Orientation tensor

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In geology, especially in the study of glacial 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 of clasts in a soil sample, which can only be compared graphically such as in a Tri-Plot (Sneed and Folk) diagram,[1][2] or as a stereographic projection.[3] The output for the orientation tensor is in the three orthogonal (perpendicular) axes of space.

Eigenvectors output from programs such as Stereo32 [4] 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.[5]


  1. ^ Graham, D., and Midgley, N., 2000. Earth Surface Processes and Landforms (25) pp 1473–1477
  2. ^ Sneed ED, Folk RL. 1958. Pebbles in the lower Colorado River, Texas, a study of particle morphogenesis. Journal of Geology 66(2): 114–150
  3. ^ GIS-stereoplot: an interactive stereonet plotting module for ArcView 3.0 geographic information system
  4. ^ Stereo32
  5. ^ Benn, D., Evans, D., 2004. A Practical Guide to the study of Glacial Sediments. London: Arnold. pp 103–107