Electrokinetic Effect in Water-Saturated Rock - Ultra and Extremely Low Frequency Electromagnetic Fields - page 323

of the size L (Scholz 1990 ). In the same approximation P is not a function of L
whence it follows that j j ek j / L =1 . Far away from the electrokinetic current
source/inhomogeneity the electric field E is proportional to the current moment
d j j ek j V , where V L 3 is the source volume. This means that

E / L 2= ;

(8.19)

where 2 = 0:18; that is, the electric field weekly depends on the inhomogene-
ity size. By contrast, for the non-fractal inhomogeneity E / L 2 .
In the model proposed by Surkov et al. ( 2002 ) the rock permeability and porosity
were assumed to decrease from the center of the inhomogeneous region towards
the periphery so that the porosity becomes close to the percolation threshold n c at
the external boundary of the inhomogeneity. The inner region of the inhomogeneity
consists of broken rocks with so high permeability and porosity that the correlation
length tends to zero in this region. This high permeable rock is surrounded by the
layer with fractal structure, where the porosity decreases down to the percolation
threshold n c . If the thickness H of this fractal layer is much smaller than the typical
size L of the inhomogeneity, then the porosity in this layer can be approximated as
follows:

n n c Cr n H: (8.20)

The porosity gradient can be estimated as n=L, where n denotes the porosity
change inside the inhomogeneity. Substituting Eq. ( 8.20 )forn into Eq. ( 8.17 ) and
taking into account that the thickness H of the fractal layer is of the order of the
correlation length we obtain that H / L =.C1/ .
The peripheral fractal region can make the major contribution to the total
current moment under the requirement that the inner region has approximately
a spherically symmetrical distribution of the electrokinetic currents because the
vector j ek averaged over the inner region becomes close to zero. In such a case, the
contribution of the fractal zone to the current moment can be estimated as follows:
d j j ek j L 2 H, where the electrokinetic current density is given by
j j ek j 0 C 0
H

= P
L :

(8.21)

Since the electric field varies directly as the current moment, we come to

E / L 1./=.1C/ : (8.22)

This theory can be applied to the earthquake preparation process in order to esti-
mate amplitude electric field variations possibly associated with the electrokinetic
phenomena in the seismo-active region.