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Global geologic maps are tectonic speedometers—Rates of rock cycling from area-age frequencies

Bruce H. Wilkinson^1,, Brandon J. McElroy², Stephen E. Kesler³, Shanan E. Peters⁴ and Edward D. Rothman³

¹ Department of Earth Sciences, Syracuse University, Syracuse, New York 13244, USA
² Department of Geological Sciences, Jackson School of Geosciences, University of Texas, Austin, Texas 78712, USA
³ Department of Geological Sciences, University of Michigan, Ann Arbor, Michigan 48109, USA
⁴ Department of Geology and Geophysics, University of Wisconsin, Madison, Wisconsin 53706, USA

Correspondence: E-mail: eustasy{at}umich.edu

Relations among ages and present areas of exposure of volcanic, sedimentary, plutonic, and metamorphic rock units (lithosomes) record a complex interplay between depths and rates of formation, rates of subsequent tectonic subsidence and burial, and/or rates of uplift and erosion. Thus, they potentially serve as efficient deep-time geologic speedometers, providing quantitative insight into rates of material transfer among the principal rock reservoirs—processes central to the rock cycle. Areal extents of lithosomes exposed on all continents from two map sources (Geological Survey of Canada [GSC] and the Food and Agricultural Organization [FAO] of the United Nations Educational, Scientific, and Cultural Organization [UNESCO]) indicate that volcanic, sedimentary, plutonic, and metamorphic rocks occupy ~8%, 73%, 7%, and 12% of global exposures, respectively.

Plots of area versus age of all mapped rock types display a power-law relation where ~6.5% of continental area is resurfaced with younger (~10% volcanic; 90% sedimentary) units every million years, and where areas of rock exposure decrease by ~0.86% for each 1% increase in outcrop age (r² = 0.90). Area-age relations for volcanic and sedimentary lithosomes are similar to the power-law distribution defined by all rock units (because ~81% of mapped area consists of these two lithologies) and reflect progressive decrease in amount of exposure with increasing age. Over the long term, continental surfaces are blanketed by new volcanic rocks and sediments at rates of ~1.5 and 12.1 x 10⁶ km²/Ma, respectively.

In contrast to power-law–distributed volcanic and sedimentary rocks that form at the Earth's surface, age-frequency distributions for plutonic and metamorphic rocks exhibit lognormal relations, with modes at ca. 154 and 697 Ma, respectively. A dearth of younger exposures of plutonic and metamorphic rocks reflects the fact that these rock types form at depth, and some duration of tectonism is therefore required for their exposure. Increasing modal ages, from Quaternary for volcanic and sedimentary successions, to early Mesozoic for intrusive rocks, to Neoproterozoic for metamorphic rocks, demonstrate that greater amounts of geologic time are required for uplift to bring more deeply formed rocks to the Earth's surface.

The two different age-frequency distributions observed for these major rock types—a general power-law age distribution for volcanic and sedimentary rocks and a lognormal distribution for plutonic and metamorphic rock ages—reflect the interplay between depths of formation and mean rates of vertical tectonic displacement. Age-frequency distributions for each of the major rock types are closely replicated by a model that presumes that individual crustal elements behave as a large population of random walks in geologic time and crustal depth, and where the processes of surficial erosion associated with tectonic uplift serve to impose an absorbing boundary on this random-walk space. Comparisons between model-predicted age-frequencies and those apparent in global map data suggest that mean rates of crustal subsidence and uplift are approximately equal in magnitude, with mean rates of vertical tectonic diffusion of lithosomes from crustal depths of formation of about half a kilometer per million years. Rates of uplift and subsidence are strongly dependent on durations of tectonic dispersion (lithosome ages); however, mean rates on the order of hundreds of meters per million years suggested by map age-frequencies are the same as would be anticipated on the basis of hundreds of published rates of erosional uplift and exhumation determined by more conventional geochronometers. This agreement suggests that geologic maps serve as effective deep-time speedometers for the geologic rock cycle.