A statistic for estimating strain with confidence intervals from deformed line distributions with an application to schists and gneisses of the Western Gneiss Region, west central Norway

It is shown how to calculate the axial ratio of the strain ellipse (Rs) from a deformed set of lines, assuming that they were initially uniformly distributed and deformed passively, using an exact but simple relationship between Rs and the mean resultant length (R̄) of the distribution. The method applies to distributions of lines modified under a general 2D deformation (−∞<Wk<∞), where Wk is the kinematical vorticity number. By using the circular variance for circular data, expressions for confidence intervals and confidence levels are calculated for strain-modified distributions of lines. These expressions indicate that confidence interval widths decrease with increasing Rs and more importantly that the method is incapable of accurately estimating low strains. The method was applied to 18 gneiss and schist samples from Jøa, west central Norway and found to produce realistic strain estimates, which are internally consistent and concur with field relationships.