The cycloid relative-motion model and the kinematics of transform faulting

Abstract

Adequate models of instantaneous plate tectonics currently exist; however, a model to describe the continuous relative motion of lithospheric plates during a finite time interval has been necessary. The small-circle relative-motion model suggests that a particle on a given plate follows a circular path around a pole of relative motion, as viewed from another plate during finite relative displacement. It can be shown that the small-circle model is not generally valid in describing the finite relative motion of plates, so this motion must trace a curve that is more complex than a circle. A new approach has been developed that permits improved modeling of finite relative plate motion. The first-order cycloid relative-motion model (CYC1) is based upon the idea that each plate is in motion around a plate-specific pole (elsewhere termed an “absolute” or “no-net-torque” pole). The observed relative motion between two plates is the result of the two plate-specific motions. Combining the two rotations, a point on one plate moves along a cycloid figure of rotation around two axes as viewed from another plate. A cycloid (a two-axis curve) is the simplest spherical curve that is more complex than a circle (a one-axis curve). The mathematical expression of cycloid relative motion involves a series of coordinate transformations. The small-circle model is a subset of the cycloid model. CYC1 indicates that significant variations in the direction and velocity of relative motion can occur even when the governing axial positions and angular velocities are constant. Hence, a variety of boundary interactions are possible during finite relative displacements that would not have been predicted by a small-circle model of finite relative plate motion. The cycloid model indicates that transform faults are not simply lines of pure slip along which crust is conserved. Systematic changes in the amount of convergence or divergence along the length of a given transform fault are predicted. This gradient is probably reflected in local boundary deformation, and is predicted to be a factor controlling the length of a given fault segment. Transform faults are generally in motion relative to the corresponding relative pole and plate-specific poles. The relative velocity along a given transform fault and the spreading rate across the adjacent ridge segments vary as the radius from the fault to its relative pole changes. The curvature of a given transform fault is also predicted to change with finite displacement, as the fault moves with respect to its relative pole. Motion of a given transform fault with respect to its relative pole and to the plates that it bounds suggests that the traces of the resulting fracture zones should be complex curves that are not symmetrical across the ridge axis. Improved modeling of finite relative plate motion should enhance understanding of the structural, stratigraphic, magmatic, and metamorphic evolution of plate margins.