Broken Sheets—On the Numbers and Areas of Tectonic Plates

The sizes and numbers of tectonic plates are thought to record the importance of plate division, amalgamation, and destruction at divergent and convergent margins. Changes in slope apparent on log area versus log frequency plots have been interpreted as evidence for discrete populations of plate sizes, but the sizes of lithospheric plates are also closely approximated by a continuous density function in which diameters of individual plates are exponentially distributed; such size frequencies are dependent only on the total area and number of designated elements. This implies that the spatial locations of plate boundaries are controlled by a myriad of complicated and interrelated processes such that the geographic occurrence of any particular boundary is largely indeterminate and thus spatially independent of the proximity of other plate boundaries. Observed breaks in slope on linearized size versus frequency plots are merely coincidental and of themselves do not support an interpretation of discrete tectonic processes operating over distinct length scales. Although a purely random distribution of plate boundaries also implicates a similar chance distribution of plate sizes, some smaller plates are indeed clustered along convergent boundaries in the southwestern Pacific. Such association of plates of similar (small) sizes suggests that locations of plate boundaries are best described as reflecting nonhomogeneous Poisson processes wherein probabilities of reaching some plate boundary vary along any Earth-surface transect. Size frequencies of continents, calderas, and many other geologic entities where dimensions are expressed as areal extent exhibit similar size-frequency distributions, suggesting that lateral occurrences of their boundaries are also largely unpredictable, thus reflecting the inherently complicated nature of processes associated with their formation.