Quantifying Anderson's fault types

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Abstract
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 Aϕ and Aψ. In their simple forms, Aϕ 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, Aϕ and Aψ agree to within 2% (or 1°), a difference of little practical significance, although Aψ has smoother analytical properties. A formulation distinguishing horizontal axes as well as the vertical axis is also possible, yielding an Aϕ ranging from −3 to +3 and Aψ 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 Aϕ and Aψ for visualizing tectonic regimes defined by regional stress fields.