Geoscience Reference
In-Depth Information
σ
∗
ω
simulation, based on the poroelastic and electric coupling
Equation (3.177) for a homogeneous and isotropic
medium that is saturated by two immiscible fluid phases,
was coded in MATLAB and COMSOL. The elasticity,
hydraulic, and electrical parameters required to solve
the problems are reported in Table 3.1. The size of the
model is 400 × 400 m
2
with a PML of 50 m surrounding
the studied domain. The fluid mixtures of air and water
are investigated, with two values of the water saturation
S
2
=02 and
S
2
=09, in which the horizontal component
of the electrical field associated with the seismic wave
propagation is perfectly proportional to the horizontal
acceleration
=
σ
3 175
0
i
ω
k
0
k
r
ρ
2
II
p
1
ω
≈
β
3 176
η
2
Therefore, the electrical field can be written as
E=
Q
V
2
σ
0
S
2
K
r
u
3 177
K
r
=
k
0
k
r
ρ
2
η
2
3 178
Equation (3.177) connects the electrical field recorded
between two electrodes and the seismic signal in terms of
the acceleration of the seismic wave. We conclude that
this proportionality depends both on the saturation state
and the hydraulic and electrical conductivities of the
medium, which are in turn related to the water content.
The ratio of the acceleration,
ü
x
, in accordance with the transfer function
in Figure 3.3 (see Figure 3.4). The advantage of this ratio
between seismic and electric fields is its usefulness to help
solve for important hydraulic and electrical parameters.
Because the origin of the seismoelectric response is due
to the existence of water in the porous medium, we also
studied the behavior of the coseismic amplitudes with
water saturation for the fluid mixtures of air and water.
We numerically simulated different values of water sat-
uration on the coseismic signal. The amplitude variations
of the electrical potential as recorded at the surface of the
earth and its maximums versus water saturation were
reported in Figure 3.5. The results obtained show an
increase in the amplitude of the coseismic electrical
ü
x
, and the electrical field is
plotted in Figure 3.3 using Equation (3.177). This result
reveals that an increase in the amplitude of the coseismic
electrical disturbance is due to an increase of the water
content. Strasher (2006) expressed this transfer equation
for the normalized seismoelectric field as a power law of
the effective saturation
E
C
0
S
0 42 ± 0 25
α
where
C
0
denotes the steady-state streaming potential coupling
in the saturated conditions. To check this proportionality
between the seismic and electric fields, a numerical
ρ
2
u
e
10
-2
10
-4
10
-6
10
-8
10
-10
Figure 3.3
The transfer function linking
the ratio of the seismoelectric field to the
acceleration of the grains versus water
saturation. This plot shows that as water
saturation increases, the coupling between
the acceleration of the grains and the
seismoelectric field also increases.
10
-12
10
-14
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
Water saturation
