Electrokinetic Effect in Water-Saturated Rock - Ultra and Extremely Low Frequency Electromagnetic Fields - page 325

As it follows from Eq. ( 8.25 ), the pore fluid pressure is directly proportional to the
volume deformation of the rock. The implication here is that the moving solid matrix
completely drags the pore fluid.
In the seismic frequency range the displacement current is negligible as com-
pared to the conduction one so that the electric potential in the homogeneous ground
is described by Eq. ( 8.13 ) whence it follows that E D C r P . Supposing that the
rock parameters are constant and taking into account Eq. ( 8.25 ), we obtain

E D CK f LJ r =Ǜ: (8.26)

For example, consider the surface quasi-harmonic Rayleigh wave propagating
along the horizontal axis x. Taking the mass velocity components V x and V z given
by Eqs. ( 7.59 ) and ( 7.60 ) one can derive the volume deformation D @ x V x C @ z V z .
Substituting this value into Eq. ( 8.26 ) gives the electric field in the ground . z 0/

LJV 0 K f !C
Ǜs 1 C l

E D .i O x C s 1 O z / exp f k R s 1 z C i .k R x !t/ g ; (8.27)

where s 1 D 1 C R =C l 1=2 , k R D !=C R is the wave number of Rayleigh wave,
and V 0 stands for the amplitude of the vertical velocity component V z .
So, the electric field oscillates in-phase with the mass velocity. The same is true
for the longitudinal wave. However, the transverse seismic wave cannot excite the
seismoelectric effect because this wave does not produce the volume deformations;
that is D 0.
To estimate the electric field amplitude, we choose the following numerical
values of the parameters: K s D 2:5 GPa, K D 0:5K s ;K f D 0:1K s , C R D 1 km/s,
C l D 3 km/s, n D 0:1, C D 10 8 10 6 V/Pa and V 0 ! D 1 mm. Substituting

these values into ( 8.27 ) we obtain the estimate E x 0.01-1 V=m which is close
to the co-seismic signal amplitude 1-10 V=m.
Now we will use the simpler way to drive one more estimate of the maximal
amplitude of seismoelectric signals. The pore pressure gradient can be roughly
estimated as follows: jr P j ıP=, where ıP is the excess of pore pressure
over the hydrostatic level and is the seismic wavelength. In order to obtain
the maximum effect we assume that the pressure variation ıP in the fluid is the
same order-of-magnitude as that in solid matrix, so that ıP=K s V 0 =C l , where
K s s C l is the solid compressibility and s is the solid matrix density. It follows
from this that ıP s C l V 0 . Hence we obtain that E max CıP= s CV 0 !.
Substituting s 2 10 3 kg/m 3 and the above values of the parameters we come
to the same estimate E max 0.02-2 V=m.
In contrast to the electric field amplitude due to the GMPs, the last estimate
essentially depends on the porosity and underground water content. At the moment
we cannot state which mechanism (that is, the GMP or seismoelectric effect) makes
the main contribution to the co-seismic electric signals observed during seismic
wave propagation. As for the magnetic component of the co-seismic signals, it
seems likely that the GMP dominates the seismoelectric effect.