The estimation of finite strain from the orientation distribution of passively deformed linear markers: Eigenvalue relationships

The eigenvalues and eigenvectors of a direction cosine dispersion matrix may be used to characterise sets of orientation measurements in either two or three dimensions. General equations are presented that relate ratios of the eigenvalues of such a measured set to the finite strain ratios of the set assuming that the original orientation distribution, before a deformation, was uniform. The measured linear features in the rock are assumed to have behaved passively during a homogeneous deformation. The application of these relationships to strain estimation is discussed and tables for the three-dimensional case are given.