Quantifying Anderson's fault types

Anderson [1905] explained three basic types of faulting (normal, strike-slip, and reverse) in terms of the shape of the causative stress tensor and its orientation relative to the Earth's surface. Quantitative parameters can be defined which contain information about both shape and orientation [Célérier, 1995], thereby offering a way to distinguish fault-type domains on plots of regional stress fields and to quantify, for example, the degree of normal-faulting tendencies within strike-slip domains. This paper offers a geometrically motivated generalization of Angelier's [1979, 1984, 1990] shape parameters ϕ and ψ to new quantities named A_ϕ and A_ψ. In their simple forms, A_ϕ varies from 0 to 1 for normal, 1 to 2 for strike-slip, and 2 to 3 for reverse faulting, and Aψ/ranges from 0° to 60°, 60° to 120°, and 120° to 180°, respectively. After scaling, A_ϕ and A_ψ agree to within 2% (or 1°), a difference of little practical significance, although A_ψ has smoother analytical properties. A formulation distinguishing horizontal axes as well as the vertical axis is also possible, yielding an A_ϕ ranging from −3 to +3 and A_ψ from −180° to +180°. The geometrically motivated derivation in three-dimensional stress space presented here may aid intuition and offers a natural link with traditional ways of plotting yield and failure criteria. Examples are given, based on models of Bird [1996] and Bird and Kong [1994], of the use of Anderson fault parameters A_ϕ and A_ψ for visualizing tectonic regimes defined by regional stress fields.