Joint seismic attributes visualization using Self-Organizing Maps Marcílio Castro de Matos marcilio@ou.edu www.matos.eng.br Kurt J. Marfurt kmarfurt@ou.edu

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

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

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

SOM map prototype vectors representation.

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.

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

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

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)

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

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°

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

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

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

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

SOM 2D  SOM 1D with 16 classes

Classes 1D SOM Classes 2D SOM + 1D SOM

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

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

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.

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 http://geology.ou.edu/aaspi/ We also would like to thank PETROBRAS for their cooperation in providing the data, support and the authorization to publish this work.