Finite tectonic strain and its error, as estimated from elliptical objects with a class of initial preferred orientations

A new inverse method is proposed to estimate strain from elliptical objects that have suffered uniform deformation with their matrix. The present method extends the applicability of strain analysis to the cases where pre-strain fabric has a class of anisotropy. Specifically, a bivariate normal distribution with the mean at the origin of the Elliott plot is expected as an approximation for the initial fabric. The method is designed to facilitate error estimation for the optimal strain ellipse. Monte Carlo tests showed that the optimal solution is accurate and numerically stable. In addition, a confidence region evaluated by the present method is also accurate, provided that the variation of initial aspect ratios was more than ∼5 times larger than the deviation of the mean from the origin.