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\centerline{\Large{\bf {Fractures and induced  anisotropy in poroelastic media.}}}
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\centerline{\Large{\bf { From the Mesoscale to the Macroscale}}}
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\centerline{{\bf \Large{ Juan E. Santos}}}
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\centerline {\bf Instituto del Gas y del Petr\'oleo, 
Facultad de Ingenier\'\i  a}
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\centerline {\bf Universidad de Buenos Aires, CONICET and} 
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\centerline{\bf Department of Mathematics, Purdue University and }
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\centerline {\bf Universidad Nacional de La Plata (UNLP)}
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\centerline{\bf {work in collaboration with J.M. Carcione (OGS), P. M. Gauzellino (UNLP) }}
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\centerline{{\bf and R. Mart\'\i  nez Corredor (UNLP)}}
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\centerline{{\bf ABSTRACT}}
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\noindent
Fractures  in a fluid-saturated poroelastic  -- Biot - medium 
can be modeled either as
a extremely thin,  highly permeable and  compliant 
porous layer or employing  suitable boundary conditions.
A Biot medium with  a  set of aligned fractures behaves as an effective 
transversely isotropic 
and viscoelastic (TIV) medium
 when  fracture distances 
are much smaller than the predominant  wavelength of the traveling waves. 
P-waves traveling in this type of Biot medium 
induce fluid-pressure gradients at fractures and mesoscopic-scale heterogeneities, 
generating fluid flow and slow (diffusion) Biot waves, 
causing attenuation and dispersion of the fast modes (mesoscopic loss).
A poroelastic medium with aligned fractures exhibits 
significant attenuation and dispersion effects due to this mechanism, 
which can properly be represented at the macroscale with 
an equivalent TIV  medium.
In the context of Numerical Rock Physics,  we apply a set of compressibility 
and shear harmonic finite-element (FE) experiments on representative samples of 
fractured highly heterogeneous Biot media   to determine the five 
complex and frequency dependent stiffnesses characterizing 
the equivalent TIV medium at the macroscale. 
The FE experiments consider 
brine or patchy brine-CO$_2$ saturated samples and 
a brine saturated sample with an heterogeneous (fractal) skeleton  with  fractures. 
We show that fractures induces strong seismic velocity and Q anisotropy, both for 
qP and  qSV waves, enhanced  either by patchy saturation
or frame heterogeneity. 
Finally we illustrate  the propagation of waves at the macroscale 
for the case of  horizontal and vertical aligned fractures  
employing the  equivalent media determined at the mesoscale.    


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