Most structural/kinematic models are inherently two-dimensional; even several recent three-dimensional models are “pseudo–three-dimensional” in that they consist of a series of parallel two-dimensional cross sections. Lack of a true three-dimensional formulation hampers our abilities to simulate three-dimensional structures such as oblique- and strike-slip faulting and displacement gradients perpendicular to the slip vector. The mathematical formulation of trishear deformation using incompressibility of flow is well suited to a solution in three dimensions. We derive one plausible velocity field for true three-dimensional flow in a triangular shear zone. This formulation allows us to simulate the deformation in oblique-slip deformation zones as well as flower structures associated with strike-slip fault zones. The strain distribution in flower structures combined with some simple mechanical assumptions suggests that faults in these zones would have a helicoidal geometry. The results of the kinematic model compare well to well-described structures in the Colorado Plateau, Andaman Sea, and Death Valley, as well as to data from analogue experiments.

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