Finite strain estimation from deformed elliptical markers: The minimized Ri¯ (MIRi) iterative method

• A method for estimating the finite strain of deformed markers is presented.
• The MIRi method furnishes finite strain Rs and max stretching direction X.
• The MIRi method provides also uncertainties on Rs and X.
• The method was tested on artificially and naturally deformed markers.
• A Matlab code is provided.

A new technique for estimating the finite strain of deformed elliptical markers is presented. This method is based on the property of the arithmetic mean Rf¯ of the deformed object aspect ratios Rf to reach its minimum value in the undeformed state when they correspond to the initial aspect ratios Ri  . The minimized Ri¯ (MIRi) iterative method furnishes the best results when, in the pre-strain state, the markers are uniformly orientated for every aspect ratio (Ri) class. A Matlab code, provided in this study, finds the best values of strain Rs and maximum stretching direction X   that minimize the arithmetic mean Ri¯ by means of several iterations. In order to define the uncertainties of Rs and X, the code: (i) re-samples h-times the original (Ri, θ) dataset; (ii) assigns random values to the initial long axis angles θ; (iii) deforms newly the synthetic dataset; (iv) re-applies the MIRi method; and finally (v) estimates the standard deviation for the (Rs, X) values. Tests of the method on synthetic aggregates of elliptical markers and two naturally deformed rocks provide strain values that are compared with estimations from other available methods.