A continuous kinematic model of plate-tectonic motions

Abstract

SUMMARY One of the many problems in the study of plate-mantle coupling is the disparity between the theory of mantle dynamics—which involves continuum physics—and the theory of plate tectonics—which employs discontinuous plates. This discordance causes a variety of difficulties in geodynamic models, e.g. infinite tractions between the plates and mantle. As motions of the Earth's surface do not involve discontinuous plates (i.e. intraplate deformation is significant and plate margins have finite width), it is necessary to adjust the plate-tectonic model to allow for continuous surface motions. Here we present a model of plate motions on a sphere using analytically continuous (i.e. infinitely differentiable) functions to describe both plate geometry and plate margin width. We first apply this model to the idealized system of a single ‘rectangular’ plate to examine the influence of plate geometry and size on kinetic-energy partitioning of plate motions on a sphere. The ratio of toroidal (strike slip and spin) kinetic energy to poloidal (convergent-divergent) kinetic energy is affected not only by the relative lengths of strike-slip and convergent-divergent margins, but also on plate size, which controls the magnitude of plate spin. For large plates, spin toroidal motion contributes a major portion of the net toroidal energy. Basic concepts from this simple illustrative model are then expanded to derive an analytically continuous model of present-day plate-tectonic motions. The plate boundary for any given plate is smoothed and expressed as a single-valued differentiable function; this function is employed to generate the analytically continuous shape function of the plate. The shape function is then used to model the plate's motion about its contemporaneous Euler pole. This technique is carried out for all the plates and their motions are superposed to yield a complete yet simplified model of present-day plate motions. We use this model to examine the influence of plate margin width on energy partitioning for the Earth's plates; this approximately indicates the extent to which energy partitioning is influenced by intraplate deformation. The calculations indicate that the introduction of finite margin width allows spin vorticity to make a larger contribution to the toroidal energy. Depending on margin width, the partitioning of energy is possibly reversed, with toroidal energy assuming a larger proportion of the net kinetic energy. The model of continuous plate motions proposed here may not only ease the disparity between the theories of plate tectonics and mantle convection, but is a first simple step toward incorporating intraplate deformation into plate tectonics.