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A mathematical model for orientation data from macroscopic elliptical conical folds


An iterative least-squares technique to fit circular and elliptical conical surfaces to orientation data from folds is presented. A statistical model is used which assumes that each data point is an observation from a Fisher distribution. The mean of this distribution is assumed to lie on the curve to be fitted. Estimates of variances and covariances for the fitting parameters are calculated, and confidence intervals for the cone axis and half apical angle are estimated from variances and covariances. A normal test with null hypothesis that the cone angle is 90° determines if a conical model fits the data better than a cylindrical model. AnF test is used to determine whether an elliptical cone is a better model than a circular cone. In this fashion, macroscopic folds are classified into cylindrical, circular conical, or elliptical conical folds. Examples of these three types of fold are given. The Wynd Syncline near Jasper, Alberta is the first natural elliptical conical fold described as such.

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Kelker, D., Langenberg, C.W. A mathematical model for orientation data from macroscopic elliptical conical folds. Math Geol 19, 729–743 (1987). https://doi.org/10.1007/BF00893011

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Key words

  • orientation data
  • circular conical folds
  • elliptical conical folds