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.
