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
Department of Earth Sciences, Syracuse University, Syracuse, New York 13244, USA
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
1
2
ABSTRACT
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). Areaage 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 × 106 km2/Ma,
respectively.
In contrast to power-law–distributed volcanic and sedimentary rocks that form at
E-mail: [email protected]
†
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 mil-
GSA Bulletin; May/June 2009; v. 121; no. 5/6; p. 760–779; doi: 10.1130/B26457.1; 18 figures; 4 tables.
760
For permission to copy, contact [email protected]
© 2009 Geological Society of America
lion 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.
INTRODUCTION
Since the first complete geologic map of England, Wales, and Scotland was scribed and published by William Smith in 1815, geologic maps
have increasingly become our most important
tools for visually representing variation in the
Earth’s surficial geologic features. Geologic
mapping serves as a linchpin of undergraduate
education in the Earth sciences, and geologic
maps now provide information on the distribution of different types of rocks and structures
for resource discovery, land use decisions, and
hazards assessments. In addition to more practical applications, geologic maps are the basis for
study of the long and rich geologic history of
continents and the planet as a whole (e.g., Veizer
and Jansen, 1979, 1985).
The possibility that geologic maps might provide quantitative insight into this history was
brought into focus by James Gilluly (1969),
who was the first to fully examine relations
between rock age and outcrop area at continental scales. Using nail scissors to cut out and
separate individual rock units represented on
geologic maps of North and South America, he
determined areas from the proportional weights
of map fragments representing each major rock
age and type. Gilluly (1969) recognized that the
log-area of rock exposure decreases with the log
of increasing age (Fig. 1). This realization led
him to conclude that: “The completeness of the
geologic record obviously diminished with the
passage of time, not simply because younger
Geologic maps are tectonic speedometers
South America
Area = 8.2 x 105 Age -0.85
r 2 = 0.85
Mean age = 800 Ma
10,000,000
Area exposed (km2 /m.y.)
rocks come to bury the older, but also because
the younger have been largely derived by the
cannibalization of the older.” Rather than being
a manifestation of lower rates of rock cycling in
the geologic past, Gilluly correctly interpreted
the pattern of decreasing rock area with increasing rock age as a manifestation of the unrelenting importance of tectonic processes of uplift
and associated erosion balanced by generally
equal amounts of subsidence and deposition that
serve to “drive” the geologic rock cycle.
Examination of Gilluly’s (1969) data (Fig. 1)
raises several other questions related to those
geologic processes that control outcrop age
and area. For example, one might wonder why
rock age and exposed area scale approximately
linearly in log-log space. Such “power-law”
relations characterize a wide range of scaleinvariant geologic data (e.g., Turcotte, 1992;
Newman, 2005). Why are area-age data on
geologic maps log-log linear?
The log-area versus log-age relationship identified by Gilluly (1969; Fig. 1) is numerically
described by both an intercept and a slope, the
former being related to amount of new outcrop
formed over some unit of time, and the latter
being related to rates of outcrop area reduction,
either through uplift and erosion or through subsidence and burial by younger units. In the case
of geologic maps, intercept and slope values
must be interrelated because the net area of continental crust has remained relatively constant
over at least the past one billion years or so (e.g.,
Pearson et al., 2007); addition of new (young)
map units to a fixed land area must therefore be
approximately balanced by equivalent loss of
older map areas.
Gilluly’s (1969) data from North America
(Fig. 1), for example, have a 1 Ma intercept of
~620,000 km2, which is ~2.9% of the total area
of the continent, and a slope of about −0.64 indicating that North American rock area is inferred
to decrease by ~0.64% for each 1% increase in
rock age. South American data (Fig. 1) define an
intercept of ~820,000 km2, or ~4.9% of the total
area of the continent, and South American rock
area decreases by ~0.85% for each 1% increase
in rock age (Fig. 1). Taken at face value, these
data suggest that rates of rock cycling in South
America are perhaps ~1.7 (4.9/2.9) times faster
than in North America, and that mean rock age
in South America is somewhat younger (Fig. 1).
Based solely on Gilluly’s study, it is not possible
to unequivocally conclude that values from the
two American continents are in fact statistically
different. Nevertheless, they do serve to exemplify the potential utility of geologic maps in
quantifying long-term rates of rock cycling. In
conjunction with the presupposition of Dutton
(1882) that “Erosion depends for its efficiency
Qt
South America
1,000,000
Tpl
North America
100,000
Sl
Or
Kt
Ms
Tpa
Pa
Tmi
Teo
10,000
Tr
Tpl
Tol
Jr
North America
Area = 6.2 x 105 Age -0.64
r 2 = 0.74
Mean age = 750 Ma
Pm
1000
Cm
100
10
1
Age (Ma)
Figure 1. Ages and areas of geologic map units exposed in North (open diamonds and black
line) and South (gray circles and gray line) America for Phanerozoic periods and epochs
(after Gilluly, 1969). Note decreasing area of outcrop with increasing age, log-log relation of
outcrop age to area, and somewhat lower slope for North American (−0.64) relative to South
American (−0.85) outcrops.
principally upon the progressive elevation of
a region,” it follows that global geologic maps
may serve as excellent recorders of first-order
rates of Earth surface-rock formation and
destruction. In order to further investigate the
efficacy of geologic maps as speedometers of
the geologic rock cycle, we therefore evaluate
the relation between areas and ages of exposed
rock units at the global scale using several newly
compiled geologic maps.
SOURCES OF DATA
Data on areas and ages of rocks exposed at
the Earth’s surface have been compiled for
various rock types, countries, and continents
(e.g., Higgs, 1949; Gilluly, 1969; Bluth and
Kump, 1991; Peucker-Ehrenbrink and Miller,
2002, 2003), but only the data of Blatt and
Jones (1975) encompass major rock types for
all continental land masses. These, however,
are based on ages determined for only 802 randomly selected points across global continents,
a sampling density of about one determination
for each 167,000 km2 (an area about the size of
Wisconsin). To obtain data with higher spatial
density, we tabulated data on areas and ages of
exposed rock bodies as mapped by the Geological Survey of Canada (GSC) and by the Food
and Agricultural Organization (FAO) of the
United Nations Education, Science, and Cultural Organization (UNESCO).
The Geological Survey of Canada Open-File
2915d, Generalized Geological Map of the World
and Linked Databases (Kirkham et al., 1995),
includes digital data in the form of geographically referenced rock-unit polygons. Associated
attribute tables contain area, age, rock type, and
name information for each of 7463 polygons
(mean map unit area of ~18,000 km2). Ages of
rock units are assigned to early, middle, late,
era- or eon-duration intervals, and are broadly
classified as plutons, mixed intrusive and metamorphic terrains, sedimentary, mixed volcanic (volcaniclastic and sedimentary), and tectonic assemblages (schist belts and mélanges).
Because time intervals are of unequal duration,
areas used in our study were normalized for
interval duration using the recent time scale of
Gradstein et al. (2004).
The Geologic World Atlas (Choubert and
Faure-Mauret, 1981), published by the United
Nations at a scale of 1:10,000,000, is a significantly more detailed source of data, but is not
in geographic information system (GIS) format.
We therefore digitally scanned each of the 18
continental map sheets and then determined
rock areas using commercial image analysis
Geological Society of America Bulletin, May/June 2009
761
Wilkinson et al.
Sedimentary
Plutonic and Metamorphic
A
Volcanic
North America
80%
60%
Relative abundance
40%
20%
FAO (1981)
Gilluly (1969)
GSC (1995)
Peucker-Ehrenbrink and Miller (2002, 2003)
Suchet et al. (2003)
Higgs (1949)
B
Earth
80%
60%
40%
software. Pixel counts for outcrop area on the
scanned images were converted to continental
surface area by scaling pixel area to real-world
area in several 1° × 1° areas over each map sheet.
These efforts resulted in the tabulation of ages,
rock types, and areas for 47,705 mapped rock
units (mean exposed area ~2900 km2), each of
which was assigned to one of 36 time bins, ranging from epochs, through lower, middle, and
upper eras or eons. Although some rock units
are assigned to one of up to 50 lithologic subdivisions, many are only resolved as volcanic,
sedimentary, plutonic, or metamorphic. As with
GSC data, FAO rock areas were normalized for
interval duration using Gradstein et al. (2004).
Here we explicitly assume that reported ages
among the four major rock groups as volcanic,
sedimentary, plutonic, and metamorphic lithosomes from either map source represent durations since extrusion, deposition, crystallization,
and peak metamorphism, respectively.
LITHOLOGIC AND AREA-FREQUENCY
DISTRIBUTIONS OF EXPOSED ROCK
UNITS
20%
FAO (1981)
Blatt and Jones (1975)
Meybeck (1987)
GSC (1995)
Gibbs and Kump (1994)
Suchet et al. (2003)
Figure 2. Relative abundances of major rock types exposed at the Earth’s surface as
tabulated in this study compared to estimates made by others for (A) North America
and for (B) all continents. Based on the Food and Agricultural Organization (FAO)
and Geological Survey of Canada (GSC) maps, North American volcanic, sedimentary, plutonic, and metamorphic rocks represent ~11%, 66%, 8%, and 14% of exposures, respectively. Globally, these values are ~9%, 73%, 7%, and 11%, respectively.
Although determination of net areal extent of
different rock types was not the primary objective of this study, our tabulations yielded these
data for all the major continents (Fig. 2 and
Table 1). Based on relative abundances of major
rock types from these two sources, volcanic,
sedimentary, plutonic, and metamorphic rocks
represent 10%–12%, 68%–65%, 9%–7%, and
13%–15% of North American exposures, and
TABLE 1. PROPORTIONS OF DIFFERENT TYPES OF ROCKS EXPOSED OVER
NORTH AMERICA AND ALL CONTINENTS TABULATED FROM THE FAO AND GSC MAPS AND FROM OTHER SOURCES
Source
FAO
GSC
Gilluly (1969)
Higgs (1949)
Peucker-Ehrenbrink
and Miller (2002,
2003)
Suchet et al. (2003)
FAO
GSC
Blatt and Jones
(1975)
Gibbs and Kump
(1994)
Meybeck (1987)
Suchet et al. (2003)
Volcanic
(%)
10
12
8
7
Sedimentary
(%)
68
65
52
88
Plutonic
(%)
9
7
21
4
Metamorphic
(%)
13
15
-
Other
(%)
191
11
Plutonic and
metamorphic
(%)
22
22
403
53
United States2
and Canada
8
67
8
16
-
25
North America
Average
10
9
58
66
10
15
-
33
21
Earth
Earth
7
10
77
70
8
6
8
15
-
16
21
Earth
8
66
9
17
-
26
Earth
7
73
4
-
-
Earth
Earth
Average
8
8
8
66
65
70
7
13
Area
North America
North America
North America
United States2
1
“Undetermined.”
Exclusive of Hawaii.
Plutonic and “undetermined.”
4
Includes 27.5% reported as “fold belts.”
Abbreviations: FAO—Food and Agricultural Organization; GSC—Geological Survey of Canada.
2
3
762
Geological Society of America Bulletin, May/June 2009
20
-
26
28
23
Geologic maps are tectonic speedometers
Lithotopes = 7462
–0.0107
Frequency = 688 e
1000
Frequency
10%–7%, 70%–77%, 6%–8%, and 15%–8%
of global exposures, respectively. Values for
North America and for all continents are in
good agreement with values reported from more
general studies by Blatt and Jones (1975), Gibbs
and Kump (1994), Gilluly (1969), Higgs (1949),
Meybeck (1987), Peucker-Ehrenbrink and
Miller (2002, 2003), and Suchet et al. (2003).
With respect to sizes of lithosome outcrop
areas, even perfunctory examination of almost
any regional geologic map leads to the general observation that there are relatively more
mapped lithosomes of small size than of large
size, that small units tend to be spatially associated with other small ones while large units are
near other large units, and that lateral lithosome
extent is commonly related to both lithology and
degree of tectonic deformation. Laterally extensive, flat-lying sedimentary and volcanic successions generally occupy one end of the spectrum,
while smaller exposures of intensely deformed
plutonic and metamorphic complexes are at the
other. It is also the case that areas of geologic
map units are, by definition, dependent on the
detail of subdivision desired by the geologistcartographer making the map. Numbers and
sizes of mapped units must sum to the total area
of the region in question. As a result, numbers
and sizes of small units must show a systematic relation to numbers and sizes of the large
units; a greater abundance of smaller outcrops,
for example, must co-occur with either fewer
numbers or smaller areas of the large. This truism requires that sizes (areas) and frequencies
(numbers) of geologic map units exhibit certain
relations to each other.
McElroy et al. (2005) described size-frequency
distributions for several types of mosaics developed across the Earth’s surface, such as large
fluvial drainage basins and geopolitical divisions
(i.e., countries), and pointed out that these distributions are similar to those exhibited by exposed
lithosome areas in global geologic maps. They
contend that these similarities emerge because
mosaic element diameters are exponentially distributed (Fig. 3). Such exponential size-frequency
distributions are the same as those arising from
the classic “broken-stick model” (e.g., Baumiller
and Ausich, 1992) in which divisions (such as
map unit boundaries) along some linear transect
(such as across a geologic map) are randomly
distributed. That is, area-frequency distributions
of individual rock types on geologic maps are
closely approximated by the distribution that
would result from the partitioning of continental
surfaces into n subregions, such that distances
between each boundary along a transect are
exponentially distributed (e.g., Fig. 3). Exponential distributions are anticipated when boundaries between different rock types occur randomly.
Rock area (km2)
r 2 = 0.934
100
10
100
200
300
400
Rock area (km2)
Figure 3. Size-frequency distributions of square roots (~diameters) of rock
body outcrop areas (diamonds) derived from the Geological Survey of
Canada (GSC) map. These represent area-frequencies of the 7460 rock
exposures that collectively make up the Earth’s 135 × 106 km2 ice-free surface. Bin sizes are 10 km2; heavy line is the best exponential fit to the data.
Hence, geologic map area-frequencies suggest
that lateral occurrences of exposed lithosome
boundaries approximately result from geologic
processes that yield a continuous random probability of crossing rock-type boundaries as one
transects a mapped surface. That is, in a statistical sense, the spatial occurrence of map unit
boundaries is largely indeterminate. For example, the 7462 areas of volcanic, sedimentary, plutonic, and metamorphic exposure mapped by the
GSC are closely approximated by a function that
describes the sizes of mosaic elements on a randomly partitioned surface. Frequency of occurrence (F) of any rock body of some given area
(A) is closely approximated (Fig. 4) by the relation in Equation 1, where N is the total number of
lithosome exposures designated over the Earth’s
surface (volcanic, sedimentary, plutonic, and
F ( A) = e − k
A/ π
(1)
metamorphic exposures are 892, 4095, 1008,
and 949, respectively), and k is the incidence of
occurrence over the Earth’s surface, expressed
as Equation 2, where
k=
Nπ
2Ta
(2)
Ta is the total area of mapped volcanic, sedimentary, plutonic, and metamorphic rock (10.1,
97.2, 8.0, and 19.8 × 106 km2, respectively).
Comparison of this theoretical size-frequency
distribution to the areal extents of volcanic, sedimentary, plutonic, and metamorphic exposures
from the GSC map yields Pearson correlation
coefficients of 0.83, 0.92, 0.79, and 0.89, respectively (Fig. 4). This good agreement suggests
that a theoretical model, in which geologic map
area is randomly subdivided, closely approximates sizes of lithologic divisions of the Earth’s
surface. Values of k, which correspond to the
probability of crossing a mapped unit boundary
per linear kilometer transect on the GSC map,
for volcanic, sedimentary, plutonic, and metamorphic rocks are 0.0121, 0.0084, 0.0142, and
0.0091 per kilometer, respectively.
Only two variables, the number of mapped
geologic units and the total area under consideration, determine the frequencies of lithosome
exposure area. Although the amount of continental land area is finite and, to a first approximation, invariant during the Phanerozoic, the
numbers of lithosome exposures may be largely
a matter of definition. Mean exposure area on
the FAO maps, for example, is ~2900 km2 (an
area ~70% the size of Rhode Island), while the
mean area on the GSC map is ~18,000 km2
(an area ~4.5 times the size of Rhode Island).
As noted above, values of k for volcanic, sedimentary, plutonic, and metamorphic exposures
on the GSC map are 12.1, 8.4, 14.2, and 9.1
per thousand linear kilometers, respectively.
In other words, the distribution of bodies of
each rock type is such that, at this scale of GSC
Geological Society of America Bulletin, May/June 2009
763
Wilkinson et al.
Lithosomes = 4095
Mean size = 21,949 km2
r 2 = 0.83
100
r 2 = 0.92
1000
100
Volcanic
10
C
Frequency
B
Sedimentary
Lithosomes = 1008
Mean size = 7381 km2
D
Lithosomes = 949
Mean size = 19,299 km2
r 2 = 0.79
100
10
10
r 2 = 0.89
Plutonic
10,000
Rock area (km2)
100
10
Metamorphic
1000
Frequency
Lithosomes = 892
Mean size = 10,381 km2
1000
Frequency
Frequency
A
10,000
Rock area (km2)
Figure 4. Areas of volcanic, sedimentary, plutonic, and metamorphic rock exposures extracted from the Geological Survey of Canada
(GSC) map. The solid lines are not regressions; they are model lines derived presuming that outcrop areas are approximately equidimensional in all directions (are roughly circular) and that land area is randomly segmented into subregions of homogeneous lithology. They are
the ideal distributions of Poisson magnitude frequencies that would result from populations of lithosome elements with randomly delimited
boundaries. Areas of such elements are dependent only on number of mapped units and total mapped area for each rock type. For each rock
type, lithosome size-frequency is closely approximated by this model distribution in which k defines the probability of exiting that rock area
(crossing some lithosome boundary) per kilometer of transect.
mapping, one would anticipate crossing about a
dozen lithologic boundaries for each thousand
kilometers of land surface traversed. While differences between these numbers reflect the fact
that exposures of mapped volcanic and plutonic rocks are somewhat smaller than those of
metamorphic or sedimentary complexes, their
absolute magnitudes more closely relate to the
continental scale of lithologic variation represented by these maps. Although more detailed
mapping of smaller areas would yield higher
values of k (volcanic, sedimentary, plutonic,
and metamorphic values from the FAO maps
are 27.4, 22.4, 33.2, and 18.2 per thousand
linear transect kilometers, respectively), the
nature of the size frequency (Fig. 4) remains
unchanged.
While lithosome exposure area data suggest that, in aggregate, continental surfaces
can be adequately described as being randomly
partitioned, in actuality there is considerable
764
nonrandom spatial structure in the distribution
of exposure sizes. Rocks of similar type are
obviously associated in space, and it therefore
follows that larger map units will be clustered
in space with larger and smaller with smaller.
Thus, the probability of crossing a map boundary (k) in a given surface transect also depends
on where that transect happens to be located, a
fact that derives from the spatially structured
distribution of crustal deformation and uplift
and subsidence apparent on any geologic map.
AGE-FREQUENCY DISTRIBUTIONS OF
EXPOSED ROCK UNITS
Age-frequency distributions of continental
rock exposures from FAO and GSC maps are
closely approximated by a power-law distribution in which the relation between logs of ages
and logs of areas defines a straight line (Fig. 5,
Equation 3) as:
A = 8.8 × 10 6 Q −0.86
(3)
with area (A) expressed in km2/Ma and rock
unit age (Q) expressed in Ma. Such a relation
describes a steady-state system in which an
“original” (intercept at 1 Ma) outcrop area of
~8,800,000 km2 decreases as it ages by ~0.86%
for each 1% increase in age. Given a total icefree continental land area of ~135 × 106 km2,
this intercept value requires that ~6.5% of continents is resurfaced with younger volcanic and/
or sedimentary rocks every million years. The
FAO and GSC data yield trends (Fig. 5) that
differ only slightly. Because the FAO maps are
approximately six times more detailed than that
of the GSC, this similarity shows that mapping
detail is not a factor in determining relations
among frequencies of different exposure areas.
When these data are divided into volcanic,
sedimentary, plutonic, and metamorphic rock
lithosome exposures (Fig. 6), it becomes apparent
Geological Society of America Bulletin, May/June 2009
10,000,000
All lithologies
1,000,000
100,000
GSC Area = 8.32 x 106 Age–0.852
10,000
FAO Area = 9.28 x 106 Age–0.862
1000
100
10
Age (Ma)
Figure 5. Log-log plot of age versus area relations from global geologic maps by the Food
and Agricultural Organization (FAO) (solid black line and open circles) and the Geological
Survey of Canada (GSC) (solid gray line and gray diamonds). Both data sets describe nearly
indistinguishable power-law relations (dashed gray line) between exposure area and age in
which outcrop area decreases by ~0.86% for each 1% increase in rock age.
Volcanic
10,000,000
Area exposed (km2/m.y.)
that the general form of the age-frequency distribution for each group is closely related to those
processes responsible for their formation. Rocks
that originate (that acquire their “age”) at the
Earth’s surface exhibit power-law distributions
with modal ages near zero, a youth reflecting
their initial abundance at or near exposed continental surfaces. Their age-frequency distributions are nearly identical to that exhibited by
all rock units (Figs. 6 and 7) because more than
80% of global outcrop consists of volcanic and
sedimentary sequences (Table 1). In contrast,
plutonic and metamorphic age-frequency distributions derived from both FAO and GSC maps
are approximately lognormal in form (Fig. 7). In
addition, the modal age of plutonic lithosomes
is markedly younger than that of metamorphic
suites (Table 2). FAO maps yield modal ages of
154 and 697 Ma for plutonic and metamorphic
lithosomes compared to 174 and 3001 Ma for
GSC maps. Globally, the most areally extensive
sedimentary and volcanic suites are the youngest, plutonic rocks have modal ages that are
mid-Phanerozoic in age, and most metamorphic
suites are older (Fig. 7). These aspects of agefrequencies are evident in data from most of the
major continents and are also apparent in geologic map data tabulated by others (Table 2).
That volcanic and sedimentary rock agefrequencies exhibit power-law distributions, and
that plutonic and metamorphic rock age-frequencies are distributed lognormally, implies a
linkage between the nature of the age-frequency
distribution and the crustal depth at which different rock types tend to form. Qualitatively,
because these map data represent rock “abundance” at the Earth’s surface, and because
volcanic and sedimentary rocks originate on
this surface, modal ages of sediments and volcanics must be very young (Figs. 7A and 7B).
In contrast, because intrusive rocks crystallized at depth and had to travel to the surface
before being designated on some geologic map,
exposed intrusive rocks must have a modal
age that is older than that of sedimentary and
volcanic rocks. Tectonic uplift and associated
denudation serve to expose intrusive rock bodies, and, depending on depths of their formation
and mean rates of uplift, significant amounts of
geologic time must pass before this can occur.
The decline in pluton area (from the Paleozoic
into the Precambrian, Fig. 7C) of rocks older
than modal age reflects the fact that tectonism
eventually serves to destroy some of these midcrustal lithosomes as they move upward through
the exposure window at the Earth’s surface or
downward where they undergo metamorphism.
Similarly, metamorphic rocks originate at even
greater crustal depths than most intrusive rocks,
and their modal ages at the surface (Fig. 7D)
Area exposed (103 km2/m.y.)
Geologic maps are tectonic speedometers
Sedimentary
Plutonic
1,000,000
Metamorphic
100,000
10,000
1000
100
1000
100
10
Age (Ma)
Figure 6. Log-log plot of relations between age and total outcrop area for major rock
groups from the Food and Agricultural Organization (FAO) maps. Note log-linear
decrease in abundance of sedimentary and volcanic rocks with increasing age similar to that for all rock types (Fig. 5) and significantly different patterns for plutonic
and metamorphic (basement) rock types. GSC—Geological Survey of Canada.
Geological Society of America Bulletin, May/June 2009
765
Wilkinson et al.
A
B
Sedimentary
600
20
Volcanic
10
200
5
C
D
8
Plutonic
15
Metamorphic
10
6
Area exposed (103 km2/m.y.)
Area exposed (103 km2/m.y.)
15
400
4
5
2
1000
100
10
1000
Age (Ma)
100
10
Age (Ma)
Figure 7. Log-age versus area relations for volcanic, sedimentary, plutonic, and metamorphic rocks from the Food and Agricultural Organization (FAO) (solid black lines) and the Geological Survey of Canada (GSC) (solid gray lines) data. Note that volcanic and sedimentary sequences
have Neogene modes, whereas the modes for intrusive complexes lie in the Paleozoic, and those for metamorphic suites lie in the Precambrian.
must, therefore, be older than intrusive rocks at
the surface. Given these qualitative distinctions,
it is likely that rock age-frequency distributions
for populations of rock bodies that formed at different depths might be used to determine mean
rates of crustal uplift and subsidence.
A STEADY-STATE MODEL
Support for the general interpretation outlined
above can be found in ages of three widespread
and abundant types of hydrothermal ore deposits.
These have been discussed elsewhere at length
(Kesler and Wilkinson, 2006, 2008; Wilkinson
and Kesler, 2007) and will be reviewed only
briefly here. The important point is that epithermal silver-gold (n = 152), porphyry copper (n
= 455), and orogenic gold (n = 66) deposits, all
of which form along continental margins during
tectonic convergence, exhibit age-frequencies
that are lognormal in form (as are plutonic and
metamorphic age-frequencies), but differ systematically with respect to their modal ages
and emplacement depths (Fig. 8). Epithermal
766
Ag-Au, porphyry Cu, and orogenic Au deposits,
which form at average depths of ~0.5, 1.9, and
10 km, exhibit age modes at ~2, 11, and 199 m.y.,
respectively, reflecting their increasing modal
age with depth of ore emplacement. Because
ages of exposed ore deposits presumably record
information about depths of ore formation and
subsequent tectonic uplift, exhumation, and
exposure, Kesler and Wilkinson (2006, 2008)
and Wilkinson and Kesler (2007) formulated a
general time-depth model of ore deposit crustal
emplacement and tectonic dispersal that is in
good agreement with observed age-frequencies.
Here, we generalize this time-depth model in
order to further examine relations between geologic map age-frequency distributions and those
continent-scale tectonic processes that give rise
to greater or lesser exposure with age.
TABLE 2. MODAL AGES OF PLUTONIC AND
METAMORPHIC ROCK LITHOSOMES TABULATED FROM DIFFERENT SOURCES*
Plutonic
Metamorphic
Source
Area
(Ma)
(Ma)
FAO
North America
127
467
FAO
Eurasia
154
529
FAO
Global
154
697
GSC
North America
107
3051
GSC
Eurasia
306
494
GSC
Global
174
3001
1
Peucker-Ehrenbrink and Miller
United States and
169
2651
(2002, 2003)
Canada
Gilluly (1969)
North America
107
–
Higgs (1949)
United States1
156
–
*Intrusive modal ages are younger than metamorphic ages in all instances.
1
Exclusive of Hawaii.
Abbreviations: FAO—Food and Agricultural Organization; GSC—Geological Survey of Canada.
Geological Society of America Bulletin, May/June 2009
Geologic maps are tectonic speedometers
Proportion of exposed deposits
Orogenic Au
n = 66, Emp Dpt = 10 km
Mode = 199 Ma
Porphyry Cu
n = 455, Emp Dpt = 1.9 km
Mode = 11 Ma
Epithermal
n = 152, Emp Dpt = 0.5 km
Mode = 3 Ma
10%
5%
100
Age (Ma)
10
Figure 8. Age-frequency plots for epithermal Ag-Au (white bars), porphyry Cu (light-gray bars), and Neoproterozoic and Phanerozoic orogenic Au (dark-gray bars) deposits based on age compilations of Garwin et al. (2005), Kesler et al. (2004), and Simmons
et al. (2005), Singer et al. (2005), and Goldfarb et al. (2005), respectively (modified from Wilkinson and Kesler, 2007). Solid lines
are least-squares, best-fit lognormal distributions to these age frequencies. Note that modal age increases with emplacement depth
(Emp Dpt), and that frequency distributions of all three types of deposits are well described by the lognormal distribution.
We begin with the simplifying assumption
that the rock cycle works at a secularly invariant rate. This presumption is probably not true
all the way back into the early Precambrian
as, forward in time, the planet gradually loses
heat needed to drive plate tectonics, and the
rock cycle should therefore slow. However, we
believe this to be a valid first-order approximation as here we are primarily interested in establishing an association between the general form
of rock age-frequencies and average rates of
rock cycling. Any shorter-term deviations from
this starting assumption (manifest as differences
between observed and model age-frequencies)
are acknowledged to record exceptions from this
assumption. The model assumes a steady-state
system with respect to: (1) rates of lithosome
formation among each of the four major rock
groups, (2) characteristic depths of rock formation in or on the Earth’s continental crust, and
(3) rates of tectonic uplift and/or depression that
serve to change the vertical positions of each
lithosome relative to the surface of the Earth’s
continental crust. Here we merely ask the first-
order question: If formation and destruction
of the commonly classified rock types were to
proceed at an invariant rate over typical depth
ranges, what constraints on average speed of the
rock cycle can be derived from areas and ages
of exposed rock bodies? Temporal evolution of
crustal depths of rock formation and rates of
rock formation or tectonism are not incorporated into nor implied in any of our models.
We formulate the model as a simple random
walk in geologic time-crustal depth space across
a numerical grid, with the horizontal axis representing elapsed time (age) and the vertical axis
representing depth beneath the continental surface (e.g., Figs. 9 and 10). Within this domain,
a hypothetical amount of rock comprising some
lateral extent is deposited or emplaced on the
surface or at some characteristic crustal depth.
In subsequent time steps, this rock then moves
vertically (up or down) as a random walk in
crustal depth and geologic time space. Any proportion of total lithosome area can be displaced
vertically a fixed distance (∆X) relative to the
Earth’s surface during each interval of model
time (∆t); it can undergo uplift, it can remain at
its current crustal depth, or it can be buried to
some greater depth. The amount of per-modelstep vertical displacement is defined here as the
“tectonic step” of the random walk.
Computationally, we emplace lithosomes over
some specified average range of crustal depths
(formation depth, Table 3), and iteratively input
different model values of: (1) the areal extent
of lithosomes that form at that mean depth per
unit time (formation rate, Table 3), and (2) the
proportion of lithosome area that experiences
uplift, stasis, or subsidence during the model run
(“Up-St-Dn,” Table 3). For each iteration, we
calculate proportions of the initially emplaced
lithosome area that is presently at different
crustal depths under different assumptions of
formation depth and subsequent tectonic dispersion (uplift, stasis, and/or subsidence). Because
here we are interested primarily in “age” frequencies of lithosome areas that have arrived at
the upper absorbing boundary (i.e., the Earth’s
erosional surface), the model is calibrated by
comparing, by conventional least-squares meth-
Geological Society of America Bulletin, May/June 2009
767
Wilkinson et al.
Crustal depth (km)
–10
2
–20
–30
E
–40
–50
–60
Depth frequency — 500 Ma
Frequency
1
2
D
Depth frequency — 1500 Ma
1
2
C
Depth frequency — 2500 Ma
1
B
Age Frequency — 0 m
A
Crustal depth (km)
–10
–20
–30
–40
–50
–60
3000
2500
2000
1500
1000
500
Age (Ma)
Figure 9. (A) Time (horizontal) versus depth (vertical) plot of random walk paths (gray lines) taken by 100 hypothetical plutonic lithosomes that were emplaced at a crustal depth of 10 km (arrow) and allowed to disperse vertically at a rate of 500 m/m.y. (B) Frequency distribution (gray curve) of “ages” (numbers of walk steps) of presently
exposed lithosomes, which is the number of thin gray lines terminating at the crustal surface (heavy horizontal
gray line in A). Like map data on plutonic and metamorphic rocks, these define a strongly skewed distribution,
here with a modal age of 58 m.y. (C–E) Depth-frequency distributions of model lithosomes of different ages.
ods, the age-frequency of “exposed” model
areas to the empirical age-frequency distributions (e.g., Fig. 11). In determining the best-fit,
age-frequency distribution of crustal rocks, we
also arrive at predictions of the amount of each
type of rock at depth in the Earth’s crust (e.g.,
Figs. 10 and 11). These include: (1) the total
areal extents and depths of each type of rock
within the model crust, (2) the modal age of
768
exposed lithosomes as derived from the model,
(3) the modal depth of each type of rock within
the model crust, and (4) the proportion of lithosomes that have been buried and preserved versus the proportion that have been uplifted and
removed by erosion over model time.
The largest uncertainty associated with this
model is making the “correct” choice of crustal
depths of formation among the four major rock
types. The choice of appropriate depth is obviously most secure for rock suites forming at the
Earth’s surface but becomes increasingly open
to discussion for those that originate at greater
crustal depths. Virtually all volcanic and sedimentary rocks now exposed at the Earth’s subaerial surface have formed essentially on that
surface, and their abrupt decrease in area with
increasing age (Figs. 6 and 7) largely reflects
Geological Society of America Bulletin, May/June 2009
Geologic maps are tectonic speedometers
A — 0 km (modal age = 0 Ma)
B — 5 km (modal age = 15 Ma)
C — 10 km (modal age = 58 Ma)
D — 15 km (modal age = 125 Ma)
E — 20 km (modal age = 218 Ma)
E
D
Crustal depth (km)
–10
C
B
–20
A
–30
–40
–50
1000
100
10
Age (Ma)
Figure 10. Time versus depth plot of random walk paths as in Figure 9, but here on the lower panel, formation is
at 20 km (arrow), and the time (horizontal) axis is plotted as a log scale. The upper panels (A–E) show frequency
distributions (gray dashed curves) of paths transected above the formation depth of 20 km. The frequency distribution in (A), for example, represents lithosome ages (walk paths intersected) along a transect at a depth of
20 km, while the frequency distribution in (E) represents lithosome ages along the surface, which is 20 km above
the formation depth. Conversely, the frequency distribution in (A) would be that expected if rock formation took
place at the Earth’s surface, as is the case for volcanic and sedimentary sequences.
subsequent area reduction by uplift and erosion
and/or subsidence and burial. Semiquantitatively, depths of emplacement of granitic plutons
are also reasonably well constrained, and many
studies interpret the tops of the shallowest of
these to intrude sedimentary successions and to
form at depths of no less than several kilometers.
The literature on maximum depths of plutonism
is more meager, but typical metamorphic lith-
ologies characteristically surround more deeply
emplaced igneous bodies. Average depths of
metamorphism are even less well constrained.
Although pressure-temperature (P-T) paths have
now been estimated for hundreds of metamorphic suites, we are unaware of any tabulation of
mean depths and/or ranges of depths for regionally metamorphosed lithosomes. Age-frequency
distributions for lithosomes conventionally
mapped as “plutonic” require a somewhat shallower average, and narrower range, of emplacement depths than those conventionally mapped
as “metamorphic,” but it is difficult to readily
arrive at more rigorous depth estimates.
However, this scarcity of data on means and
ranges of depths of origination for plutonic and
metamorphic suites is not fatal to the use of the
random tectonic walk model for understanding
Geological Society of America Bulletin, May/June 2009
769
Wilkinson et al.
map-unit, age-frequency distributions. There
are two main reasons for this reprieve. First, any
uncertainty associated with estimating means
and ranges of actual crustal depths of rock formation primarily affects the random walk model
by increasing or decreasing theoretical estimates
of the amount (distance) of vertical displacement
needed to bring some map-derived, rock-unit
modal age to the Earth’s surface (e.g., Fig. 7;
Table 2). In other words, the depths at which
different lithosomes form and their modal ages
(e.g., Fig. 7) are only related (in the model calculation) by the requisite amounts of vertical rates
of tectonic movement needed to bring these two
parameters into agreement. Given some modal
age, overestimation or underestimation of formation depth will merely translate into larger or
smaller tectonic steps, respectively, that serve to
disburse all, and ultimately expose some, of this
population of lithosomes.
Second, and related to these dependencies
between tectonic step size and emplacement
depth, here we are primarily concerned with a
determination of some mean rate of continental
tectonism that serves to drive the global geologic rock cycle. Thus, it follows that rates of
rock uplift and erosion or subsidence and burial
that serve to control age-frequency distributions for any one of the four major lithosome
types should also operate at the same rate for
the other three. If so, we can then proceed by
determining the best fit between model and
map age-frequency distributions simultaneously
(e.g., Fig. 11) while assuming a similar tectonic
step for each, and then determine if means and
ranges of formation depths seem reasonable in
light of independent geologic data (Table 3).
MODEL RESULTS
Best agreement between model and observed
age-frequency curves (Fig. 11) is found when
the tectonic step for the vertical dispersion of
lithosomes is about half a kilometer per million years when there is no significant bias
to the tectonic random walk (uplift ≅ stasis ≅
subsidence), and when volcanic, sedimentary,
plutonic, and metamorphic associations are
presumed to originate at crustal depths of 0.2
± 0.3, 0.1 ± 0.1, 10.0 ± 3.1, and 25.0 ± 5.1 km,
respectively (Table 3). The FAO area-frequency
distribution for volcanic rock (Fig. 11), for
example, is most closely matched with a model
distribution derived when presuming: (1) that
rates of uplift (33%), stasis (34%), and subsidence (33%) are about equivalent; (2) that
volcanic rocks originate at the Earth’s surface
(200 ± 300 m); and (3) that volcanic lithosomes
form at a rate of ~2 × 106 km2/m.y. (Table 3).
These values result in a model age-frequency
770
TABLE 3. MAP DATA 1 AND MODEL2 PARAMETERS
FOR AGE-FREQUENCIES OF GLOBAL ROCK TYPES (FIG. 11)
Volcanic
Sedimentary
Plutonic
Metamorphic
33-34-33
29-41-30
34-32-34
36-28-35
Up-St-Dn2
%
Formation
0.2 ± 0.3
0.1 ± 0.1
10.0 ± 3.1
25.0 ± 5.1
km
2
depth
2,053,932
39,545,996
4,186,012
6,353,460
km2/Ma
Formation rate2
Modal age2
0
0
142
953
Ma
4.0%
3.8%
39.3%
61.7%
%
Extant2
2
96.0%
96.3%
60.7%
38.3%
%
Eroded
2
0.077%
0.088%
0.060%
0.045%
%
Exposed
m/Ma
Modal
Surficial
Surficial
70
26
(Formation depth
exhumation
divided by modal age)
rate2
Tectonic
532
511
539
552
m/Ma
step2
Model exposed2
5,995,331
132,474,490
9,528,877
10,748,329
km2
Actual exposed1
9,738,735
104,277,071
10,168,638
11,471,408
km2
Note: Up-St-Dn refers to proportions of tectonic movement up, stationary, or down with each time step;
formation rate is lateral lithosome area per unit time; extant, eroded, and exposed are relative to total
lithosome area; modal exhumation rate is formation depth divided by modal age.
with a modal age of 0 Ma (in agreement with
map data), and suggest that, of all volcanic lithosomes ever formed, ~4% are currently buried
beneath the Earth’s surface, and ~96% have
been destroyed by subsequent erosion (Table 3).
The tectonic step needed to derive this best-fit,
volcanic rock model age-frequency is 532 m of
vertical displacement per million years, and the
model amount of exposed volcanic lithosome
(0.08% of all volcanic rocks produced) is ~6 ×
106 km2 (compared to a FAO-mapped area of
~9.8 × 106 km2). Similar metrics are derived for
sedimentary, plutonic, and metamorphic lithosomes (Fig. 11; Table 3).
Biases to Tectonic Diffusion
Formulation of the general random-walk
model presumes that total areas of model lithosomes experience equal magnitudes of uplift,
stasis, or subsidence with each time interval
(Figs. 9 and 10). However, when applying
the model to data on age-frequency distributions, we had no compelling reason a priori to
believe that this equality was appropriate. During model runs, biases to random walks were
therefore unconstrained, and crustal dispersion
was allowed to range from 100% subsidence
to 100% stasis to 100% uplift, and all possible
combinations thereof (but summing to 100%).
Somewhat surprisingly, closest agreement to
observed age-frequency distributions for each
of the four major rock types considered here
(Fig. 11) was achieved when proportions of
uplift, stasis, and subsidence were about the
same (Table 3). In other words, the model of
random tectonic diffusion is in closest agreement with geologic map data and has no
important bias toward or away from the Earth’s
surface; neither uplift nor subsidence has
predominated during the formation and sub-
sequent aggregate dispersion of crustal rocks,
at least at the global scale.
This conclusion is somewhat surprising in
view of the fact that rocks are probably most
rapidly “cycled” along convergent orogens,
and these are regions that might be thought to
be the focus of uplift and exposure, particularly
with respect to plutonic and metamorphic associations. How can it be that rocks that are primarily uplifted and destroyed along convergent
margin settings exhibit map age-frequencies
suggesting that they also experience nearly
equal amounts of subsidence? The most likely
explanation is that orogenic convergence also
acts to thicken the crust, causing significant
amounts of burial both by subsidence and
thrusting, as well as uplift and erosion (e.g.,
Haschke et al., 2002; Pedreira et al., 2003).
Tectonic Diffusion, Map Areas, Geologic
Time, and Crustal Depth
Several aspects of the geologic rock cycle are
clarified by relations apparent from data on the
geologic maps discussed here: (1) volcanic and
sedimentary lithosome area-frequency distributions exhibit primarily power-law distributions,
while those for plutonic and metamorphic lithosomes are closely lognormal in form; (2) modal
ages for each of the four major rock groups
increase with depth of rock formation; (3) sedimentary and volcanic distributions experience
area loss (by erosion and burial) from the time
of rock formation, whereas those of plutonic
and metamorphic rocks reflect a (younger than
modal age) time interval of uplift and exhumation prior to subsequent area loss by erosion and
burial; and (4) age-frequencies for each of the
major rock types are closely approximated by
distributions anticipated for lithosomes forming
at characteristic crustal depths that then undergo
Geological Society of America Bulletin, May/June 2009
Geologic maps are tectonic speedometers
A
B
20
Sedimentary
Volcanic
15
400
10
200
5
C
D
15
8
Plutonic
Metamorphic
10
6
4
5
Area exposed (103 km2/m.y.)
Area exposed (103 km2/m.y.)
600
2
1000
100
10
1000
Age (Ma)
100
10
Age (Ma)
Figure 11. Log-age versus area relations for volcanic, sedimentary, plutonic, and metamorphic rocks from the Food
and Agricultural Organization (FAO) (1981; solid gray lines) data and best-fit, random-walk model approximations
(e.g., Figs. 10A–10E). Model parameters derived from each curve are listed in Table 3. All four model curves are
derived when presuming that global rates of uplift and subsidence are approximately equal (there is no bias to the
random walk) and that global rates of vertical tectonism are approximately a few hundred meters per million years.
largely random uplift and subsidence at rates on
the order of about half a kilometer per million
years. Fuller understanding of these relations
necessitates additional consideration of variations in three interrelated geologic parameters—
lithosome area, crustal depth, and geologic time.
Systems of random walks (e.g., Figs. 9
and 10) exhibit many characteristics of agefrequencies derived from geologic maps. With
increasing number of time steps (age), lithosome paths become increasingly dispersed relative to their original formation depth. At any
specified number of time steps (age), lithosome
depths comprise normally distributed populations relative to their starting depths, and depth
variance increases linearly with time (e.g.,
Figs. 9C–9E). Moreover, increase in variance
(V) of the normally distributed depth population is only dependent on age (A) and lateral
(tectonic) step size per unit time (T) as:
2
V = TA2 .
3
(4)
The normal distribution of rock lithosomes at
any crustal depth (x) is therefore approximated
by the probability density function:
f (x) =
(x µ)
−
1
e 2V ,
2 πV
−
2
(5)
where µ is the mean of the distribution (crustal
depth of lithosome formation).
The net effect of such tectonic depth dispersion is that, with increasing age, the population
of vertical distances (depths) of lithosomes from
their original depth of rock formation and the
present Earth’s subaerial surface behave in a predictable manner (Fig. 12). Moreover, presumption of mean volcanic and sedimentary rock formation at the Earth’s surface, and mean plutonic
and metamorphic rock formation at depths of
~10 and ~25 km, respectively (Table 3), yields
good agreement between observed and modeled
age-frequencies (Fig. 11) when T is about half a
kilometer per million years.
OTHER MEASURES OF ROCK-CYCLE
“SPEED”
Volcanic, sedimentary, plutonic, and metamorphic rock age-frequencies from both FAO
and GSC maps suggest that first-order aspects
of the geologic rock cycle primarily proceed in
a conceptual system where tectonic processes
act to progressively disperse bodies of crustal
rock vertically relative to continental surfaces.
This expression of tectonic diffusion, coupled
with Earth-surface erosion that acts as an
efficient absorbing boundary, serves to effectively describe the major features of map agefrequencies (Fig. 11). Importantly, the rather
significant differences in the general structure
of volcanic, sedimentary, plutonic, and metamorphic rock age-frequencies (Figs. 6 and 7)
are each closely approximated (Fig. 11) when
presuming that the “step” size of an unbiased
(uplift ≅ stasis ≅ subsidence) random tectonic
walk (Figs. 9 and 10) is on the order of about
half a kilometer per million years (Table 3).
Because compiling even approximate error
estimates for data and assumptions employed
in the derivation of this value is probably not
possible, the best that can be said is that geologic maps suggest mean rates of tectonism on
the order of a few hundreds of meters per million years.
Continental Tectonism from Rates of Erosion
As context for this inferred amount of vertical tectonism, estimates of volumetric fluxes
of sediment to the Phanerozoic global sedimentary reservoir from data in Ronov (1980)
Geological Society of America Bulletin, May/June 2009
771
Wilkinson et al.
4%
80
3%
35
2%
1%
0%
30
25
20
D
1
ep 5
th
70
Depth frequency
Lithosome area
5%
10
60
50
e
e
Ag
(k 5
m
qu
rf e
20
10
)
0
y
nc
a)
40
30
ge
A
(M
0
Figure 12. Random walks in age-depth-frequency space (e.g., Fig. 9) showing the proportion of hypothetical lithosomes (Z axis) as a function of age (X axis) that are constantly emplaced at a crustal depth of 5 ± 0.5 km (Y axis).
The X-axis parallel slice at a depth of 0 km (green line) is the (approximately lognormal, e.g., Fig. 11C) agefrequency distribution of currently exposed lithosomes that formed at a crustal depth of 5 km. Arrow is located
at the modal age of 17 Ma. Lines normal to “Age” (e.g., blue line) are depth-frequency distributions of lithosomes
of various ages (e.g., Figs. 9C–9E). Heavy yellow line at an emplacement depth of 5 km follows the approximately
power-law age (X axis) -frequency (Z axis) trend of rock (such as volcanic and sedimentary, Fig. 11A) now exposed
at the Earth’s surface (which is approximately their depth of formation).
and independent estimates of total areas of
subaerial continental crust undergoing erosion
from Scotese and Golonka (1992) allow for
calculation of mean rates of continental denudation over the past ~542 m.y. of Earth history.
These range from a middle Triassic low of
~4 m/Ma to a Pliocene high of ~53 m/Ma and
an average of ~16 m/Ma for all of Phanerozoic
time (Wilkinson, 2007). Similarly, a literature
on the general magnitude of riverine sediment
fluxes (e.g., Summerfield and Hulton, 1994;
Syvitski et al., 2005), suggests that the current
annual riverine flux of weathering products to
global oceans is equivalent to that required to
reduce all subaerial land surfaces by ~62 m/
Ma. Assuming that the rock volume–derived
and river flux–derived values are approximately
correct (that continent-wide denudation occurs
at rates on the order of a few tens of meters per
million years), it is important to note that these
rates are about an order of magnitude lower
than the rates inferred from geologic map agefrequencies (hundreds of meters per million
years). Why are rates of continental erosion that
772
are determined from sedimentary rock volumes
and modern river sediment loads only a fraction
of those determined from age-frequencies of
the Earth’s exposed rock lithosomes? The reason for this disparity is that erosion rates from
rock volumes and river fluxes are both determined across the entirety of exposed continental (land) surfaces, whereas those “rock cycle”
processes of uplift, erosion, and volcanism that
serve to impart the greatest change to map areafrequencies have largely operated along the
Earth’s major orogenic belts. The magnitude of
this difference (tens of meters per million years
across all continents versus hundreds of meters
per million across orogens) suggests that areas
of active rock cycling (orogens) on average
have comprised ~10% of continental areas over
the entirety of Phanerozoic time.
Oceanic Tectonism from Rates of Spreading
The most widely cited records of global tectonic rates that might be compared to our estimates from data on geologic maps are those
related to the rate (and changes therein) of
seafloor spreading. Such lateral movement of
the Earth’s major tectonic plates embodies a
significant expression of mantle convection,
and many authors contend that spreading rates
control a wide variety of geophysical, geobiological, and geochemical processes, including
mantle heat loss (e.g., Kominz, 1984), sea-level
change (e.g., Gaffin, 1987), transgression and
regression (e.g., Pitman, 1978), carbon cycling
(Berner et al., 1983), and seawater chemistry
(Sandberg, 1975; Hardie, 1996). Based on area
versus age relations for oceanic crust, it appears
that rates of divergence have varied little, at least
over the past several hundred million years.
Expressed as area, seafloor has formed at a rate
of ~3.4 km2/yr (Rowley, 2002). Expressed as
length, global half-spreading has occurred at a
rate of ~2.0–2.5 cm/yr (20–25 km/Ma) over this
time interval (Conrad and Lithgow-Bertelloni,
2007). Because these rates are largely derived
from maps of global seafloor area versus age
(e.g., Müller et al., 1997), they are philosophically analogous to our rates derived from ages
Geological Society of America Bulletin, May/June 2009
Geologic maps are tectonic speedometers
Continental Tectonism from Rates of Uplift
and Exhumation
Other attempts to quantify amounts of tectonic movement have focused on determining rates of crustal uplift and exhumation by
employing a wide range of geochronometers.
Although the terms “uplift” and “exhumation”
have been used rather loosely in the geologic
literature, the sum of these processes generally
equates with rates of rock displacement relative
to the geoid (e.g., England and Molnar, 1990).
In an attempt to summarize vertical displacement estimated from such studies, we have
tabulated 754 durations and vertical amounts of
change from over 200 recent papers containing
the phrases “exhumation rate” and/or “uplift
rate” as a keyword or phrase in their title. Durations and amounts of crustal movement examined in these papers were inferred from a variety of geomorphic, geochemical, and isotopic
techniques including 40Ar/39Ar, U-Pb, Rb-Sr,
Sm-Nd, apatite helium (AHe), zircon helium
(ZHe), apatite fission track (AFT), zircon fission track (ZFT), 10Be, 26Al, electron spin resonance (ESR), optically stimulated luminescence
(OSL), and 14C methods. Changes range from a
few meters per million years over durations of
a few billion of years (e.g., Precambrian, Canadian Shield; Flowers et al., 2006) to tens of
kilometers per million years over durations of
a few million years (e.g., Pliocene, Papua New
Guinea; Baldwin et al., 2004).
Several aspects of these data merit note.
First, rates determined from amounts and durations of inferred change exhibit an approximate
lognormal distribution with mean and modal
values of 877 m/Ma and 1000 m/Ma, respectively (Fig. 13A). The shape of this distribution
itself probably does not illustrate any important geological corollary. These data comprise
measures of various erosional processes that
are ultimately related to ambient conditions of
climate and/or crustal tectonism, and decreasing numbers of measured rates in excess of
~1 km/Ma along the upper bound of the distribution (Fig. 13A) may therefore indeed
reflect some upper limit of such processes at
A
All rates, n = 754
Mean = 877 m/Ma
80
60
Number of measurements
and areas of the major rock groups exposed on
the Earth’s continents. Conversely, rates of oceanic crust generation and destruction primarily
record the effects of lateral tectonism, whereas
those derived from continents largely reflect rates
of vertical uplift and subsidence. In a context of
rates of tectonic deformation of the Earth’s lithosphere, these two processes are intimately interrelated. The mean rate of lateral oceanic crust
tectonism is ~40 times that occurring during the
vertical deformation of continental crust.
40
20
B
Durations <5012 yr, mean = 3636 m/Ma
Durations >5012 yr, mean = 210 m/Ma
50
40
30
20
10
1
100
10,000
1,000,000
Rate (m/Ma)
Figure 13. Frequency distribution of (A) 754 “uplift” and “exhumation” rates and (B) frequency distribution of rates determined over durations less than 5012 yr (median age of the
data—dark gray bars) and over durations greater than 5012 yr—open bars). Note that all
exhibit an approximate lognormal distribution. The mean rate of the short-duration population is 3636 m/Ma, whereas the mean rate of the long-duration population is 210 m/Ma.
these time scales of consideration. The lower
bound of rate-frequencies, on the other hand,
is almost surely related to sampling bias. These
studies encompass the use of geochronometers
that, by choice and application, are designed to
record some inferred amount of change. Fewer
values reflecting lower amounts and durations
of change almost surely reflect a decreasing
likelihood of study in areas that are approximately stationary.
More importantly, separation of the 754 values on the basis of a median duration (5012 yr)
into two populations containing equal number of measurements (377), and constructing
rate-frequency distributions for each subset
(Fig. 13B), demonstrates that each also exhibits an approximately lognormal distribution,
but with significantly different average rates.
Those linear changes measured over durations
of less than 5012 yr (n = 377) have a mean of
3636 m/Ma while those determined over time
spans in excess of 5012 yr (n = 377) have a
mean of only 210 m/Ma (Fig. 13B). This difference requires that rate of change is critically
dependent upon duration of observation.
The nature of this effect is apparent when rates
of “uplift” and “exhumation” are plotted relative
to durations of change for the entire population
of values. Collectively, these define a power-law
trend of decreasing rate of change with increasing time interval of change as Equation 6.
R = 170 D −0.31
(6)
where R is the rate in m/Ma and D is the
duration in units of Ma. In other words, rate
decreases by ~0.3% with each 1% increase in
process duration such that mean rates of vertical
change in the Earth’s surface due to processes
of rock “uplift” and “exhumation” decreases
by ~2 orders of magnitude (3000 to 20 km/
Ma) over the range of durations (months to billions of years) encompassed here (Figure 14).
Such dependence of inferred rate on dura-
Geological Society of America Bulletin, May/June 2009
773
Wilkinson et al.
Coseismic
10
m/Ma tectonic steps
kil
Modal rates
om
Rate (m/Ma)
100,000
et
er
s
UHP
1000
10
10
0.
0.1
1
Uplift rates
m
illi
m
Exhumation rates
0.000001
1
0.0001
et
0
ce
nt
er
0.01
im
1
et
er
1
m
m
et
er
s
et
er
100
Duration (Ma)
Figure 14. Log-log scatter plot of 754 uplift (open circles) and exhumation (gray diamonds) durations and
rates determined from various geochronometers and geomorphic data. Dashed diagonals are amounts
of equal uplift and exhumation (as length). Note that these define a trend (heavy black line) of decreasing rate with increasing duration of measurement (rate decreases ~0.3% for each 1% increase in duration). For reference, highest (darkly shaded circles and diamonds) at short and long durations represent
rates of coseismic uplift and exhumation of ultra high-pressure (UHP) terrains, respectively. Solid black
squares are per-million-year rates of tectonism that yield the best fits between North American (Food and
Agricultural Organization [FAO] and Geological Survey of Canada [GSC], Gilluly, 1969; and PeuckerEhrenbrink and Miller, 2002, 2003) and global (FAO and GSC) geologic map areas. Shaded squares are
modal rates (formation depth divided by modal age) for the same lithosomes.
tion of (ultimately tectonic) change has been
noted previously with respect to other natural
systems. Many processes (such as uplift and
exhumation) that proceed with a high degree of
irregularity (such as that occurring along a random walk) exhibit similar negative power-law
relations between net rate and the duration of
time over which rate is established. This relation has been well documented for Earth surface progressions such as sediment deposition
(Sadler, 1981), erosion (Gardner et al., 1987),
and biological evolution (Gingerich, 1994).
With these 754 values of uplift and exhumation serving as context, it is now possible to ask
the question: how do these magnitudes of uplift
and exhumation compare with vertical rates of
tectonic dispersion inferred from geologic map
774
volcanic, sedimentary, plutonic, and metamorphic age-frequencies? Before answering that
question, it should be noted that agreement
between model and measured map area agefrequencies (Fig. 11) allow for the estimation of
two distinct but interrelated measures of crustal
uplift and denudation. These are: (1) the average amount of tectonic uplift or subsidence (step
size in the random walk) experienced by each
lithosome per unit time and (2) for plutonic or
metamorphic lithosomes that yield modal ages
significantly different from times of rock formation, the amount of time necessary to bring the
largest number of lithosomes of some particular
age (the modal age of the frequency distribution)
to the Earth’s surface. This second value gives
an indication of the magnitude of the mean rate
of exhumation that occurs over the “lifetimes”
of exposed lithosomes.
In the first case, because ages for rock bodies have uncertainties of least a million years,
we computed time steps in the tectonic random
walk model at that (1 Ma) interval of time. For
walk steps of this duration, the amount of vertical movement necessary for arriving at agreement between model and observed volcanic,
sedimentary, plutonic, and metamorphic frequencies is on the order of about half a kilometer per million years (Table 4). This value is
the average size of tectonic “steps” experienced
by rock bodies during vertical crustal displacement over a period of 1 m.y. in duration. The
fact that step values for each rock type are about
the same is perhaps more than coincidental as,
Geological Society of America Bulletin, May/June 2009
Geologic maps are tectonic speedometers
broadly speaking, most rock bodies, regardless
of lithology, are primarily “cycled” along convergent margin orogens.
In the second, but related case, observed and
model age-frequency distributions (Fig. 11)
also provide an estimate of mean rates of
erosional denudation necessary to expose the
greatest number of plutonic and metamorphic
lithosomes at Earth’s surface. These rates of
“modal” exhumation, which are derived from
modal ages and emplacement depths (Table 4)
are about an order of magnitude lower than
rates estimated as the 1-m.y.–duration tectonic
steps for these same rock bodies, and again
make obvious the fact that net exhumation
rates are critically dependent on durations of
observation.
Qualitatively, the reason for this dependence
is perhaps most apparent from inspection of
paths taken by random walks (e.g., Figs. 9 and
10). Consider those paths (in depth and time
space) that begin at some depth but eventually
arrive at the absorbing barrier (the Earth’s erosional surface). Routes of short duration (by
necessity) also extend over short distances,
and resultant “rates” (∆distance/∆time) are
therefore high. In contrast, those routes (from
greater depths) are of longer duration, reflecting the increasing numbers of steps both toward
and away from the absorbing barrier; as a
result, net unit change in depth per unit change
in age is progressively lower. The dependence
of global uplift and exhumation rates on duration of observation (Fig. 14) merely reflects
the high degree of temporal irregularity that is
characteristic of global tectonic and denudational processes.
OTHER CONSEQUENCES OF
TECTONIC DIFFUSION
Agreement between model and observed
age-frequencies suggests that tectonic movement serves to vertically disperse continental
rock bodies relative to their initial depth of
formation by a process directly analogous to a
random walk in two dimensions. This is not to
imply that any single rock body will randomly
move up and/or down during its entire geologic
history. Rather, random dispersion reflects the
net movement experienced by all members
of the aggregate lithosome population; some
will certainly undergo more or less continual
uplift; others will experience prolonged intervals of stability; while still others will undergo
prolonged long periods of subsidence, with or
without later uplift. The net effect of all of these
histories in time-depth space, however, is that
collectively, age-frequencies of plutonic and
metamorphic rocks that formed at depth now
Source
FAO
GSC
Gilluly (1969)
PeuckerEhrenbrink
and Miller
(2002, 2003)
FAO
GSC
TABLE 4. MODAL EXHUMATION RATES AND TECTONIC STEPS
Exhumation rate
Area
(m/Ma)
Tectonic step (m/Ma)
Plu
Met
Vol
Sed
Plu
North America
137
61
323
188
809
North America
172
10
177
120
884
North America
76
19
467
449
428
Met
928
146
448
United States2
and Canada
149
12
513
379
762
196
Eurasia
Eurasia
40
42
48
42
355
347
163
125
371
410
461
784
FAO
Earth
70
26
532
511
539
552
GSC
Earth
89
16
212
147
637
452
Note: Modal exhumation rates (ER) and per-one-million-year tectonic steps (TS) for volcanic (Vol),
sedimentary (Sed), plutonic (Plu), and metamorphic (Met) outcrops on global, North American, and Eurasian
geologic maps.
1
“Undetermined.”
2
Exclusive of Hawaii.
Abbreviations: FAO—Food and Agricultural Organization; GSC—Geological Survey of Canada.
take on a characteristic lognormal distribution,
whereas volcanic and sedimentary rocks that
formed on continental surfaces exhibit a characteristic power-law distribution (Fig. 11).
Volcanic and Sedimentary Rock AgeFrequencies
The linear nature of volcanic and sedimentary rock age-area distributions (Figs. 15A–
15D) merits additional comment. As pointed
out by Newman (2005), a number of characteristics of random walks are distributed according to power-laws. One of these is a randomly
fluctuating process that undergoes what is colloquially referred to as a “gambler’s ruin”; such
runs have a power-law distribution of possible
lifetimes. Imagine a random path defined by a
walker who takes steps to the left or to the right.
If the walker starts at a position zero, the probability that the walker returns to this position
after some number of steps is the “first return
time” of the walk. We might consider the ages
of volcanic and/or sedimentary exposures in
a similar manner, in that these are units that
originate at a depth of zero (relative to continental surfaces), but eventually (by definition)
return to the same surface. Durations (first
return times) of such histories exhibit a powerlaw distribution with a slope of ~2/3 (theoretically, there is ~0.66% decrease in return
time-frequency for each 1% decrease in return
time duration). In reality, power-law slopes
of volcanic and sedimentary age-frequencies
(Figs. 15A–15D) are closer to unity. Actual
area of exposure at any rock age is somewhat
less than would be anticipated for a gambler’s
ruin, probably because real-world sequences of
volcanic and sedimentary rock do not experience abrupt vertical “steps” during their geo-
logic random walk. Geologic map data are only
resolved to epoch-duration intervals and, at this
scale, some erosion undoubtedly occurs prior to
subsidence and burial, while additional erosion
and/or burial is currently reducing the areas of
exposed lithosomes. Although such processes
serve to increase power-law slopes, they do
not obviate the conclusion that, like those lognormal distributions characteristic of plutonic
and metamorphic rocks, these age-frequencies
are also readily interpreted in the context of an
Earth’s crust behaving tectonically as a random
walk with an absorbing (erosional) boundary.
Area Reduction by Erosion and Burial
The logarithms of exposed areas of volcanic
and sedimentary rock decrease linearly with
the logarithms of ages, and the logarithms of
exposed areas of plutonic and metamorphic
bodies show a similar decrease across time
spans that are older than their modal ages
(e.g., Fig. 11). As noted by Gilluly (1969), this
decrease reflects the progressive uplift, erosion,
and destruction of some exposed lithosomes
and the progressive subsidence and burial of
others by younger (volcanic and sedimentary)
rocks. Which process, uplift and erosion or
subsidence and burial, is the more important
in the progressive dwindling of exposed rock
area with age on geologic maps? Knowledge of
total areas of volcanic and sedimentary lithosomes (extending throughout their subsurface
extent) has been determined by Ronov (1978a,
1978b, 1980) and coworkers. These papers
include estimations of the entirety (surface and
subsurface) of areal extents and thicknesses of
Phanerozoic volcanic and sedimentary successions on each major continent (except Antarctica) parsed by lithology. Because total areal
Geological Society of America Bulletin, May/June 2009
775
Wilkinson et al.
A
Volcanic outcrop
B
FAO maps
Sedimentary outcrop
10,000,000
FAO maps
100,000
100,000
10,000
1000
6
Area = 1.48 x 10 Age
r2 = 0.86
C
Volcanic outcrop
7
Area = 1.21 x 10 Age
r2 = 0.87
D
GSC map
-0.97
Sedimentary outcrop
1000
10,000,000
GSC map
100,000
1,000,000
10,000
100,000
10,000
1000
Total area (km2/Ma)
-1.05
Exposed area (km2/Ma)
10,000
5
Area = 8.68 x 10 Age
2
r = 0.86
E
-1.01
Total volcanic lithosome area
Ronov (1980)
7
Area = 2.23 x 10 Age
2
r = 0.88
F
-1.17
1000
Total sedimentary lithosome area
Ronov (1980)
100,000,000
1,000,000
10,000,000
100,000
5
Area = 9.93 x 10 Age
r2 = 0.26
1000
100
Age (Ma)
10
-0.30
7
Area = 3.15 x 10 Age
r2 = 0.17
1000
100
-0.397
1,000,000
Total area (km2/Ma)
Area exposed (km2/Ma)
1,000,000
10
Age (Ma)
Figure 15. Log-log plots of age versus area relations for volcanic (A and C) and sedimentary rock (B and D) outcrops for the Food and
Agricultural Organization (FAO) (A and B) and Geological Survey of Canada (GSC) (C and D) maps, and similar plots of total (exposed
and subsurface) lithosome area (E and F) from data in Ronov (1978a, 1978b, 1980). Straight lines are best-fit power-law regressions through
the data. Note that all four outcrop data sets define a slope of about −1.0 (~1% decrease in area for each 1% increase in age), whereas slopes
from data on total lithosome areas are on the order of about −0.35 (~0.35% decrease in area for each 1% increase in age). This difference
suggests that decreasing volcanic and sedimentary outcrop area with increasing age is primarily (70%) a result of burial by younger units,
rather than by erosion.
776
Geological Society of America Bulletin, May/June 2009
Geologic maps are tectonic speedometers
account for only a few percent of bulk continental crust, and only predominate lithologically in
the uppermost few kilometers (Fig. 16).
While this realization is probably not surprising to geologists, it brings into focus the
fact that rocks that form near the Earth’s surface inherently have a much higher probability
of erosional destruction than those that form at
greater crustal depths. Because random-walk
models applied to geologic map data allow for
estimates of amounts of surviving (buried) and
eroded (absorbed) lithosomes, it is possible to
compare relations between crustal depths of
formation and proportions of all lithosomes
that now survive at various depths in continental crust (e.g., Fig. 17). From the map data and
model parameters discussed above (Table 3),
it appears that the amount of surviving rock
increases by ~4% for each kilometer increase
in crustal depths of formation. At the end of
2007, Georef listed some 3000 journal articles
with “crystalline basement” as a title (869) or
keyword (2356) term; the omnipresence of
older plutonic-metamorphic (“crystalline”)
associations at greater (”basement”) crustal
depths is a fundamental geologic axiom. Its
veracity, however, is derived only in part from
the fact that plutonic and metamorphic lithosomes originate at crustal depth. Crystalline
rocks primarily predominate at greater depths
because of their much greater potential for
preservation.
Bulk Lithologic Composition of the Upper
Continental Crust
A final comment about geologic map frequency distributions derives from the observation first made by Gilluly (1969) that log
areas of surviving exposure decrease linearly
with the log of increasing age. Gilluly’s (1969)
slopes for North and South America (−0.67 and
−0.98, respectively; Fig. 1) are not notably different from those derived here for the entire
Earth from the FAO and GSC global maps
(−0.86 and −0.85, respectively; Fig. 5). Taking
either of these latter relations as characteristic
of mapped global exposures, the simplest relation that describes remaining global outcrop
area (Ar ) global as a function of age (t) is:
As discussed above, age-frequency distributions of the major rock groups are closely
mimicked when presuming that the enumerable
structural elements that collectively make up
continental crust essentially behave as a population of largely independent tectonic blocks
experiencing random vertical displacement
relative to the Earth’s surface. Because crustal
diffusion models simulating such a system also
result in the determination of hypothetical paths
taken by all rock lithosomes, it is possible to
sum the totality of each rock type over all model
depths in order to estimate the bulk lithologic
composition of continental crust (Fig. 16).
This approximation suggests that while those
continental lithologies traditionally mapped as
being some form of “metamorphic” rock only
make up between 10% and 20% of continental
exposures (Table 1), these lithologies comprise
fully ~90% of continental crustal volume. Sedimentary units, on the other hand, while making
up 60%–70% of global exposures (Table 1),
5
Depth (km)
extents of volcanic and sedimentary lithosomes
decrease with increasing age, and because this
decrease is completely unrelated to burial by
younger units, these data allow for an estimation of that portion of map areas decrease that
is driven solely through processes of exposure
and erosion. From these data sources (Ronov,
1978a, 1978b, 1980), we calculate the size
(volume) of the Phanerozoic volcanic (105 ×
106 km3) and sedimentary (533 × 106 km3) continental rock reservoir to be ~638 × 106 km3;
~16% and 84% of the total, respectively. These
values are of the same proportional magnitude as areas of currently exposed volcanic
and sedimentary rock as determined from the
FAO (8% and 92%) and GSC (12% and 88%)
maps. More importantly, when total areas
of volcanic and sedimentary lithosomes are
plotted relative to rock age, the resulting data
define power-law trends with slopes of about
−0.3 and −0.4, respectively (Figs. 15E and
15F). These slopes require that uplift and erosion alone serves to decrease total volcanic and
sedimentary sequence areas by ~0.3% to 0.4%
for each 1% increase in rock age. Importantly,
these slopes are about one-third those defined
by analogous plots of exposures on geologic
maps (about −1.0; Figs. 15A–15D), and serves
to demonstrate that the ubiquitous decrease
in map area of exposed continental rock with
increasing age is primarily (~2/3) due to burial
by younger volcanic sedimentary successions,
and only secondarily (~1/3) due to exposure
and erosion.
Volcanic (2%)
10
Sedimentary (4%)
15
Plutonic (3%)
20
Metamorphic (91%)
25
30
20%
40%
60%
80%
Percent of lithologies
Figure 16. Model-derived estimate of the proportional lithologic composition of continental
crust with depth from Food and Agricultural
Organization (FAO) global maps. Values in
parentheses are proportional totals integrated
over the entire depth range; arrows at top
indicate actual proportions of outcrop at the
Earth’s surface from the FAO maps (Table 1).
Primeval Residuals
Ar = A0 t −0.86
(7) ,
where A0 is the FAO and GSC map intercepts
(Fig. 5). These values are the typical amount of
new map area generated by volcanism and sediment deposition: ~9 × 106 km2/m.y. (Fig. 5). To
the degree that this relation can be realistically
extrapolated back in geologic time, some 6 ×
103 km2 of 4 b.y. rock (an area about the size
of Delaware) should be exposed on the Earth’s
surface. Moreover, calculation of the relative
proportions of volcanic, sedimentary, plutonic,
and metamorphic exposure with time (Fig. 18)
suggests that this 4 b.y. crust might consist of
generally subequal proportions (~36%, 24%,
and 37%, respectively) of sedimentary, plutonic, and metamorphic rocks. Loss of volcanic and sedimentary area through erosion and
burial naturally serve to decrease area with age,
but, in the latter instance, sedimentary cover is
sufficiently large at the start, that loss over the
past ~4 b.y. is approximately balanced by uplift
and exposure of plutonic and metamorphic
basement rocks (Fig. 18). In other words, areas
of geologic units now exposed at the Earth’s
continental surfaces decrease in net area at a
rate of ~0.85% per 1% increase in their age. As
such, there is no compelling reason, at least on
the basis of these data, not to expect the presence of some Delaware-sized fragment or fragments of primal continental crust somewhere
at the modern Earth’s surface (e.g., Bowring
and Williams, 1999). Moreover, the probabilities that this fragment is sedimentary, plutonic,
and/or metamorphic in lithologic constitution
are nearly equal.
Geological Society of America Bulletin, May/June 2009
777
Wilkinson et al.
Proportion surviving
ACKNOWLEDGMENTS
70%
% Surviving = 0.040 e0.121 Depth
60%
r2 = 0.745
We sincerely thank Sarah Smalheer, Erin Dimaggio,
Marit Gamberg, Tammara Gipprich, Emily Johnson,
Jaye Kain, Tracy Kolb, Kelly Wells, and David Whipp
for assistance in compiling much of the map area–agefrequency data that serves as the basis of this study. The
focus of this study profited from discussions with John
Prucha and Pat Bickford; Bryce Hand, Andrew Hynes,
Linda Ivany, Karl Karlstrom, James Metcalf, Scott
Miller, Jon Pelletier, and Jan Veizer read early drafts
of the manuscript and offered many helpful comments
and suggestions. This work was supported by National
Science Foundation grant EAR-99-02849.
50%
40%
30%
20%
REFERENCES CITED
10%
5
10
15
20
25
Mean depth of formation (km)
Proportion of exposures
Figure 17. Model-derived estimates of volcanic, sedimentary, plutonic, and metamorphic lithosome preservation (Y
axis) relative to inferred mean depths of rock formation (X
axis) from Food and Agricultural Organization (FAO) and
Geological Survey of Canada (GSC) maps. Volcanic and
sedimentary rocks—open diamonds; plutonic lithosomes—
lightly shaded diamonds; metamorphic suites—dark-gray
diamonds. Note that preservation potential increases with
increasing inferred crustal depths of formation. These data
define a trend suggesting that lithosome survival increases
by ~4% for each kilometer increase in depth of formation.
80%
Volcanic
60%
Sedimentary
Plutonic
40%
Metamorphic
20%
1000
100
10
Age (Ma)
Figure 18. Proportions of rock outcrop lithologies from the Food and Agricultural Organization (FAO) global maps. Arrows denote approximate proportion of exposures expected at
~4 b.y. Note that metamorphic, plutonic, and sedimentary lithosomes are present in generally subequal amounts.
778
Baldwin, S.L., Monteleone, B.D., Webb, L.E., Fitzgerald, P.G.,
Grove, M., and Hill, E.J., 2004, Pliocene eclogite exhumation at plate tectonic rates in eastern Papua New Guinea:
Nature, v. 431, p. 263–276, doi: 10.1038/nature02846.
Baumiller, T.K., and Ausich, W., 1992, The broken-stick
model as a null hypothesis for crinoid stalk taphonomy
and as a guide to the distribution of connective tissue in
fossils: Paleobiology, v. 18, p. 288–298.
Berner, R.A., Lasaga, A.C., and Garrels, R.M., 1983, The carbonate-silicate geochemical cycle and its effect on atmospheric carbon dioxide over the past 100 million years:
American Journal of Science, v. 283, p. 641–683.
Blatt, H., and Jones, R.L., 1975, Proportions of exposed
igneous, metamorphic, and sedimentary rocks: Geological Society of America Bulletin, v. 86, p. 1085–
1088, doi: 10.1130/0016-7606(1975)86<1085:POEIM
A>2.0.CO;2.
Bluth, G.J.S., and Kump, L.R., 1991, Phanerozoic paleogeology: American Journal of Science, v. 291, p. 284–308.
Bowring, S.A., and Williams, I.S., 1999, Priscoan (4.00–
4.03 Ga) orthogneisses from northwestern Canada:
Contributions to Mineralogy and Petrology, v. 134,
p. 3–16, doi: 10.1007/s004100050465.
Choubert, G., and Faure-Mauret, A., 1981, editors, Atlas
géologique du monde: Paris, Commission de la
carte géologique du monde, Bureau de cartographie
géologique internationale, United Nations Educational,
Scientific and Cultural Organization 22 sheets.
Conrad, C.P., and Lithgow-Bertelloni, C., 2007, Faster
seafloor spreading and lithosphere production during the mid-Cenozoic: Geology, v. 35, p. 29–32, doi:
10.1130/G22759A.1.
Dutton, C.E., 1882, Tertiary history of the Grand Canyon district, with atlas: U.S. Geological Survey Monograph 2,
264 p.
England, P.C., and Molnar, P., 1990, Surface uplift, uplift
of rocks, and exhumation of rocks: Geology, v. 18,
p. 1173–1177, doi: 10.1130/0091-7613(1990)018<1173:
SUUORA>2.3.CO;2.
Flowers, R.M., Bowring, S.A., and Reiners, P.W., 2006, Low
long-term erosion rates and extreme continental stability documented by ancient (U-Th)/He dates: Geology,
v. 34, p. 925–928, doi: 10.1130/G22670A.1.
Gaffin, S., 1987, Ridge volume dependence on seafloor generation rate and inversion using long term sea-level change:
American Journal of Science, v. 287, p. 596–611.
Gardner, T.W., Jorgensen, D.W., Shuman, C., and Lemieux,
C.R., 1987, Geomorphic and tectonic process rates:
Effects of measured time interval: Geology, v. 15, p. 259–
261, doi: 10.1130/0091-7613(1987)15<259:GATPRE>
2.0.CO;2.
Garwin, S., Hall, R., and Watanabe, Y., 2005, Tectonic setting,
geology, and gold and copper mineralization in Cenozoic
magmatic arcs of southeast Asia and the west Pacific terranes, in Hedenquist, J.W., Thompson, J.F.H., Goldfarb,
R.J., and Richards, J.P., eds., One hundredth anniversary
volume (1905–2005): Economic Geology and Bulletin of
the Society of Economic Geologists, v. 100, p. 891–930.
Gibbs, M.T., and Kump, L.R., 1994, Global chemical erosion
during the last glacial maximum and the present: Sensitivity to changes in lithology and hydrology: Paleoceanography, v. 9, p. 529–543, doi: 10.1029/94PA01009.
Geological Society of America Bulletin, May/June 2009
Geologic maps are tectonic speedometers
Gilluly, J., 1969, Geological perspective and the completeness of the geologic record: Geological Society of
America Bulletin, v. 80, no. 11, p. 2303–2312, doi: 10.
1130/0016-7606(1969)80[2303:GPATCO]2.0.CO;2.
Gingerich, P.D., 1994, Quantification and comparison of
evolutionary rates: American Journal of Science,
v. 293, p. 453–478.
Goldfarb, R.J., Baker, T., Dubé, B., Groves, D.I., Hart,
C.J.R., and Gosselin, P., 2005, Distribution, character,
and genesis of gold deposits in metamorphic terranes,
in Hedenquist, J.W., Thompson, J.F.H., Goldfarb, R.J.,
and Richards, J.P., eds., One hundredth anniversary
volume (1905–2005): Economic Geology and Bulletin of the Society of Economic Geologists, v. 100,
p. 407–450.
Gradstein, F.M., Ogg, J.G., and Smith, A.G., eds., 2004, A
geologic time scale: Cambridge University Press.
Hardie, L.A., 1996, Secular variation in seawater chemistry:
An explanation for the coupled secular variation in the
mineralogies of marine limestones and potash evaporites
over the past 600 m.y: Geology, v. 24, p. 279–283, doi:
10.1130/0091-7613(1996)024<0279:SVISCA>2.3.CO;2.
Haschke, M., Siebel, W., Guenther, A., and Scheuber, E.,
2002, Repeated crustal thickening and recycling during the Andean Orogeny in North Chile (21°–26° S):
Journal of Geophysical Research, v. B107, p. 1–18.
Higgs, D.V., 1949, Quantitative areal geology of the United
States: American Journal of Science, v. 291, p. 284–308.
Kesler, S.E., and Wilkinson, B.H., 2006, The role of exhumation in the temporal distribution of ore deposits:
Economic Geology and the Bulletin of the Society of
Economic Geologists, v. 101, p. 919–922.
Kesler, S.E., and Wilkinson, B.H., 2008, Earth’s copper
resources estimated from tectonic diffusion of porphyry copper deposits: Geology, v. 36, p. 255–258, doi:
10.1130/G24317A.1.
Kesler, S.E., Hall, C.M., Russell, N., Piñero, E., Sánchezi,
C.R., Pérez, R.M., Moreira, J., and Borges, M., 2004,
Age of the Camagüey silver-gold district, Cuba: Tectonic evolution and preservation of epithermal mineralization in volcanic arcs: Economic Geology and the
Bulletin of the Society of Economic Geologists, v. 99,
p. 869–886.
Kirkham, R.V., Chorlton, L.B., and Carrière, J.J., 1995,
compilers, Generalized geology of the world, in Generalized geological map of the world and linked databases: Geological Survey of Canada Open-File 2915d
(CD-ROM).
Kominz, M.A., 1984, Oceanic ridge volume and sea level
change—An error analysis, in Schlee, J.S., ed., Interregional unconformities and hydrocarbon accumulation:
American Association of Petroleum Geologists Memoir 36, p. 109–127.
McElroy, B.H.J., Wilkinson, B.H., and Rothman, E.D.,
2005, Tectonic and topographic framework of politi-
cal division: Mathematical Geology, v. 37, p. 197–206,
doi: 10.1007/s11004-005-1309-2.
Meybeck, M., 1987, Global chemical weathering of surficial
rocks estimated from river dissolved loads: American
Journal of Science, v. 287, p. 401–428.
Müller, R.D., Roest, W.R., Royer, J.-Y., Gahagan, L.M., and
Sclater, J.G., 1997, Digital isochrones of the world’s
ocean floor: Journal of Geophysical Research, v. 102,
p. 3211–3214, doi: 10.1029/96JB01781.
Newman, M.E.J., 2005, Power-laws, Pareto distributions,
and Zipf’s law: Contemporary Physics, v. 46, p. 323–
351, doi: 10.1080/00107510500052444.
Pearson, D.G., and Parman, S.W., Nowell, and G. M., 2007,
A link between large mantle melting events and continent growth seen in osmium isotopes: Nature, v. 449,
p. 203–209.
Pedreira, D., Pulgar, J.A., Gallart, J., and Diaz, J., 2003,
Seismic evidence of Alpine crustal thickening and
wedging from the western Pyrenees to the Cantabrian
Mountains (north Iberia): Journal of Geophysical
Research, v. B108, p. 1–21.
Peucker-Ehrenbrink, B., and Miller, M.W., 2002, Quantitative bedrock geology of the conterminous United
States of America: Geochemistry Geophysics Geosystems, v. 3, p. 1–4.
Peucker-Ehrenbrink, B., and Miller, M.W., 2003, Quantitative bedrock geology of Alaska and Canada: Geochemistry Geophysics Geosystems, v. 4, p. 1–10.
Pitman, W.C., 1978, Relationship between eustacy and stratigraphic sequences of passive margins: Geological Society of America Bulletin, v. 89, p. 1389–1403, doi: 10.11
30/0016-7606(1978)89<1389:RBEASS>2.0.CO;2.
Ronov, A.B., 1978a, The Earth’s sedimentary shell: Quantitative patterns of its structure, compositions, and
evolution: International Geology Review, v. 24, no. 11,
p. 1313–1363.
Ronov, A.B., 1978b, The Earth’s sedimentary shell: Quantitative patterns of its structure, compositions, and evolution (part 2): International Geology Review, v. 24,
no. 12, p. 1365–1388.
Ronov, A.B., 1980, The Earth’s sedimentary shell: quantitative patterns of its structures, compositions, and evolution, in Yaroshevskiy, A.A., ed., The 20th V.I. Vernadskiy lecture: The Earth’s sedimentary shell: Moscow,
Nauka, p. 1–80; also, American Geological Institute
Reprint Series 5, p. 1–73.
Rowley, D.B., 2002, Rate of plate creation and destruction:
180 Ma to present: Geological Society of America Bulletin, v. 114, p. 927–933, doi: 10.1130/0016-7606(2002)
114<0927:ROPCAD>2.0.CO;2.
Sadler, P.M., 1981, Sediment accumulation rates and the
completeness of stratigraphic sections: The Journal of
Geology, v. 89, p. 569–584.
Sandberg, P.A., 1975, New interpretations of Great Salt Lake
ooids and of ancient non-skeletal carbonate mineralogy:
Sedimentology, v. 22, p. 497–537, doi: 10.1111/j.13653091.1975.tb00244.x.
Scotese, C.R., and Golonka, J., 1992, Paleogeographic atlas:
PALEOMAP Progress Report 20-0692, Department of
Geology, University of Texas at Arlington, 34 p.
Simmons, S.F., White, N.C., and John, D.A., 2005, Geological characteristics of epithermal precious and base
metal deposits, in Hedenquist, J.W., Thompson, J.F.H.,
Goldfarb, R.J., and Richards, J.P., eds., One hundredth
anniversary volume (1905–2005): Economic Geology
and Bulletin of the Society of Economic Geologists,
v. 100, p. 485–522.
Singer, D.A., Berger, V.I., and Moring, B.C., 2005, Porphyry copper deposits of the world: Database, maps,
and preliminary analysis: U.S. Geological Survey
Open-File Report 2005-1060 (http://pubs.usgs.gov/
of/2005/1060/).
Suchet, P.A., Probst, J., and Ludwig, W, 2003, Worldwide
distribution of continental lithology: Implications
for the atmospheric/soil CO2 uptake by continental
weathering and alkalinity river transport to the oceans:
Global Biogeochemical Cycles, v. 17, p. 1–13, doi:
10.1029/2002GB001891.
Summerfield, M.A., and Hulton, N.J., 1994, Natural controls of fluvial denudation rates in major world drainage basins: Journal of Geophysical Research, v. 99,
p. 13,871–13,883, doi: 10.1029/94JB00715.
Syvitski, J.P.M., Vörösmarty, C.J., Kettner, A.J., and Green,
P., 2005, Impact of humans on the flux of terrestrial
sediment to the global coastal ocean: Science, v. 308,
p. 376–380, doi: 10.1126/science.1109454.
Turcotte, D.L., 1992, Fractals and chaos in geology and geophysics: Cambridge Press, 221 p.
Veizer, J., and Jansen, S.L., 1979, Basement and sedimentary recycling and continental evolution: The Journal
of Geology, v. 87, p. 341–370.
Veizer, J., and Jansen, S.L., 1985, Basement and sedimentary recycling 2: Time dimension to global tectonics:
The Journal of Geology, v. 93, p. 625–643.
Wilkinson, B.H., 2007, Impact of humans on continental sedimentation and erosion: Geological Society of
America Bulletin, v. 119, p. 140–156, doi: 10.1130/
B25899.1.
Wilkinson, B.H., and Kesler, S.E., 2007, Tectonism and
exhumation in convergent margin orogens—Insights
from ore deposits: The Journal of Geology, v. 115,
p. 611–627, doi: 10.1086/521606.
MANUSCRIPT RECEIVED 30 APRIL 2008
REVISED MANUSCRIPT RECEIVED 3 SEPTEMBER 2008
MANUSCRIPT ACCEPTED 12 SEPTEMBER 2008
Printed in the USA
Geological Society of America Bulletin, May/June 2009
779