A continuous plate tectonic model using geophysical data to estimate plate-margin widths, with a seismicity-based example

A continuous kinematic model of present-day plate motions is developed which (1) provides more realistic models of plate shapes than employed in the original work of Bercovici & Wessel (1994), and (2) provides a means whereby geophysical data on intraplate deformation is used to estimate plate-margin widths for all plates. A given plate's shape function (which is unity within the plate and zero outside the plate) can be represented by analytic functions as long as the distance from a point inside the plate to the plate's boundary can be expressed as a single-valued function of azimuth (i.e. a single-valued polar function). To allow sufficient realism to the plate boundaries, without the excessive smoothing used by Bercovici & Wessel, the plates are divided along pseudo-boundaries; the boundaries of plate sections are then simple enough to be modelled as single-valued polar functions. Moreover, the pseudo-boundaries have little or no effect on the final results. The plate shape function for each plate also includes a plate-margin function which can be constrained by geophysical data on intraplate deformation. We demonstrate how this margin function can be determined by using, as an example data set, the global seismicity distribution for shallow (depths less than 29 km) earthquakes of magnitude greater than 4. Robust estimation techniques are used to determine the width of seismicity distributions along plate boundaries; these widths are then turned into plate-margin functions, that is analytic functions of the azimuthal polar coordinate (the same azimuth-of which the distance to the plate boundary is a single-valued function). The model is used to investigate the effects of 'realistic' finite-margin widths on the Earth's present-day vorticity (i.e. strike-slip shear) and divergence fields as well as the kinetic energies of the toroidal (strike-slip and spin) and poloidal (divergent and convergent) flow fields. The divergence and vorticity fields are far more well defined than for the standard discontinuous plate model and distinctly show the influence of diffuse plate boundaries such as the northeast boundary of the Eurasian plate. The toroidal and poloidal kinetic energies of this model differ only slightly from those of the standard plate model; the differences, however, are systematic and indicate a greater proportion of spin kinetic energy in the continuous plate model.