Geoscience Reference
In-Depth Information
solid phase (in Pa). The passage of the wave generates a
confining pressure fluctuation,
P
, on a representative ele-
mentary volume of the rock, more precisely on the elastic
skeleton. This change in confining pressure generates in
turn a change in the pore fluid pressure and therefore the
flow of the pore water according to Darcy
describe the effects of coseismic field and seismoelectric
conversion. We start with the coseismic field associated
with the traveling of a compressional pressure (P-)wave
in a homogeneous material. Figures 1.21, 1.22, and 1.23
show three snapshots showing the propagation of such a
wave between a seismic source and a geophone collo-
cated with an electrode (the reference for the electrical
potential at the electrode is taken to infinity). We see
an electrical signal at the position of the electrode only
when the seismic wave arrives at this location. Therefore,
the coseismic electrical field is only localized in the spatial
support of the seismic wave.
Figure 1.24 shows a snapshot of the electrical potential
distributionwhen a seismic wave hits an interface between
twomedia of differentmechanical and electrical properties.
In this example, the two layers are only characterized by a
difference inelectrical conductivity. Theseismoelectriccon-
version at the interface is similar to the one that would be
generated by a dipole distribution located along the inter-
face in the first Fresnel zone of then seismic wave. The con-
cept of Fresnel zone will be discussed further in Chapter 4.
s law. More-
over, the flow of pore water relative to the solid phase
generates a source current density given by
'
Q
V
k
0
η
f
∇
J
S
=
Q
0
V
w
=
−
p
1 117
where
w
denotes the Darcy velocity discussed in Section
1.2. In getting Equation (1.117), we have neglected the
inertial terms, and therefore, this equation considers only
low-frequency disturbances (below 1 kHz).
1.4.3 Numerical example of the coseismic
and seismoelectric conversions
We use now the acoustic approximation, implemented in
the finite-element package COMSOL Multiphysics, to
Normalised pressure (
t
= 88.5 ms)
Normalised electric potential (
t
= 88.5 ms)
200
200
5
5
100
100
0
0
0
0
−100
−100
−5
−5
−200
−100
0
100
200
−200
Electrode
−200
Geophone
offset(m )
Electrode
−200
−100
0
100
200
−200
−100
0
100
200
Offset (m)
Recorded potential at electrode
Recorded pressure at geophone
4
4
2
2
0
0
−2
−2
−4
−4
0
100
200
300
0
100
200
300
Time (ms)
Time (ms)
Figure 1.21
Synthetic example computed with the acoustic approximation to demonstrate the effect of the coseismic electrical
field. A seismic source generates a pressure wave in a homogeneous material. We see here the normalized pressure (left panel)
and the normalized electrical potential (right panel) at time 88.5 ms. The star represents the seismic source. (
See insert for
color representation of the figure
.)
