The limitations of three-dimensional kinematic vorticity analysis

The kinematic vorticity number (W_k) can be calculated for three-dimensional as well as two-dimensional geologic deformations. For steady-state deformations, W_k can be correlated to and analyzed in terms of finite strains. The analysis shows that assumptions commonly made for two-dimensional deformations are not applicable to three-dimensional deformations. A single W_k describes an infinite number of three-dimensional deformations. Further, even knowledge of flow apophyses orientation, instantaneous stretching axes orientation, and/or W_k are not sufficient to describe deformation. Three-dimensional deformations also require knowledge of the deformation ‘type’ or boundary conditions of deformation (e.g. transpression). Hence, in addition to being difficult to estimate, the value of knowing W_k for three-dimensional deformations is greatly reduced compared with plane strain. The most useful methods of determining W_k from naturally deformed rocks are presented.