Cycloid kinematics of relative plate motion

Abstract

The trajectory of a point on one plate as observed from another plate is generally a complex curve and not a small circle around a single axis of relative motion, as is commonly assumed. The shape of the relative-motion path is given the general name “spherical cycloid” because of its morphological similarity to cycloid planetary trajectories described by early astronomers. The cycloid relative-motion model predicts that the following phenomena occur during finite displacements: (1) the relative velocity and the curvature of the trajectory of a point on one plate relative to another plate varies systematically; (2) plates wobble relative to one another, and (3) the angle of convergence and/or divergence varies systematically along the length of any given transform fault. The small-circle relative-motion model, whereby transform faults have been considered “lines of pure slip” along which crust is “conserved,” is not generally valid for finite relative displacements.