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2.0 A 100 MPa B 150 MPa 1.5
1.0
1.5 0.5
Transition Probability (10-3 /km)1.0
log Exceedence0.5

log ExceedenceC200 MPaD250 MPa

E 1.0 1.0

0.6 0.5 0.5
0.5
0.4 678 67 8
0.3
0.2 log Area (km2) log Area (km2)

100 MPa Tp = 0.108 Ys-1.14
150 MPa R2 = 0.95
200 MPa
250 MPa

100 150 200 250

Yield Stress (MPa)

Figure 4. (A–D) Convection in 3D spherical models of mantle convection (inset Earth models) and the logarithm of plate size
versus log exceedance (cumulative count) (colored lines) for yield stresses of 100, 150, 200, and 250 MPa from Mallard et al.
(2016). (E) Transition probabilities for broken sheets calculated for the 18 arrays of plate area and number (colored lines in
[A–D]). Relations between model yield stresses and transitions probabilities defined an approximate power law relation
between stress at model plate boundaries and degree of plate fragmentation.

clustering of plates is around the equatorial mechanisms of plate formation and is geographic association of larger and
North Bismarck plate off Papua New destruction might exhibit a degree of vari- smaller plates, merely enforces the suppo-
Guinea (23 neighbors within 5,000 km). ation along a theoretical length scale. At a sition that those factors responsible for the
Association of smaller plates in the south- longer scale, it is generally accepted, for generation of differing plate numbers,
western Pacific could reflect a greater example, that larger plates bearing conti- sizes, and locations, both in time and in
importance of such processes of plate frac- nental crust tend to aggregate over cold space, must reflect a concatenation of
ture, particularly when overriding plates downwellings, leading to overheating of many complex processes, but that these
are oceanic lithosphere, in ways that are the mantle, which in turn gives rise to the processes also operate with differing geo-
not associated with convergence when the tensional fragmentation of continents (e.g., graphic and/or temporal intensity across
overriding plate is continental lithosphere, Gurnis, 1988). Conversely, at a shorter the Earth’s surface.
as is found along the eastern Pacific. scale, subduction zones may tend to pro-
However, fragmentation alone is a uni­ duce smaller plates (e.g., Mallard et al., IMPLICATIONS
directional process that serves to abruptly 2016), particularly when subduction-
decrease plate sizes and somewhat obvi- related back-arc volcanism develops into As a first approximation, the Earth’s
ates considerations of size changes that oceanic spreading centers (e.g., Bird, lithosphere generally comprises a ran-
might arise through subduction, spreading, 2003); microplates may also be produced domly broken sheet wherein the occur-
or suturing. along seafloor spreading centers when rences of plate boundaries are spatially
propagating rifts pass by each other (e.g., independent but somewhat geographically
Although identification of “populations” Hey et al., 1985). Other processes of plate clustered across the southwestern Pacific.
of large and small plates defined by appar- generation and destruction are less sensi- This suggests that the processes of
ent linear runs in log size versus log tive to length scale; plates of any size can spreading, suturing, fragmentation, and
exceedance space may indeed be spurious, be amalgamated during continental colli- subduction, which ultimately result in
this does not preclude an interpretation sion and/or destroyed by subduction. differing plate areas as well as contiguous
that plate-center convection and plate-mar- areas of granitic crust (i.e., continents),
gin tectonism have differentially influ- That plate areas are in general agree- are irreconcilably complex while also
enced plate size histories. There is much ment with the premise that the Earth’s lith- exhibiting some degree of spatial and
support for the premise that the osphere is randomly fragmented, yet there temporal heterogeneity across the Earth’s

8 GSA Today | June 2018