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that these methods could be used for much greater
depths (several kilometers in the case of the electroseismic
method). The seismoelectric method has also been used
for a variety of applications in near-surface geophysics
(for instance, Migunov & Kokorev, 1977; Fourie, 2003;
Kulessa et al., 2006). Mikhailov et al. (2000) described
crosshole seismoelectric measurements in a small-scale
laboratory experiment with vertical and inclined fractures
located between the source and the receivers. They
recorded not only the coseismic electric signals generated
by the seismic wave arriving at the receivers but also the
EM wave associated with the Stoneley wave excited in
the fracture. They claimed that a tomography image with
the travel times extracted from the seismoelectric mea-
surements could be possibly constructed.
Several modeling attempts have been developed to
comprehend both the seismoelectric and electroseismic
effects. Neev and Yeatts (1989) developed a theory of
these effects, but as discussed by Pride (1994), this theory
was incomplete. The model developed in the seminal
paper of Pride (1994) couples fully the Biot
-
Frenkel the-
ory to the Maxwell equations via a source current density
of electrokinetic origin. This model was obtained by
volume averaging the local Navier
-
Stokes and Nernst
-
Planck equations as well as the Maxwell equations. It
has opened the door to numerical modeling of both the
coseismic and seismoelectric conversions using finite-
difference or finite-element methods and was used to
assess the usefulness of these methods for various appli-
cations (e.g., White, 2005; White & Zhou, 2006). The
model introduced by Pride has been the fundamental tool
used to model the electroseismic and seismoelectric
responses of porous rocks in the last two decades (see
Haartsen & Toksoz, 1996; Haartsen & Pride, 1997;
Garambois & Dietrich, 2001, 2002, for some examples).
This approach is however open to some criticisms as
discussed later in this topic in Chapter 2. Pride
Various authors have used the finite-difference tech-
nique to simulate the 2D seismoelectric response of a
heterogeneous medium, taking into account all the
poroelastic wave modes (fast and slow P-waves and shear
(S-)wave) and their coseismic electrical signals plus the
seismoelectric conversions (note that the isochoric shear
wave does not produce any coseismic electrical field
in perfectly homogeneous porous media). Pain et al.
(2005) presented a 2D mixed finite-element algorithm
to solve the poroelastic Biot equations including the
electrokinetic coupling in order to study the sensitivity
of the seismoelectric method to material properties, like
porosity and permeability of geological
formations
surrounding a borehole.
Several works have focused on producing some full
waveform modeling of the seismoelectric signals using
Pride
s theory (see, for instance, Grobbe et al., 2012;
Grobbe & Slob, 2013). The code developed by Niels
Grobbe, electroseismic and seismoelectric modeling
(ESSEMOD), is able to model all existing seismoelectric
source
'
s theory)
in layered media, considering fully coupled Maxwell
equations. This code can be also used to model seismo-
electric laboratory configurations of a sample in a water
tank (i.e., fluid/porous medium/fluid transitions; see
Smeulders et al., 2014). This code can also be used to gen-
erate all required fields for the theoretical interferometric
seismoelectric Green
-
receiver combinations
(using Pride
'
s function retrieval. This allows,
for instance, to improve the signal-to-noise ratio of the
weak seismoelectric conversions (or interface response
fields). By applying interferometric techniques (e.g.,
Schoemaker et al., 2012), stacking inherently takes place
with possible signal-to-noise ratio improvements as well.
Along a similar idea, Sava and Revil (2012) introduced
recently a simplified poroacoustic formulation to describe
the seismoelectric coupling in porous media, and they
introduce a new method called seismoelectric beam-
forming. The idea is to focus seismic waves on a grid of
specific points and to use the seismoelectric conversion
to image heterogeneities in mechanical and electrical
properties (see Chapter 6). The poroacoustic approxima-
tion allows handling the computation of the seismoelec-
tric signals in very complex geometries very quickly,
and the beamforming approach is used to enhance the
seismoelectric conversion over the coseismic signals.
Most of the current efforts in seismoelectric theory are
also directed to understand the seismoelectric conver-
sions in unsaturated or in porous media saturated by
'
s model
is unable to describe correctly the surface conductivity,
the frequency dependence of the conductivity of the
material, and the quadrature conductivity of porous
rocks. It is not based on the electrical double layer theory
(only the diffuse layer is accounted for), and therefore,
some fundamental elements are missing in this theory.
That said, Pride has been the first to provide the complete
set of macroscopic equations, and his model can easily
be corrected to account for the missing components
(induced polarization and frequency dependence of the
electrical conductivity).
'
