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0
C
jr
P
j
V
4r
2
ıB
:
(10.41)
This estimate differs from that given Eq. (
10.39
) by replacement of C and V by
C and V , respectively. Taking the volume of the EQ focal zone V
D
10
3
km
3
,
distance r
D
50 km, C
C and values of other parameters we obtain ıB
max
4
pT; that is, several orders of magnitude greater than the previous value obtained in
the framework of the model by Fenoglio et al. (
1994
,
1995
). Certainly this result
directly follows from the large value of the focus volume V .
Notice that the numerical estimates of the ULF signal cover a wide range of
amplitudes because of the lack of information on the rock structure at higher depths,
i.e. rock permeability, underground water content, crack distribution over size and
orientation, and so on.
In Chap.
8
we have demonstrated that the electrokinetic effect in a fractal porous
medium results in power law dependence of electric field variations on the source
size L. According to Eqs. (
8.19
) and (
8.22
) this dependence can vary depending
on the structure of fractal pore space, transport critical exponents and correlation
length critical exponent . Now we consider the model of an earthquake hypocenter
zone in which the electrokinetic current is considered as a by-product of the fluid
filtration in the fractal pore network above percolation threshold (Surkov et al.
2002a
; Surkov and Tanaka
2005
). The typical size of EQ focal zone L can be related
with the EQ magnitude M by the known empirical rule (Kanamori and Anderson
1975
):
log L
D
0:5M
1:9
(10.42)
where L is measured in kilometers. Combining Eqs. (
8.19
) and (
10.42
) yields
log E
D
aM
C
b
(10.43)
where a
D
1
=.2/
0:09. Combining Eqs. (
8.22
) and (
10.42
), we come
to the same dependence where a
D
0:5
f
1
.
/=.1
C
/
g
0:31.Herewe
have used the following critical exponents :
D
1:6 and
D
0:88 derived from
numerical simulations on 3D grids (Staüffer
1979
; Feder
1988
). By contrast, in the
case of non-fractal focal zone we obtain that a
D
1. Although the value a
D
0:31
is very close to the observational one (a
0:34-0:37) reported by Varotsos et al.
(
1996
), we cannot relate the electrokinetic phenomena and pre-seismic activity with
confidence primarily due to a paucity of actual observations and the complexity of
the ULF electric field variations in the near-surface atmospheric layer.
The physical mechanisms treated above, i.e. the geomagnetic field perturbation
and the electrokinetic effect, seem to be the most promising and creditable to
explain, in principle, the co-seismic electromagnetic phenomena and pre-seismic
ULF electromagnetic noise. Both mechanisms have to be stimulated by pre-seismic
activity, which is accompanied by an enhancement of underground fluid migration,
by rock fracture and an increase of the crack number in the vicinity of fault zone.
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