BROKEN SHEETS – ON THE NUMBERS AND AREAS OF TECTONIC PLATES AND OTHER TILES

Sizes and numbers of tectonic plates are thought to record the importance of different processes 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 two or three discrete populations of plate sizes that reflect lithospheric fragmentation associated with processes of mantle convection and plate boundary tectonics. However, the size distribution of lithospheric plates is closely approximated by a continuous density function that is only dependent on the total area and number of designated elements. This reflects the fact that the position and orientation of plate boundaries are largely controlled by a myriad of complicated and interrelated processes such that the geographic occurrence of any particular boundary is spatially indeterminate; that is, any boundary is independent of the proximity of other plate margins. Observed breaks in slope of linear trends in log size versus log frequency plots are merely coincidental, and of themselves do not support an interpretation of distinct tectonic processes operating over such easily-delineated length scales. However, smaller plates are found to be clustered along convergent boundaries in the southwestern Pacific suggesting that locations of plate boundaries are best described as comprising a heterogeneous Poisson system in which the intensity of processes of plate accretion, amalgamation, fragmentation, and destruction are distributed non-uniformly across the Earth’s lithosphere. Size frequencies of continents, calderas, and countries, as well as many other entities where dimensions are expressed as lateral extent, exhibit similar size frequency distributions that also reflect the inherently complicated nature of the systems by which they were formed.