Vector Analysis of Ice Fabric Data
COLD REGIONS RESEARCH AND ENGINEERING LAB HANOVER NH
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The mechanical properties of ice are strongly affected by crystal texture and c-axis alignment. In this report we develop a general quantitative method for analysis of uniaxial crystal orientation data. These data are represented as unit vectors from the origin with endpoints on the surface of a unit sphere. An orthogonal least-squares error measure is used to develop equations that define the closest plane and line through the data. The resulting eigenvalue problem is identical to that obtained by other investigators using different methods. However, we identify an implicit assumption in the method, and observe that the error measure represents physical distance and quantifies the goodness-of-fit of the idealized structures to the data. For comparison, a parallel development is presented of classical dependent-variable least squares. A method is developed to transform the data and the results for viewing on Schmidt nets drawn in the best plane and the predominant basal plane of a sample, in addition to the standard xy-plane. Applications of the analysis to sea ice samples include both numerical and Schmidt net presentations of results. C-axis orientation, Orthogonal least-squares, Sea ice, Crystal fabric analysis, Schmidt nets.
- Snow, Ice and Permafrost
- Numerical Mathematics