Primary lineations: Groove casts, Liscomb Island, Nova Scotia
Crenulation lineation: Windermere Supergroup, Crowsnest Pass area
Intersection lineation, Halifax, NS
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The the vector components (l,m,n) of a line with plunge (P) and trend (T) are given by:
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.
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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
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Vector dot product
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Vector cross product
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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
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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
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Point plot vs Contour plot
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Contour plot: 1% circle method |
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Contour plot: Starkey method
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Contour plot: Gaussian method, single point
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Gaussian plot
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Vector sum
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Resultant R = |R|
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Vector mean
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Mean resultant r = R/n
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Critical Values for the Rayleigh test of uniformity
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Cone of Confidence on the mean direction
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38 fold hinges from Stellarton NS
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Direction cosine matrix
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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
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The modified Flynn plot indicates the relative magnitudes of the 3 eigenvectors
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http://www-texdev.mpce.mq.edu.au/GeoMath/ |
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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