Estimation of the tectonic strain ratio from the mean shape of deformed elliptical objects

By considering computer models representing suites of passive elliptical markers subjected to homogeneous deformation, the relationship between the strain ellipse shape (Rs equals 1 plus e//1/1 plus e//2) and mean final axial-ratio of the markers is investigated. Random and uniform models in terms of the choice of pre-tectonic initial axial-ratios (Ri) and marker-orientation are considered. The arithmetic mean (R), geometric mean (G) and harmonic mean (H) of the final axial-ratios (Rf equals long/short axis) are calculated and it is found that R departs the most from Rs. The closest of the means to the value of Rs is given by H. Using H as an estimate of Rs always gives rise to an error when the markers had a non-circular original shape. However this error diminishes relatively with increase in Rs and decrease in Ri. For the initial clast shapes present in coarse-grained detrital sedimentary rocks and Rs equal or greater than 2. 5, H allows an estimation of Rs within 10% error