Geoscience Reference
In-Depth Information
Wave propagation
Electromagnetic disturbances
Acoustic: 1 P-wave
Elastic: 1 P-wave, 1 S-wave
Poroelastic, Newtonian luid: 2 P-waves, 1 S-wave
Poroelastic, Maxwell luid: 2 P-waves, 2 S-wave
+
Maxwell equations
Low frequency: quasi-static regime
Intermediate frequencies: diffusive regime
High frequencies: Propagative regime
Description of the seismic source
Seismoelectric effects
Type I: Co-seismic ields
Type II: Seismoelectromagnetic conversions
Type III: Disturbances associated with the seismic source
Figure 1.18
General concept of seismoelectric disturbances. Seismoelectricity combined the propagation of seismic (compressional
and rotational) waves in porous materials. These porous materials are considered to be composites with phases carrying a net charge
density (the material as a whole is neutral). The mechanical equations are coupled to the Maxwell equations through a source current
density and a source of momentum. Three types of seismoelectric disturbances can be observed: Type I corresponds to the
electromagnetic fields traveling with the seismic wave itself (coseismic fields). Type II corresponds to the electromagnetic disturbances
associated with the passage of a seismic wave through a macroscopic heterogeneity (seismoelectric conversion). Type III corresponds to
the electromagnetic fields associated with a seismic source. S corresponds to shear wave, while P corresponds to compressional
(pressure) wave (the letters P and S are also used in terms of arrival time: primary and secondary waves).
rheology of the material and its dispersive properties. In
this topic, we will consider various rheological behaviors
leading to different types and numbers of waves. For
instance, the acoustic theory applied to porous media
can only be used to describe, in an approximate way,
the propagation of compressional (
P
for pressure) waves
in porous media. A refinement of this theory is to con-
sider the elastic case. The elastic case implies that two
types of seismic waves are generated: pressure (P-)waves
and shear (S-)waves. That said, porous media are com-
posite of mineral and fluids, so a more complicated the-
ory exists to describe more accurately seismic wave
propagation in porous media. This corresponds to the
theory of poroelasticity.
A macroscopic linear poroelastic theory of wave prop-
agation has been first proposed by Biot (1962a, b). Micro-
scopic theories of poroelasticity have been also proposed
by various authors, but they will not be reviewed in this
topic. The poroelastic theory proposed by Biot leads to
two P-waves (a slow P-wave and a fast one) and one
S-wave. Revil and Jardani (2010) generalized the Biot
the biotheory is asymmetric in its equations as the fluid
does not sustain shear stresses. Whatever the theory
used, the propagation of the seismic waves through a
porous material is responsible for a movement of the
water with respect to the solid phase. In the presence
of an electrical double layer, this relative displacement
is the source for an electrical current density. This current
density acts a source term in the Maxwell equations
generating EM disturbances. These EM disturbances
are described by the Maxwell equations, which takes
the general form of the coupled telegraph equations for
the electrical and magnetic fields (these partial differen-
tial equations contain propagative and diffusive terms). If
we consider low-frequency seismic waves, the time-
dependent terms can be dropped from the telegraphist
s
equations, and we end up with Poisson equations for the
electrical and magnetic fields. Three types of EM distur-
bances can be generated: Type I corresponds to the EM
fields traveling with the seismic waves themselves. These
are generally called the coseismic fields and can only be
observed in the volume directly affected by the propaga-
tion of the seismic waves. Type II corresponds to EM
effects associated with the passage of seismic waves
through a macroscopic heterogeneity (seismoelectric
conversion). They can be remotely observed, away from
'
-
Frenkel theory to the case where the fluid can sustain
shear stresses. This theory will be developed in
Chapter 2. It yields to two P-wave and two S-wave prop-
agation models and provides a symmetric theory, while
