Shape fabrics in populations of rigid objects in 2D: Estimating finite strain and vorticity

Shape fabrics of elliptical objects in rocks are usually assumed to develop by passive behaviour of inclusions together with the surrounding material leading to shape-based strain analysis methods belonging to the Rf/ϕ family. By deriving the probability density function for populations of rigid ellipses deforming in a general 2D deformation, a method is developed which can be used to estimate both finite strain and the kinematic vorticity number. Statistical parameters are theoretically derived and their behaviours under various kinematic conditions are investigated. The maximum likelihood method from statistics is used to produce a numerical method for estimating deformation parameters from natural populations. A simulation study demonstrates that finite strain can be estimated well for both low and high applied finite strains, whereas the kinematic vorticity number is well estimated only in the case of high finite strains (Rs > 40), and that large sample numbers (≈1000) are required.