Semivariogram application to a matrix

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AndrewPBentle
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My name is Andrew Bentley, a Geology student of Temple University. I am currently working on a thesis that uses a geostatistical technique that uses semivariograms on ground-penetrating radar (GPR) data.

I would have posted this in the Earth Science section but all my issues are in the Mathematical and Statistical side of things. I am having an issue (more like a lack of knowledge) on how to apply a formula to a matrix of information.

My matrix contains columns of trace data (the number of 'soundings' of GPR data as it moves across the ground) and rows of amplitude with depth corresponding to particular soundings. My hope is to use semivariograms of my GPR data to differentiate dune types via their internal architecture. To do this I will look at the plotted semivariogram data and use the size of the "range" to determine a threshold.

So my question is, how do I run a formula through a matrix of data? I am using MatLab for all my calculations. If anyone has readings I can find online on such a subject, that would be very useful as well.

I very much appreciate your help.

Andrew Bentley
 
Attachments
  • Two GPR radar cross-section profiles, each 50 m wide and 4.5 m deep, labelled Barchan (top) and Parabolic (bottom), with annotated features including truncation, water table, downlap, point-source diffractions and hummocky reflections.
    Screen Shot 2012-03-15 at 12.20.13 PM.jpg
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  • White mathematical formula on black background: γ(h) = (1/2N) Σ from i=1 to N of [z(xᵢ + h) − z(xᵢ)]², the semivariogram estimator.
    Screen Shot 2012-03-15 at 10.59.59 AM.png
    7.3 KB · Views: 418
  • Two side-by-side GPR radar sections with blue diagonal reflector lines and horizontal dotted reference lines, each marked with a black arrow labelled h pointing down and to the right.
    Screen Shot 2012-03-17 at 2.35.52 PM.jpg
    33.9 KB · Views: 461
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AndrewPBentle said:
To do this I will look at the plotted semivariogram data and use the size of the "range" to determine a threshold.

I don't understand what "size of the range" means. Can you give an example? - perhaps show a 3 by 3 matrix and explain what the size of the range is iin that case.

Are we facing a image recognition problem? Do you essentially have pictures (described by a matrices of data) and you want to classify each of them as being a particular type of dune?

Or are you processing each matirx of data to obtain a smaller set of numbers and trying to use those numbers to classify the dunes?
 
Size of the range refers to an attribute of the blotted semivariogram data. I have just actually figured out my issue. I wrote s script that allows the semivariogram to work on a line by line basis of the matrix at hand.

I will be looking into image recognition next.

Thank you.