JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, B01411, doi:10.1029/2002JB002284, 2004
Steady state erosion of critical Coulomb wedges with
applications to Taiwan and the Himalaya
G. E. Hilley1 and M. R. Strecker
Institut für Geowissenschaften, Universität Potsdam, Potsdam, Germany
Received 1 November 2002; revised 14 July 2003; accepted 2 October 2003; published 23 January 2004.
[1] Orogenic structure appears to be partially controlled by the addition to and removal of
material from the mountain belt by tectonic accretion and geomorphic erosion,
respectively. We developed a coupled erosion-deformation model for orogenic wedges
that are in erosional steady state and deform at their Coulomb failure limit. Erosional
steady state is reached when all material introduced into the wedge is removed by erosion that is
limited by the rate at which rivers erode through bedrock. We found that the
ultimate form of a wedge is controlled by the wedge mechanical properties, sole-out depth
of the basal decollement, erosional exponents, basin geometry, and the ratio of the added
material flux to the erosional constant. As this latter ratio is increased, wedge width
and surface slopes increase. We applied these models to the Taiwan and Himalayan
orogenic wedges and found that despite a higher flux of material entering the former, the
inferred ratio was larger for the latter. Calculated values for the erodibility of each wedge
showed at least an order of magnitude lower value for the Himalaya relative to Taiwan.
These values are consistent with the lower precipitation regime in the Himalaya relative to
Taiwan and the exposure of crystalline rocks within the Himalayan orogenic wedge.
Independently determined rock erodibility estimates are consistent with the accretionary
wedge sediments and metasediments and the crystalline and high-grade metamorphic
rocks exposed within Taiwan and the Himalaya, respectively. Therefore differences in
rock type and climate apparently lead to key differences in the erosion and hence orogenic
INDEX TERMS: 1824 Hydrology: Geomorphology (1625);
structure of these two mountain belts.
8110 Tectonophysics: Continental tectonics—general (0905); 8020 Structural Geology: Mechanics; 8102
Tectonophysics: Continental contractional orogenic belts; 8107 Tectonophysics: Continental neotectonics;
KEYWORDS: critical Coulomb wedge, fluvial bedrock incision, Himalaya, Taiwan
Citation: Hilley, G. E., and M. R. Strecker (2004), Steady state erosion of critical Coulomb wedges with applications to Taiwan and
the Himalaya, J. Geophys. Res., 109, B01411, doi:10.1029/2002JB002284.
1. Introduction
[2] Many recent studies [e.g., Dahlen and Suppe, 1988;
Dahlen and Barr, 1989; Barr and Dahlen, 1989; Beaumont
et al., 1992; Willett and Beaumont, 1994; Willett, 1999;
Horton, 1999; Beaumont et al., 2001; Willett and Brandon,
2002] show that erosional processes exert an important
control on the structure of orogens. Specifically, the construction of high topography creates gravitational body
forces that may favor the migration of deformation to
lower-elevation areas [e.g., Willett and Beaumont, 1994;
Royden, 1996]. Where erosional processes are efficient
relative to tectonic accretion, material is transported from
the interior to the exterior of an orogen, reducing the
topography and gravitational load. In this case, deformation
and orogenic structure may be focused in a relatively small
area [Willett, 1999]. However, where erosional processes are
1
Now at Department of Earth and Planetary Sciences, University of
California, Berkeley, California, USA.
Copyright 2004 by the American Geophysical Union.
0148-0227/04/2002JB002284$09.00
inefficient, accreted material is stored in the orogen’s
interior, resulting in the continual migration of deformation
toward its margins [e.g., Royden, 1996].
[3] The relationship between topographic slope and the
triangular geometry of an orogenic wedge was first explored
by considering brittle, cohesionless orogenic wedges that
deform at their Coulomb failure limit [Davis et al., 1983;
Dahlen, 1984]. In addition, Dahlen and Suppe [1988] and
Dahlen and Barr [1989] recognized that erosion may act to
modify the deformation within such wedges and their
geometries by removing material from their interiors. As
this removal occurs, two effects are seen: (1) the wedge
grows in width until all of the material accreted to the toe of
the orogen is removed by erosional processes acting along
its surface, and (2) the orogenic wedge adjusts its internal
kinematics to accommodate the local variations in erosion
rates [Dahlen and Barr, 1989]. In these studies, two simple
erosion laws were prescribed in which a uniform erosion
rate was specified to erode the entire width of the orogen,
and this erosion rate was allowed to vary as a function of
elevation [Dahlen and Barr, 1989]. Recently, a series of
geodynamic modeling studies have revisited these interac-
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tions between surface processes and tectonics by considering more complicated rheological conditions [e.g., Willett,
1999; Beaumont et al., 2001]. The results have been
quantitatively compared to the Taiwanese orogenic wedge
[e.g., Dahlen and Barr, 1989] and qualitatively compared to
the Southern Alps of New Zealand and the Olympic
Mountains in Washington State, USA, for example [Willett,
1999]. These studies highlight the importance of erosional
processes in determining tectonic deformation patterns and
thermochronologic age distributions [Willett and Brandon,
2002]. However, the simple treatment of erosion in these
studies may hamper quantitative tests of these models that
relate the orogen’s geometry directly to rock erodibility or
climatic conditions. For example, Dahlen and Barr [1989]
found that erosion rates inferred for Taiwan based on its
geometry were consistent with those inferred by fission
track studies of this island. However, these quantities cannot
be related directly to landscape attributes such as rock
erodibility and climate, and so for example, cannot be used
to predict the effect of the exposure of different rock types
within the wedge on its geometry. Likewise, the treatment
of erosion as a simple power law in which the erosion rate is
linearly proportional to orogen slope and catchment area
[e.g., Willett, 1999] neglects a more complex power law
dependence on these factors that appears to be required by
detailed field studies of bedrock channels [e.g., Howard and
Kerby, 1983; Whipple et al., 1999; Whipple and Tucker,
1999; Sklar and Dietrich, 1998, 2001]. Because these
geodynamic models have shown that exhumation patterns
and orogenic forms are sensitive to spatial variations in
erosional power within the orogen, properly characterizing
the relations between channel slope and catchment area are
essential to make quantitative comparisons between tectonically active mountain belts and process-based models.
Instead of these simple erosional models, many workers
have endorsed fluvial bedrock incision as the rate-limiting
erosion process in orogens [e.g., Whipple et al., 1999].
Studies that relate the rate of erosion in bedrock channels to
channel slope and catchment area suggest that erosion may
not be linearly proportional to channel slope and catchment
area [e.g., Howard and Kerby, 1983; Sklar and Dietrich,
1998] and may vary depending on the processes that act to
erode the channel bed [Whipple et al., 2000].
[4] In this study, we constructed a coupled model of
bedrock fluvial incision and topographic loading of the crust.
This approach allows us to directly examine dependence of
wedge geometry on factors such as the types of rocks exposed
in the orogen and the climatic conditions acting to erode the
wedge. We used the critical Coulomb wedge (CCW) theory
[Davis et al., 1983; Dahlen et al., 1984; Dahlen, 1984] and
simple models of mass accretion in an orogenic wedge to
constrain the relationship between deformation and topography. We focused on the condition in which all material
accreted to the orogen by tectonic processes is removed by
erosion (hereafter referred to as a steady state orogen). We
found that the orogenic wedge geometry is related to the ratio
of the mass flux of tectonically accreted material and the
bedrock incision erosion constant. As this ratio increases,
orogenic width increases. This steady state coupled erosiondeformation model is applied to Taiwan and the Himalaya,
which are interpreted to be in tectonic and erosional steady
state [Suppe, 1981; Hodges, 2000; Hodges et al., 2001].
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Good agreement was found between the inferred values of
the erosional constants, the rock types exposed in each
orogen, and independently determined values of erodibilities
of similar rocks [Stock and Montgomery, 1999]. Interestingly,
while the tectonic accretion of material to the Taiwan
orogenic wedge is significantly larger than along the Himalaya, easily eroded accretionary complex sediments and
abundant precipitation result in a narrower orogen than the
dryer Himalaya, which comprises rocks of lower erodibility.
2. Model Formulation
[5] We combine the CCW model [Davis et al., 1983;
Dahlen, 1984] with models of tectonic accretion of material
[DeCelles and DeCelles, 2001] and erosion by bedrock
incision [e.g., Howard and Kerby, 1983; Seidl and Dietrich,
1992]. This work examines a subset of conditions whose
complete formulation is presented by Hilley et al. [2003].
We model the relationship between topography and deformation by assuming that the orogenic wedge is approximately triangular in cross section, a situation that arises in
cohesionless wedges that deform at their Coulomb failure
limit [e.g., Davis et al., 1983; Dahlen, 1984] (Figure 1). In
this case, the decollement is planar until it reaches the its
sole-out depth (D in Figure 1). Under these conditions, the
width is related to the basal fault dip of the wedge (b) and D.
Likewise, the surface slope (a) of the orogenic wedge
remains constant along its width. Convergence may be
accommodated by introduction of material into the back
of the wedge (left side in Figure 1), incorporation of
foreland material into the front of the wedge, and/or stable
sliding of the wedge over the foreland. The mass added to
the wedge from the first two of these mechanisms may be
removed from the wedge by erosion or may induce a change
in the cross-sectional area of the wedge. Therefore the
wedge geometry (as gauged by its cross-sectional area) is
controlled by the rates of addition of mass to and removal of
mass by material accretion and erosion, respectively.
[6] First, we relate the surface slope to the decollement
geometry using the critical Coulomb wedge (CCW) theory
[Davis et al., 1983; Dahlen et al., 1984; Dahlen, 1984]. In
this formulation, lithostatic loading increases with surface
slope and fault dip. The theory predicts that an orogenic
wedge is in mechanical equilibrium when the resolved
tractions along the fault surface are equal to the failure limit
along the surface as defined by the Coulomb Failure Criterion [Davis et al., 1983; Dahlen, 1984]. The relationship
between the surface slope (a) and fault dip (b) at this critical
condition is expressed most simply as [Dahlen, 1984]
a þ b ¼ yb yo ;
ð1Þ
where yb and yo is the angle between the base and surface
of the wedge and the maximum principle compressive
stress, respectively. For subaerial orogenic wedges, yb and
yo depend on the friction of the wedge (m) and the fault
plane (mb), the Hubbert-Rubey fluid pressure ratio within the
orogenic wedge (l) and along its basal decollement (lb),
and a. Complete expressions for these parameters are given
by Dahlen [1984].
[7] We show an example of the relationship between a
and b in Figure 2 [Davis et al., 1983; Dahlen, 1984], when m
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Figure 1. Schematic model depiction. Orogenic wedge has mechanical properties, m, mb, l, and lb,
converges with the foreland and its rear at velocity, vf and vr, respectively, accretes a thickness Tf and Tr of
material from the foreland and rear, respectively, into the wedge, soles out at depth D, and is eroded
according to the erosional parameters K, ka, h, m, and n. Figure modified after Hilley et al. [2003].
and mb are fixed to 1.1 and 0.85, respectively. Solid lines in
Figure 2 show combinations of a and b that lead to critically
deforming wedges for different l and lb. Measured a, b
relations for Taiwan and the Himalaya are shown for
reference. Generally, an inverse relationship between the
surface slope and basal decollement angle is observed when
a wedge is at its failure limit. Therefore, as the fault dip
steepens, the surface slopes must shallow to maintain a
wedge that deforms at its critical limit. Importantly, wedges
that are in mechanical and erosional equilibrium will plot
along one of these lines, given m, mb, l, and lb. As the pore
pressure ratios within the wedge and along its base increase
(l and lb), or the basal decollement friction decreases (mb),
this reduces the ability of the wedge to support a large
topographic load and the surface slope must shallow, all else
being equal [Davis et al., 1983].
[8] The erosional component of our model considers the
material fluxes entering and leaving the wedge from tectonic accretion and erosional removal of material, respectively. If the density of material does not change as material
is accreted to the wedge, the material flux entering the
wedge is equal to the product of the convergence velocity
(v) and the thickness of accreted material (T) relative to and
entering the front and rear of the wedge, respectively
[DeCelles and DeCelles, 2001]:
vT ¼ vf Tf þ vr Tr :
rock erodibility and climate [Howard and Kerby, 1983;
Howard et al., 1994; Stock and Montgomery, 1999]:
dz
¼ KAm S n :
dt b
ð3Þ
Here the power law exponents (m, n) may partially
encapsulate the processes acting to erode the channel bed
[Whipple et al., 2000]. In particular, hydraulic lifting of
blocks from the channel may tend to favor low values of m
and n, while processes such as cavitation may result in
higher values [Whipple et al., 2000]. To express A in terms
ð2Þ
where vf and Tf and vr and Tr are the wedge convergence
velocities relative to and thicknesses of accreted material of
the foreland and rear of the wedge, respectively.
[9] This tectonically accreted material is at least partially
removed by erosion. Following the work of others [Whipple
et al., 1999; Whipple and Tucker, 1999, 2002; Whipple,
2001], we consider the relief traversing the orogenic wedge
to be limited by the rate of fluvial incision into bedrock. This
rate is thought to be a power function of the channel slope
(S), the catchment area (A, a proxy for discharge [Howard et
al., 1994]), and a constant (K) that represents the effects of
Figure 2. Relationship between orogenic wedge surface
slope (a) and wedge decollement angle (b) when wedge is
at its Coulomb failure limit. Model lines show expected
relations when m = 1.1 and mb = 0.85. An inverse
relationship between b and a is observed when b is small.
The a-b relations and their uncertainties are plotted for the
Taiwan and Himalayan orogenic wedges. Figure modified
after Davis et al. [1983].
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Figure 3. Contoured base 10 logarithm values of vT/K, highlighting the effect of changing ka for
different values of m and n. Mechanical stability lines for a wedge in which m = 1.1; mb = 0.85; and l =
lb = 0, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.97 are shown for reference (lines are the same as in Figure 2).
of the downstream profile position (x), we relate the source
area to the upstream profile length [Hack, 1957]:
A ¼ ka xh ;
ð4Þ
where ka and h are constants that depend on the catchment
geometry. As h increases, larger amounts of source area are
collected for a given downstream distance than when h is
low. Therefore increases in h result in more square geometry
basins than low values of h. By combining equations (3)
and (4), we express the rate of change of the channel
elevation in terms of the downstream profile distance, x:
dz
¼ Kkam xhm S n :
dt b
ð5Þ
[10] By assuming that wedges grow in their mechanically
critical state according to equation (1), accrete material
according to equation (2), and erode by fluvial bedrock
incision (equation (5)), Hilley et al. [2003] derive an
expression for the temporal rate of change of the basal
decollement angle as a function of the erosional and
mechanical parameters of the wedge:
2
1
db
D tan a D2 cot2 bgðbÞ D2 csc2 b
¼
þ
dt
sin b cos b
2 cos2 f ðbÞ
2
hm ðhmþ1Þ
Kka D
cotðhmþ1Þ bS n
;
vT hm þ 1
ð6Þ
where f(b) and g(b) are functions that relate the value and
temporal rate of change of a as a function of b [Dahlen,
1984; Hilley et al., 2003].
[11] In this paper, we consider the special condition in
which all material entering the wedge from tectonic accretion is removed by erosion and, hence, its cross section
remains invariant with time. Under these circumstances, db/
dt = 0 and the first term on the right-hand side of
equation (6) may be eliminated. Rearranging this equation
and letting S = tana, we cast the ratio of the material flux of
accreted material and the erosion constant (vT/K) as a
function of the erosional parameters of the wedge:
vT kahm Dhmþ1 cothmþ1 b tann a
¼
:
K
hm þ 1
ð7Þ
Equation (7) requires that for a given set of (a, b) pairs and for
erosional and basin geometry constants, there is a single
value of vT/K that will lead to a wedge in which erosion is
sufficient to remove all accreted material. Values of vT/K
larger and smaller than this result in growing and shrinking
wedges, respectively. Wedges in mechanical and erosional
steady state must satisfy the two conditions imposed by
equations (1) and (7), respectively. Therefore, for wedges in
which the basal sole-out depth is constant (i.e., don’t grow
self-similarly) a unique combination of a and b exist that
allow wedges to be in both mechanical and erosional steady
state. This pair can be determined graphically by locating the
intersection of the CCW functions (equation (1) and Figure 1)
and those derived from equation (7). While many orogenic
wedges may adjust to changes in erosion by deepening their
wedge sole-out depth, we first consider the case of fixed D
and then determine the effects of changing D on the required
vT/K ratio that produces wedges in which accretion is
balanced by erosion.
3. Model Results
[12] We explored the relationship between erosional
parameters and steady state orogenic wedge geometries
using equation (7). We varied the free parameters in our
model (ka, h, and D), and computed vT/K values for all a, b
pairs between the range 0 a, b 25 that were required
to maintain a steady state erosional wedge. In each case, we
fixed two of the three free parameters to constant default
values while varying the other over a full range of their
potential values. Default values for the parameters are ka = 5,
h = 1.6, and D = 20 km. In addition, a full range of power
law bedrock incision exponents were explored (1/3 m 5/4, 2/3 n 5/2) [e.g., Whipple et al., 2000]. For
reference in each of the plots that follow, we show the
mechanical stability lines computed in Figure 2 (m = 1.1;
mb = 0.85; l = lb = 0, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.97).
However, our results may easily extrapolated to other
mechanical wedge conditions by superposing the appropriate mechanical stability limits and finding the intersection
between these functions and those presented.
3.1. Variation in ka
[13] Figure 3 shows the effect of changing ka on the steady
state erosional geometry of the wedge. In Figures 3 – 5 values
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Figure 4. Contoured base 10 logarithm values of vT/K, highlighting the effect of changing h for
different values of m and n. Mechanical stability lines for a wedge in which m = 1.1; mb = 0.85; and l =
lb = 0, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.97 are shown for reference (lines are the same as in Figure 2).
of the base 10 logarithm of vT/K are contoured for each
value of the changing parameter. For example, dashed lines
in Figure 3, first column, show the isolines of vT/K
between 106 and 109 when ka = 2, h = 1.6, D = 20 km,
and m = 1/3, n = 2/3. Increases in vT/K represent greater
convergence velocities, larger thickness of accreted material, and/or smaller K due to exposure of less erodible rock
types and/or lowered erosional capacity due to reduced
precipitation.
[14] In all models with fixed D, higher values of vT/K lead
to orogenic wedges with higher surface slopes and lower
wedge decollement angles. These low-angle decollements
lead to wider orogenic wedges if D is held constant. Figure 3
indicates that for similar values of vT/K, large ka values result
in steeper stable decollements and shallower surface slopes
than small values. In these and all subsequent models, as m
and n increase, larger values of vT/K are required to produce
similar a, b combinations. This results from the fact that as
erosional exponents increase, the erosion rate increases for
fixed values of the catchment area and local slope of the
channel at each point. Therefore the amount of material
accreted to the wedge must increase or the erosional efficiency must decrease to maintain a constant topographic
form. Both of these factors lead to the increase in vT/K for
constant a, b when the exponents are increased.
3.2. Variation in h
[15] We show the effect of changing h on the vT/K values
for a range of (a, b) pairs in Figure 4. Previous studies
suggest that this value varies over a narrow range between
1.67 and 1.92 [Hack, 1957; Maritan et al., 1999; Rigon et
al., 1996]. We consider a conservative range of h between
1.3 and 1.9 in our models. As with ka, high values of
h require lower values of vT/K for fixed values of a and b
to maintain the wedge in an erosional steady state. For the
range in h explored, the variation of vT/K for fixed a, b pairs
is larger than for the range in ka that was modeled. Increasing
m and n require larger values of vT/K to produce a topographic form similar to their lower valued counterparts.
3.3. Variation in D
[16] The effects of changing D are shown in Figure 5. We
chose values for the sole-out depth of 5, 10, and 20 km,
representing movement along a plastically deforming weak
decollement [e.g., Stocklin, 1968], the depth to the brittleplastic transition in areas of high to moderate heat flow
[Brace and Kohlstedt, 1980], and the depth to the brittleplastic transition when heat flow is low. As D increases, the
absolute size of the steady state wedge increases, allowing
greater storage of material in the wedge as material is
accreted and eroded from its extremes. This results in high
Figure 5. Contoured base 10 logarithm values of vT/K, highlighting the effect of changing D for
different values of m and n. Mechanical stability lines for a wedge in which m = 1.1; mb = 0.85; and l =
lb = 0, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.97 are shown for reference (lines are the same as in Figure 2).
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Figure 6. Simplified geologic map of Taiwan. Westward underthrusting of the Eurasian Plate (EP)
beneath the Philippine Sea Plate (PSP) at 70– 82 mm/yr has resulted in the formation of a west vergent
fold-and-thrust belt that is actively accreting material of the EP. Geology compiled from Suppe [1987]
and maps of Taiwan Geological Survey. Structures based on work by Suppe [1987] and Davis et al.
[1983] and geologic map relations.
b and lower a values when D is large. As in other models,
as m and n increase, so must the values of vT/K to maintain
constant (a, b) relations within the wedge.
4. Application to Taiwan and the Himalaya
4.1. Tectonics, Geology, Topography, and Climate
of the Taiwan and Himalayan Orogenic Wedges
[17] Numerous studies within the Taiwan and Himalayan
orogens constrain the tectonics, geology, topography, climate, and mechanical properties of these two wedges.
Below, we review each of these aspects to deduce appro-
priate inputs to our steady state erosion-deformation wedge
model.
4.1.1. Taiwan
[18] The island of Taiwan lies between the Philippine Sea
Plate (PSP) and the Eurasian Plate (EP) in eastern Asia
(Figure 6). North and eastward directed subduction thrusts
the PSP beneath the EP and the EP beneath the PSP, along
E-W and N-S trending subduction margins, within the
northern, and central and southern parts of the island,
respectively. Therefore the northern section of the island
records a shift in subduction polarity at a triple junction that
is migrating southward with time [Suppe, 1987]. For the
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Figure 7. Taiwanese wedge geometries considered in this study. For simplicity, we only consider
forewedge erosion in this study and treat the potential contribution of erosion from the retrowedge as an
additional material flux leaving the wedge. Cross section modified after Davis et al. [1983, and references
therein].
purposes of this study, we will only consider the effects of
westward directed overthrusting of the PSP onto the EP that
is the dominant plate tectonic regime throughout most of the
island, while neglecting the potential complications that
arise from the southward migration of the shift in subduction polarity with time. Measurements of the convergence
between the EP and PSP vary between 70 mm/yr [Seno,
1977; Minster and Jordan, 1979; Ranken et al., 1984; Seno
et al., 1993] and 82 mm/yr [Yu et al., 1997], directed NWSE. The onset of underthrusting varies depending on the
location along the island. In the north, stratigraphic studies
indicate that the arc-continent collision began 4 Ma,
whereas it appears to be beginning presently at the southernmost tip of the island [Suppe, 1987].
[19] Underthrusting of the EP beneath the PSP throughout the majority of the island leads to uplift and exhumation
of the subduction accretionary prism and volcanic arc to the
east. The geology of this area is well constrained by both
surface and subsurface geologic and petroleum exploration
studies [e.g., Suppe, 1981, 1984, and references therein].
The salient geologic features of the island for this study are,
from west to east, are as follows:
[20] 1. Cenozoic clastic sediments and metasediments
constitute the bulk of the exposed rocks in western and
central Taiwan (exposed area 60– 70 km wide from NWSE). These deposits record the deformation, uplift, erosion,
and deposition around the EP-PSP accretionary wedge
complex. Neogene units comprise 5 to 6 km thick unmetamorphosed to weakly metamorphosed sediments, whereas
Paleogene sediments at their lowest structural level consist
of greenschist grade slates and phyllites [Suppe et al., 1976].
[21] 2. A pre-Oligocene unconformity separates these
sediments from pre-Cenozoic quartzites and slates within
the Hsuehshan Range and Central Mountains in eastern
Taiwan (exposed area 10– 20 km wide from NW-SE) that
constitute the basement of this area, which are often
exposed by NNE striking backthrusts.
[22] 3. In the easternmost sector of the island, west
verging reverse faults juxtapose ophiolitic fragments and
arc remnant material with the basement of the 10-km-wide
Coastal Range. These rocks likely represent sections of
South China Sea crust and the Luzon volcanic arc, which
formed above, and in response to the subduction of the EP
beneath the PSP [Suppe et al., 1981].
[23] Geologic units and their relationships indicate several important properties of this orogen. First, sediments
exposed in western Taiwan constitute a westward migrating
orogenic wedge that is composed of sediments from the EP
and incorporates material by underplating of EP sediments.
Second, this westward verging wedge (prowedge) is mirrored by an eastward verging orogenic wedge (retrowedge)
whose basal decollement is apparently the backthrust of a
larger, westward verging structure. Global Positioning System velocities [Yu et al., 1997] in this area indicate that
material that is accreted to the westward verging wedge is
eroded from the prowedge and may be transported through
the drainage and structural divide into the eastward verging
retrowedge. Third, exposed rocks generally become more
structurally competent, and presumably more difficult to
erode, to the SE. The Cenozoic clastic sediments constitute
most of the width of the westward verging orogenic wedge,
with only limited exposure of pre-Cenozoic crystalline
rocks along the topographic crest of the wedge in a zone
not exceeding 20 km in width.
[24] The topography of Taiwan reflects the present high
denudation and precipitation regimes. The width and height
of the mountain belt grow steadily from south to north for
120 km [Suppe, 1987] from the southern tip of the island.
North of this point, the mountain belt is consistently 90 km
wide and appears to be in a flux steady state in which all
material accreted to the westward verging orogenic wedge is
removed by erosion [Suppe, 1981; Deffontaines et al., 1994;
Willett and Brandon, 2002]. Peak elevations within the
Central Range exceed 4 km [Suppe, 1987], while surface
slopes along the westward flanks of the island range from
2.6 – 3.2 [Davis et al., 1983; Suppe, 1980, 1981]. The
cross-sectional geometry typical of the Taiwanese orogenic
wedge is shown in Figure 7. The topographic crest of
Taiwan is located along the eastern section of the island
where the metamorphic rocks are exposed. This NE-SW
topographic asymmetry may be explained by the rapid
eastward advection of material through the forewedge
[Willett et al., 2001], or alternatively, the exposure of lowerodibility crystalline rocks along the eastern margin of the
orogen, which leads to the migration of the drainage divide
to areas where these rocks are exposed. Currently, up to
4 m/yr of precipitation falls on the island. High exhumation rates produced by the high rock uplift, high precipitation, and low rock erodibility conditions are documented at
decadal, Holocene, and 1 Myr timescales by suspended and
dissolved stream load measurements [Li, 1975], uplifted
Holocene reefs and marine terraces [Peng et al., 1977], and
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Figure 8. Geologic map of the Himalaya. Ongoing collision of India with respect to Asia has produced
15.5– 19.5 mm/yr of convergence between the two. The orogenic wedge is constituted by, from northeast to
southwest, ophiolites and sutures, metamorphosed sedimentary rocks from the Tethys basin, high-grade
metamorphic rocks of the High Himalayan Crystalline, lower-grade metamorphic rocks of the Lesser
Himalaya, and sedimentary foreland deposits of the Subhimalaya. Various volcanic and crystalline rocks
are included within these units. Geology and structures simplified after Hodges et al. [2000, and references
therein].
apatite, sphene, and zircon fission track thermochronology
[Liu, 1982], respectively. Exhumation rates over these timescales are 5 – 6, 5, and 5 –9 mm/yr, respectively.
4.1.2. Himalayan Orogenic Wedge
[25] Northward translation of India with respect to Eurasia
and the resulting continental collision has produced one of
the most spectacular active mountain belts on Earth [e.g.,
Molnar and Tapponnier, 1975]. This collision has been
ongoing since 50 Ma [Rowley, 1996; Searle et al., 1997;
Ratschbacher et al., 1994] and has resulted in a total of 1800
and as much as 2750 km of relative displacement between
India and Eurasia in the western and eastern Himalaya,
respectively [Dewey et al., 1989]. Global Positioning System
(GPS) reoccupations of sites across the Himalaya indicate
that the current rate of convergence is 17.5 ± 2 mm/yr [Bilham
et al., 1997], and most of the resulting interseismic contraction is concentrated in the northern parts of the Himalaya
[Jackson and Bilham, 1994; Bilham et al., 1997]. However,
studies of uplifted and warped Quaternary terraces along the
southern margin of the Nepalese Himalaya record similar
deformation rates [Lave and Avouac, 2000]. Therefore, while
high interseismic strain may accumulate within the core of the
Himalaya, it is apparently released primarily along its southern margin. This continued contraction within the Himalaya
has produced an orogenic wedge 250 km in width, from
northeast to southwest [DeCelles and DeCelles, 2001].
[26] The geology of the Himalayan orogenic wedge is
shown in Figure 8. The regional geology reflects the progressive incorporation of material into and exhumation of the
wedge from northeast to southwest. The major lithotectonic
units exposed in the wedge are, from northeast to southwest:
[27] 1. Ophiolites and crystalline batholiths represent the
suture between the Indo-Eurasian plates and the eroded
remnants of the volcanic arc that formed behind the
northward directed subduction [Dewey and Bird, 1970;
Tapponnier et al., 1981].
[28] 2. These rocks are thrust onto a thick section of
sedimentary rocks that represent the deposition of material
into the Tethys basin prior to collision [Şengör et al., 1988;
Gaetani and Garzanti, 1991].
[29] 3. A series of high-grade metamorphic rocks are
juxtaposed with these metasediments by a low-angle normal
fault within the orogen’s interior [e.g., Caby et al., 1983;
Burg et al., 1984; Burchfiel et al., 1992; Searle, 1986;
Herren, 1987; Valdiya, 1989]. These rocks are bounded to
the southwest by a north dipping low-angle thrust system
[e.g., Hodges, 2000] and comprise a fault-bounded wedge
whose structural thickness varies along strike between 3.5
and 11.7 km.
[30] 4. The high-grade metamorphic rocks supersede
weakly to moderately metamorphosed clastic sediments of
the Lesser Himalaya 8 to 10 km thick, and form a series of
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Figure 9. Two modeled Himalayan wedge geometries considered in this study. Model 1 assumes a
simple wedge geometry originally calculated by Davis et al. [1983] and recently used by DeCelles and
DeCelles [2001]. Model 2 assumes a crustal-scale ramp beneath the High Himalaya [e.g., Cattin and
Avouac, 2000, and references therein], allowing the wedge to penetrate to a depth of 40 km.
fold-and-thrust nappes [e.g., Schelling, 1992; Hodges,
2000].
[31] 5. Rocks at the periphery of the orogen belong to the
Subhimalaya and consist of Tertiary siltstones and sandstones, and lower Miocene to Pleistocene clastic sediments
that represent the deposition of material in front of the
advancing orogenic wedge [e.g., Burbank et al., 1997;
DeCelles et al., 1998].
[32] These structures are bounded by a set of thrust faults
that daylight intermittently, resulting in both faulting and
folding at the surface [Nakata, 1989; Yeats et al., 1992].
Important for this study, the lithologies exposed within the
orogenic wedge consist of a large fraction of crystalline and
metamorphic rocks (Figure 8). The structural competency of
these rocks generally decreases to the southwest; however,
the areal extent of each rock type indicates that the weakly
metamorphosed sediments and uplifted foreland rocks of
the Lesser Himalaya and Subhimalaya, respectively, constitute a small fraction of the wedge relative to the crystalline
and metasedimentary rocks to the northeast.
[33] The long-lived Indo-Eurasian collision has produced
a mountain belt 250 km wide with elevations in excess of
8 km. Two end-member models exist for the geometry of the
Himalayan orogenic wedge. The first geometry explored
(hereafter referred to as model 1) assumes a simple wedge
geometry (Figure 9). In this model, surface slopes of the
orogenic wedge range from 3.5– 4.5, while basal decollement dips range between 2 and 3 [Ohta and Akiba, 1973;
Seeber et al., 1981; Schelling, 1992; DeCelles et al., 1998].
More recent structural and geophysical studies indicate that
this simple wedge geometry may not completely characterize the geometry of the deforming wedge. Data synthesized
by Cattin and Avouac [2000] suggest the presence of a
crustal-scale ramp under the High Himalaya (this model
hereafter referred to as model 2), with an average decollement dip between 10 and 12 (Figure 9). We also recalculated the average surface slope in this case by considering the
mean topography between the front of the wedge and the
rigid backstop of the Tibetan Plateau. In this case, average
surface slopes are between 1 and 2 for the entire wedge. In
addition, the internally drained Tibetan Plateau lies northeast
of the externally drained Himalaya; therefore, the orogen
consists of only a forewedge whose eroded material is
deposited directly into the Himalayan foreland to the southwest. Precipitation along the range front averages between 1
and 3 m/yr and decreases to the northeast due to the presence
of high topography. On the basis of a synthesis of the
geologic history, calculations of the distribution of potential
energy gradients in Asia, and topographic analyses, Hodges
[2000] and Hodges et al. [2001] speculated that the
Himalayan orogenic wedge is in a quasi-steady state in
which material introduced into the wedge by tectonic
accretion is removed by erosion or tectonic exhumation.
4.2. Model Parameters
[34] To interpret the topography and structural geometries
of the Taiwan and Himalayan orogenic wedges in terms of
our coupled erosion-deformation model, basin hydrologic
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Figure 10. Basin area and channel length relationships for (left) Taiwan and (right) the Himalaya.
Regression of these data constrain h and ka to be 1.7 and 4.9 and 1.65 and 9.4, in Taiwan and the
Himalaya, respectively. Data computed using Hydro1K digital elevation model.
parameters (ka and h), the accretionary material flux (vT),
and the mechanical properties of the wedge (mb, m, lb, and l)
must be constrained. We directly constrained h and ka using
topographic analyses of the western slopes of the Taiwan
orogenic wedge (Figure 10, left). We used the Hydro1K 1
km topographic data set to define the basin area and channel
length relationships encapsulated in ka and h. We solved for
these parameters using a brute force approach in which rootmean-square (RMS) misfit values between observed and
predicted (equation (4)) basin area-channel lengths were
calculated for different combinations of ka and h to find
those values that produced the lowest RMS values. Best fit
values for the steady state section of the Taiwan orogenic
wedge were h = 1.7, ka = 4.9. The accretionary material flux
(vT) entering the Taiwan wedge was constrained by Suppe
[1981], who indicated that a flux of 500 m2/yr of eroded
rocks is incorporated into the orogenic wedge by frontal
accretion. To account for the removal of material from the
retrowedge, we use relative GPS velocities to estimate a
conservative range of the material flux that travels through
and is eroded from the retrowedge. This flux was then
subtracted from the total accreted flux to determine that
eroded from the forewedge. Our calculations indicate that
between 276 and 333 m2/yr is eroded from the forewedge
(Appendix A). Regional cross sections from Davis et al.
[1983]; Suppe [1980, 1981] indicate that the depth to the
base of the wedge is 11.5 km. The mechanical properties
of the westward verging orogenic wedge have been constrained by formation tests and sonic log measurements
during petroleum exploration [Suppe and Wittke, 1977;
Suppe et al., 1981; Davis et al., 1983]. Using these
measurements, Davis et al. [1983] estimate the HubbertRubey fluid pressure ratios within the wedge and along the
basal decollement to be l = lb = 0.675 ± 0.05. Finally, an
analysis of the surface and basal decollement slopes in this
wedge yield a wedge internal friction of m = 1.1 when the
friction along the basal decollement is assumed to obey
Byerlee’s friction law (mb = 0.85 [Byerlee, 1978; Dahlen,
1984]).
[35] Within the Himalayan orogenic wedge, analyses of
the basin area to channel length relations were conducted
in the manner described above. The current relationships
along the Himalayan mountain belt produce best fit h and ka
values of 1.65 and 9.4, respectively (Figure 10, right). The
accretionary material flux entering the Himalayan orogenic
wedge probably constitutes several components. First,
7 km of foreland material is accreted to the front of the
orogenic wedge [DeCelles and DeCelles, 2001] at a rate
between 15.5 and 19.5 mm/yr [Bilham et al., 1997]. Therefore the cross-sectional material flux due to frontal accretion
is between 109 and 137 m2/yr. In addition, Hodges [2000]
and Hodges et al. [2001] explain the contemporaneous
movement of normal and reverse faults bounding the northern and southern margins of the Higher Himalayan crystalline rocks, respectively, by the extrusion of lower Tibetan
crust southward into the Himalaya. Extensional movement
along the top of this potentially extruded section commenced
in the Miocene (15 Ma) and has produced a minimum of
40 km of displacement [Hodges, 2000, and references
therein]. Finally, the structural thickness of the extruded
section is between 3.5 and 11.7 km perpendicular to the
transport direction of material. Therefore we estimate that a
flux of 31 m2/yr may be added to the Himalayan orogenic
wedge through the extrusion of Tibetan lower crust. Because
this extrusion remains controversial, we add this material
flux to the maximum estimate of the material flux into the
wedge. Consequently, a conservative bound on vT entering
the Himalayan orogenic wedge that accounts for the full
range of tectonic models of deformation within the wedge is
between 109 and 168 m2/yr. We calculated vT/K values for
the two end-member geometries discussed above (model 1
and model 2). For the model 1 wedge geometry, we followed
DeCelles and DeCelles [2001] by calculating the depth to
the basal decollement beneath the surface trace of the
drainage divide by extrapolating the average 6 decollement dip across the 250 km width of the orogen, yielding
D = 13 km. For model 2, we simplified the crustal ramp
structure as a planar, triangular wedge with an average basal
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Figure 11. Observed (gray boxes) and predicted a, b relationships for the Taiwan orogenic wedge.
Solid lines show mechanical stability limits computed by Davis et al. [1983] and Dahlen [1984]. Dotted
lines contour base 10 logarithm of vT/K that is required to produce an orogenic wedge in which all
tectonically accreted material is erosionally removed from the wedge.
decollement dip that reflected the average observed by Cattin
and Avouac [2000]. The mechanical properties of the Himalayan orogenic wedge are not as well defined as those in
Taiwan. However, the wedge geometry of the Himalaya
imply that if l = lb, mb = 0.85 according to Byerlee’s friction
law, and m = 1.1, lb = 0.76 [Davis et al., 1983].
4.3. Results
[36] We show the results of the application of our model to
the Taiwan and Himalayan orogenic wedges in Figures 11
and 12, respectively. In Figures 11 and 12, dotted lines are
the contoured base 10 logarithm value of vT/K and solid
lines are the mechanical stability limits of the orogenic
wedges. Figures 11 and 12 show the effect of changing m
and n on values of vT/K required to produce the different
(a, b) pairs. In general, higher vT/K values are required to
produce the a, b relations observed in the Himalaya relative
to the Taiwan orogenic wedge. For the Taiwan wedge, base
10 logarithm values of vT/K between 7.1– 7.4, 7.3 – 7.5, and
13.3– 13.7 are required when m = 1/3, n = 2/3, m = 0.4,
Figure 12. Observed (gray boxes) and predicted a, b relationships for the Himalayan orogenic wedge.
Solid lines show mechanical stability limits computed by Davis et al. [1983] and Dahlen [1984]. Dotted
lines contour base 10 logarithm of vT/K that is required to produce an orogenic wedge in which all
tectonically accreted material is erosionally removed from the wedge. (top) Wedge parameters defined
originally by Davis et al. [1983] and utilized by DeCelles and DeCelles [2001]. (bottom) Crustal ramp
model summarized by Cattin and Avouac [2000].
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Table 1. Inferred vT/K and K Values for Taiwan and Himalayan Orogenic Wedge
m = 1/3, n = 2/3
Minimum
Maximum
vT/K
K
1.4 107
1.3 105
2.1 107
2.4 105
vT/K
K
5.1 107
6.2 107
vT/K
K
2.9 107
2.0 106
m = 0.4, n = 1
Minimum
m = 5/4, n = 5/2
Maximum
Minimum
Maximum
Taiwan
2.0 107
8.3 106
3.3 107
1.6 105
1.8 1013
5.4 1012
5.1 1013
1.7 1011
1.8 108
3.3 106
Himalaya Model 1
9.0 107
2.9 107
3.7 108
1.9 106
4.2 1014
1.6 1014
6.6 1015
4.0 1013
5.5 107
5.8 106
Himalaya Model 2
3.9 107
1.2 106
9.0 107
4.3 106
5.2 1013
3.3 1013
3.3 1014
3.2 1012
n = 1, and m = 5/4, n = 5/2, respectively. In the Himalaya,
the base 10 logarithms of this value range between 7.7– 8.5,
7.9– 8.6, and 14.7– 15.8 when m = 1/3, n = 2/3, m = 0.4,
n = 1, and m = 5/4, n = 5/2, respectively. Interestingly, the
effects of the deeper wedge sole-out depths implied by the
model 2 wedge geometry were roughly offset by the steeper
basal decollement geometry. This resulted in similar vT/K
values for model 1 and model 2 wedges, despite their
disparate geometries. While the poorly constrained mechanical properties of the Himalayan orogenic wedge may cause
shifts in the solid lines in Figure 12, the geomorphic
isolines are solely the product of the geometry of the
wedge. Therefore this fundamental observation of high
and low values of vT/K required to produce the Himalayan
and Taiwan orogenic wedges does not change with changing wedge mechanical properties.
[37] Table 1 shows the range in vT/K values required to
produce the geometry of each wedge when they are in
erosional steady state. In general, vT/K increases with
increasing m and n. Using the constraints on vT described
above, we calculated a range of K values required to produce
steady state geometries for Taiwan and the Himalaya.
Because vT is significantly larger for Taiwan, larger K values
are necessary to produce vT/K values that are less than those
observed in the Himalaya. Inferred mean K values for
Taiwan are 1.9 105, 1.2 105, and 1.2 1011 when
m = 1/3, n = 2/3, m = 0.4, n = 1, and m = 5/4, n = 5/2,
respectively. Mean K values from Himalaya model 1 are
2.0 106, 1.1 106, and 2.1 1013 when m = 1/3, n =
2/3, m = 0.4, n = 1, and m = 5/4, n = 5/2, respectively. Mean
K values for the Himalaya model 2 geometry are 3.9 106,
2.8 106, and 2.26 1012 when m = 1/3, n = 2/3, m = 0.4,
n = 1, and m = 5/4, n = 5/2, respectively.
5. Discussion
[38] Our models highlight the important role of changing
tectonic rates and erosional processes in controlling deformation in actively deforming, externally drained orogens.
First, rock type erodibility and precipitation may exert
strong controls on the orogenic structure. When rocks are
difficult to erode and/or precipitation is low, larger wedges
must be built in order to produce surface slopes that are
sufficient to remove material introduced by accretion.
Second, as the accreted material flux (vT) increases, so does
the size of the wedge, as steeper wedge slopes are required
to evacuate this larger input of material. Therefore wedges
subjected to low precipitation that expose low-erodibility
rocks should be wider than their high precipitation, high
erodibility counterparts, if all other properties are fixed. This
phenomenon was identified by Dahlen and Barr [1989] in
Taiwan; however, because the erosion rate is specified
directly in their models, it is not possible to attribute this rate
to specific factors such as the exposed rock type and to
validate consistency between these landscape and climatic
parameters and those measured elsewhere by independent
means. In addition, this observation has been made in the
Bolivian Andes [Horton, 1999], where narrow and wide
portions of the orogen are associated with high and low
precipitation, respectively. In addition, Schlunegger and
Simpson [2002] suggested that the lateral growth of the Alps
is related to the exposure of less erodible rocks in their core.
Both observations and conditions in the Himalaya and
Taiwan are consistent with the basic conclusion of our model
that reduced erodibility (either by rock type exposure or
climate) or increased material input to the wedge leads to
wider orogenic wedges.
[39] Our analysis of Taiwan and the Himalaya highlight
the important role of the exposure of different rock types in
the orogenic wedge on its structure. The material input into
the Taiwan orogenic wedge is significantly larger than that
entering the Himalaya (500 m2/yr versus 110– 170 m2/yr).
However, the inferred values of vT/K are far lower for
Taiwan than the Himalaya. This leads to lower inferred K
values in the Himalaya relative to Taiwan. This is qualitatively consistent with the observations that the Himalaya
receives lower average precipitation than Taiwan [World
Meteorological Organization, 1981] and exposes crystalline
and high-grade metamorphic rocks, rather than the accretionary wedge sediments present in Taiwan. Interestingly,
the only systematic study that inferred rock type erodibilities for a variety of lithologies determined best fit power
law exponents m = 0.4 and n = 1, and K values to be
between 4.8 105 – 4.7 104 and 4.4 10 – 7 – 1.1 106 for volcaniclastics and mudstones, and granitoid and
metasedimentary rocks, respectively [Stock and Montgomery, 1999]. When similar power law exponents are used in
our models, these values quantitatively agree with our
estimates of 8.3 106 – 1.6 105 and 2.9 107 –
1.9 106 determined for Taiwan and the Himalaya,
respectively. We conjecture that the K value in Taiwan is,
and should be, lower than that inferred for volcaniclastics
and mudstones, due to the exposure of lightly metamorphosed rocks within the prowedge. K values inferred for the
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Himalaya agree well with those determined for similar
metasedimentary and crystalline rocks. However, while
the Taiwan wedge appears to be in a steady state form,
the Himalayan orogenic wedge may not have reached the
steady state postulated by Hodges [2000] and Hodges et al.
[2001]. The fact that this orogenic wedge is growing into
the foreland at 3 mm/yr [DeCelles and DeCelles, 2001]
argues that the wedge is not yet in steady state, although it
may be close to this condition [Hilley et al., 2003]. In this
case, estimated K values are maximum estimates. In any
case, even substantial decreases in K would be broadly
consistent with independent estimates for these rock types
being eroded in an arid climate. These adjustments do not
change the qualitative conclusion that the dryer climate and
exposure of crystalline rocks in the core of the Himalayan
wedge may lead to a vastly different orogenic geometry
than that observed in Taiwan.
[40] It is worth pointing out that the Taiwanese orogenic
wedge appears to be growing in a self-similar manner in
which the fault angle and surface slope remain fixed with
time and the decollement flattening depth increases as
material is accreted to the wedge [e.g., Davis et al.,
1983]. In these cases, the temporal evolution of the wedge
may not be well characterized by equation (6), as this
formulation assumes that the wedge grows by a reduction
in the decollement angle rather than a deepening of the soleout depth. However, our steady state parameterization
(equation (7)) allows us to generalize this equation to
wedges that grow by any combination of decollement
flattening and self-similar growth. In this case, the steady
state geometry of the wedge is not influenced by how the
wedge grows, but instead depends only on the three
independent variables that capture the geometry of the
wedge (a, b, and D). Therefore, while the application of
the temporal growth of these wedges must be taken with
care when wedges grow self-similarly, our steady state
results should be insensitive to the way in which the wedge
grows into its steady state geometry. However, complimentary formulations applying the bedrock power law incision
model to the growth of orogenic wedges that grow selfsimilarly have been produced (K. X. Whipple and B. J.
Meade, Dynamic coupling between erosion, rock uplift, and
strain partitioning in two-sided, frictional orogenic wedges
at steady state: An approximate analytical solution, submitted to Journal of Geophysical Research, 2003, hereinafter
referred to as Whipple and Meade, submitted manuscript,
2003). By combining our model results with these studies, a
full range of wedge development by both decollement
flattening (this work and Hilley et al. [2003]) and self-similar
growth (Whipple and Meade, submitted manuscript, 2003)
can be explored and applied to a wide range of orogens.
[41] Our findings and those of others [e.g., Davis et al.,
1983; Dahlen, 1984; Hilley et al., 2003] allow the temporal
development of orogenic wedges whose decollement soleout depth remains fixed to be represented graphically
(Figure 13). Triangular orogenic wedges at any time in
their developmental history plot as a point on this a, b
diagram. First, the works of Davis et al. [1983] and Dahlen
[1984] define the stability lines of a brittle-elastically
deforming triangular orogenic wedge that is at its Coulomb
failure limit (Figure 13, A, solid lines). This theory predicts
the possible wedge geometries for a set of mechanical
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Figure 13. Schematic graphical depiction of the development of orogenic wedges. Solid lines (A) show stability
limits calculated by Davis et al. [1983] and Dahlen [1984].
Arrows on these lines (B) show transient wedge development when it grows in its critical state, as formulated in
Hilley et al. [2003]. Dashed lines (C) show condition under
which wedge is in erosional equilibrium. Intersection of
these lines with mechanical stability lines (solid circles)
indicate an orogen’s geometry when it is in mechanical and
erosional steady state.
parameters; however, it provides no information as to the
specific location on these lines an orogenic wedge will plot.
Second, Hilley et al. [2003] developed a transient coupled
erosional-tectonic wedge development model that shows the
direction and rate at which points move along these lines
(Figure 13, B, arrows on solid line), given the mechanical
properties, erosional parameters, and initial geometry of the
wedge. In the simple case of a wedge with no surface
topography, the wedge geometry will initially plot at the
point labeled (1). As material is added to the wedge,
the surface topography steepens, accelerating erosional
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processes (2). This acceleration in erosion reduces the rate
at which the wedge widens with time. This particular model
assumes that wedges grow in their mechanically critical
state. However, other models [e.g., Willett, 1992] may be
used to estimate the path of points within this diagram when
the wedge does not grow in its critical condition. In these
cases, the trajectory of points may deviate from the mechanical stability lines [Davis et al., 1983; Dahlen et al.,
1984; Willett, 1992]. In the case that the wedge grows selfsimilarly (‘‘self-similar growth’’; fixed alpha and beta) and
in its mechanically critical state, the point representing the
wedge geometry will not move from a single point on this
diagram. Instead, increases in the depth to the basal decollement with time causes the vT/K base 10 logarithm contours
to rotate counterclockwise in Figure 13 until the erosional
flux balances the tectonic accretion rate. Finally, the wedge
geometry will approach its steady state form (3) in which
erosion is sufficient to remove all material accreted to the
wedge. This study shows the ultimate form of the wedge
when it is in its erosional steady state form (Figure 13, C,
dashed lines). When the wedge is in mechanical and
erosional steady state, the orogenic wedge geometry plots
at the intersection of the vT/K contour and the mechanical
stability line appropriate for a specific orogenic wedge
(Figure 13, solid circles). Using these diagrams, the development and ultimate geometry of orogenic wedges that gain
material by accretion and lose material by bedrock fluvial
incision may be understood.
[42] Finally, it is important to acknowledge the assumptions of our estimated values of vT and our model formulations. For the Taiwanese orogenic wedge, vT was
estimated by Suppe [1981] to be 500 m2/yr based on
balanced cross sections that sample accretion over several
million years. However, in the Himalaya, wedge accretion
rates were based on geodetic measurements and the thickness of accreted foreland material and the potential lower
crustal Tibetan channel (Appendix A). While the geodetic
rates may only sample instantaneous accretion rates, no
further information exists regarding the material fluxes
entering the Himalayan wedge. In addition, the application
of geodetic rates to wedge accretion rates over longer
timescales has been successfully employed previously
[e.g., DeCelles and DeCelles, 2001].
[43] For simplicity, the formulations of Davis et al. [1983]
and Dahlen [1984] assume that the wedge has a simple
triangular cross section and deforms brittle-elastically at the
Coulomb failure limit of the wedge. In real orogens, plastic
deformation within the wedge and deviations in this simple
geometry may confound the simple relationships presented.
In addition, we neglect isostasy in our analysis and assume
that heterogeneities in mechanical and erosional properties
within the wedge may be represented by average, homogeneous values. Isostasy may increase the decollement angle
and reduce the surface slope to maintain the inverse relationship predicted between fault dip and surface slope [Davis et
al., 1983]. Both isostasy and heterogeneity within orogens
are important factors, and so their incorporation into our
models provides a fruitful direction of future research.
However, as shown by Davis et al. [1983], Dahlen [1984],
and DeCelles and DeCelles [2001], simple wedge models
apparently capture the first-order features of the structures of
many orogens.
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[44] In addition, it is important to note that all terms
related to the mechanical properties of the wedge have
vanished from our formulation (equation (7)), as long as
we assume that the wedge maintains a triangular cross
section. More complex rheologies may lead to the violation
of this geometry [e.g., Willett, 1999]; however, where an
approximately triangular wedge geometry can be demonstrated, our model can be employed. Therefore, because we
estimate the geometry of the wedge a priori, the steady state
geometry is independent of the rheological properties, and
isostatic adjustments should be encapsulated within the
derived estimates of vT/K, allowing us to discard many of
the mechanical and isostatic processes and parameters that
may be difficult to constrain by field data.
[45] Two of the largest uncertainties in our analysis
include the assumption of mechanical and erosional steady
state, and the broad application of the bedrock power law
incision model to an entire orogen. First, few wedges likely
exist that are in this steady state condition, and the Taiwan
orogen is probably the best example of this phenomenon
[Suppe, 1981]. Because this steady state condition is likely
the exception to the rule, the direct applicability of our
models to other orogens may be limited. However, our
results provide important information about the state toward
which mountain belts tend to evolve. In many areas of the
world and ancient orogens, information on steady state
behavior does not exist. However, as this study and those
of others [e.g., Willett, 1999; Hilley et al., 2003] have
shown, erosion may nevertheless exert important controls
on deformation within and topographic form of many
orogens. Our results provide a valuable heuristic guide for
interpreting changes in orogenic structure with respect to
these erosional factors in settings where tectonic and erosional rates may not be available.
[46] Second, we assume that the rate-limiting process in
orogenic wedges is bedrock fluvial incision [Whipple et al.,
1999]. Other erosional processes may be important in
denuding the orogenic wedge; however, many of these
other processes (e.g., glacial transport) are less well understood than bedrock erosion. Instead of including less well
constrained processes, we followed the approach of many
[e.g., Whipple et al., 1999; Whipple and Tucker, 1999;
Kirby and Whipple, 2001; Whipple and Tucker, 2002] by
using the power law as our rate-limiting orogen-scale
erosion process. However, there are several important
limitations of the bedrock power law incision model that
warrant discussion. The erodibility parameter (K) may be
influenced by rock type [Stock and Montgomery, 1999], the
distribution of fractures within the bedrock [e.g., Whipple et
al., 2000], allometric changes within the channel, the
relations between catchment area and effective discharge
in the channel [Whipple and Tucker, 1999; Sklar and
Dietrich, 1998], the power law exponents [Sklar and
Dietrich, 1998], and sediment input from hillslopes [Sklar
and Dietrich, 1998, 2001; Whipple and Tucker, 2002].
Many of the factors that control the value of K remain only
qualitatively or poorly understood, limiting the predictive
capability of the bedrock incision model. As an example,
Sklar and Dietrich [1998, 2001] found that sediment input
from hillslopes may exert a strong control on the rate of
bedrock incision, and this sediment input may be modulated
by the effects of climate and uplift rate [Montgomery and
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HILLEY AND STRECKER: STEADY STATE EROSION OF CRITICAL COULOMB WEDGES
Dietrich, 1994; Fernandes and Dietrich, 1997; Whipple and
Tucker, 2002]. Also, incision rates may be related to the
amount of excess transport capacity that these bedrock
channels may contain after sediment has been transported
(the ‘‘over-capacity’’ model of Kooi and Beaumont [1994]).
However, we do not consider these models because they
tend to predict unrealistic stream profile geometries relative
to those observed in nature [Whipple and Tucker, 2002].
Stock and Montgomery [1999] analyzed a series of bedrock
channels in different parts of the world that were cut into
various types of bedrock and found that the primary
controlling factor of K appeared to be lithology. The
consistency between our inferred K values and those estimated for similar rock types indicates that while there are a
plethora of factors included in K, temporal averaging over
the timescales applicable to orogen-scale development may
fold many of these factors into a bulk lithology factor in
which specific and perhaps covarying erosional mechanisms may be captured by a single effective rock type.
Therefore, while our formulations presented will change
with greater understanding of these erosional processes, the
heuristic results of our analysis may be unaffected.
6. Conclusions
[47] We developed a coupled erosion-deformation model
that is used to understand how deformation within and
erosion of an orogenic wedge are linked. The model
assumes that the wedge (1) has a triangular cross section,
(2) gains mass either from underplating of foreland sediments or injection of material into the back of the wedge,
(3) looses mass removed by erosional processes whose rates
are limited by fluvial bedrock incision, (4) is in a steady
state form in which all material that is tectonically introduced into the wedge is removed by erosion, and (5) is at its
Coulomb failure limit. Under these assumptions, the morphology of the steady state wedge is controlled by its
mechanical properties (m, mb, l, lb), the basin hydrologic
parameters (ka and h), the erosional exponents (m and n),
the sole-out depth of the basal decollement (D), and the
ratio of the flux of tectonically added material to the
erosional constant (vT/K).
[48] In general, increasing values of vT/K produce steady
state orogenic wedges that are wider than their low vT/K
counterparts. Increases in this parameter may result from
increasing material flux introduced into the wedge, the
exposure of less-erodible rock types within the wedge,
and/or decreased erosional power due to reduced precipitation and runoff. Our results highlight the role of erosion, and
by inference, the importance of climate and rock type
exposure in determining orogenic structure. While a steady
state condition may not be satisfied in most orogens, our
analysis provides important heuristic results that may be
used to interpret both active and ancient orogens in terms of
the accretion and erosion of material from the wedge where
information about the controlling processes and their rates
may be unavailable or erased.
[49] We applied these models to the Taiwan and Himalayan orogenic wedges, which may be in tectonic and erosional steady state. In the case of Taiwan, previous work has
found that erosion rates inferred from fission track analyses
are consistent with those required to explain wedge steady
B01411
state geometry [Dahlen and Barr, 1989]. However, these
studies do not allow direct comparison of the inferred rock
resistance to fluvial bedrock incision with those exposed
within the island. Our analysis demonstrates that large values
of vT/K are required to explain the structural and topographic
relations in the Himalaya relative to Taiwan. However,
independent estimates of the material flux entering the
Himalaya relative to Taiwan are substantially lower and
require an order of magnitude smaller K acting to erode this
wedge. This reduced K value in the Himalaya is consistent
with the lower precipitation and exposure of less erodible
rock types within this wedge relative to Taiwan. Our
calculated K values are consistent with those determined
independently for similar rock types. Therefore differences
in rock type and climate apparently lead to key differences in
the erosion, and hence, structure of these two mountain belts.
Appendix A: Estimation of Material Leaving
Retrowedge in Taiwan
[50] To calculate the range of material fluxes eroded from
Taiwan’s eastward verging retrowedge, we calculated the
velocity of the Luzon arc remnants relative to the prowedge
and retrowedge drainage divide using Global Positioning
System measurements [Yu et al., 1997] to determine the
velocity of material moving out of the wedge at its eastern
boundary. We found that material moves out of the wedge’s
eastern boundary at a horizontal velocity of 36– 48 mm/yr.
We assumed a maximum rock uplift rate of 10 mm/yr
throughout the retrowedge. This value was chosen as a
conservative maximum estimate of rock uplift rates, and so
a reduction in this value slightly reduces the material flux
leaving the retrowedge and increases that eroded from the
prowedge. Using these values, we determined the velocity
component perpendicular to the wedge surface and integrated
this velocity along its length. By assuming that all material
moving through the orogenic system is removed by erosion,
leaving the cross-sectional geometry of the orogen unchanged, these calculations indicate that between 168 and
224 m2/yr of material moves through the surface slope of the
retrowedge. By assuming that all material moving through
the orogenic system is removed by erosion, we equated
erosional removal with this amount. The total estimated
accreted material flux was estimated to be 500 m2/yr;
therefore between 276 and 333 m2/yr is removed from the
prowedge before reaching the boundary between the prowedges and retrowedges. This estimate is consistent with
fluxes calculated from GPS-derived decollement slip rates
beneath the western portion of the island [Hsu et al., 2003].
[51] Acknowledgments. G.H. acknowledges support from the
Alexander von Humboldt Foundation and the DAAD IQN program for
support of his research at Potsdam. M.S. acknowledges support by the
German Research Council (DFG) grant STR 373/-3. Also, G.H. thanks
Vince Matthews for introducing him to the critical Coulomb wedge and
astutely suggesting its utility in understanding orogen-scale tectonic and
landscape development. We gratefully acknowledge Edward Sobel for
commentary onan earlydraft ofthis manuscript.In addition,FritzSchlunegger,
Terence Barr, and Jean Braun all provided valuable reviews that improved
the manuscript. Finally, we would like to acknowledge comments on the
manuscript by Roland Bürgmann that improved our analyses.
References
Barr, T. D., and F. A. Dahlen (1989), Brittle frictional mountain building:
2. Thermal structure and heat budget, J. Geophys. Res., 94, 3923 – 3947.
15 of 17
B01411
HILLEY AND STRECKER: STEADY STATE EROSION OF CRITICAL COULOMB WEDGES
Beaumont, C., P. Fullsack, and J. Hamilton (1992), Erosional control of
active compressional orogens, in Thrust Tectonics, edited by K. R.
McClay, pp. 1 – 18, Chapman and Hall, New York.
Beaumont, C., R. A. Jamieson, M. H. Nguyen, and B. Lee (2001), Himalayan tectonics explained by extrusion of a low-viscosity crustal channel
coupled to focused surface denudation, Nature, 414, 738 – 742.
Bilham, R., K. Larson, and J. Freymuller (1997), Indo-Asian convergence
rates in the Nepal Himalaya, Nature, 386, 61 – 64.
Brace, W. F., and D. L. Kohlstedt (1980), Limits on lithospheric stress
imposed by laboratory experiments, J. Geophys. Res., 85, 6248 – 6252.
Burbank, D. W., R. A. Beck, and T. Mulder (1997), The Himalayan foreland basin, in The Tectonic Evolution of Asia, edited by A. Yin and
M. Harrison, pp. 149 – 188, Cambridge Univ. Press, New York.
Burchfiel, B. C., Z. Chen, K. V. Hodges, Y. Liu, L. H. Royden, C. Deng,
and J. Xu (1992), The South Tibetan detachment system, Himalayan
orogen: Extension contemporaneous with and parallel to shortening in
a collisional mountain belt, Spec. Pap. Geol. Soc. Am., 269, 41 pp.
Burg, J. P., M. Brunel, D. Gapais, G. M. Chen, and G. H. Liu (1984),
Deformation of leucogranites of the crystalline Main Central Sheet in
southern Tibet (China), J. Struct. Geol., 6, 535 – 542.
Byerlee, J. (1978), Friction of rocks, Pure Appl Geophys, 116, 615 – 626.
Caby, R., A. Pêcher, and P. Le Fort (1983), Le grande chevauchement
central Himalayen: Nouvelles données sur le métamorphisme inverse á
la base de la Dalle du Tibet, Rev. Géogr. Phys. Géol. Dyn., 24, 89 – 100.
Cattin, R., and J.-P. Avouac (2000), Modeling mountain building and the
seismic cycle in the Himalaya of Nepal, J. Geophys. Res., 105, 13,389 –
13,407.
Dahlen, F. A. (1984), Noncohesive critical Coulomb wedges: An exact
solution, J. Geophys. Res., 89, 10,125 – 10,133.
Dahlen, F. A., and T. D. Barr (1989), Brittle frictional mountain building:
1. Deformation and mechanical energy budget, J. Geophys. Res., 94,
3906 – 3922.
Dahlen, F. A., and J. Suppe (1988), Mechanics, growth, and erosion of
mountain belts, Spec. Pap. Geol. Soc. Am., 218, 161 – 178.
Dahlen, F. A., J. Suppe, and D. Davis (1984), Mechanics of fold-and-thrust
belts and accretionary wedges: Cohesive Coulomb theory, J. Geophys.
Res., 89, 10,087 – 10,101.
Davis, D., J. Suppe, and F. A. Dahlen (1983), Mechanics of fold-and-thrust
belts and accretionary wedges, J. Geophys. Res., 88, 1153 – 1172.
DeCelles, P. G., and P. C. DeCelles (2001), Rates of shortening, propagation, underthrusting, and flexural wave migration in continental orogenic
systems, Geology, 29, 135 – 138.
DeCelles, P. G., G. E. Gehrels, J. Quade, P. A. Kapp, T. P. Ojha, and B. N.
Upreti (1998), Neogene foreland basin deposits, erosional unroofing, and
the kinematic history of the Himalayan fold-and-thrust best, western
Nepal, Geol. Soc. Am. Bull., 110, 2 – 21.
Deffontaines, B., J. Lee, J. Angelier, J. Carvalho, and J.-P. Rudant (1994),
New geomorphic data on the Taiwan orogen: A multidisciplinary
approach, J. Geophys. Res., 99, 20,243 – 20,266.
Dewey, J. F., and J. M. Bird (1970), Mountain belts and the new global
tectonics, J. Geophys. Res., 75, 2625 – 2647.
Dewey, J. F., S. Cande, and W. C. Pitman (1989), Tectonic evolution of the
India/Eurasian collision zone, Eclogae Geol. Helv., 82, 717 – 734.
Fernandes, N. F., and W. E. Dietrich (1997), Hillslope evolution by diffusive processes: The timescale for equilibrium adjustments, Water Resour.
Res., 33, 1307 – 1318.
Gaetani, M., and E. Garzanti (1991), Multicyclic history of the northern India
continental margin (northwest Himalaya), AAPG Bull., 75, 1427 – 1446.
Hack, J. T. (1957), Studies of longitudinal stream profiles in Virginia and
Maryland, U.S. Geol. Surv. Prof. Pap., 294-B.
Herren, E. (1987), Zanskar shear zone: Northeast-southwest extension within the Higher Himalayas (Ladakh, India), Geology, 15, 409 – 413.
Hilley, G. E., M. R. Strecker, and V. A. Ramos (2003), Erosional growth of
critical Coulomb wedges applied to the Aconcagua fold and thrust belt,
Argentina, J. Geophys. Res., 108, doi:10.1029/2002JB002282, in press.
Hodges, K. V. (2000), Tectonics of the Himalaya and southern Tibet from
two perspectives, Geol. Soc. Am. Bull., 112, 324 – 350.
Hodges, K. V., J. M. Hurtado, and K. X. Whipple (2001), Southward
extrusion of Tibetan crust and its effect on Himalayan tectonics,
Tectonics, 20, 799 – 809.
Horton, B. K. (1999), Erosional control on the geometry and kinematics of
thrust belt development in the central andes, Tectonics, 18, 1292 – 1304.
Howard, A. D., and G. Kerby (1983), Channel changes in badlands, Geol.
Soc. Am. Bull., 94, 739 – 752.
Howard, A. D., M. A. Seidl, and W. E. Dietrich (1994), Modeling fluvial
erosion on regional to continental scales, J. Geophys. Res., 99, 13,971 –
13,986.
Hsu, Y.-J., M. Simons, S.-B. Yu, L.-C. Kuo, and H.-Y. Chen (2003), A twodimensional dislocation model for interseismic deformation of the Taiwan mountain belt, Earth Planet. Sci. Lett., 211, 287 – 294.
B01411
Jackson, M., and R. Bilham (1994), Constraints on Himalayan deformation
inferred from vertical velocity fields in Nepal and Tibet, J. Geophys. Res.,
99, 13,897 – 13,912.
Kirby, E., and K. X. Whipple (2001), Quantifying differential rock-uplift
rates via stream profile analysis, Geology, 29, 415 – 418.
Kooi, H., and C. Beaumont (1994), Escarpment evolution on high-elevation
rifted margins: Insights derived from a surface processes model that
combines diffusion, advection, and reaction, J. Geophys. Res., 99,
12,191 – 12,209.
Lave, J., and J.-P. Avouac (2000), Active folding of fluvial terraces across
the Siwaliks Hills, Himalaya of central Nepal, J. Geophys. Res., 105,
5735 – 5770.
Li, Y. H. (1975), Denudation of Taiwan island since the Pliocene Epoch,
Geology, 4, 105 – 107.
Liu, T.-K. (1982), Fission-track study of apatite, zircon, and sphene from
Taiwan and its tectonic implication (in Chinese), Ph.D. thesis, Natl.
Taiwan Univ., Taipei.
Maritan, A., A. Rinaldo, R. Rigon, A. Giacometti, and I. RodriguezItrube (1999), Scaling laws for river networks, Phys. Rev. E., 53,
1510 – 1515.
Minster, J. B., and T. H. Jordan (1979), Rotation vectors for the Philippine
and rivera plates (abstract), Eos Trans. AGU, 60, 958.
Molnar, P., and P. Tapponnier (1975), Cenozoic tectonics of Asia: Effects of
a continental collision, Science, 189, 419 – 426.
Montgomery, D. R., and W. E. Dietrich (1994), A physically based model
for the topographic control on shallow landsliding, Water Resour. Res.,
30, 1153 – 1171.
Nakata, T. (1989), Active faults of the Himalaya of India and Nepal, in
Tectonics of the Western Himalayas, edited by L. L. Malinconico and R. J.
Lillie, Spec. Pap. Geol. Soc. Am., 232, 243 – 264.
Ohta, Y., and C. Akiba (Eds.) (1973), Geology of the Nepal Himalayas,
Himalayan Comm. of Hokkaido Univ., Saporro, Japan.
Peng, T. H., Y. H. Li, and F. T. Wu (1977), Tectonic uplift rates of the
Taiwan island since early Holocene, Mem. Geol. Soc. China, 2, 57 – 69.
Ranken, B., R. K. Cardwell, and D. E. Karig (1984), Kinematics of the
Philippine Sea plate, Tectonophysics, 3, 555 – 575.
Ratschbacher, L., W. Frisch, G. Liu, and C. Chen (1994), Distributed
deformation in southern and western Tibet during and after India-Asia
collision, J. Geophys. Res., 99, 19,917 – 19,945.
Rigon, R., I. Rodriguez-Iturbe, A. Maritan, A. Giacometti, D. Tarboton, and
A. Rinaldo (1996), On Hack’s law, Water Resour. Res., 32, 3367 – 3374.
Rowley, D. B. (1996), Age of initiation of collision between India and Asia:
A review of stratigraphic data, Earth Planet. Sci. Lett., 145, 1 – 13.
Royden, L. (1996), Coupling and decoupling of crust and mantle in
convergent orogens: Implications for strain partitioning in the crust,
J. Geophys. Res., 101, 17,679 – 17,705.
Schelling, D. (1992), The tectonostratigraphy and structure of the eastern
Nepal Himalaya, Tectonophysics, 11, 925 – 943.
Schlunegger, F., and G. Simpson (2002), Possible erosional control on
lateral growth of the European central Alps, Geology, 30, 907 – 910.
Searle, M., R. I. Corfield, B. Stephenson, and J. McCarron (1997), Structure of the north Indian continental margin in the Ladakh-Zanskar Himalayas: Implications for the timing of obduction of the Spontag ophiolite,
India-Asia collision and deformational events in the Himalaya, Geol.
Mag., 134, 297 – 316.
Searle, M. P. (1986), Structural evolution and dequence of thrusting in the
High Himalyan, Tibetan-Tethys and Indus suture zones of Zanskar and
Ladakh, western Himalaya, J. Struct. Geol., 8, 923 – 936.
Seeber, L., J. G. Armbruster, and R. C. Quittmeyer (1981), Seismicity and
continental subduction below the Himalayan arc, in Zagros-Hindu KushHimalaya Geodynamic Evolution, Geodyn. Ser., vol. 3, edited by H. K.
Gupta and F. M. Delany, pp. 215 – 242, AGU, Washington, D. C.
Seidl, M. A., and W. E. Dietrich (1992), The problem of channel erosion
into bedrock, in Functional Geomorphology, edited by K. H. Schmidt and
J. de Ploey, Catena Suppl., 23, 101 – 124.
Şengör, A. M. C., D. Altiner, A. Cin, T. Ustaömer, and K. J. Hsu
(1988),
Origin and assembly of the Tethyside orogenic collage at the expense of
Gondwana Land, Geol. Soc. Spec. Publ., 37, 119 – 181.
Seno, T. (1977), The instantaneous rotation vector of the Philippine Sea
plate relative to the Eurasian plate, Tectonophysics, 42, 209 – 226.
Seno, T., S. Stein, and A. E. Gripp (1993), A model for the motion of the
Philippine Sea plate consistent with NUVEL-1 and geological data,
J. Geophys. Res., 98, 17,941 – 17,948.
Sklar, L. S., and W. E. Dietrich (1998), River longitudinal profiles and
bedrock incision models: Stream power and the influence of sediment
supply, in Rivers Over Rock: Fluvial Processes in Bedrock Channels,
Geophys. Monogr. Ser., vol. 107, edited by K. Tinkler and E. E. Wohl,
pp. 237 – 260, AGU, Washington, D. C.
Sklar, L. S., and W. E. Dietrich (2001), Sediment and rock strength controls
on river incision into bedrock, Geology, 29, 1087 – 1090.
16 of 17
B01411
HILLEY AND STRECKER: STEADY STATE EROSION OF CRITICAL COULOMB WEDGES
Stock, J. D., and D. R. Montgomery (1999), Geologic constraints on
bedrock river incision using the stream power law, J. Geophys. Res.,
104, 4983 – 4993.
Stocklin, J. (1968), Structural history and tectonics of Iran: A review, AAPG
Bull., 52, 1229 – 1258.
Suppe, J. (1980), Imbricated structure of western foothills belt, southcentral Taiwan, Pet. Geol. Taiwan, 17, 1 – 16.
Suppe, J. (1981), Mechanics of mountain building and metamorphism in
Taiwan, Mem. Geol. Soc. China, 4, 67 – 89.
Suppe, J. (1984), Kinematics of arc-continent collision, flipping of subduction, and back-arc spreading near Taiwan, Mem. Geol. Soc. China, 6, 21 –
33.
Suppe, J. (1987), The active Taiwan mountain belt, in The Anatomy of
Mountain Ranges, edited by J.-P. Schaer and J. Rodgers, pp. 227 – 293,
Princeton Univ. Press, Princeton, N. J.
Suppe, J., and J. H. Wittke (1977), Abnormal pore-fluid pressure in relation
to stratigraphy and structure in the active fold-and-thrust belt of northwestern Taiwan, Pet. Geol. Taiwan, 14, 11 – 24.
Suppe, J., Y. Wang, J. G. Liou, and W. G. Ernst (1976), Observations of
some contacts between basement and Cenozoic cover in the Central
Mountains, Taiwan, Geol. Soc. China Proc., 19, 59 – 70.
Suppe, J., J. G. Liou, and W. G. Ernst (1981), Paleogeographic origins of
the Miocene East Taiwan ophiolite, Am. J. Sci., 281, 228 – 246.
Tapponnier, P., et al. (1981), The Tibetan side of the India-Eurasia collision,
Nature, 294, 405 – 410.
Valdiya, K. S. (1989), Trans-Himadri intracrustal fault and basement upwarps south of the Indus-Tsangpo suture zone, Spec. Pap. Geol. Soc.
Am., 232, 153 – 168.
Whipple, K. X. (2001), Fluvial landscape response time: How plausible is
steady-state denudation?, Am. J. Sci., 301, 313 – 325.
Whipple, K. X., and G. E. Tucker (1999), Dynamics of the stream-power
river incision model: Implications for height limits of mountain ranges,
landscape response timescales, and research needs, J. Geophys. Res., 104,
17,661 – 17,674.
Whipple, K. X., and G. E. Tucker (2002), Implications of sediment-fluxdependent river incision models for landscape evolution, J. Geophys.
Res., 107(B2), 2039, doi:10.1029/2000JB000044.
B01411
Whipple, K. X., E. Kirby, and S. H. Brocklehurst (1999), Geomorphic
limits to climate-induced increasees in topographic relief, Nature, 401,
39 – 43.
Whipple, K. X., G. S. Hancock, and R. S. Anderson (2000), River incision
into bedrock: Mechanics and relative efficacy of plucking, abrasion, and
cavitation, Geol. Soc. Am. Bull., 112, 490 – 503.
Willett, S. D. (1992), Dynamic and kinematic growth and change of a
Coulomb wedge, in Thrust Tectonics, edited by K. R. McClay, pp.
19 – 31, Chapman and Hall, New York.
Willett, S. D. (1999), Orogeny and orography: The effects of erosion
on the structure of mountain belts, J. Geophys. Res., 104, 28,957 –
28,981.
Willett, S. D., and C. Beaumont (1994), Subduction of Asian lithospheric
mantle beneath tibet inferred from models of continental collision,
Nature, 369, 642 – 645.
Willett, S. D., and M. T. Brandon (2002), On steady states in mountain
belts, Geology, 30, 175 – 178.
Willett, S. D., R. Slingerland, and N. Hovius (2001), Uplift, shortening and
steady state topography in active mountain belts, Am. J. Sci., 301, 455 –
485.
World Meteorological Organization (1981), Climatic Atlas of Asia, Geneva.
Yeats, R. S., T. Nakata, A. Farah, M. Fort, M. A. Mirza, M. R. Pandey, and
R. S. Stein (1992), The Himalayan frontal fault system, Ann. Tectonicae,
6, 85 – 98.
Yu, S.-B., H.-Y. Chen, and L.-C. Kuo (1997), Velocity of GPS stations in
the Taiwan area, Tectonophysics, 274, 41 – 59.
G. E. Hilley, Department of Earth and Planetary Sciences, 377 McCone
Hall, University of California, Berkeley, CA 94720-4767, USA. (hilley@
seismo.berkeley.edu)
M. R. Strecker, Institut für Geowissenschaften, Universität Potsdam,
Karl-Liebknecht-Str. 24-25, Postfach 601553, D-14415 Potsdam, Germany.
17 of 17