Vector analysis of ice-fabric data

Abstract

AbstractThe mechanical properties of ice are strongly affected by crystal texture and c-axis alignment. In this paper, we develop a general quantitative method for analysis of uniaxial crystal-orientation data. These data are represented as unit vectors from the origin with end points 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, here we identify an implicit assumption in the method, and observe that the error measure represents physical distance and quantifies the goodness of fit to the data of idealized structures. Also, 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.