Electromagnetic Effects Resulted from Natural Disasters - Ultra and Extremely Low Frequency Electromagnetic Fields - page 372

JV
4r 3 ;ıB

0 JV
4r 2 ;

E (10.3)

where V denotes the volume of EQ focus. Substituting Eq. ( 10.2 )forJ D J e into
Eq. ( 10.3 ), we obtain

ıB
0 r ;ıB

0 † c RV
2r 2 Rt

E : (10.4)

Taking the numerical values of the parameters t D 10 3 s, R D 1 mm, R=R D
0:01; † c D 10 3 C=m 2 , V D 10 3 km 3 , D 10 3 S/m, and distance r D 50 km we
come to the following estimates: E 30 nV/m and ıB 2 pT.
The charges are actually randomly distributed on the crack sides forming the
so-called fluctuating alternating-sign mosaic. Thus the mean value of the surface
charge density at the crack sides can be much smaller than the maximal value of
† c which is typical for separate points of fresh crack sides. In this picture the used
value † c D 10 3 C=m 2 appears as being overestimated.
However the main difficulty of this theory is incoherence of electromagnetic
microfields produced by individual dipoles/charged cracks because the space
orientation of dipole vectors is random rather than ordered. This means that the
amplitude of the total field is proportional to the square root of the crack number but
not to the crack number N. Taking the notice of a very large value of N, the above
estimate of the microfracturing effect can decrease by many orders of magnitude.
In the other model (Vallianatos and Tzanis 1998 ; Tzanis and Vallianatos 2002 ),
the main emphasis is on the motion of charged edge dislocations associated with
the microfacturing process in the EQ focus. The majority of the edge dislocation is
assumed to slip parallel to the applied shear stresses thereby producing a maximal
value of the current. Since there may be several types of the charged dislocations
with opposite charges, we suppose the excess of certain type of dislocation.
Consider, for simplicity, only one type of such dislocations, the current density due
to edge dislocation motion reads

J d D q d N d V d ; (10.5)

where q d is the charge per unit dislocation length, and N d is the number of
dislocation per unit area. The mean dislocation velocity V d is related to the strain
rate P " through

P " D bN d V d ; (10.6)

where b stands for the absolute value of Burgers vector. Combining Eqs. ( 10.5 ) and
( 10.6 ) leads to

J d D q d P "=b: (10.7)