From jcarcione@ogs.trieste.it Fri May  8 11:48:51 2009
Date: Fri,  8 May 2009 11:11:09 +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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Juan, 

> I undestand, but how we send a plane wave with an incident angle?
> As I said before, in well logging I was putting 2 sources and a
> distance related to the wavelength and firing them with a delay so that I
> could see a wavefront with the energy concentarte in one direction, but it
> is not a "pure" direction.

 
In the time domain, we have used a point source and a set of receivers 
at different angles. We had to be careful with the angle. The difference
between the phase and energy angles is explained in the draft I sent you. 
The attached paper may be useful but when there is attenuation the eqs. 
are more general. 


> 
> I assume what you are saying is what I said above, take a layered media
> and "tilt" the layers for example at  45 degrees angle, then impose a
> normal stress at the top. Is not true that this gives us a 45 incidence
> angle?
> 
> may be  we need to take a  representative sample to be rectangular and
> larger in the  x-direction than in the z-direction to have  many layers
> with  relatively the same length.
> 

Yes, a flat sample. 


> 
> The code I have is 2D and has only 1st order absorbing BC.
> I have been asking for the last 2 years to Patricia to implement the PML
> in our code. She says that she knows how but she did not implemented the
> PML yet.
>

I have implemented the PML and it is that not impressive. The last version, 
C-PML (see Komatitsch and Martin) is a particular version of my memory 
variable approach for describing attenuation we introduced in the 80's. 
I guess that the implementation in the w-domain is trivial, since you 
avoid the additional differential equations and it is just a multiplication 
by a complex kernel anytime you have an spatial derivative


> 
> OK, let us continue the discussion on what to do first and how.
> 
> 
> The 1srt thing that worries me  is that we do not know if performing
> oscillatory tests on a layered viscoelastic media will work or not.
> 
> To check that,  Stefano may write a 1D code similar to the oscillatory
> code   we have now but having viscoelastic  layers  instead of
> poroelastic.
> 
> Then we apply the stress at the top bry and fix the material at the botom
> and see if we get what is known from theory, I assume that the paper  of
> 92 in Geophys. Prospec. can give the Q's for normal incidence to check the
> 1D code.
> 
> Jose: let me know what you think about this. If you agree that this is
> step one in order to discard  or not oscillatory tests, I may write a
> latex file with the differential 1D model and the boundary conditions and
> the finite element procedure, that is very easy in this case.
> 
> Remenber that we need to take a sample with enough layers but small enough
> so that is the domain is homogeneous there is negligible dispersion.
> 
> 

Consider the draft I sent you. We may test p33 or p55 (normal to the 
stratification). They are eqs. 4_2 and 4_3. Both are geometric averages
of the single properties. Q is given by eq. (14). At normal incidence 
the phase and energy angle is the same so there is no problem with the 
angle. This is a first test. 

-- Jose' 




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