Abstract
Finite strain estimation is a widely used technique for the study of rock deformation in structural geology. One particular algorithm proposed by Shimamoto and Ikeda uses the ‘average shape matrix’ of deformed markers. This paper provides a detailed error analysis for resulting strain estimates in two dimensions. When the number of markers exceeds 100, estimators of components of the strain tensor are shown to have an approximately Gaussian distribution with variances that increase with their mean. Equal variance estimators are obtained by applying a log transform for the elongation and an arcsin transformation for the orientation estimates. Confidence interval formulae for strain tensor components are proposed. Lithology specific constants arising in these formulae are estimated from undeformed samples. The results are validated by application to simulated data as well as observational data from thin sections of sandstone sampled from SE Ireland.
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