This book presents the theory of waves propagation in a fluid-saturated
porous medium (a Biot medium) and its application in Applied Geophysics.
In particular, a derivation of absorbing boundary conditions in
viscoelastic and poroelastic media is presented, which later is employed
in the applications.
The partial differential equations describing the propagation of waves
in Biot media are solved using the Finite Element Method (FEM).
Waves propagating in a Biot medium suffer attenuation and dispersion
effects. In particular the fast compressional and shear waves are
converted to slow diffusion-type waves at mesoscopic-scale
heterogeneities (on the order of centimeters), effect usually occurring
in the seismic range of frequencies.
In some cases, a Biot medium presents a dense set of fractures oriented
in preference directions. When the average distance between fractures is
much smaller than the wavelengths of the travelling fast compressional
and shear waves, the medium behaves as an effective viscoelastic and
anisotropic medium at the macroscale.
The book presents a procedure determine the coefficients of the
effective medium employing a collection of time-harmonic compressibility
and shear experiments, in the context of Numerical Rock Physics. Each
experiment is associated with a boundary value problem, that is solved
using the FEM.
This approach offers an alternative to laboratory observations with the
advantages that they are inexpensive, repeatable and essentially free
from experimental errors.
The different topics are followed by illustrative examples of
application in Geophysical Exploration. In particular, the effects
caused by mesoscopic-scale heterogeneities or the presence of aligned
fractures are taking into account in the seismic wave propagation models
at the macroscale.
The numerical simulations of wave propagation are presented with
sufficient detail as to be easily implemented assuming the knowledge of
scientific programming techniques.
