Primary lineations: Groove casts, Liscomb Island, Nova Scotia


Crenulation lineation: Windermere Supergroup, Crowsnest Pass area


Intersection lineation, Halifax, NS


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.


Unconformity surface between subvertical Horton Group (Mississippian) and gently dipping Fundy Group (Triassic) - Walton NS


Fault, North Sea coast


Fold axial surfaces, cleavage planes. Ordovician Davidsville Group, Nfld










Vector dot product

Vector cross product

a.b = abcosθ

is a number equal to abcosθ where a and b are the magnitudes of a and b and θ is the angle between the vectors.

Dot product can be used to find the angle between two lines or planes

a x b = c

is a third vector mutually perpendicular to the first two, with magnitude absinθ where a and b are the magnitudes of a and b

Cross product can be used to find the line perpendicular to two other lines or the line of intersection of two planes




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