From jcarcione@ogs.trieste.it Tue May  5 13:53:12 2009
Date: Tue,  5 May 2009 12:27:02 +0200
From: Jose' M. Carcione <jcarcione@ogs.trieste.it>
To: Juan E Santos <santos@math.purdue.edu>
Cc: Stefano Picotti <spicotti@ogs.trieste.it>,
     Jose' Carcione <carcione@ogs.trieste.it>
Subject: Re: fractures + oscillatory tests

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Hola Juan, 

There is good thesis about modeling a fracture in a Biot medium. 
You may download it from here. 

http://repositories.cdlib.org/lbnl/LBL-29257/

Then, there is the double-porosity theory of Berryman, Pride, and 
co-workers. This is an effective medium theory of the Biot type. 
The simulations can be compared to the moduli obtained by this 
theory. See Pride2004.pdf.

But before doing this, I would like, if possible, to compute 
the complex modulus of a periodic (or not) medium made a isotropic
viscoelastic layers and obtain the quality factor vs angle. This 
is a hot topic and if it is possible to do it with the harmonic 
experiments, then we have something important, since Q anisotropic
processing is started to be included into practice (see Tsvankin 
paper attached ani_att.pdf). 

-- Jose' 

ps. I include a draft to give an idea. We attempted to do it with 
waves but did not succeed (Backus.pdf). 



-- 
Jose' M. Carcione
Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS)
jcarcione@ogs.trieste.it -- jcarcione@libero.it
http://www.lucabaradello.it/carcione/


Quoting Juan E Santos <santos@math.purdue.edu>:

> 
> Stefano:
>          besides implementing the oscilaltories tests  faster in 2D and
> then in 3D, I was thinking on including fractures inside the
> representative   sample. People like Schoenber lately has implemented the
> fractures as boundary conditions including jumps in displacements or
> velocities and cont. of stress, but I beleive that since the fracture is
> at least 2 orders of magnitude greater than the pore size, may be we can
> include the fracture as a fluid medium within the Biot medium  represented
> as an inviscid or a viscous fluid, with appropiate Boundary cond.
> 
> Then may be we can obtain the displacements discontinuity BC  compressing
> the samples as we do now and plot the discontinuity as function of the
> fracture aperture,  change   of the plane wave modulus  as function
> of the presence or not of fractures at a given frequency etc.
> 
> Let me know  what you think about this approach.Ii believe that we can use
> the computer as virtual laboratory and represent real rocks, what you can
> not do with analytical methods, they are OK to check our code later.
> 
>                                               regards, Juan
> 
> 
> 
> 
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> 


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