The limitations of three-dimensional kinematic vorticity analysis

The kinematic vorticity number (Wk) can be calculated for three-dimensional as well as two-dimensional geologic deformations. For steady-state deformations, Wk 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 Wk describes an infinite number of three-dimensional deformations. Further, even knowledge of flow apophyses orientation, instantaneous stretching axes orientation, and/or Wk 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 Wk for three-dimensional deformations is greatly reduced compared with plane strain. The most useful methods of determining Wk from naturally deformed rocks are presented.