stanford-imaging team mailing list archive

[Michael Cardiff <michaelcardiff@xxxxxxxxxxxxxx>]

Hi Hatef -

on 1) I will work on getting you the FFT code shortly. I just want to
make sure that it is decently commented and still gives the expected
results. As usual, please bug me if you do not hear from me soon.

With regards to 2) - I would recommend using more of the data (or at
least, less than 1m spacing, if possible). The reason is that, even
though the closely-spaced positioning of the sources and receivers
will result in many tests that sample the same near-borehole grid
cells, there will be differences in the travel time through individual
grid blocks due to the slightly different positions, which adds extra
information to the inversion. I have not played around with this too
much (it is really more of a "gut" sense), but I suspect that 1m would
be too coarse.

For previous models, I will have to look back at them but I believe I
was using 20cm grid resolution. It was definitely close to that. Since
the C well ring encloses ~20m, and the aquifer is ~20m thick that
would mean the model had roughly (20m/20cm)^3 cells, or 1e6 cells. I
think it may have been slightly less than this, but it was in that
neighborhood of 5e5 - 1e6 cells.

In regards to 3) - that sounds like a promising strategy. However, do
you think you will be able to capture the range of possibilities for a
20m x 20m x 20m aquifer with only 1000 or so realizations? I guess we
will just have to see what the misfit looks like for the "best" models
using the realization-based strategies. Of course, if you have
significant prior info in the form of, e.g., the porosity logs, this
may help out a lot.

And yes, please keep in touch as well! I will be interested to hear
more about your methods soon!

Best,
Mike

On Mon, Feb 21, 2011 at 5:31 PM, Hatef Monajemi <monajemi@xxxxxxxxxxxx> wrote:
> 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
> ________________________________
> 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
> 1910 University Drive, MS-1536
> Boise State University
> Boise, ID 83725-1536
> phone: 208-426-4678
> fax:     208-426-3888
> email: michaelcardiff@xxxxxxxxxxxxxx
> http://earth.boisestate.edu/michaelcardiff
>



-- 
Michael Cardiff, Ph.D.
Assistant Research Professor
Center for Geophysical Investigation of the Shallow Subsurface (CGISS)
Department of Geosciences
1910 University Drive, MS-1536
Boise State University
Boise, ID 83725-1536
phone: 208-426-4678
fax:     208-426-3888
email: michaelcardiff@xxxxxxxxxxxxxx
http://earth.boisestate.edu/michaelcardiff