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Article
Volume 12, Number 4
1 April 2011
Q04002, doi:10.1029/2010GC003459
ISSN: 1525‐2027
Topography, the geoid, and compensation mechanisms
for the southern Rocky Mountains
D. Coblentz
Geodynamics Group, Los Alamos National Laboratory, MS D443, Los Alamos, New Mexico 87545,
USA ([email protected])
C. G. Chase
Department of Geosciences, University of Arizona, Tucson, Arizona 85721, USA
K. E. Karlstrom
Department of Earth and Planetary Sciences, University of New Mexico, Albuquerque, New Mexico
87131, USA
J. van Wijk
Department of Earth and Atmospheric Sciences, University of Houston, Houston, Texas 77204‐5007,
USA
[1] The southern Rockies of Colorado are anomalously high (elevations greater than 2800 m), topographi-
cally rough (implying active uplift), and underlain by significant low‐velocity anomalies in the upper mantle
that suggest an intimate relationship between mantle geodynamic processes and the surface topography. The
region is in isostatic equilibrium (i.e., near‐zero free‐air gravity anomaly); however, the poor correlation
between the high topography and crustal thickness makes the application of simple compensation models
(e.g., pure Heiskanen or Pratt‐Hayford) problematic. Knowledge of how the current topography of the
Rockies is isostatically compensated could provide constraints on the relative role of sublithospheric buoyancy versus lithospheric support. Here we evaluate the geoid and its relationship to the topography (using the
geoid‐to‐elevation ratio (GTR) in the spatial domain and the admittance in the frequency domain) to constrain
the mechanism of compensation. We separate the upper mantle geoid anomalies from those with deeper
sources through the use of spherical harmonic filtering of the EGM2008 geoid. We exploit the fact that at
wavelengths greater than the flexural wavelength where features are isostatically compensated, the geoid/
topography ratio can be used to estimate the depth of compensation and the elastic thickness of the lithosphere. The results presented below indicate that the main tectonic provinces of the western United States
have moderate geoid/topography ratios between 3.5 and 5.5 m/km (∼3.9 for the southern Rockies, ∼4.25
for the Colorado Plateau, and ∼5.2 for the Northern Basin and Range) suggesting shallow levels of isostatic
compensation. In terms of the elastic thickness of the lithosphere, our results indicate an elastic thickness of
less than 20 km. These value support the notion that a major portion of the buoyancy that has driven uplift
resides at depths less than 100 km and that upper mantle processes such as small‐scale convection may play
a significant role in the buoyant uplift of the southern Rockies (as well as other actively uplifting areas of
the western United States). Further support for this hypothesis is provided by high coherence for the geoid‐
topography relationship for nearly all wavelengths between 50 and 1000 km.
Components: 9800 words, 8 figures.
Keywords: topography; geoid; Rocky Mountains.
Copyright 2011 by the American Geophysical Union
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Index Terms: 8120 Tectonophysics: Dynamics of lithosphere and mantle: general (1213); 8175 Tectonophysics: Tectonics
and landscape evolution; 8122 Tectonophysics: Dynamics: gravity and tectonics.
Received 2 December 2010; Revised 17 February 2011; Accepted 22 February 2011; Published 1 April 2011.
Coblentz, D., C. G. Chase, K. E. Karlstrom, and J. van Wijk (2011), Topography, the geoid, and compensation mechanisms
for the southern Rocky Mountains, Geochem. Geophys. Geosyst., 12, Q04002, doi:10.1029/2010GC003459.
1. Introduction
[2] Our understanding of how the high topography
of mountain ranges is compensated at depth is
incomplete except for the most simplistic cases (e.g.,
balanced one‐dimensional columns and cartoon
illustrations of the lithosphere). Reality is a much
more complicated mix of the principal compensation
mechanisms such as thickening a constant density
crust (Airy), lateral changes in density of crust (Pratt)
and the support of topographic loads by elastic
stresses within the lithospheric plate overlying a
weak, fluid asthenosphere (flexural support). The
dominance of the Airy‐type compensation in earlier
studies stems in large part from early crustal structure studies that indicated that most high mountain
ranges have a thick root/crust. In such a situation the
free‐air gravity anomaly is small and approaches
zero for the longest wavelengths. In contrast, the
Bouguer gravity anomaly is nonzero, reflecting the
crustal root, and strongly correlated with topography
at long wavelengths. To a first order these observation hold true for a majority of the Earth’s mountain
ranges. It is only with the arrival of recent, more
detailed, seismic studies (e.g., the EarthScope project in the western United States) and evaluations of
the intraplate stress field [Zoback and Mooney,
2003] that sufficient information has become available to raise serious question about the applicability
of the Airy model of compensation. Thus, while it is
generally accepted that mountain belts are underlain
by “roots” that are less dense than the surrounding
mantle, it is becoming more and more apparent that
the roots are not large enough to appeal to a purely
Airy mechanism of compensation. Indeed, one of
the principal conclusions of Zoback and Mooney
[2003] was that for most continental areas there
exists no clear relationship between elevation and
crustal thickness and pure Airy‐type correlation
between elevation and crustal thickness is limited to
continental regions with either very thick (>55 km)
or very thin (<20 km) crust. The implication is that
mantle buoyancy may be a significant contributor
to surface elevation, a suggestion made more than
40 years ago [Thompson and Talwani, 1964].
[3] This is particularly the case for the actively
deforming western U.S. Cordillera. The western
United States is characterized by regionally high
elevation typically exceeding 1.5 km and recent
deformation and uplift which invites evaluation
of the relationship between topography and the
underlying geodynamics driving continental uplift.
The southern Rocky Mountains in Colorado (SRM)
and the Colorado Plateau (CP) regions are particularly intriguing, given the debate surrounding the
uplift dynamics of the CP and the anomalously high
and actively deforming SRM. Both of these provinces are characterized by a present‐day lithosphere that is a composite of structures that formed
during lithospheric assembly and during later
modification, including active tectonism. Recent
modeling results suggest that while the CP and the
SRM are quite distinct in geology and physiography, they share recent uplift which is hypothesized
to be driven by small‐scale and relatively shallow
mantle flow and buoyancy [van Wijk et al., 2010].
This influence from the upper mantle is consistent
with the observation that the Tertiary epeirogenies in
the western United States are coincident with mafic
igneous activity and suggests that continental swells
such as the southern Rockies are associated with
sublithospheric processes (possibly akin to a variation on mantle hot spots) in the same manner as
oceanic swells [Crough, 1979; Eaton, 1986, 2008;
Suppe et al., 1975].
[4] Much of the high elevation of the SRM coincides
with thin or attenuated continental crust, which
suggests that anomalous buoyancy of the mantle
plays an important role in the topographic support.
An emerging hypothesis from the recently completed CREST (Colorado Rocky Mountain Experiment and Seismic Transect) experiment [Aster et al.,
2009] is that 100 km‐scale mantle velocity domains
correlate with regions undergoing differential uplift
in the SRM and CP and, more generally, that surface
topography is being shaped by mantle flow and
buoyancy at various scales. Significant upper mantle
low‐velocity features beneath the Aspen region and
San Juan Mountains appear to coincide with Proterozoic lithospheric structures within the Colorado
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Figure 1. P and S velocity model depth slices at 60 km (first row) and cross sections from 0 to 660 km (second through
fourth rows) from linear inversion of relative traveltime delays across a network of 167 CREST, USArray, and other
broadband seismic stations located in central Colorado (J. R. MacCarthy, personal communication, 2011). These
high‐resolution images of the upper mantle reveal large seismic velocity variations on a 50–100 km scale and are suggestive of interpretations relating the velocity anomalies to surface topographic features that are of the same spatial scale.
mineral belt. This region is characterized by high
and rough topography, recent (5–10 Ma), rapid
exhumation, and the lowest Bouguer gravity anomalies in the western United States. Recent integration
of EarthScope Transportable Array (TA) and
PASSCAL/Flexible Array seismic data beneath the
SRM and High Plains reveals an extraordinary
image of the velocity complexities in the upper
mantle including a fascinating array of blobs and
dipping pipe‐like features extending to the 410 km
discontinuity beneath Gunnison, CO and Chama,
NM [Hansen et al., 2011]. Details of the upper
mantle velocity anomalies along several profiles
across the central Colorado Rockies from the
CREST data are shown in Figure 1. These high‐
resolution 3‐D upper mantle images reveal large
seismic velocity variations on a 50–100 km scale
and are suggestive of interpretations relating the
velocity anomalies to surface topographic features
that are of the same spatial scale.
[5] Several studies have noted that the topography
of the SRM correlates better with the seismic
velocity anomalies in the upper mantle than with
crustal thicknesses [Humphreys and Dueker, 1994;
Karlstrom and Humphreys, 1998] which supports
the notion that isostatic compensation in this region
takes place largely in the mantle. A more recent
analysis of the receiver function images collected
during the CREST experiment [Hansen et al., 2011]
has shown that the SRM is not associated with
thickened crust, suggesting upper mantle support of
the high topography. Furthermore, it appears that
the Colorado Plateau and SRM have an average
lithospheric thickness of about 80 km which is
thinner than generally accepted continental litho-
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spheric average of 100 km which is observed further
to the east under the Great Plains [Abt et al., 2010;
Yuan and Romanowicz, 2010]. The relationship
between the surface topography, crustal thickness
and upper mantle processes in central Colorado
remains poorly understood and constraints on the
compensation mechanism provided by an analysis
of the geoid is germane for resolving the contentious
issues surrounding the lithospheric structure. Other
studies, in particular the analysis of Rayleigh wave
tomography [Li et al., 2002], have concluded the
relationship between the elevated topography with
mantle velocities is not as strong as the correlation
with crustal anomalies.
[6] In this study we build on the previous investigations into the coupling between elevation and
thermal field in the context of isostasy and its role
in continental deformation in convergent orogens
[Sandiford and Powell, 1990; Zhou and Sandiford,
1992] and the lithospheric density moment as a
source of intraplate stress and associated deformation at both global and tectonic plate scales
[Coblentz et al., 1994]. We present the results of an
evaluation of the upper mantle geoid and its relationship to the topography of the SRM in an effort to
help resolve the controversy of how the topography
is compensated and constrain the various geodynamic models being postulated to explain the
observed upper mantle velocity anomalies beneath
the SRM. We evaluate the geoid‐to‐topography
ratio (GTR) for various compensation models using
one dimensional isostatically balanced lithospheric
density models to place constraints on the plausible
lithospheric structure. This is followed by an interpretation of the coherence and admittance of the
relationship between the topography and the gravity/
geoid fields in an attempt to distinguish between
topography that is compensated by lithospheric
variations and those that are supported by flexure of
the lithospheric plate [Dorman and Lewis, 1970;
Forsyth, 1985]. Our estimates for the mechanism
and depth of compensation beneath SRM places
strong constraints on the depth at which the buoyancy resides and help resolve the attendant issues
surrounding uplift mechanisms in the western
United States.
2. Topography, Gravity, and the Geoid
[7] The high topography of the SRM is a dominant
feature of the western United States (Figure 2a) and
is part of a larger north‐south striking, long‐
wavelength topographic swell (topography with
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l > 250 km is shown in Figure 2b) that extends
for more than 1000 km from central New Mexico
into Wyoming. This long‐wavelength “swell” cuts
across major structural features in the crust including the northeast trending paleosubduction sutures
inherited from the assembly of the North American
plate, the northwest striking trends of the Ancestral
Rocky Mountains, and the northeast trending
Colorado Mineral Belt (see discussions by Eaton
[1986, 2008]). From a geophysical point of view
the lithosphere in the SRM region has been more
intensely studied than any other orogenic system
(with the possible exception of the Alps and parts
of the Andes) and provides the data necessary to
evaluate and understand how the topographic load
of the southern Rockies is compensated.
[8] As is well established by the principle of
isostasy, topographic loads at the Earth’s surface are
compensated by mass deficits and excesses within
the Earth’s interior; Watts [2001] provides a comprehensive review of the development of the concept
of isostasy. The small free‐air gravity anomaly
throughout the western United States indicates
that most of the tectonic provinces, including the
Colorado Plateau and the Rockies are in a state of
isostatic equilibrium. Thus, given the very long
wavelength topographic features of the CP and the
SRM, simple isostatic models can be employed to
constrain the first‐order compensation mechanisms.
The principle of parsimony suggests beginning with
consideration of the Airy‐Heiskanen compensation (with purely crustal thickness variations) as the
dominant compensation mechanism. For the simplest crustal model, a surface elevation of 2800 m
will correspond with a crustal thickness of more than
48 km (assuming a crustal density of 2800 kg/m3
and mantle lithospheric density of 3300 kg/m3).
However, the analysis of recent seismic imaging
[Hansen et al., 2011] indicates that the crustal
thickness under the high topography in the Aspen
region of central Colorado is about 42 km or more
than 5 km thinner than predicted by Airy‐Heiskanen
compensation. This crustal thickness, combined
with the lack of correlation between the highest
topography and the largest Bouguer gravity anomalies, is evidence that the compensation mechanism
beneath central Colorado is more complex. The
situation calls for either a combination of both
Airy‐Heiskanen and Pratt‐Hayford isostasy (see
discussions by Martinec [1994a, 1994b]) or
involvement of the whole lithosphere in the isostatic
compensation (that is, a depth of compensation in
the range of 100–150 km as suggested by Martinec
[1994b]). As a result, in order to achieve more
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Figure 2. Spatial variations in the (a) topography, (b) filtered topography (low‐pass l > 250 km), (c) upper mantle‐
lithospheric geoid (see text for details), and (d) Bouguer gravity anomaly in the southern Rockies region of the western
United States. White lines delineate the principal tectonic boundaries of the Basin and Range, Colorado Plateau, and
southern Rockies.
accurate estimates of the vertical distribution of
compensating mass anomalies, isostatic calculations
must consider the mantle lithosphere as well as the
crust [Sandiford and Powell, 1990].
[9] The question of how the topographic load of
the Rockies is compensated cannot be resolved by
consideration of the Bouguer gravity anomalies
alone. While gravity analyses have long been used
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to constrain crustal structure in the western United
States [Li et al., 2002; Thompson and Zoback,
1979], use of geoid anomalies (which are variations in the gravitational potential) are much better
suited to the purpose of detecting where the compensating masses are located in the subsurface.
Geoid anomalies caused by long‐wavelength isostatically compensated continental topography are
proportional to the elevation multiplied by the mean
depth of compensation (that is, they are proportional
to the local dipole moment of the density‐depth
distribution [Haxby and Turcotte, 1978]) and can be
used to evaluate and constrain the subsurface distribution of mass associated with various topographic loads and features. Because the geoid
reflects the gravitational dipole moment it is more
sensitive to deeper sources than the gravity field,
reflecting the fact that the geoid anomaly observed at
the surface caused by a point mass buried at depth d
decreases in amplitude as 1/d, whereas the gravity
anomaly of the same point mass decays as 1/d2. This
makes the study of geoid anomalies more useful for
discerning depths of isostatic compensation. In
continental settings, the geoid has primarily been
used to deduce regional tectonic stresses from the
variations of gravitational potential energy [Jones
et al., 1996, 1998; Sonder and Jones, 1999].
Recently, geoid anomalies have been used to constrain deep continental structure as well [Doin et al.,
1996; Ebbing et al., 2001].
[10] There is a trade‐off, however, to the advantages
of the depth sensitivity of geoid anomalies. Mantle
heterogeneities produce long‐wavelength, high‐
amplitude anomalies that dominate the geoid and
consequently the observed geoid anomaly is the
combination of mass anomalies in both the lithosphere and deeper mantle. Thus it is imperative to
separate the upper mantle geoid anomalies from
those with deeper sources, especially those that arise
in the lower mantle before using the geoid for
understanding the distribution of masses in the
lithosphere. We accomplish this by removing all
spherical harmonic terms of degree less than 7 and
applying a one‐sided cosine taper to harmonic terms
from degree 7 to 11 (see Chase et al. [2002] for
details). This filter allows removal of all anomalies
with spatial wavelengths greater than 3000 km and
limits the sources of the anomaly to depths less than
about 600 km. This geoid field (which we refer to as
the “upper mantle‐lithospheric geoid”) is shown in
Figure 2c and appears to be appropriate for the
southwestern North America, in that the average
geoid value with crust near sea level is zero both on
the west coast and the Gulf of Mexico (see Chase
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et al. [2002, Figure 4] for a more regional view of
this geoid). It is important to note that this geoid is
also consistent with the natural choice for a reference lithospheric column that has a near‐zero geoid
associated with zero elevation; a feature that is
exploited below in the discussion of partitioning
deformational strain between the crust and mantle
lithosphere.
[11] Haxby and Turcotte [1978] showed that in
the limit of long‐wavelength and complete isostatic
compensation, the geoid anomaly caused by density
variations above the depth of compensation is proportional to the vertical dipole moment of the mass
distribution above the depth of compensation:
2G
DN ¼
g
ZD
zDð zÞdz
S
where DN is the geoid anomaly; G, Newton’s
gravitational constant; g, the value of gravitational
acceleration on the reference ellipsoid; D, the depth
of compensation (the depth below geoid at which
pressure becomes equal beneath columns in isostatic
balance, or here, where lateral density differences
cease); S, the surface elevation; z, the depth; and
Dr(z) the lateral difference in density from a reference lithosphere, including crust. There are two
important implications of this formulation that are
germane to this study: (1) the geoid anomaly over
continents should increase both with increasing
elevation and increasing average depth of compensation [Turcotte and Mcadoo, 1979; Turcotte and
Schubert, 2002] and (2) for a particular elevation,
the greater the depth extent of the isostatic “root” (or
the deeper the source of buoyancy) the larger the
resulting geoid anomaly. The linear relationship
between gravity and topography can be used in a
variety of ways for geodynamic applications. Two
application of interest are of interest here. First, for a
region where both the topography and gravity are
measured over an area that is several times greater
than the flexural wavelength (i.e., >∼100 km), the
gravity‐topography transfer function relationship
(also referred to as the admittance or “isostatic
response function”) can be evaluated to extract
information about the isostatic state of the lithosphere. This approach has also been used to evaluate
the flexural rigidity of the lithosphere [McNutt and
Menard, 1982] and to estimate the elastic thickness of the lithosphere [Banks et al., 1977; Dorman
and Lewis, 1972; McKenzie and Bowin, 1976;
McNutt and Menard, 1979; Watts, 1978]. A second
application is for wavelengths greater than the
flexural wavelength and where features are iso6 of 18
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statically compensated, in which case the geoid/
topography ratio (GTR) can be used to estimate the
depth of compensation in the spatial domain [Haxby
and Turcotte, 1978]. A low GTR value (in the range
of 2–4 m/km) indicates the topography is shallowly
supported by thickened crust (dominantly Airy
compensation), and intermediate GTR (in the range
of 5–7 m/km) suggests deeper compensation that is
related to lithospheric thinning [Crough, 1978] and a
high GTR value (greater than ∼7 m/km) is reflective
of dynamic support from sublithospheric sources
such as mantle convection. As will be discussed
below, however, these general values for GTR and
corresponding depths of compensation (without
reference to the surface elevation) are applicable
only to Pratt‐Hayford isostasy; for other mechanisms of compensation including Airy‐Heiskanen
and pure lithospheric thinning there is a linear correlation between the GTR and surface elevation.
3. Compensation Mechanisms
in the Western United States
[12] The
near‐zero free‐air gravity anomaly
throughout the western United States is indicative of
long‐wavelength isostatic equilibrium and allows
the use of isostatically balanced lithospheric columns for understanding the relative geometries
of the crust and mantle lithosphere that result in
plausible models for compensating the topography.
It is clear that compensation is a process that incorporates the whole lithosphere; see, for example,
the discussion about the case of the Colorado Plateau
in [Coblentz et al., 2007]. As a result, in order to
achieve more accurate estimates of the vertical distribution of compensating mass anomalies, isostatic
calculations must consider the mantle lithosphere as
well as the crust.
[13] The fc‐fl diagram [Coblentz and Stüwe, 2002;
Sandiford and Powell, 1990] provides a convenient
way to evaluate how vertical strains in the lithosphere may be decoupled between crustal and
mantle components. Following Sandiford and
Powell [1990] we defined the fc as the ratio of
deformed to referenced crustal thickness and fl as
the ratio of the deformed to reference total lithospheric thickness. This approach using 1‐D vertical
columns to represent the lithosphere so “deformed”
in this case is the vertical strain of the lithospheric
column. For example, fc = 2.0 implies a doubling of
the crustal thickness from the reference thickness to
the “deformed” thickness. The origin of the fc‐fl
plane (where fc = fl = 1.0) corresponds to an unde-
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formed “equilibrium” lithosphere where there is
no vertical strain. This is also the state that the crust
and lithosphere will tend toward in the absence of
deformational forces [Sandiford and Powell, 1990].
Completely undeformed lithosphere lies at the center of the of the fc‐fl plane with larger and smaller
values of fc and fl corresponding to thicker and
thinner crustal or lithospheric thicknesses, respectively. Here we assume a reference lithospheric
column as 30 km of 2800 kg/m3 crust overlying
mantle lithosphere with a density of 3300 kg/m3
extending to a depth of 100 km.
[14] Deformational paths in the fc‐fl plane tend to
be closed paths, starting at the origin and returning
there eventually. Three typical deformational paths
are shown in Figure 3. Deformation that involves
only a change in crustal thickness without a change
in the mantle lithospheric thickness, follows path A
with fl = 1 until the crust is nearly doubled ( fc approaches 2.0). The surface elevation in response to
this crustal thickening increases to a height of 4 km
with a corresponding geoid anomaly of about 20 m.
Alternatively, the case of thermal thinning (Path B)
leads to a reduction in the mantle lithosphere thickness with no substantial change in crustal thickness.
In this case, fc = 1 and fl < 1 and the deformation
path in the fc‐fl plane is vertical, parallel to the fc axis.
Path B in Figure 3 illustrates the response in the
surface elevation (∼1.6 km) and geoid anomaly
(5 m) associated with this type of lithospheric
deformation. It clear from many recent studies (see
review by Coblentz and Stüwe [2002]) that lithospheric deformation often involves a hybrid of
these two cases. In the case of isostatic continental
plateaus, lithospheric strain is typically partioned
between crustal thickening ( fc > 1) and overall
lithospheric thinning ( fl < 1). Path C in Figure 3
illustrates this type of composite deformation ( fc =
1.6 and fl = 0.61, defining crustal thickening to
48 km and mantle lithosphere thinning to 61 km).
The resulting surface elevation is ∼3.7 km with a
geoid anomaly ∼20 m. Below, we employ the
fc‐fl approach to quantifying lithospheric strain
of balanced 1‐D isostatic columns (an appropriate
approach given the very long wavelength topographic features under consideration) to evaluate
the compensation mechanism for the southern
Rockies and its neighboring tectonic provinces.
[15] Figure 4 illustrates the GTR‐elevation values
for the four fundamental compensation mechanisms: (1) Pratt, (2) pure Airy ( fc > 1, fl = 1, corresponding to only crustal thickening, path A in
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Figure 3. (a) The fc‐fl space [Sandiford and Powell, 1990; Coblentz and Stüwe, 2002] contoured for surface elevation,
geoid, and geoid‐elevation ratio based on deformation of the reference column shown in Figure 3b. Three deformation
paths are illustrated: path A is pure crustal thickening ( fc > 1 and fl = 1), path B is pure mantle lithospheric thinning ( fc =
1 and fl < 1), and path C is a distributed strain case with both crustal thickening ( fc > 1) and mantle lithospheric thinning
( fl < 1). (b) The lithospheric crust and mantle geometries resulting from these three cases. See text for discussion.
spheric ( fc = 1, fl < 1, path B in Figure 3), and (4) a
combined strain path ( fc > 1, fl < 1, corresponding
to combined crustal thickening and mantle lithospheric thinning, path C in Figure 3). Also plotted
in Figure 4 are the relative GTR‐elevation values
for the Colorado Plateau (CP), southern Rocky
Mountains (SRM), Northern Basin and Range (NBR),
and Yellowstone (YS) to facilitate the evaluation of
plausible compensation mechanisms.
[16] Pratt‐type compensation (Figure 4a) yields a
constant GTR value independent of surface elevation and for the mantle density contrast assumed
here (r = 3300 km) a low GTR value (∼3 m/km)
indicates shallow compensation supported by thickened crust (depth of compensation = 50 km), an
intermediate GTR of ∼4–5 m/km corresponds to
deeper compensation (∼75 km), and a GTR value
∼6 m/km corresponds to deep support (depth of
compensation = 100 km). In the context of Pratt
compensation, the topography of Yellowstone
requires a very deep compensation depth of greater
than about 120 km while the Colorado Plateau and
southern Rockies can be supported with near crustal
compensation depths of 55 km and 68 km, respec8 of 18
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Figure 4. The predicted GTR‐elevation values for the four fundamental compensation mechanisms: (a) Pratt, (b) pure
Airy ( fc > 1, fl = 1, corresponding to only crustal thickening (path A in Figure 3)), (c) thinning of the mantle lithosphere
(thermal thinning) with fc = 1, fl < 1 (path B in Figure 3), and (d) a combined strain path ( fc > 1, fl < 1, corresponding to
combined crustal thickening and mantle lithospheric thinning (path C in Figure 3)). Also plotted are the relative GTR‐
elevation values for the Colorado Plateau (CP), southern Rocky Mountains (SRM), Northern Basin and Range (NBR),
and Yellowstone (YS).
tively. We note that the Northern Basin and Range
has a significantly deeper Pratt depth of compensation of about 87 km.
[17] In contrast to Pratt compensation, the other
three compensation mechanisms considered have
a linear relationship between the GTR values and
the surface elevation (z). The GTR for Airy compensation is proportional to h2 and therefore the Airy
GTR is a function of h with a relatively small slope
(Figure 4b). The Airy GTR is also dependent on the
Lo (the reference lithospheric thickness) with a GTR
variation of about 1.25 m/km as Lo ranges from
60 km to 120 km. We note that given the crustal and
mantle lithospheric density variations used here (rc =
2750 kg/m3 and rc = 3300 kg/m3), only the NBR
province has GTR and surface elevation values that
fall with the plausible ranges of Airy GTR. That is,
the geoid for SRM is too low relative to the surface
elevation for Airy compensation to be a viable
compensation mechanism for the Rockies.
[18] The GTR for thermal thinning (Figure 4c;
mantle lithospheric thinning, fl < 1; and constant
crustal thickness, fc = 1) differs significantly from
the Airy GTR and is characterized by a steep, negative slope with respect to z. This results from the
fact that the thermal density contrast resulting from
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required crustal (30 km) and mantle lithospheric
geometries (NBR Ld = 54 km, CP Ld = 36 km) are
inconsistent with known crustal and mantle lithospheric thicknesses for these provinces (i.e., zcrust =
35 km in the NBR and ∼43 km in the CP and
zlithosphere = ∼65 km and ∼98 km in the NBR and CP,
respectively [Coblentz et al., 2007]). In the case of
the southern Rockies, the observed surface elevation
cannot be achieved through thinning of the mantle
lithosphere alone, eliminating the plausibility of
this compensation mechanism for supporting the
topography of the Rockies.
[19] As discussed in the Introduction, and high-
Figure 5. The location in fc‐fl space of plausible lithospheric geometries (indicated by the diamonds for the
NBR, circles for the CP, triangles for YS, and squares
for the SRM) for the four principal tectonic provinces
of the western United States at consistent observed
GTR‐elevation values. The initial total lithospheric thickness (Lo) for the initial reference column is indicted.
While plausible geometries for most of the tectonic
provinces are tightly clustered, the NBR is poorly constrained in terms of plausible mantle lithospheric thicknesses. Furthermore, we note that in contrast to the
neighboring provinces, the southern Rockies province
requires a thin initial lithospheric thickness of about
80 km.
fl < 1 is much smaller than the crustal density contrast. This compensation mechanism has an upper
elevation limit (designated by the termination of
the curves in Figure 4c) that corresponds to the fl
value that produces a mantle lithospheric thickness
equal to the reference crustal thickness (30 km), i.e.,
where the mantle lithosphere disappears entirely. In
the case of a reference lithospheric with a thickness
of 100 km fl is limited to 0.30 and the maximum
surface elevation is about 1.6 km. As illustrated
in Figure 4c, the GTR‐elevation values of the NBR,
CP and YS fall within the plausible ranges of the
thermal thinning model. For example, the 2.4 km
average surface elevation and ∼7 m/km GTR of
Yellowstone can be produced by pure mantle lithospheric thinning of a 175 km reference lithosphere
with a thinning factor of fl = 0.44 (producing a final
lithospheric thickness, Ld, of 77 km with an undeformed crust of 30 km). While the same deformational mechanism operating on a thinner reference
lithosphere (Lo = 120 km) results in GTR‐elevation
values for the NBR and the CP that are consistent
with observed geoid and elevation values, the
lighted by the results of the GTR‐elevation values
for the pure mantle thinning case, the most likely
lithospheric deformation scenarios in the western
United States involve both crustal and mantle lithospheric strain. Relative to the reference lithospheric
column, the tectonic provinces in the western United
States are characterized by a combination of crustal
thickening (fc > 1) and lithospheric thinning (fl < 1),
and follow a deformation along path C in Figure 3.
The GTR values are dependent on both the initial
reference lithospheric thickness and the fc‐fl deformation path. The GTR‐elevation values for the path
with fc varying from 1.0 to 1.5 as fl varies from 1.0
to 0.4 (roughly path C in Figure 3) are shown in
Figure 4d. The lithospheric thinning results in a
negative slope of the GTR as a function of elevation
but the slope is less pronounced than for the pure
thermal thinning case. For this particular deformation path, the GTR‐elevation values of the four
provinces can be reproduced by varying the initial
lithospheric thickness (Lo).
[20] Plausible crustal and mantle lithosphere strains
(as indicated by locations in fc‐fl space) that correspond with the observed GTR‐elevation values for
the Colorado Plateau, Northern Basin and Range,
Yellowstone, and the southern Rocky Mountains
is shown in Figure 5. Here we have explored the
solution space by evaluating a suite of initial lithospheric values (Lo) in the range of 60 to 140 km and
calculating the fc‐fl ranges that generate the observed
GTR‐elevation values for the four tectonic provinces. Lithospheric thickness values (Lo) vary from
more than 140 km for Yellowstone to more intermediate values for the NBR (Lo = 110–120 km) and
the CP (Lo = 90–100 km) and relatively thin values
for the SRM (Lo = 80 km). While the range of
plausible fc‐fl values for the provinces are generally
tightly clustered, the exception is the Northern Basin
and Range where a large number of fc‐fl combinations satisfies the observed GTR values. We note
that crustal thickness in the range of 32 to 37 km and
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overall lithospheric thickness values of about 52 to
90 km are indicated. Because the generally accepted
lithospheric thickness in the Northern Basin and
Range is about 65 km, the range of fc‐fl values
delineated by the green‐filled circles (corresponding
to a lithospheric than thinned from 120 km to a range
of 60 to 72 km with) are the most plausible. The
crustal thicknesses of the other three provinces
considered fall in the range of 40 to 44 km which is
consistent with the minimum end of the generally
accepted values. This analysis indicates that with the
exception of the Colorado Plateau, the major tectonic provinces of the western United States have all
undergone more than 40 km of lithospheric thinning
during their tectonic evolution.
4. Coherence and Admittance Analysis
[21] Because compensation mechanisms eventually
produce responses at different wavelengths it is not
an easy task to separate the relative role of short‐
(isostatic) versus long‐wavelength (flexure) compensation of topography using the 1‐D analysis in
section 3. To help estimate the relative roles of these
two mechanisms, we turn next to an evaluation of
the admittance and coherence functions (or the
spectral measure of the gravity/geoid to topography
relationship in the frequency domain).
[22] The spectral relationship between topography
and gravity has been used in many studies to evaluate the form of isostatic compensation in continental regions [Banks et al., 1977; Bechtel et al.,
1990, 1999; Dorman and Lewis, 1970; Forsyth,
1985; Londe, 1990; McKenzie and Bowin, 1976;
Pilkington, 1990] in particular to help constrain
estimates of the elastic thickness of the lithosphere.
A similar analysis using the geoid has been commonly used to investigate the depth and mechanism
of isostatic compensation in ocean plateaus and swells
[Cserepes et al., 2000; Grevemeyer, 1999; Sandwell
and Renkin, 1988; Sandwell and MacKenzie, 1989;
Wessel, 1993].
[23] Other works have been focused on the viscous
mantle flow associated with thermal convection and
induced dynamic topography [Panasyuk and Hager,
2000]. Here we evaluate the coherence and admittance between the gravity (free air and Bouguer) and
geoid fields and the topography along four profiles
through the southern Rockies (38°N, 38.5°N, 39°N,
and 39.5°N) extending from 117°W to 100°W. A
composite image of the profiles (Figure 6a) illustrates the strong (qualitative) correlation between the
10.1029/2010GC003459
Bouguer gravity, the geoid, the upper mantle velocity
anomaly at 110 km [Schmandt and Humphreys,
2010], and topography across the southern Rockies
(that is, the highest topography corresponds to the
lowest Bouguer gravity anomaly, a pronounced
negative Vp velocity anomaly, and the highest geoid
anomaly). As noted previously, the free‐air gravity
anomaly is near zero across most of this region
(indicative of isostatic equilibrium). In order to
include as much short‐wavelength geoid information
as possible, we have used the harmonic expansion from EGM2008 [Pavils et al., 2008] which
contains spectral information out to degree/order
2190 (corresponding to a spatial wavelength of
about 18 km). Because this geoid is sensitive to
sources in the upper mantle (harmonic depth cutoff
of about 700 km), we have renamed this geoid the
“Upper Mantle‐Lithospheric Geoid.” The spectral
power of the Bouguer gravity, free‐air gravity, geoid
and topography along the 38.5°N is shown in
Figure 6b. All four share a characteristic red spectra
(i.e., greater power at longer wavelengths) with the
gravity fields (on the order of tens to hundreds of
mGal) having significantly more spectral power
than the topography (in the range of 0 to 4 km) and
geoid (in the range of 0 to 10 m). We note that the
spectral power of both the gravity and the topography‐geoid fields converge at wavelengths on the
order of the lithospheric thickness; at ∼110 km for
the Bouguer and free‐air gravity fields and ∼90 km
for the geoid‐topography fields.
[24] Any load on the lithosphere can, in general, be
expressed as a Fourier series of different wavelength
loads [Dorman and Lewis, 1970]. In the Fourier
domain, the admittance, Z(k), is the ratio between the
gravity anomaly, G(k), caused by a topographic load
on an elastic plate and the magnitude of the topography, H(k), where G(k) and H(k) are the Fourier
transforms of the Bouguer anomaly and the topography, respectively, and k is the wave number
(k = 2p/l):
Gðk Þ ¼ ZðkÞHðkÞ
Thus the admittance represents a ratio of the
amplitudes between gravity anomaly and topography. The coherence, on the other hand, is a measure
of the correlation between the gravity anomaly and
the topography; or more formally, the square of the
correlation coefficient in the frequency domain
between the two signals. The coherence and admittance and between the gravity/geoid fields and
the topography for the four profiles are shown in
Figure 7.
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Figure 6. (a) Variations in the free‐air and Bouguer gravity anomalies, topography, upper mantle velocity anomaly at
110 km [Schmandt and Humphreys, 2010], and the upper mantle‐lithospheric geoid (see text for explanation) along four
profiles centered on 38.5°N, 38.5°N, 39°N, and 39.5°N. The composite profiles illustrate the strong correlation between
the high topography, upper mantle velocity anomaly, geoid, and Bouguer gravity across the southern Rockies. (b) The
spectral power for the Bouguer gravity, free‐air gravity, geoid, and topography along the 38.5°N profile illustrating the
characteristic red spectra of these fields.
[25] The coherence between the Bouguer gravity
and topography is particularly useful for evaluating
the elastic thickness of the lithosphere (Te). Theoretical curves for various values of the elastic
thickness (assuming a uniform load on the surface of
the lithosphere and a crustal thickness of 30 km) are
shown as the light blue lines in Figure 7a for a range
of Te values (20 to 50 km). Large topographic loads
will flex even very strong plates (i.e., Te = 50 km);
isostatic compensation produces a large Bouguer
anomaly and a coherence that approaches unity
(for very long wavelengths). Shorter‐wavelength
features, in contrast, will be adequately supported by
the plate’s mechanical strength, generating little or
no associated Bouguer anomaly. Thus the coherence approaches zero for short wavelengths. The
wavelength corresponding to the transition between
coherent and incoherent gravity and topography
provides a direct indication of the flexural rigidity
(see discussion by Forsyth [1985], particularly on
the subject of surface versus internal loading of the
lithosphere). The wavelength corresponding to a
coherence of about 0.5 provides an estimate of the
length scale at which isostatic compensation begins
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Figure 7. The (left) coherence and (right) admittance between the potential fields and topography: (a) Bouguer gravity,
(b) free‐air gravity, and (c) geoid along the four profiles shown in Figure 6. Light blue lines in the Bouguer gravity‐
topography coherence plot are theoretical curves for various values of the elastic thickness (assuming a uniform load on
the surface of the lithosphere and Moho thickness of 30 km). Theoretical admittance curves are shown in the Bouguer
gravity‐topography admittance plot for values of ro = 2700 kg/m3, dr = 670 kg/m3, and zc = 35 km. The dark blue
curve is the admittance curve for the pure Airy compensation case which corresponds to a flexural rigidity of zero.
(d) Coherence between the Bouguer and free‐air gravity anomaly (blue) and Bouguer gravity anomaly and the geoid
(red) illustrating the sharp dropoff in the coherence at wavelengths greater than 100 km.
to prevail over mechanical support (as load size
increases). As indicated by the theoretical curves in
Figure 7, the transition wavelength for strong/thick
plate can be as large as 600 km (for Te = 50 km) and
will be considerable less for weak/thin plates (e.g.,
about 275 km for Te = 20 km). In the case of the
profiles considered here, loads with l ∼ 225 km
delineate the transition from mechanical to isostatic
compensation. Referencing the theoretical curves in
Figure 7, this is suggestive of an elastic thickness of
less than 20 km.
[26] The admittance also depends on the elastic
thickness and can be viewed as a filter which predicts the gravity anomaly given the topography
[McKenzie and Bowin, 1976]. As discussed by
Forsyth [1985] the isostatic response function for
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a model of a thin elastic plate loaded on top by
topography of density ro is:
QðkÞ ¼ 2 o G expðk zc Þ=
where
10.1029/2010GC003459
geoid relationship most likely located in the upper
mantle.
5. Discussion
[29] Using the fact that at long wavelengths the GTR
4
¼ 1 þ D k = g
where G is defined as the gravitational constant;
D, the flexural rigidity of the plate; g, the gravitational acceleration; dr, the density contrast at
the compensation interface (e.g., the crust‐mantle
density contrast), and zc the depth to the density
contrast (e.g., the crustal thickness). Theoretical
admittance curves for values of ro = 2700 kg/m3,
dr = 670 kg/m3, and zc = 35 km, are shown as light
blue curves in the admittance plot in Figure 7.
The dark blue curve is the admittance curve for the
pure Airy compensation case which corresponds to
a flexural rigidity of zero. The gravity anomaly
produced by topography with l < ∼200 km is
less than about 10 mGal/km and is consistent with
a Te < 20 km.
[27] For wholly uncompensated topography the
free‐air anomaly rather than the Bouguer gravity
will correlate with topography [Lambeck et al.,
1988; McKenzie and Fairhead, 1997]. We note,
however, that the coherence between the free‐air
gravity and the topography (Figure 7b) is similar to
Bouguer gravity coherence (particularly at wavelengths less than 200 km). For wavelengths greater
than 300 km, however, the coherence of the free
air and topography is significantly less than the
Bouguer gravity‐topography coherence. Consistent
with the general observation that the free‐air gravity
anomaly is near zero for most of the region
[Thompson and Zoback, 1979] the free‐air admittance is near zero for all wavelengths.
[28] In contrast to the gravity fields, the coherence
between the geoid and topography is high (greater
than 0.75 for most wavelengths along the four profiles) substantiating the notion that there is a strong
correlation between the geoid and topography.
Figure 7 illustrates that this is the case for nearly all
wavelengths of topography (we do note, however,
there is considerable scatter in the coherence for the
most northern of the profiles considered (39.5°N).
The admittance between the geoid and topography
is low (<2 m/km) for wavelengths less than about
200 km, and increases significantly to the range of
3–4 m/km at longer wavelengths. This is suggestive of significant, deep sources for the topography‐
can be used to constrain the depth and mode of
compensation [Sandwell and Renkin, 1988] we have
evaluated various mechanisms by which the high
topography of the southern Rocky Mountains can
be isostatically compensated. Within the framework of the neighboring tectonic provinces there are
several commonalities that have important tectonic
implications.
[30] We first considered the geoid‐elevation ratios
based on first‐order 1‐D isostatically balanced
lithospheric columns. Using this approach, several
generalities can be applied. In general, features with
a GTR greater than ∼6 m/km are sublithospherically
compensated and are dynamically supported by
convective stresses [McKenzie et al., 1980]; that
is, supported by dynamic topography generated by
convection. The relatively high GTR value computed for Yellowstone (∼7 m/km) is consistent with
this scenario. Low GTR values (<2 m/km) are
associated with shallowly (<50 km) Airy or Pratt‐
type compensated plateaus [Angevine and Turcotte,
1983]. We note that none of the western U.S. tectonic provinces considered here fit this category.
Finally, intermediate GTR values in the range of
2–6 m/km reflect average compensation depths of
50–80 km and suggests reheating of the lower lithosphere [Crough, 1978]. Given that we find such
GTR values for the western United States (∼3.9 for
the southern Rockies, ∼4.25 for the Colorado Plateau, and ∼5.2 for the Northern Basin and Range),
some kind of mantle lithospheric thinning in conjunction with crustal thickening is the most plausible
compensation mechanism in the western United
States. The notion that lithospheric strain is partioned between the crust and mantle lithosphere
is supported by previous investigations [Sandiford
and Powell, 1990].
[31] While isostatic elevation changes can be the
result of either crustal or mantle lithosphere mechanisms, our analysis of the geoid‐topography relationship indicates that variations in the thickness of
both the crust and mantle lithosphere are required to
produce the modern elevation of the western United
States in general and the southern Rockies in particular. In the case of the central Rockies, a combination of a thick crust (∼45 km) in conjunction
with significant thinning of the mantle lithosphere
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Figure 8. Spatial correlation between (a) the topography, (b) crustal thickness (a composite based on CRUST 5.1 and
seismic results from analysis of the EarthScope transportable Array (TA), the PASSCAL/Flexible Array, and the
CREST experiment), (c) the upper mantle Vp velocity anomalies at 110 km [Schmandt and Humphreys, 2010], and
(d) the calculated geoid‐elevation ratios from this study. We note that the crustal thickness under the southern Rockies is
“nonthickened” in the sense that observed values of 42–45 km are at odds with the high‐standing topography.
since the Oligocene (30 Ma) (presumably related to
delamination of a denser upper mantle or thermal
erosion) can explain the recent and pronounced
uplift. In terms of the neighboring provinces, we find
that the Colorado Plateau topography can be supported by a combination of relatively undisturbed
mantle lithosphere with significant crustal thickening (Figure 5); in the Northern Basin and Range,
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in contrast, a wide range of mantle lithospheric
strains in combination with moderate crustal thickening satisfies the observed GTR information. As
expected, mantle thinning plays a large role for
Yellowstone (with more than 50 km of thinning
of initial very thick lithosphere. In general we find
that with the exception of the Colorado Plateau,
the major tectonic provinces of the western United
States have all undergone more than 40 km of lithospheric thinning during their tectonic evolution.
[32] Recent studies that evaluated the role of the
crustal portion of lithospheric buoyancy and concluded that pure Airy‐type correlation between
elevation and crustal thickness (i.e., thicker crust
associated with higher elevation), exists only where
the crust is very thick (>55 km) or very thin, less than
20 km [Zoback and Mooney, 2003]. The important
tectonic implication is that non‐Airy lithospheric
compensation is more common than traditionally
thought. This is indeed the case for the southern
Rockies where the emerging picture of a tectonic
setting where the observed crustal thicknesses
(Figure 8b) are not big enough to compensated the
high topography (Figure 8a) by purely Airy compensation. The lack of “sufficient” crustal roots
beneath the central Rockies in conjunction with the
existence of profound upper mantle velocity variations (Figure 8c) and high coherence between
the geoid and the topography (Figure 7) supports
the notion that the anomalous upper mantle in the
western United States (and the associated mantle
buoyancy) is a significant contributor to surface
elevation (a notion dating back many years to
Thompson and Talwani [1964]).
[33] Our conclusion that upper mantle dynamic
processes play an important role in the support of
the topography of the central Rocky Mountains
raises the question of supporting, but plausible,
geodynamic scenarios for the region. An assumption that observed upper mantle velocity variations
(Figure 8c) are purely thermal, anelastic velocity‐
temperature mapping of velocity anomalies constrains the anomalies to be 200–300°C warmer than
a 1300°C mantle adiabat for a pyrolitic mantle
composition [Cammarano et al., 2003; Moucha
et al., 2009; van Wijk et al., 2010]. Such thermal
heterogeneity at short scales requires advective
transport of warmer than normal mantle rising from
a deep thermal boundary layer. At larger scales,
inversion of a global seismic traveltime and geodynamic surface observables for a mantle thermal/
composition model [Simmons et al., 2009] find
the southwestern United States to be a region of
upwelling warm mantle from the base of the mantle
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[Moucha et al., 2009]. A plausible hypothesis then,
is that complex small‐scale upper mantle convection
and resulting buoyancy variations are driving of
dynamic uplift (on the order of 400–800 m [van Wijk
et al., 2010]) in many parts of the western United
States and is actively reshaping the physiographic
characteristics of western U.S. tectonic provinces.
This observation is consistent with recent Apatite
fission track thermochronology that shows rapid
exhumation in the Rockies starting 10–6 Ma at
modern elevations ranging from 1.5 to 3 km,
requiring Neogene tectonic uplift [Karlstrom et al.,
2008, 2010].
6. Conclusions
[34] Within the framework of the assumptions made
for this study, we draw two principal conclusions:
(1) a major portion of the buoyancy that has driven
uplift in the southern Rockies resides at depths less
than 100 km and that upper mantle processes such
as small‐scale convection may play a significant
role in the buoyant uplift of the southern Rockies (as
well as other actively uplifting areas of the western
United States) and (2) the high coherence for the
geoid‐topography relationship for nearly all wavelengths between 50 and 1000 km suggests an intimate relationship between upper mantle dynamic
processes and the surface topographic character.
Acknowledgments
[35] This work has benefited from productive conversations with
a number of investigators. In particular, we acknowledge the
insightful comments and suggestions provided by the CREST
working group (including but not limited to Ken Dueker, Rick
Aster, Jonathan MacCarthy, Andres Aslan, and Sheri Kelley).
Randy Keller and an anonymous reviewer are thanked for insightful comments. Jonathan MacCarthy is thanked for providing Figure 1. This manuscript is released under Los Alamos
National Laboratory LAUR‐10‐08105.
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