that at far distance the electromagnetic precursor of acoustic wave
(see Sect. 7.2.4 ) has the same shape and polarization for all the cracks while the
next stage of the signal which associates with the acoustic wave arrival, consists
of co-seismic oscillations, whose frequency and phase depend on the inclination of
geomagnetic field, the crack size and the crack plane orientation. In an early study
of the crack-generated GMPs, Surkov et al. ( 2003 ) took into account only the initial
part of the signals, that is the coherent part, in order to avoid some mathematical
complexities.
Here we follow the more accurate model (Surkov and Hayakawa 2006 ), which
allows for an accidental character in the moments of the crack growth and formation.
When calculating the net electromagnetic signal produced by all the cracks, we take
into consideration both coherent and incoherent/co-seismic parts of the signals. The
model includes such important details as random crack orientation, distribution of
the crack sizes, and the attenuation of the acoustic waves.
According to Scholz ( 1990 ), the region of a preparing EQ can occupy the area
with size of about several hundred kilometers. Accumulation of tectonic energy
before an EQ results in the generation of a system of cracked zones with sizes