**Cycloid Tectonics: Kinematics of Transform Faulting
Reevaluated**

**Vincent S. Cronin**

Euler's theorem is commonly invoked to demonstrate that the displacement of a continent from one position to another position can be described as a rigid rotation around a vertical axis through the center of the earth. Transform faults have been thought to be small circles around an axis of (finite) relative motion. This assumption is not generally valid. The Eulerian axis generally does not describe the actual path of a plate's motion between two discrete, relative positions (information that is essential to understand the stress, deformation, and displacement history along a plate boundary), so this type of instantaneous axis does not necessarily have geological significance. While an instantaneous axis of relative motion can be determined for a given plate pair using s ismic data, the finite path along which a reference point on one plate moves relative to another moving plate is a spherical cycloid: a figure of rotation that typically has two or three axes. The curvature of a cycloid path changes systematically with time, as does the reference point's relative velocity. The relative motion trajectories of multiple points on a rigid plate trace a family of cycloids having a common wavelength and frequency but differing in amplitude and/or phase. Cycloid relative motion virtually precludes the possibility that discrete, "pure" strike-slip plate boundaries exist along which "crust is conserved." Systematic changes in the angle of relative convergence or divergence occur along the length of a given transform fault through time, regardless of its shape. Th resulting horizontal stress gradient is sufficient to generate structures of economic significance adjacent to transform faults involving continental crust.

AAPG Search and Discovery Article #91038©1987 AAPG Annual Convention, Los Angeles, California, June 7-10, 1987.