- Orientation Tensor
Orientation Tensor / Eigenvectors & Eigenvalues
In
geology , especially in the study ofglacial till , eigenvectors and eigenvalues are used as a method by which a mass of information of a clast fabric's constituents' orientation and dip can be summarized in a 3-D space by six numbers. In the field, a geologist may collect such data for hundreds or thousands ofclasts in a soil sample, which can only be compared graphically such as in a Tri-Plot (Sneed and Folk) diagram [Graham, D., and Midgley, N., 2000. Earth Surface Processes and Landforms (25) pp 1473-1477] , [Sneed ED, Folk RL. 1958. Pebbles in the lower Colorado River, Texas, a study of particle morphogenesis. Journal of Geology 66(2): 114–150] , or as a Stereonet on a Wulff Net [ [http://dx.doi.org/10.1016/S0098-3004(97)00122-2 GIS-stereoplot: an interactive stereonet plotting module for ArcView 3.0 geographic information system] ] . The output for the orientation tensor is in the three orthogonal (perpendicular) axes of space.Eigenvectors output from programs such as Stereo32 [ [http://www.ruhr-uni-bochum.de/hardrock/downloads.htm Stereo32] ] are in the order E1 > E2 > E3, with E1 being the primary orientation of clast orientation/dip, E2 being the secondary and E3 being the tertiary, in terms of strength. The clast orientation is defined as the Eigenvector, on a compass rose of 360°. Dip is measured as the Eigenvalue, the modulus of the tensor: this is valued from 0° (no dip) to 90° (vertical). Various values of E1, E2 and E3 mean different things, as can be seen in the book 'A Practical Guide to the Study of Glacial Sediments' by Benn & Evans, 2004 [Benn, D., Evans, D., 2004. A Practical Guide to the study of Glacial Sediments. London: Arnold. pp 103-107] .
ee also
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Eigenvalue, eigenvector and eigenspace , page on the other uses of Eigenvectors.References
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