SFT and the Earth's Tectonic Plates

Copyright 1998-2005 UC

Have the earth's tectonic plates passed through a sequential fragmentation process?

We tested this hypothesis by starting out with the National Geographics excellent map (April 1995) entitled "The Earth's Fractured Surface," which presented all the known boundaries of the earth's tectonic plates. From this Winkel Tripel Projection, we replotted the boundaries on equal-area projections: the Peters projections to about 60o N and S latitude, and the Lambert projection of both poles. We measured the areas of 30 plates with a precision planimeter, and thus obtained the area of each plate in square kilometers (Table 1). We then estimated the thickness of each plate to obtain their volumes. Next we estimated the density of each plate to obtain their masses. Finally, we plotted the mass distribution of the plates and compared it to the "sequential fragmentation" theory (Brown and Wohletz, J. Applied Phys 78(4)).

The result was that the mass distribution of the earth's tectonic plates showed a rather broad peak that poorly fit a single Sequential Fragmentation curve (Figure 1). This result indicates that the distribution of tectonic plate masses is not related to a discrete fragmentation mechanism. It also points to the fact that there are too few plates to really perform a distribution analysis of the type we hypothesized.

Assuming that two or more fragmentation events did contribute to the size distribution of the plates, we simply converted their area into a length representing their equivalent diameter. Applying the SFT software, using the conversion in length of 1000 km = 1 mm, we plotted the size distribution (Figure 2) that shows 4 modes that explain over 95% of the observed variance. The dominant mode (79%) corresponds to major plates, having an equivalent diameter of 9700 km. The largest plates form a minor mode (11%) as do the smallest plates (5 and 4 %). All of these modes with exception of the smallest have positive dispersion (gamma) values, indicating that aggregation may have played role in which smaller plates combined early in earth's history to form larger plates with evidence not manifested by today's geophysical/geological observations.

Table 1. Plate Area

Plate Area (Square Kilometers)
African 61,334,000
Antarctic 60,916,000
Arabian 5,010,900
Australian 47,152,000
Caribbean 3,319,000
Cocos 2,860,000
Eurasian 67,811,000
Indian 11,920,000
Juan de Fuca 252,000
Nazca 15,630,000
North American 75,888,000
Pacific 103,280,000
Philippine 5,447,000
Scotia 1,651,000
Somali 16,667,000
South American 43,617,000
Bismark microplate 286,000
Burma microplate 1,110,000
Caroline microplate 1,720,000
Easter microplate 133,000
Explorer microplate 18,400
Fiji microplates 1,144,000
Galapagos microplate 12,000
Gorda microplate 69,600
Juan Fernandez microplate 96,000
Mariana microplate 364,000
Rivera microplate 73,000
Solomon microplate 254,000
South Sandwich microplate 166,000

Tonga microplate


Figure1. Histogram showing the number of plates per logarithmic mass

Figure 2. Results using SFT program to analyze subpopulations of the tectonic plate size
distribution curve. Four subpopulations are evident: Major plates (>9000 km in equivalent
equivalent diameter) minor plates (<5000 km in equivalent diameter). The horizontal axis
is a "phi" conversion of plate diameters, and the vertical axis represents the percentage of the
earth's crust represented by each size mode.

W. K. Brown
5179 Eastshore Drive
Lake Alamanor, CA 96173

K. H. Wohletz
Group EES-1, MS-D462
Los Alamos National Laboratory
Los Alamos, NM 87545