The the vector components (l,m,n) of a line with plunge (P) and trend (T) are given by:

  • l = sin T cos P

  • m = cos T cos P

  • n  = -sin P

The three components are called direction cosines because each is the cosine of the angle between the line and an axis.

Planes as vectors: plane normals

To do the same kinds of things with planes, we use the normal or pole to the plane.

Point plot vs Contour plot

Contour plot: 1% circle method

Contour plot: Starkey method

Contour plot: Gaussian method, single point

Gaussian plot

Vector sum

Resultant R = |R|

Vector mean

Mean resultant r = R/n

Critical Values for the Rayleigh test of uniformity

Cone of Confidence on the mean direction

38 fold hinges from Stellarton NS

Direction cosine matrix

The direction cosine matrix yields 3 eigenvectors. (Analogous to strain axes for a non-rotational deformation matrix.)

Associated with each is an eigenvalue

E1 = 0.46         E2 = 7.11       E3 = 29.42

The relative sizes of the eigenvalues indicate the strength of clustering about each eigenvector

The modified Flynn plot indicates the relative magnitudes of the 3 eigenvectors

www.ipc.shizuoka.ac.jp

http://www-texdev.mpce.mq.edu.au/GeoMath/

Diagrams showing fabrics developed by deformation of random populations of passive markers. Ramsay, J. G., and Huber, M. I., 1983, The Techniques of Modern Structural Geology. Volume 12: Folds and Fractures. Academic Press. Reproduced under license from Cancopy; further reproduction prohibited