[CIG-SEISMO] time reversed computation in specfem2d

[Carl Tape]

Hi Jorg,

I think these questions pertain more to the process of how the adjoint 
procedure works for seismic wave propagation, rather than the details of 
the codes.  The two papers that Dimitri mentioned step through the 
procedure: Tromp et al. (2005) and Tape et al. (2007).  In short, though, 
the procedure does not involve chanding the sign of deltat.  (This IS done 
in practice to recreate the forward wavefield in the 3D code, so that you 
do not have to store the wavefield at every time step -- see Liu and Tromp 
(2006).)  It involves using the forward solver with one 
source-time-function for the real source and a different 
source-time-function ("adjoint source") placed at the station.  For a 
forward simulation alone, we typically use a delta function as the 
source-time-function.  The delta function has unresolved frequencies, so 
then you need to filter these out in post-processing.  For the adjoint 
simulations, though, we do use "smooth" source-time-functions as you 
mentioned.

I hope these papers are informative enough in conveying the procedure. 
Maybe after you check those out we could discuss the implementation 
details.  If you have questions, let me know.

I did the work shown within the two GJI papers starting in 2003 using a 
version of a SEM 2D code, prior to an SVN version of SPECFEM2D.  Life 
would have been easier if I switched to "the" SPECFEM2D and started using 
SVN right away, since there are many features of the inverse problem (not 
the forward problem) that are used within my work that are not yet 
implemented into SPECFEM2D.  Hopefully I can help Christina bring at 
least the essential parts into the code for the adjoint simulations. 
It is not at all a matter of "cut and paste" though -- we just need to 
find a few weeks of time to do this.

Carl Tape
Caltech (now Harvard)

On Thu, 30 Apr 2009, pge05bqw at studserv.uni-leipzig.de wrote:

> Hello,
> thanks for your answers. My aim is to simulate time reversed seismic
> wave propagation in random media. There should be absorbing and non
> absorbing bounderies. This is in preparation for my physics diploma
> thesis. I'm sorry if I ask silly questions because I'm quite new to
> (computational) geophysics.
> How does the source function matter for the adjoint simulation, if I
> run a forward simulation first? (The temporal extent of the source
> function should of course be small compared to the running time)I
> thought it would be enough to change the sign of the "deltat" in the
> second loop only. (which seems to work for the only time loop in 1D)
> The routines of the 3D adjoint code appear to be much more complicated
> than that.
> But if someone of you has allready implemented it, it would be nice if
> you could make it available.
> Best regards,
> Jörg
>
> Zitat von Chris Morency <cmorency at Princeton.EDU>:
>
>> Hi,
>>
>> Can you give me some more specificities about your experiment ? You
>> said you are running a time reversed experiment. How do you define
>> your source function ?
>> Do you have absorbing boundaries ? Is a homogeneous/heterogeneous model ?
>>
>> For your information, we are upgrading specfem2D. The new package
>> will have acoustic/elastic/poroelastic capabilities, adjoint method
>> and Frechet derivatives calculation will also be included.
>>
>> Christina
>>
>
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