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Broken Sheets—On the Numbers and
Areas of Tectonic Plates

Bruce H. Wilkinson, Department of Earth Sciences, Syracuse University, Syracuse, New York, 13244, USA, eustasy@umich.edu;
Brandon J. McElroy, Department of Geology & Geophysics, University of Wyoming, Laramie, Wyoming, USA; and
Carl N. Dummond, Department of Physics, Purdue University Fort Wayne, Fort Wayne, Indiana 46805-1499, USA

ABSTRACT unpredictable, thus reflecting the inher- comprise a single continuous power law
ently complicated nature of processes distribution of size frequency, but with the
The sizes and numbers of tectonic associated with their formation. proviso that a finite Earth surface area
plates are thought to record the impor- imposes an upper limit on larger plate
tance of plate division, amalgamation, and INTRODUCTION areas. Like Bird (2003), Morra et al. (2013)
destruction at divergent and convergent concluded that plate sizes consist of large
margins. Changes in slope apparent on log The outer brittle layer of the Earth con- and small populations, and that this differ-
area versus log frequency plots have been sists of lithospheric plates that move over the ence in plate areas persists back in time at
interpreted as evidence for discrete popu- relatively weak asthenosphere. Larger-scale least several tens of millions of years.
lations of plate sizes, but the sizes of litho- aspects of plate movement are the surficial Mallard et al. (2016) employed spherical
spheric plates are also closely approxi- manifestations of mantle convection in the models of mantle convection to examine
mated by a continuous density function in deeper Earth, but local processes of defor- the geodynamical processes that drive the
which diameters of individual plates are mation may be only indirectly related to tessellation of the Earth’s lithosphere and
exponentially distributed; such size fre- regional stress fields. Because size frequen- concurred with Bird (2003) and Morra et
quencies are dependent only on the total cies from brittle fragmentation might be al. (2013) that plate areas comprise several
area and number of designated elements. manifest as self-similar (fractal) power laws distinct populations. Harrison (2016) pro-
This implies that the spatial locations of (e.g., Davydova and Uvarov, 2013), it is posed an additional 107 plates as subdivi-
plate boundaries are controlled by a myr- important to know the relationships between sions of the 52 plates proposed by Bird
iad of complicated and interrelated pro- lithospheric rheology and degree of frag- (2003); he also interpreted several changes
cesses such that the geographic occur- mentation, as well as the degree to which the of slope in log-log plots of plate number
rence of any particular boundary is largely breakup of the lithosphere reflects the versus area as reflecting the presence of
indeterminate and thus spatially indepen- dynamics of mantle convection versus local several size populations.
dent of the proximity of other plate bound- interactions along plate boundaries. This is
aries. Observed breaks in slope on linear- particularly so as models of the evolution of While the designation of any particular
ized size versus frequency plots are tectonic plates are extended over ever- region as a discrete “plate” is somewhat of
merely coincidental and of themselves do increasing spans of geologic time (e.g., an evolving enterprise (e.g., Zhang et al.,
not support an interpretation of discrete Domeier and Torsvik, 2014; Matthews et al., 2017), the actuality of either single
tectonic processes operating over distinct 2016; Merdith et al., 2017). (Sornette and Pisarenko, 2003) or multiple
length scales. Although a purely random (Anderson, 2002; Bird, 2003; Mallard et
distribution of plate boundaries also impli- One approach to this question derives al., 2016; Harrison, 2016) populations of
cates a similar chance distribution of plate from considerations of the numbers and plate sizes is important to interpreting the
sizes, some smaller plates are indeed clus- sizes of the tectonic plates. Anderson manifestation of causative tectonic pro-
tered along convergent boundaries in the (2002), for example, noted that fracture cesses. If sizes of tectonic plates are read-
southwestern Pacific. Such association of patterns tend to self-organize such that ily characterized by a single frequency
plates of similar (small) sizes suggests mud cracks, frozen ground, basalt col- distribution, be it fractal or otherwise, an
that locations of plate boundaries are best umns, and other natural features exhibit interpretation of multiple processes operat-
described as reflecting nonhomogeneous similar patterns. He argued that tectonic ing at distinct length scales is not sup-
Poisson processes wherein probabilities plates therefore might consist of semi-rigid ported. Conversely, if plate area-frequen-
of reaching some plate boundary vary larger polygons separated by (at times dif- cies are best described by multimodal
along any Earth-surface transect. Size fuse) boundary zones of deformation sur- distributions, then interpretations linking
frequencies of continents, calderas, and faced by smaller elements. Bird (2003) populations of large plates to processes
many other geologic entities where presented a global data set interpreted as occurring at convective length scales (e.g.,
dimensions are expressed as areal extent embodying several fractal subpopulations Lenardic et al., 2006) and populations of
exhibit similar size-frequency distribu- of plate sizes, each manifest as an approxi- smaller plates to the generation of litho-
tions, suggesting that lateral occurrences mately linear trend in log area versus log spheric fragments at the edge of plate
of their boundaries are also largely occurrence–frequency space. Sornette and boundaries are entirely reasonable.
Pisarenko (2003) argued that plate sizes

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