stanford-imaging team mailing list archive

[Hatef Monajemi <monajemi@xxxxxxxxxxxx>]

Hi Mike, 

Thanks for your email. Couple of things: 

1) It would be helpful if I can have the FFT-based code for generating unconditional realizations. Currently, I am using a very crude Karhunen Loeve Expansion (KLE) based code for generating unconditional realizations that I had from past. This code is not cable of generating unconditional realization for high resolutions models and I was thinking to move towards FFT-based methods that Arvind was talking about. Now, that you have the code, that will certainly save some time for me. Although, Arvind once told me that he has some ideas for exploiting KLE to generate unconditional realization without using the whole prior covariance matrix. I hope he moves to 3D soon. I have his code for 2D. As long as I understand, Arvind's methodology for reducing costs is affected by the cardinality of the problem. So, He needs to change some stuff to move to 3D I guess. He certainly can comment more on this. 

2) what is the current resolution of the model you are considering? Did you get to 10^6 grid cells? The reason I ask is that the data we currently have is taken with pretty 
fine resolution ( it seems they were moving the receiver down the borehole 25 cm in each trial and the vertical scale is about 17 m deep). So, According to this resolution in collecting data, it is not convincing to use low resolution models unless you ignore some data. I was thinking to , initially, take data for each 1 m instead of 25 cm (which means 17 spots for receiver). But I am certainly interested to move to higher resolutions as this is the goal. 

3) In regards to inversion, I doubt we will have problem if we use the methods we are currently developing. We are trying to reduce the size of matrix to be inverted from # of observations to number of realizations which are usually much less that the former (usually O(10^2-10^3) based on the problem size). The porosity logs show pretty smooth functions, therefore, I would not be worried about the inversion. BUT we will have to wait and see. 

4) In response to your comment on sequential inversion of data, I must say, yes. You may deal with each measurement at a time which changes the matrix to be inverted to a scalar and hence no need to worry about inversion. In terms of time, I doubt you would save any. You will, however, save memory this way as you do not deal with the inversion of 200,000 by 200,000 matrix. 

Please keep in touch so as to combine powers! 

Bests, 
Hatef 
----- Original Message -----
From: "Michael Cardiff" <michaelcardiff@xxxxxxxxxxxxxx> 
To: "Hatef Monajemi" <monajemi@xxxxxxxxxxxx> 
Cc: stanford-imaging@xxxxxxxxxxxxxxxxxxx, "Peter K Kitanidis" <peterk@xxxxxxxxxxxx> 
Sent: Sunday, February 20, 2011 4:22:42 PM 
Subject: Re: [Stanford-imaging] Realizations in 3D Large Scale Computations (Arvind) 

Hi Hatef - 

I have a 3D code, based on the FFT-based methods, that can generate 
unconditional realizations with 1million + grid-cells. We can discuss 
this if you're interested in using it. Of course, if Arvind has code 
for doing unconditional realizations using his techniques, I'd be 
curious about those as well! 



For the data, I believe in the early inversions I was trying I was 
using about half the data. Based on discussions with Baptiste, some of 
the datasets are more noisy than others, so I just picked some of the 
slices that he had indicated were more reliable. 

Another strategy, of course, would be to just randomly select a subset 
of the data. 200,000 measurements is a bit much for doing 
geostatistical approaches, since the inverted matrices (HQHt+R HX; HX 
0) are non-sparse and even a (# measurements x # measurements) matrix 
will be quite cumbersome to store. Around 100,000 could be manageable 
on a machine with a lot of RAM. 

The size of this dataset is actually what got me thinking about 
sequential data inclusion methods... perhaps using the techniques you 
are planning, you could successively incorporate more and more 
measurements? 

Feel free to let me know what you're thinking and we can brainstorm further... 

-Mike 

On Sat, Feb 19, 2011 at 6:12 PM, Hatef Monajemi <monajemi@xxxxxxxxxxxx> wrote: 
> Hello , 
> 
> I wonder if Arvind has already developed the code for generating 
> unconditional realizations in 3D at least for structured grid. 3D 
> calculation seems to be more in need of methods that save storage. 
> 
> Also, Mike, can you give us an estimate of the size of problem you are 
> considering for 3D inversion of GPR data in BHRS. There is around 200,000 
> measurements of travel time and I wonder if you are using all or a subset of 
> that. 
> 
> Please reply all so that people can keep track of what research is going on 
> in the team. 
> 
> Thanks, 
> Hatef 
> 
> -------------- 
> Hatef Monajemi 
> PhD Student 
> Environmental Fluid Mechanics and Hydrology 
> Department of Civil and Environmental Engineering 
> Stanford University 
> 473 Via Ortega, Y2E2 Bldg, Room M25 
> Stanford, CA 94305 
> Email: monajemi@xxxxxxxxxxxx 
> Web: http://www.stanford.edu/~monajemi/ 
> 
> 
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-- 
Michael Cardiff, Ph.D. 
Assistant Research Professor 
Center for Geophysical Investigation of the Shallow Subsurface (CGISS) 
Department of Geosciences 
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