Semivariogram application to a matrix

In summary, Andrew Bentley is a Geology student at Temple University and is working on a thesis that uses a geostatistical technique. He has a question about how to apply a formula to a matrix of data, and is looking into image recognition.
  • #1
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
 

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  • #2
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?
 
  • #3
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.
 

1. What is a semivariogram and how is it used in matrix analysis?

A semivariogram is a statistical tool used to analyze the spatial variability of a variable in a matrix. It measures the degree of similarity between data points based on their distance and direction from each other. In matrix analysis, the semivariogram is used to study the spatial autocorrelation of a variable and identify any spatial patterns or trends.

2. How do you calculate a semivariogram for a matrix?

To calculate a semivariogram for a matrix, you first need to define a lag distance, which is the distance between data points that will be compared. Then, the difference between data points at each lag distance is calculated and squared. The average of these squared differences is then plotted against the lag distance, creating a semivariogram curve.

3. What is the significance of the sill and range in a semivariogram?

The sill and range are important parameters in a semivariogram as they provide information about the spatial structure of the variable being analyzed. The sill represents the maximum variability in the data, while the range indicates the distance at which the data points become uncorrelated. These values are useful in understanding the spatial pattern and variability of the variable in the matrix.

4. Can semivariogram analysis be used for any type of matrix data?

Yes, semivariogram analysis can be applied to any type of matrix data as long as it meets the assumptions of stationarity and isotropy. Stationarity means that the statistical properties of the data do not change over space, and isotropy means that the spatial structure is the same in all directions. If these assumptions are met, semivariogram analysis can be used to analyze the spatial variability of the data.

5. How can semivariogram analysis be useful in practical applications?

Semivariogram analysis can provide valuable insights in various practical applications, such as agriculture, environmental monitoring, and urban planning. It can help identify areas with similar characteristics, detect spatial trends or anomalies, and guide decision-making processes. For example, in agriculture, semivariogram analysis can be used to optimize crop yield by identifying areas with similar soil properties for planting.

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