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z
z
¢
y
′
ʱ
y
x
,
x
′
--
z
0
Fig. 8.4
A model of plane-stratified medium with inclined high-permeable layers. The
horizontal
cylinder
represents a source of excess fluid pressure in pores
considered model of the plane-stratified medium. Despite the constant value ,
the magnetic variations have shown to appear both in the atmosphere and in the
conducting ground. This result follows from the Maxwell equations and the tensor
relationship between the electrokinetic current and the pore pressure gradient.
In the general case, considering the macro-anisotropical media, we can thus
conclude that the scalar parameters C should be replaced by the streaming potential
tensor C which depends on the structure of pore space and the presence of
preferential directions for the underground fluid flow. Moreover the scalar Onsager
relations (
8.10
) transform to the tensor ones in such a way that the scalar coefficients
should be replaced by L
12
D
L
21
DO
C, L
22
DO
, and L
11
D
O
k= where
O
, C,
and
O
k stand for the tensors of the rock conductivity, of streaming potential, and of
rock permeability, respectively.
8.1.4
Electrokinetic Effect in Fractal Media
Taking into account that the dry rock conductivity is much smaller than that
of the groundwater, we consider the model of porous rock which contains the
non-conductive solid matrix and the channels and pores filled by the conducting
underground water. As we have noted above, the isolated pores and cracks cannot
be the conductor for the fluid flow as well as for the electrokinetic current. Only
those cracks and channels which create a connected system or cluster are capable of
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