1. Joint seismic attributes visualization using Self-Organizing Maps
Marcílio Castro de Matos
Kurt J. Marfurt

2. Motivation: self organizing example
1- Choosing the attributes
Ex: The ratio between length and width L W L W
Bananas have high ratio
Blueberries have ratio close to one
2- Clustering

3. Summary
SOM review
SOM 1d
SOM 2d  SOM 1d
SOM 2d colormap
SOM3d  RGB

4. Kohonen Self Organizing Maps
Input Data: Cartesian coordinates of 3 gaussians centralized in [0,0,0] in red; [3,3,3] in blue and [9,0,0] in green. The “+” signals represent the vectors prototypes.
Input DATA MATRIX: 03 attributes with length 3000 x y z
... 13
Winner prototype vector
Training neighboohood 7
91 (13x7) prototype vectors

5. SOM map prototype vectors representation.

6. U-matrix
Unified Distance Matrix (U-matrix) gives the distances between the neighboring map units. …
Red color indicates long distances, and blue color indicates short distances.
This U-matrix representation gives an impression of “mountains” (long distances) which divide the map into “fields” (dense parts) or clusters.
Each cluster represents different classes.

7. Clustering of the SOM abstraction
Abstraction level1
Abstraction level 22
N samples
(input data) M
prototype vectors
C classes
>>
>>

8. Kohonen Self Organizing Maps
Attr 2
Attr 1
Class1
Class3
Class2
Pre-image of prototype
vectors from target space
1-D target space
2-D source
space

9. Kohonen Self Organizing Map
K-means clusters
K-means clustering tend to be attracted to the extreme values and are not ordered in a topological sequence.
Kohonen Self Organizing Map
17 classes indicated by black dots; red dotted lines correspond to the ordering of the classes. Note that the classes defined by K-means clustering tend to be attracted to the extreme values and are not ordered in a topological sequence. Conversely, SOM-defined classes are in a sequence, so the process is less sensitive to the number of classes and noise and generates a better-organized seismic facies map. (After Coleou et al., 2003)
SOM-defined classes are in a sequence, so the process is less sensitive to the number of classes
(Coleou et al. 2003)

10. Summary
SOM review
SOM 1d
SOM 2d  SOM 1d
SOM 2d colormap
SOM3d  RGB

11. 1D Self-Organizing Map 12 classes
A color equidistant from each other has been got from the HSV circle and has been assigned to each class. It has not been taken into account the distance between the prototype vectors.
Classes 0°
30°
60°
90°
120°
150°
180°
210°
240°
270°
300°
330°

12. 1D Self-Organizing Map 12 classes
The distance among HSV color are proportional to the distance of the prototype vectors. This creates a smoother way to visually the classification result.
HSV (Varying Hue, at fixed Saturation and Value) colormap
Classes

13. Principal component projection of the data and the prototype vectors
Classes
Taking into account the distance among the prototype vectors
Classes 0°
30°
60°
90°
120°
150°
180°
210°
240°
270°
300°
330°
Don’t taking into account the distance among the prototype vectors

14. 1D Self-Organizing Map 256 classes
Principal component projection of the data and the prototype vectors

15. Summary
SOM review
SOM 1d
SOM 2d  SOM 1d
SOM 2d colormap
SOM3d  RGB

16. SOM 2D  SOM 1D with 16 classes

17. Classes
1D SOM
Classes
2D SOM +
1D SOM

18. SOM 2D  SOM 1D with 256 classes
2D SOM colored prototype vectors and 1D SOM prototype vectors trajectory (white line)
Classes

19. Summary
SOM review
SOM 1d
SOM 2d  SOM 1d
SOM 2d colormap
SOM3d  RGB

20. SOM 3D colormap
RGB cube
The RGB color model mapped to a cube. The horizontal x-axis as red values increasing to the left, y-axis as blue increasing to the lower right and the vertical z-axis as green increasing towards the top. The origin, black, is hidden behind the cube.

21. Acknowledgements
The first two authors would like to thank the support from the University of Oklahoma Attribute-Assisted Seismic Processing and Interpretation Consortium and its sponsors.
Attribute-Assisted Seismic Processing and Interpretation
We also would like to thank PETROBRAS for their cooperation in providing the data, support and the authorization to publish this work.