Global geologic maps are tectonic speedometers— Rates of rock cycling from area-age frequencies Bruce H. Wilkinson1†, Brandon J. McElroy2, Stephen E. Kesler3, Shanan E. Peters4, and Edward D. Rothman3 1Department of Earth Sciences, Syracuse University, Syracuse, New York 13244, USA 2Department of Geological Sciences, Jackson School of Geosciences, University of Texas, Austin, Texas 78712, USA 3Department of Geological Sciences, University of Michigan, Ann Arbor, Michigan 48109, USA 4Department of Geology and Geophysics, University of Wisconsin, Madison, Wisconsin 53706, USA ABSTRACT the Earth’s surface, age-frequency distribu- lion years suggested by map age-frequencies tions for plutonic and metamorphic rocks are the same as would be anticipated on the Relations among ages and present areas of exhibit lognormal relations, with modes at basis of hundreds of published rates of ero- exposure of volcanic, sedimentary, plutonic, ca. 154 and 697 Ma, respectively. A dearth sional uplift and exhumation determined by and metamorphic rock units (lithosomes) of younger exposures of plutonic and meta- more conventional geochronometers. This record a complex interplay between depths morphic rocks refl ects the fact that these agreement suggests that geologic maps serve and rates of formation, rates of subsequent rock types form at depth, and some duration as effective deep-time speedometers for the tectonic subsidence and burial, and/or rates of tectonism is therefore required for their geologic rock cycle. of uplift and erosion. Thus, they potentially exposure. Increasing modal ages, from Qua- serve as effi cient deep-time geologic speed- ternary for volcanic and sedimentary succes- INTRODUCTION ometers, providing quantitative insight into sions, to early Mesozoic for intrusive rocks, rates of material transfer among the principal to Neoproterozoic for metamorphic rocks, Since the fi rst complete geologic map of Eng- rock reservoirs—processes central to the rock demonstrate that greater amounts of geologic land, Wales, and Scotland was scribed and pub- cycle. Areal extents of lithosomes exposed on time are required for uplift to bring more lished by William Smith in 1815, geologic maps all continents from two map sources (Geolog- deeply formed rocks to the Earth’s surface. have increasingly become our most important ical Survey of Canada [GSC] and the Food The two different age-frequency dis- tools for visually representing variation in the and Agricultural Organization [FAO] of the tributions observed for these major rock Earth’s surfi cial geologic features. Geologic United Nations Educational, Scientifi c, and types—a general power-law age distribu- mapping serves as a linchpin of undergraduate Cultural Organization [UNESCO]) indicate tion for volcanic and sedimentary rocks education in the Earth sciences, and geologic that volcanic, sedimentary, plutonic, and and a lognormal distribution for plutonic maps now provide information on the distribu- metamorphic rocks occupy ~8%, 73%, 7%, and metamorphic rock ages—refl ect the tion of different types of rocks and structures and 12% of global exposures, respectively. interplay between depths of formation and for resource discovery, land use decisions, and Plots of area versus age of all mapped rock mean rates of vertical tectonic displacement. hazards assessments. In addition to more practi- types display a power-law relation where Age-frequency distributions for each of the cal applications, geologic maps are the basis for ~6.5% of continental area is resurfaced with major rock types are closely replicated by a study of the long and rich geologic history of younger (~10% volcanic; 90% sedimentary) model that presumes that individual crustal continents and the planet as a whole (e.g., Veizer units every million years, and where areas of elements behave as a large population of and Jansen, 1979, 1985). rock exposure decrease by ~0.86% for each random walks in geologic time and crustal The possibility that geologic maps might pro- 1% increase in outcrop age (r2 = 0.90). Area- depth, and where the processes of surfi cial vide quantitative insight into this history was age relations for volcanic and sedimentary erosion associated with tectonic uplift serve brought into focus by James Gilluly (1969), lithosomes are similar to the power-law dis- to impose an absorbing boundary on this who was the fi rst to fully examine relations tribution defi ned by all rock units (because random-walk space. Comparisons between between rock age and outcrop area at conti- ~81% of mapped area consists of these two model-predicted age- frequencies and those nental scales. Using nail scissors to cut out and lithologies) and refl ect progressive decrease apparent in global map data suggest that separate individual rock units represented on in amount of exposure with increasing age. mean rates of crustal subsidence and uplift geologic maps of North and South America, he Over the long term, continental surfaces are are approximately equal in magnitude, with determined areas from the proportional weights blanketed by new volcanic rocks and sedi- mean rates of vertical tectonic diffusion of of map fragments representing each major rock ments at rates of ~1.5 and 12.1 × 106 km2/Ma, lithosomes from crustal depths of formation age and type. Gilluly (1969) recognized that the respectively. of about half a kilometer per million years. log-area of rock exposure decreases with the log In contrast to power-law–distributed vol- Rates of uplift and subsidence are strongly of increasing age (Fig. 1). This realization led canic and sedimentary rocks that form at dependent on durations of tectonic disper- him to conclude that: “The completeness of the sion (lithosome ages); however, mean rates geologic record obviously diminished with the †E-mail: [email protected] on the order of hundreds of meters per mil- passage of time, not simply because younger GSA Bulletin; May/June 2009; v. 121; no. 5/6; p. 760–779; doi: 10.1130/B26457.1; 18 fi gures; 4 tables. 760 For permission to copy, contact [email protected] © 2009 Geological Society of America Geologic maps are tectonic speedometers rocks come to bury the older, but also because the younger have been largely derived by the cannibalization of the older.” Rather than being South America 10,000,000 5 -0.85 a manifestation of lower rates of rock cycling in Area = 8.2 x 10 Age r2 = 0.85 Qt the geologic past, Gilluly correctly interpreted Mean age = 800 Ma South America the pattern of decreasing rock area with increas- ing rock age as a manifestation of the unrelent- 1,000,000 /m.y.) Tpl ing importance of tectonic processes of uplift 2 and associated erosion balanced by generally North America equal amounts of subsidence and deposition that 100,000 Kt Tpa Sl serve to “drive” the geologic rock cycle. Ms Or Pa Examination of Gilluly’s (1969) data (Fig. 1) Tmi Tpl Teo raises several other questions related to those Tol 10,000 geologic processes that control outcrop age Jr and area. For example, one might wonder why Tr North America rock age and exposed area scale approximately Pm Area = 6.2 x 105 Age-0.64 2 linearly in log-log space. Such “power-law” (km exposed Area 1000 r = 0.74 relations characterize a wide range of scale- Cm Mean age = 750 Ma invariant geologic data (e.g., Turcotte, 1992; Newman, 2005). Why are area-age data on geologic maps log-log linear? 100 10 1 The log-area versus log-age relationship iden- tifi ed by Gilluly (1969; Fig. 1) is numerically Age (Ma) described by both an intercept and a slope, the Figure 1. Ages and areas of geologic map units exposed in North (open diamonds and black former being related to amount of new outcrop line) and South (gray circles and gray line) America for Phanerozoic periods and epochs formed over some unit of time, and the latter (after Gilluly, 1969). Note decreasing area of outcrop with increasing age, log-log relation of being related to rates of outcrop area reduction, outcrop age to area, and somewhat lower slope for North American (−0.64) relative to South either through uplift and erosion or through sub- American (−0.85) outcrops. sidence and burial by younger units. In the case of geologic maps, intercept and slope values must be interrelated because the net area of con- tinental crust has remained relatively constant principally upon the progressive elevation of and Agricultural Organization (FAO) of the over at least the past one billion years or so (e.g., a region,” it follows that global geologic maps United Nations Education, Science, and Cul- Pearson et al., 2007); addition of new (young) may serve as excellent recorders of fi rst-order tural Organization (UNESCO). map units to a fi xed land area must therefore be rates of Earth surface-rock formation and The Geological Survey of Canada Open-File approximately balanced by equivalent loss of destruction. In order to further investigate the 2915d, Generalized Geological Map of the World older map areas. effi cacy of geologic maps as speedometers of and Linked Databases (Kirkham et al., 1995), Gilluly’s (1969) data from North America the geologic rock cycle, we therefore evaluate includes digital data in the form of geographi- (Fig. 1), for example, have a 1 Ma intercept of the relation between areas and ages of exposed cally referenced rock-unit polygons. Associated ~620,000 km2, which is ~2.9% of the total area rock units at the global scale using several newly attribute tables contain area, age, rock type, and of the continent, and a slope of about −0.64 indi- compiled geologic maps. name information for each of 7463 polygons cating that North American rock area is inferred (mean map unit area of ~18,000 km2). Ages of to decrease by ~0.64% for each 1% increase in SOURCES OF DATA rock units are assigned to early, middle, late, rock age.