growth and erosion of fold-and-thrust belts with an application to the aconcagua fold...

Growth and erosion of fold-and-thrust belts with an application

to the Aconcagua fold-and-thrust belt, Argentina

G. E. Hilley1 and M. R. StreckerInstitut fur Geowissenschaften, Universitat Potsdam, Potsdam, Germany

V. A. RamosDepartment de Geologia, Universidad de Buenos Aires, Buenos Aires, Argentina

Received 1 November 2002; revised 26 August 2003; accepted 11 September 2003; published 23 January 2004.

[1] The development of topography within and erosional removal of material from anorogen exerts a primary control on its structure. We develop a model that describes thetemporal development of a frontally accreting, critically growing Coulomb wedge whosetopography is largely limited by bedrock fluvial incision. We present general resultsfor arbitrary initial critical wedge geometries and investigate the temporal development ofa critical wedge with no initial topography. Increasing rock erodibility and/or precipitation,decreasing mass flux accreting to the wedge front, increasing wedge sole-out depth,decreasing wedge and basal decollement overpressure, and increasing basal decollementfriction lead to narrow wedges. Large power law exponent values cause the wedgegeometry to quickly reach a condition in which all material accreted to the front of thewedge is removed by erosion. We apply our model to the Aconcagua fold-and-thrust belt inthe central Andes of Argentina where wedge development over time is well constrained.We solve for the erosional coefficient K that is required to recreate the field-constrainedwedge growth history, and these values are within the range of independently determinedvalues in analogous rock types. Using qualitative observations of rock erodibilities withinthe wedge, we speculate that power law exponents of 1/3 � m � 0.4 and 2/3 � n � 1characterize the erosional growth of the Aconcagua fold-and-thrust belt. This generalmodel may be used to understand the development of mountain belts where orogenicwedges grow as they deform at their Coulomb failure limit. INDEX TERMS: 8010 Structural

Geology: Fractures and faults; 8102 Tectonophysics: Continental contractional orogenic belts; 8020 Structural

Geology: Mechanics; 1815 Hydrology: Erosion and sedimentation; 1824 Hydrology: Geomorphology (1625);

KEYWORDS: critical Coulomb wedge, fluvial bedrock incision, Sierra Aconcagua, Argentina

Citation: Hilley, G. E., M. R. Strecker, and V. A. Ramos (2004), Growth and erosion of fold-and-thrust belts with an application to

the Aconcagua fold-and-thrust belt, Argentina, J. Geophys. Res., 109, B01410, doi:10.1029/2002JB002282.

1. Introduction

[2] Field and modeling studies increasingly show that theinteraction between topographic construction, erosionalprocesses, and deformation at least partially controls thestructure of orogens [e.g., Beaumont et al., 1992, 2001;Horton, 1999; Willett, 1999; Willett and Brandon, 2002]. Inparticular, studies by Davis et al. [1983], Dahlen et al.[1984], and Dahlen [1984] showed that topography andstable structural geometries are linked in an orogenicwedge. By inference, erosional processes removing materialfrom orogens may alter the mechanical balance betweenorogenic slopes and deformation, and hence influence the

development of deformation within the orogenic wedge[e.g., Dahlen and Suppe, 1988; Dahlen and Barr, 1989].[3] Numerical models that explicitly link plate tectonic

convergence rates, temperature dependent rheologies, anderosional processes have been used to explore the generalinteraction between deformation and erosion [e.g., Willett,1999; Willett and Brandon, 2002]. These models demon-strate that erosion may exert an important control on thedeformation, thermal structure, and thermochronologic agedistributions within orogens [Willett and Brandon, 2002]. Inaddition, fully coupled thermomechanical erosion modelsthat allow heterogeneous material properties within the crusthave been successfully employed to model conditions asdiverse as the South Island, New Zealand [Beaumont et al.,1996; Pysklywec et al., 2002], the Pyrenees [Beaumont etal., 2000], the Swiss Alps [Pfiffner et al., 2000], and thegeneral problems of episodic accretion of terranes [Ellis etal., 1999]. The geodynamic models have provided valuableinsight into the relative roles of accretion, rheology, anderosion in the development of these orogens. However,

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, B01410, doi:10.1029/2002JB002282, 2004

1Now at Department of Earth and Planetary Science, University ofCalifornia, Berkeley, California, USA.

Copyright 2004 by the American Geophysical Union.0148-0227/04/2002JB002282$09.00

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these models suffer from at least two limitations: (1) Theircomplexity allows exploration of a wide variety of mechan-ical, thermal, and erosional conditions that may be appro-priate for real mountain belts; however, this samecomplexity limits quantitative comparisons with field dataand formal inversions for model parameters; and (2) theerosion laws employed are exceedingly simple (and perhapsunrealistic [Whipple and Tucker, 2002]) relative to thecomplexity allowed for the rheologies in these models. Thislatter limitation complicates model-based interpretations ofthe role of erosion on orogenic structure and may prohibitthe comparison of erosional parameters used within thesemodels to values that have been determined elsewhere forspecific erosional processes [e.g., Stock and Montgomery,1999].[4] Alternatively, simple kinematic models have been

used to understand how orogenic wedges may change theirforms with time [e.g., DeCelles and DeCelles, 2001]. Thesemodels lack the complex and realistic rheologies treated inthe coupled thermomechanical-erosional models; however,their formulation allows geologic data, such as relativeconvergence velocities and thickness of accreted forelandmaterial, to be directly used to understand how orogenicwedges develop. Using orogenic wedge geometries andfrontal wedge propagation rates from the Bolivian Andesand Himalaya, DeCelles and DeCelles [2001] found rea-sonable correspondence between their model and the field-measured quantities of wedge tip propagation rates andorogenic widths. The simple form of these models opensthe possibility for quantitatively determining model param-eters based on field data. However, as with the coupledthermomechanical-erosional models, these kinematic modelstreat erosion as a simple function whose parameters cannotbe directly compared to erosional constants determineddirectly from geomorphic erosional studies. In particular,erosion is required to remain constant in space and time,which neglects the potentially important acceleration oferosional processes as slopes within the orogen steepen inresponse to prolonged uplift [e.g., Ahnert, 1970].[5] In this paper, we construct a simple kinematic model

of orogenic wedge growth in which realistic erosion lawsare used to examine the development of wedge geometry tovarying erosional conditions. This simplicity provides sev-eral important advantages to previous models. First, geo-logic information determined in the field may be directlyused to model wedge growth. Second, the simplicity of ourmodel allows us to formally invert geologic data to deter-mine the unknown rate constants in the analysis, andspecifically, the erosional constants acting to denude thewedge. Because these rate constants apply to specificerosional processes, they can be directly compared toindependently derived estimates of these values to providea direct and quantitative test of the influence of erosion onorogen geometry. In addition, we can use these formulationsto explicitly explore effects such as changing climate andvariable rock-type erodibility on orogenic structure.[6] We used the bedrock power law incision model

[Howard and Kerby, 1983; Whipple et al., 1999; Whippleand Tucker, 1999, 2002] as our primary orogenic-scaleerosion process [Whipple et al., 1999], and merged thiswith the Critical Coulomb Wedge (CCW) [Davis et al.,1983; Dahlen, 1984] and kinematic frontal accretion

[DeCelles and DeCelles, 2001] models to consider thedevelopment of a critically growing orogenic wedge sub-jected to erosion and frontal accretion of material. Using aseries of forward models of wedge development, we foundthat this growth is profoundly influenced by the erosionalexponents, and when these values are low, rock erodibilityand climate may play a strong role in the development ofthe wedge. Finally, we tested this model using field obser-vations from the Aconcagua fold-and-thrust belt (AFTB) inthe central Andes of Argentina, where geologic field studiesconstrain the growth of the wedge [Ramos et al., 2002;Giambiagi and Ramos, 2002]. Using this history of wedgedevelopment, we solve for the poorly known bedrockerosional constant for different values of the power lawexponents. We speculate that lower power law exponentsapply to this wedge based on comparisons of qualitativeobservations of the relative erodibilities of different rocktypes exposed within the wedge with our model results. Wefound that our model well represents orogenic growth ofthis wedge, and where judiciously applied, may be used tounderstand the coupled deformation-erosion response ofother orogenic wedges.

2. General Model Description

[7] Many studies have sought to explain the relationshipbetween stable topography and structural geometries inaccretionary wedges and fold-and-thrust belts by idealizingan orogen as a simple wedge geometry (Figure 1). In thiscase, the decollement flattens at the back of the wedge(hereafter referred to as the ‘‘decollement sole-out depth’’).Likewise, the surface slope of the orogenic wedge maintainsa uniform slope along its width. Convergence between theorogenic wedge and the foreland may be accommodated byintroduction of material into the back of the wedge (left sidein Figure 1), incorporation of foreland material into the frontof the wedge, and/or stable sliding of the wedge over theforeland. The mass added to the wedge from the first two ofthese mechanisms may be removed from the wedge by avariety of surficial processes or may induce a change in thecross-sectional area of the wedge. Therefore the wedgegeometry (as gauged by its cross-sectional area) is con-trolled by the rates of addition and removal of mass bymaterial accretion and erosion, respectively.[8] We simplify the process of wedge growth by assum-

ing that the wedge deforms at its Coulomb failure limit[e.g., Davis et al., 1983] during its entire development. Thisassumption allows us to explicitly link the surface slope ofthe wedge (a in Figure 1) to its basal fault angle (b inFigure 1) at all times during orogenic development. Wedgesmay undergo phases of subcritical and supercritical growthdue to changes in wedge frictional properties or porepressures over time [e.g., DeCelles and Mitra, 1995].However, consideration of these types of fluctuations arebeyond the scope of this study, and so to a first order, weexpect the wedge to remain at its critical taper during mostof its history. We fix our reference coordinate system to thebackstop of the wedge (left side in Figure 1) and assumethat mass enters the front of the wedge by accretion of athickness of foreland material, T at the velocity that theforeland converges with respect to the back of the wedge, v.The depth at which the basal wedge decollement flattens at

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the back of the wedge is fixed to D, and thus the wedgegrows as the average decollement angle decreases ratherthan self-similar growth [e.g., Davis et al., 1983]. Finally,we assume that the rate-limiting process of removal fromthe surface of the wedge corresponds to the rate at whichrivers can incise bedrock [e.g., Whipple et al., 1999]. Thisincision rate is idealized as a power function that dependson the upstream contributing area, the local channel slope,two power law exponents, m and n that may be related tothe processes eroding the channel bed [e.g., Whipple et al.,2000], and an erodibility factor, K. K includes the effects ofdownstream allometric changes in the channel geometry,effective precipitation, and the resistance of bedrock tofluvial incision [Whipple and Tucker, 1999]. Therefore Kgenerally tends to decrease with increasing resistance ofbedrock to erosion [Stock and Montgomery, 1999] anddecreasing effective precipitation [Whipple and Tucker,1999]. Finally, the geometry of the watersheds drainingthe orogen is encapsulated in the parameters ka and h [Hack,1957].[9] By combining the tectonic and erosional fluxes of

material entering and leaving the wedge [DeCelles andDeCelles, 2001; Whipple et al., 1999; Whipple and Tucker,1999] with the kinematic equations of critical wedge growth[e.g., Dahlen, 1984; DeCelles and DeCelles, 2001], we canexpress the rate of change of the average fault decollementangle as a function of the mechanical and erosional prop-erties of the wedge:

dbdt

¼ �D2 tanasin b cos b

þ D2 cot2 bg bð Þ2 cos2 f bð Þ � D2 csc2 b

2

� ��1

� vT � KkahmD hmþ1ð Þ cot hmþ1ð Þ bSn

hmþ 1

� �ð1Þ

where f(b) and g(b) are functions that relate the surfaceslope of the wedge to the decollement angle and the rate ofchange of the surface slope to the wedge decollement angle,respectively. A detailed description of the derivation of thisexpression, and the parameters in equation (1) and theirphysical significance is provided in Appendix A and thenotation section of this paper. When an initial wedgegeometry is prescribed, equation (1) may be numerically

integrated to determine the temporal development of themodel wedge.

3. Assumptions and Limitations of the Model

[10] There are several assumptions of our model thatwarrant discussion. First, we simplify the coupled ero-sional-mechanical system by assuming that the wedgegrows continuously in its critical state. In many orogens,preexisting structures may cause deformation to move indiscrete steps toward the foreland [e.g., Strecker et al.,1989; DeCelles and Mitra, 1995]. Also, orogenic wedgesmay begin their histories in noncritical states and developtoward criticality as material is incorporated into thewedge [Willett, 1992]. We neglect these effects in ourmodel to elucidate the first-order features of developingwedges without introducing additional model parametersthat may be difficult or impossible to constrain with fieldobservations. Second, when the depth of flattening iscontrolled by the brittle-plastic transition in the crust, bmay decrease continuously near this depth, rather thanabruptly flatten as the geometry of our model requires.Therefore our models only apply to orogenic wedgeswhere this ideal geometry is approximated. Third, ourmodels assume that the material accreted to the wedgedoes not change its density as it is incorporated into theorogen. Compaction of foreland material may increase thedensity of this material, decreasing the volume fluxentering the wedge. However, the relatively small changein vT that results from this effect likely does notinfluence the first-order features observed in our models.Fourth, we assume that the wedge is both mechanicallyand erosionally homogeneous. However, orogens oftenexpose disparate rock types with different mechanical anderosional properties. In addition, orographically controlledprecipitation may alter the erosional capacity of differentsections of the orogen [e.g., Willett, 1999]. These spatialheterogeneities in mechanical and erosional propertiespresent fruitful paths of future research on the couplederosional-tectonic development of orogenic wedges; how-ever, assessing complex variations in these properties arebeyond the scope of this work. Finally, we considerbedrock incision to be the primary erosional agent that

Figure 1. Schematic model depiction. Orogenic wedge has mechanical properties, m, mb, l, and lb,converges with the foreland at velocity, v, accretes a thickness T of foreland material into the wedge, solesout at depth D, and is eroded according to the erosional parameters K, ka, h, m, and n. The portion of thewedge’s cross-sectional area above and below the foreland is Aa and Ab, respectively.


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limits the topography in the orogenic wedge. Likewise,the mean wedge slopes in our models mimic those of thebedrock channels. In many high-altitude portions of anorogen, glacial transport may be an important erosionalprocess. Also, the spatial distribution of exposed bedrockwithin channels may change in space and time [Montgomeryet al., 1996], leading to ‘‘mixed’’ bedrock-alluvial channels[Whipple and Tucker, 2002]. The mechanics of bedrockchannels have been only recently explored [e.g., Howardand Kerby, 1983; Seidl and Dietrich, 1992; Whippleand Tucker, 1999, 2002], and research on these mixedbedrock-alluvial channels is only in its infancy. In addition,quantitative rules for relating incision to basin propertiesand uplift for glacial transport have been elusive [Whippleet al., 1999]. Therefore we followed currently establishedtransport rules for modeling erosional removal from bed-rock channels, rather than include more complex and lesswell understood processes.

4. Model Results

4.1. Model Parameter Values

[11] We used the model of critical wedge growth toexplore the impacts of changing each of the modelparameters on the rate of change of the basal decollementangle (db/dt), wedge propagation rate (dW/dt), and wedgewidth (W) through time. A number of the parameters inequation (1) are not varied in our forward models forreasons of simplicity. In this study, we fix ka = 4 and h =1.4. We assume that within the wedge, the coefficient offriction (m = tan f) is equal to 0.85, as predicted byByerlee’s friction law [Byerlee, 1978], although theeffective friction may be greater in the wedge due tocohesion [Dahlen et al., 1984]. In addition, we do notallow the Hubbert-Rubey fluid pressure ratio within andoutside of the wedge to differ (l = lb).[12] We varied the erosion power law exponents (m and n),

rock erodibility (K), volume flux per unit width ofaccreted material (vT), depth at which the decollementflattens (D), the wedge and basal Hubbert-Rubey fluidpressure ratio (l and lb), and the coefficient of frictionof the basal decollement mb = tan fb. We chose a rangefor each of these values encountered in the field, and thevalues used in our forward models are shown in Table 1.On the basis of theoretical and field studies, the ratio ofm/n is close to 0.5; however, the value of n likely rangesbetween 2/3 and 7/2 [e.g., Whipple et al., 2000]. For ourreference value, we considered m and n values of 0.4and 1, respectively [Stock and Montgomery, 1999]. Stockand Montgomery [1999] investigated a series of bedrock

channels and found that K varies primarily with rock typeover possibly three orders of magnitude. Their studyprovided average K values of 1 � 10�4, 6 � 10�6,and 1 � 10�6 for mudstones/volcaniclastics, basalt flows,and granitoid/metasedimentary rocks mainly in humidregions, respectively. In addition, lower precipitationmay lead to a decrease in the discharge in channelsand lower values of K [Howard et al., 1994]. We chosevolume fluxes (vT) that represent the accretion of 2, 5,10, and 15 km of foreland material at convergencevelocities similar to the Himalayan orogenic wedge(v 17.5 mm/yr [Bilham et al., 1997; DeCelles et al.,1998; Powers et al., 1998]). We varied the depth to thebasal decollement (D) between 10 and 25 km. The lowvalue of D may characterize wedges in which thepresence of weak evaporite layers result in pressure-independent plastic flow at the base of the wedge [e.g.,Stocklin, 1968], whereas large values of D represent theupper depth bound for the location of the brittle-plastictransition in cool continental crust [Brace and Kohlstedt,1980]. We vary the Hubbert-Rubey fluid pressure ratiobetween 0 and 0.9 to represent dry and wet wedges,respectively. Finally, we let the coefficient of friction ofthe basal decollement (mb) vary between 0.85 and 0.2,representing those that obey Byerlee’s friction law andweak decollements, respectively. Four of these fiveparameters were fixed to their reference values, shownin Table 1, while the other was varied. These baseconditions represent a basaltic lithology eroded by theinfluence of moderate (1000 mm/yr) precipitation [Stockand Montgomery, 1999], the volume flux estimated to beentering the Himalayan orogenic wedge [DeCelles andDeCelles, 2001, and references therein], a moderate todeep brittle-plastic transition, a wedge with little fluidoverpressure, and a wedge with a basal decollement thatobeys Byerlee friction.[13] Finally, we calculated the rate of change of the

average basal decollement angle (db/dt) and the propaga-tion rate of the wedge toward the foreland (dW/dt) as afunction of b, and constructed example histories of aninitially flat-surfaced wedge over time, calculating dW/dtand W as a function of time. We examined the relativeresponse times of the wedge as each parameter changes.We qualitatively define the response time as the timebetween initiation of wedge growth and the time at whichthe propagation rate of the wedge decreases to a valueclose to zero. This gauges the length of time required foraccretion to be approximately balanced by erosion. Wefocus on the transient behavior of the growing or shrink-ing critical wedge in this paper, with the results of asteady state analysis of this model presented by Hilleyand Strecker [2003].

4.2. Variation in K

[14] The effects of changing K are shown in Figures 2and 3. Negative and positive db/dt values correspond towedges that widen and narrow with time, respectively.Low K values require high topographic slopes to evac-uate an equivalent amount of material per time relative towedges undergoing vigorous erosion (Figure 2). There-fore most of the material accreted to the wedge slowlyincreases the topographic slope of the wedge and causes

Table 1. Model Parameters Used in Forward Models of Wedge

Growth

Parameter Base Value Value 1 Value 2 Value 3 Value 4

m 0.4 1/3 0.4 5/4n 1 2/3 1 5/2K, m1 – 2m/yr 5 � 10�6 1 � 10�7 1 � 10�6 1 � 10�5 1 � 10�4

vT, m2/yr 122.5 35 87.5 175 262.5D, km 20 10 15 20 25l,lb 0 0 0.5 0.8 0.9mb 0.85 0.2 0.4 0.6 0.85


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Figure 2. Effect of changing erodibility constant (K) on (top) db/dt and (bottom) dW/dt for variouspower law exponents, m and n (left, middle, and right). See text and Table 1 for unvarying parametervalues.

Figure 3. Effect of changing erodibility constant (K) on the history of (top) dW/dt and (bottom) wedgewidth W over 10 Myr of model time for an initially flat wedge. The effects of changing power lawexponents, m and n, are shown in the each of the columns.


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the wedge to grow at a relatively constant dW/dt, withlittle erosional removal of material. However, as thewedge slopes become steep and erosion more effective,successively larger volumes of material accreted to thefront are removed as the wedge widens and b decreases,resulting in rapidly decreasing wedge propagation rates.[15] Figure 2 highlights the importance of the initial

critical wedge geometry on the rate and directionof wedge growth. Orogenic wedges that start theirhistory with relatively steep surface slopes (e.g., ‘‘A’’in Figure 2) result in a larger erosional flux thanaccreted flux entering there. In this case, the wedgeloses volume as the average basal decollement steepensand surface slopes diminish. In addition, the wedgepropagation rate is often large when the initial surfacegeometry of the wedge is steep sloped. Conversely, awedge that starts its tectonic history with no initialtopography (point ‘‘B’’ in Figure 2) will consequentlylose little material by erosion until slopes are developedthat cause significant erosion. In this case, the initialpropagation rate of the wedge tip represents that duesolely to frontal accretion. However, as the wedgegrows, erosion becomes progressively more efficient untilthe amount of material accreted to the wedge is balancedby erosional removal of material.

[16] The propagation rate and wedge width history of aninitially flat-surfaced wedge is shown in Figure 3. First, theresponse time of the wedge increases with decreasing K,because propagation rates close to those expected in theabsence of erosion (at t = 0) are sustained for longer periodsof time. The prolonged high propagation rates lead to largewedge widths over time. For example, in the case that m =1/3, n = 2/3, and K = 1 � 10�4, the wedge geometrychanges little during its history and quickly attains ageometry that does not change with time. This rapidresponse time results from the fact that the invariantgeometry is close to that of the initial wedge geometry.Therefore only a limited amount of accretion is necessary toprovide the material required by this narrow wedge. Incontrast, when K = 1 � 10�7, propagation rates and wedgewidths are both large after 10 Myr of model time. The highpropagation rates at the end of the model time suggest thatthe wedge may not reach a geometry in which frontalaccretion is balanced by erosion for several tens of millionsof years. Under these extremely low erosion conditions, thetime at which surficial erosion becomes a significant agentof mass transport from the wedge may be far longer than thelife of the orogen itself.[17] In this and all model parameter variations hereafter,

the power law incision exponents m and n exert a first-order

Figure 4. Effect of changing accreted volume flux (vT) on (left) db/dt and (right) dW/dt. See text andTable 1 for unvarying parameter values.

Figure 5. Effect of changing accreted volume flux (vT) on the history of (left) dW/dt and (right) wedgewidth W over 10 Myr of model time.


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control on the response of the wedge. Because the effectof the power law exponents on the wedge behavior issimilar for a wide range of varied parameters, we do notshow the effects of changing m and n on wedge growth inFigures 4–11. In these cases, we present only the wedgegrowth behavior for m = 0.4, n = 1. In the auxiliarymaterial1, we include a series of figures that document theeffect of changing m and n the wedge’s growth for allmodel parameters investigated.[18] Large values of the power law exponents increase

the efficiency of erosion, thus small changes in the surfaceslope of the wedge result in large changes in the erosionalflux removed from the wedge. For example, when m = 5/4,n = 5/2, wedge propagation rates change rapidly withchanging fault geometry. Because the erosional flux is higheven at low surface slopes, steep fault geometries andhence narrow wedges lead to erosion that is efficientenough to remove all accreted material (Figure 2). As mand n increase, the response time and width of thewedge at each point in time decrease (Figure 3). In thesecases, the short response time of the wedge leads them torapidly adjust to changes in wedge or erosional parametersand reflect recent rates of frontal accretion, erosion bysurface processes, and intrinsic wedge properties (m, mb, l,and lb).

4.3. Variation in vT

[19] The effect of the changing accreted flux per unit wedgewidth of material into the wedge is shown in Figures 4 and 5.Large values of vT result in both larger db/dt and dW/dt thantheir smaller counterparts (Figure 4).When vT is large, higherwedge surface slopes are required to evacuate all of theaccreted material; therefore, low angle decollements arefavored when the accreted volume flux is large. Wedgeswhose initial surface slopes and basal decollements areinitially steep and shallow, respectively, change their widthsmore rapidly than those in which orogenesis begins withsubtle initial topography and steep decollement angles.[20] Figure 5 shows the propagation rate and wedge

width history of a wedge with no initial topography. The

response time of the wedge varies little with vT, butinstead is primarily dependent onm and n (auxiliary materialitems 1 and 2)1. After 10 Myr of model time, erosionalprocesses with power law exponents of m = 0.4, n = 1remove approximately all accreted material through erosiveprocesses.

4.4. Variation in D

[21] Effects of changing the depth at which the basaldecollement flattens (D) are shown in Figures 6 and 7.Small values of D lead to reduced wedge cross-sectionalareas for a constant decollement dip. These smaller wedgeareas cannot store large volumes of material; therefore, theychange their geometry more rapidly in response to aconstant accreted flux than larger wedges. This results inlarge and small db/dt when D is small and large, respec-tively. Likewise, wedge propagation rates are large when thedecollement flattening depth is small.[22] Figure 7 shows the complex temporal history of a

series of initially flat wedges as D is varied. All otherparameters equal, wedges whose decollments flatten atlower depths have larger cross-sectional areas, and thustake longer to respond to changes in the erosion and/oraccretion. Therefore, while larger values of D result insmaller initial propagation rates, these decay slowlyrelative to the case when D is small. As a result, wedgeswith large D may become wider over time than wedgeswith small D.

4.5. Variation in L and Lb

[23] We show how the wedge geometry changes as l, lbis changed in Figures 8 and 9. Large l, lb result in morenegative values of db/dt for any given b. Large l results inlower surface slopes for a fixed decollement angle relativeto their small l counterparts [Davis et al., 1983]. Thisreduction in the wedge’s surface slope and cross-sectionalarea allows storage of smaller volumes of accreted materialand reduces the erosive power in the wedge at a given faultdip. Both these factors conspire to produce increased faultangle changes and wedge propagation rates for a givendecollement angle.[24] The effect of changes in l on the history of wedge

development is shown in Figure 9. As l increases, so does

Figure 6. Effect of changing sole-out depth (D) on (left) db/dt and (right) dW/dt for various power lawexponents. See text and Table 1 for unvarying parameter values.

1Auxiliary material is available at ftp://ftp.agu.org/apend/jb/2002JB002282.


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the response time of the wedge. Finally, high fluid pressureratios tend to ultimately form wider wedges, as shallowerbasal decollement geometries are required to produce sur-face slopes and erosive power sufficient to remove accretedmaterial from the wedge.

4.6. Variation in Mb

[25] Finally, we varied mb to determine its effect on thedevelopment of the wedge (Figures 10 and 11). Small mbresults in a shallow decollement. These low decollementangles result in large wedge cross-sectional areas, evenwhen the topography is initially flat. Simultaneously, lowerdecollement friction coefficients result in subtle surfaceslopes for each b and hence low erosive power. These twoeffects act in opposite directions: the larger cross-sectionalarea of the wedge favors lower wedge propagation rates,while the lower surface slopes diminish the erosive flux andfavor high propagation rates. In general, large values of mblead to more negative values of db/dt. Peak wedge propa-gation rates are equivalent for all values of mb; however,high basal decollement friction coefficients sustain thepropagation rates over a broader range of b (Figure 10).[26] The history of an initially flat wedge (Figure 11)

illustrates the changing importance of the effects of dimin-ished slope for each value of b on the wedge’s cross-sectionalarea and erosional capacity. At the beginning of orogenesis,wedges with low values of mb (mb = 0.2) have lower

propagation rates than those with large mb (mb = 0.85), asthe enhanced cross-sectional area of the low mb wedge mustaccrete large amounts of material to change its basal decolle-ment angle. However, the rapidly increasing slopes ofwedges with large mb increase the erosional capacity of thebedrock channels, resulting in a relatively rapid reduction inthe propagation rate of the wedge. After 2 Myr of modeltime, propagation rates of the low-mbwedges are significantlygreater than their weak counterparts. Ultimately, the weak(low mb) wedges become wider than those that are strong.

5. Application of Model to AFTB

5.1. Geologic Setting

[27] The AFTB is a thin-skinned fold-and-thrust belt thatforms an integral part of the Argentine Andean Cordillera.The study area is an ideal natural laboratory for studying theerosional impact on wedge growth because geologic studiesin the area constrain the growth history of this fold-and-thrust belt [e.g., Giambiagi and Ramos, 2002; Ramos et al.,2002]. The AFTB lies between 32�300S and 33�000S, over atransition between flat and steep subduction [Barazangi andIsacks, 1976, 1979; Stauder, 1973] of the oceanic NazcaPlate. The area consists of three principal tectonic provincesthat reflect the progressive widening and eastward migrationof the AFTB orogenic wedge (Figure 12). From west toeast, the three structural provinces are the Cordillera Prin-

Figure 7. Effect of changing sole-out depth (D) on the history of (left) dW/dt and (right) wedge widthWover 10 Myr of model time.

Figure 8. Effect of changing Hubbert-Rubey fluid pressure ratio in the wedge and along the basaldecollement (l, lb) on (left) db/dt and (right) dW/dt. See text and Table 1 for unvarying parameter values.


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cipal, Cordillera Frontal, and the Precordillera [e.g., Ramoset al., 2002]. Below, we review the development of each ofthese zones to construct a temporal history of deformationwithin and migration of the AFTB orogenic wedge.[28] The Cordillera Principal (Figure 12) consists of a

Jurassic-Neogene sequence that unconformably overliespre-Jurassic basement rocks. The basement includes meta-morphic rocks and partly metamorphosed black shales thatare intruded by Carboniferous and Permian granitoids,which are in turn unconformably overlain by a thick sectionof Permo-Triassic volcanic rocks [Polanski, 1964]. TheJurassic-Paleocene strata mainly include deformed evapor-ites, red beds, platform limestones, shales, mudstones and,siltstones [Alvarez et al., 1997; Alvarez and Ramos, 1999;Alvarez et al., 2000; Pangaro, 1995; Aguirre-Urreta, 1996;Tunik, 1999, 2001; Giambiagi and Ramos, 2002]. Defor-mation within the Cordillera Principal had begun at about20 Ma [Ramos et al., 2002; Giambiagi and Ramos, 2002;Cegarra and Ramos, 1996] and ceased around 8.5 Ma[Giambiagi et al., 2001].[29] The Cordillera Frontal (Figure 12) mainly comprises

pre-Jurassic basement rocks, with isolated remnants ofNeogene sediments, which crop out east of its foothills.Uplift within the Cordillera Frontal had commenced by8.5 Ma and had ceased in both the Cordillera Principal

and Cordillera Frontal by 5.9 Ma [Ramos et al., 1999;Giambiagi et al., 2001]. Therefore uplift of the FrontalCordillera likely took place between 9 and 6 Ma.[30] Thrusting in the Precordillera has exposed Neogene

synorogenic deposits derived from the eastward advancingorogenic wedge of the Cordillera Fontal and Cambro-Ordovician carbonates [e.g., von Gosen, 1992; Verges etal., 2001]. In the area, uplift likely commenced at 5 Ma[Ramos et al., 2002] and had ceased around 2 Ma [Godoy,1999; Ramos et al., 1997, 2002]. Also, Quaternary defor-mation has been documented farther south [Sarewitz, 1988].[31] Deformation thus migrated eastward within the Cor-

dillera Principal between 20 and 9 Ma, uplifted the Cordil-lera Frontal between 9 and 6 Ma, and continued to migrateeastward into the Precordillera between 5 and 2 Ma. Wesynthesized balanced cross sections and structural analysesto constrain the propagation rates of the AFTB [Ramos etal., 2002], convergence rate between the AFTB orogenicwedge and the foreland, and wedge accretion parametersthroughout the three-stage history of the orogenic wedge(Figure 13). In section 5.2, shortening and wedge propaga-tion rates are reported relative to the back of the wedge,following the convention of DeCelles and DeCelles [2001].Balanced cross sections in the Cordillera Principal indicateconvergence rates between 5.5 and 5.75 mm/yr [Cegarra

Figure 9. Effect of changing Hubbert-Rubey fluid pressure ratio in the wedge and along the basaldecollement (l, lb) on the history of (left) dW/dt and (right) wedge width W over 10 Myr of model time.

Figure 10. Effect of changing basal decollement coefficient of friction (mb) on (left) db/dt and (right)dW/dt. See text and Table 1 for unvarying parameter values.


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and Ramos, 1996] during the first stage of deformation(20–9 Ma). During this period, wedge propagation ratesare on the order of 2.5 mm/yr [Ramos et al., 2002].Retrodeformed structural sections within the CordilleraPrincipal indicate that a thickness of 8 km of forelandmaterial was accreted to the wedge as it advanced eastward

[Giambiagi and Ramos, 2002]. Following this phase ofdeformation, convergence was accommodated along adeeper decollement level and deformation abruptly movedto the eastern margin of the Cordillera Frontal [Ramos et al.,2002] approximately 40 km to the east of the CordilleraPrincipal. This deeper decollement incorporated a thickness

Figure 11. Effect of changing basal decollement coefficient of friction (mb) on the history of (left) dW/dtand (right) wedge width W over 10 Myr of model time.

Figure 12. Shaded relief map with principal lithotectonic units of the AFTB overlain. The Principal,Frontal, and Precordilleras represent the progressive migration of deformation from the west to east,respectively. Section A-A0 shows location of schematic tectonic section shown in Figure 13. Geologicdata are taken from Giambiagi and Ramos [2002]. Shaded relief topographic base is from GTOPO30(1 km pixel) digital elevation model.


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of 14 km of foreland basin and basement material into theorogenic wedge and exposed pre-Jurassic basement withinthe Cordillera Frontal. On the basis of these constraints,Ramos et al. [2002] calculate a wedge propagation rate of13.3 mm/yr during uplift of the Frontal Cordillera between9 and 6 Ma. Structural sections presented by Ramos et al.[1996] indicate that between 36 and 37 km of displacementwas accommodated between the foreland and the back ofthe wedge in the Frontal Cordillera. Hence, during this time,convergence rates within the Frontal Cordillera wereapproximately 12.1 mm/yr [Giambiagi and Ramos, 2002].Between 5 and 2 Ma [Giambiagi and Ramos, 2002, andreferences therein] relatively high wedge propagation ratesof 9.1 mm/yr [Ramos et al., 2002] were observed. Thicksequences of the Neogene foreland basin and underlyingrocks (16 km) were incorporated into the wedge duringthis last important stage of deformation [Giambiagi and

Ramos, 2002]. During this time, convergence rates betweenthe wedge backstop and the foreland were 10 mm/yr[Ramos et al., 1996; Giambiagi and Ramos, 2002].

5.2. Model Results

[32] We modeled the development of the Aconcaguaorogenic wedge using the three stage history describedabove. The different phases of deformation exposed differ-ent rock types with disparate erodibilities. Our estimatedmodel parameters for the wedge properties are presented inTable 2 and expanded upon in Appendix B. The range inwidths of the orogenic wedge before each phase of defor-mation was calculated by subtracting the product of dW/dtand the time increment of the deformation from the currentwedge width of 175 km. Using the history of the wedgegeometry, we solved for the unknown rock erodibilityparameter (K) by minimizing the difference between the

Figure 13. Schematic tectonic section highlighting three-stage growth of the AFTB orogenic wedge.Vertical black lines show inferred position of drainage divide. From 15 to 9 Ma, frontal accretion offoreland material incorporated a thickness of 4–6 km of sediment into the wedge. Flattening of thesubducting slab to the west around 9 Ma led to incorporation of greater thicknesses (16–18 km) offoreland material into the wedge. Finally, westward migration of deformation between 6 and 2 Mauplifted the Precordillera, exposing Neogene basin sediments and Paleozoic rocks. During this last phaseof deformation, the position of the drainage divide is poorly constrained and may lie up to 60 km east ofthe western extent of the AFTB. Section modified after Ramos et al. [2002] and Giambiagi and Ramos[2002].


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range of field-determined and model wedge widths aftereach period of deformation.[33] Our forward models indicate that m and n are impor-

tant parameters in determining the growth of the wedge andso we explored the effect of different sets of these values onthe growth of the AFTB. Table 3 shows the best fit K valuesfor different combinations of m and n. Errors in these valuesrepresent uncertainties introduced by ranges in wedge prop-agation rates reported by Ramos et al. [2002]. Generally, asmand n increase, Kmust decrease to produce equivalent wedgegeometries. When m and n are low, mean rock-type erodi-bilities decrease and increase after the first and second phasesof deformation, respectively. However, when m = 5/4, n =5/2, a continual decrease in K over the wedge’s history isrequired to produce the inferred wedge geometry.[34] Using these ranges in K, we calculated dW/dt over the

history of the orogenic wedge and compared these values tothose determined in the field. (Figure 14). As m and nincrease, the propagation rate decreases more quickly thanfor low values of the exponents. In the case of low andmoderate values ofm and n (1/3�m� 0.4, 2/3� n� 1),K isgreatest during the first stage of deformation, decreasesduring the second, and increases slightly during the third.However, whenm = 5/4, n = 5/2, K decreases during all threestages of deformation.

6. Discussion

6.1. Uncertainties in the Bedrock Power Law IncisionModel

[35] There are several important uncertainties in the bed-rock power law incision model that must be addressed in anystudy that attempts to understand orogen-scale topography inthis context. First, as Sklar and Dietrich [1998] point out,bedrock incision may be a complicated function of hydraulicgeometry, uplift, basin parameters, climate, and hillslopesediment supply to the channel. Second, K encapsulates theeffects of allometric changes in channel geometry withdischarge, sediment flux entering the channel, the relation

between effective discharge and drainage basin area, and theresistance of bedrock to fluvial erosion. Most of these factorslikely change with m, but to date, no comprehensive studyhas been conducted that defines this scaling relationship.Contrary to the work of others [e.g., Sklar and Dietrich,1998;Whipple and Tucker, 1999], we chose not to scale U/Kby 1/n in our forward models to maintain a constant topo-graphic form for changing n, as it is not apparent that theunknown scaling law of K and m supports this approach.Instead, we fixed K to values determined by Stock andMontgomery [1999] for n = 1, m = 0.4. If increasing powerlaw exponent values reduce the value of K, our modelsoverestimate and underestimate the voracity of erosion inwedge development when the exponents are high and low,respectively. While these scaling problems lead us to viewour conclusions as preliminary and subject to change uponfurther work, all studies that strive to understand orogen-scale relief using the power law bedrock incision modelsuffer from this deficiency. Nevertheless, our work is novelin that it includes the effects of realistic values ofm and n (andtheir ratio) in a coupled model that investigates the feedbacksbetween deformation, rock erodibility, and climate.

6.2. General Model Results

[36] Our results expand the work of Davis et al. [1983],Dahlen [1984], and DeCelles and DeCelles [2001]. In theoriginal CCW formulation, a locus of (a, b) pairs waspredicted for a set of mechanical wedge parameters m, mb, l,and lb. Any wedge at its critical failure limit falls on a linerelating a to b (line in Figure 15); however, the CCW theorydid not predict wedge development over time or theirultimate (a, b) pair. Willett [1992] used a finite elementmethod to model elastic-plastic wedge growth in responseto convergence in the absence of erosion. We add theerosional component to the CCW theory to understandcontrolling factors and rates at which orogens progress fromtheir initial states to those in which all material added to thewedge is evacuated by erosion. In this way, our modelpredicts both the line on which stable a,b pairs of anorogenic wedge will lie and how a point representing thedevelopment of the orogen moves along that line in re-sponse to accretion of foreland material and erosion.[37] b and dW/dt in our model decay with time as the

wedge grows toward its stable configuration. Decrease in bover time has been noted in many orogens [e.g., Mitra,1997] and has been explained by the successive incorpora-tion of increasingly structurally competent rocks into thewedge [Mitra, 1997; DeCelles and DeCelles, 2001]. Be-cause D relates the wedge area directly to the db/dt in ourmodels, the change in wedge cross-sectional area for agiven change in b increases dramatically as b decreases.In the absence of erosion, material accreted to the wedgecauses its cross-sectional area to change at a constant rate,requiring db/dt to decrease as the wedge widens. This effect

Table 2. Model Parameters and Propagation Rates for the AFTB

Model Parameter 20–9 Ma 9–6 Ma 5–2 Ma 20–2 Ma Referencea

m 0.982 1mb 0.85 2l 0.7 1lb 0.7 1ka 4 1h 1.4 1v, mm/yr 5.5–5.75 12.2 10 1,3,4T, km 8 14 16 3,4,5dW/dt, mm/yr 2.5 13.3 9.1 4

aReferences: 1, this study; 2, Byerlee [1978]; 3, Ramos et al. [2002]; and4, Giambiagi and Ramos [2002]; 5, Ramos et al. [1996].

Table 3. Best Fit K Values for Observed History of AFTB

Deformation Stage m = 1/3, n = 2/3 m = 0.4, n = 1 m = 5/4, n = 5/2

Stage I (20–9 Ma) 1.1 ± 0.04 � 10�5 1.1 ± 0.04 � 10�5 8.6 ± 0.3 � 10�10

Stage II (9–6 Ma) 6.1 � 10�6 5.2 � 10�6 1.2 � 10�10

Stage III (5–2 Ma) 7.1 � 10�6 5.3 � 10�6 6.4 � 10�11


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is augmented when erosion removes material from thewedge and decreases the rate of volume addition to thewedge. Because erosional efficiency increases as bdecreases, the rate of change in cross-sectional area of the

wedge will decrease as it grows. Therefore these twoconspiring processes may provide alternative or compli-mentary hypotheses that explain decreases in b and db/dtwith time in orogenic wedges.[38] Finally, our model results show the important role of

both climate and the m and n in determining the growth andlateral extent of orogenic wedges. As climate becomes dryerand/or rocks less erodible, wedge propagation rates increaseand wedges widen. Conversely, where erosional efficiencyis high, narrow orogens whose propagation rates decayrapidly in time might be expected. The magnitude of theseeffects is strongly controlled by the choice of m and n. Inour forward models, when these values are high (e.g., m =5/4, n = 5/2), the wedge builds little topography, faultgeometries remain close to their steep extremes throughouttheir history, and wedges adjust virtually instantaneously tochanges in climate and/or wedge properties. However, lowvalues (e.g., m = 1/3, n = 2/3) allow significant topographyto be built before erosional efficiency becomes importantand a wide range of wedge responses to typical erosional ormechanical perturbations may be observed.

6.3. AFTB Calibration Study

[39] The validity of our modeling results and their appli-cability to natural systems is supported by the time-spacerelationships of wedge development in the AFTB. Betweenthe first (20–9 Ma) and second (9–6 Ma) stage of defor-mation in the AFTB, deformation likely moved discretelytoward the foreland in a series of steps that uplifted the

Figure 14. Modeled and observed propagation rateswithin the AFTB over time. Regions outlined by heavyblack lines show field-determined ranges of the wedgepropagation rate, while gray regions show range of modelresults. Model results are presented as fields to express therange of possibilities produced by geologic uncertainties inforeland-wedge convergence velocity (v). Results for powerlaw erosion exponents of (top) m = 1/3, n = 2/3, (middle)m = 0.4, n = 1, and (bottom) m = 5/4, n = 5/2.

Figure 15. Schematic depiction of the development of acritical Coulomb wedge subject to bedrock incision. Lineshows the conditions under which the wedge deforms at itsCoulomb failure limit [Davis et al., 1983]. Awedge with noinitial topography (A) will accrete material and increase itscross-sectional area and surface slope. As the surface slopeincreases, erosional processes remove larger amounts ofaccreted material, causing the change in cross section of thewedge to decelerate with time. Conversely, wedges withinitially steep surface slopes (B) undergo more erosion thanaccretion. This causes a decrease in the wedge’s cross-sectional area and surface slopes until erosion balancesaccretion.


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Cordillera Frontal. These discrete events led to wedgethickening and out-of-sequence thrusting in the higherportions of the wedge. These steps violate the assumptionsof our model of critical growth of the wedge. However, theysteps appear small and frequent enough to approximate acontinuous migration of the wedge tip within the toleranceof our model assumptions. Also, the drainage divide mayhave shifted eastward during the last phase of deformation.Provenance studies [e.g., Giambiagi and Ramos, 2002;Giambiagi et al., 2001] suggest that most or all of thewedge drained to the east between 15 and 6 Ma (Figure 13).However, at an unknown time between 6 Ma and thepresent, the drainage divide migrated to the east. Becausethe timing of this migration is unknown, we assume forsimplicity that the eastward movement of the divide tookplace after cessation of deformation in the AFTB. Thisassumption may cause a underestimation of the K valuesinferred during the final stage of deformation. Lacking anydirect information regarding the timing of divide migrationand noting the uncertainties in the K values during the finalphase of deformation, we nevertheless regard our estimatesof K during this final stage as a representative range ofvalues applicable to this wedge.[40] Despite the many simplifying assumptions of our

orogenic wedge model, the determined K values for theAFTB are within the range of those reported when m = 0.4,n = 1. Stock and Montgomery [1999] estimated K values offor a variety of lithologies determined best fit power lawexponents m = 0.4 and n = 1, and K values to be between4.8 � 10�5 � 4.7 � 10�4, 3.8 � 10�6 � 7.6 � 10�6 and4.4 � 10�7 �1.1 � 10�6 for volcaniclastics and mudstones,basalts, and granitoid and metasedimentary rocks, respec-tively. While the combinations of rocks exposed in theAFTB are not directly comparable, the sandstones/mud-stones and platform carbonates, metamorphic basement andcombination of these and foreland sediments in our modelyielded mean K values of 1.1 � 10�5, 5.2 � 10�6 and 5.3 �10�6, respectively. These estimates are consistent withsediment/metasedimentary rocks with a crystalline compo-nent, metamorphic/crystalline basement, and a mixture ofthese rocks with foreland basin sediments, respectively.While Stock and Montgomery’s [1999] estimates span awide range of K values for each rock type, the wedgepropagation rates and widths are quite sensitive to this value(Figures 2 and 3). Therefore it is not unreasonable to expectthat if the effects of erosion were not properly captured inour models, our inverted K values may be orders ofmagnitude different than those determined for similar rocktypes.[41] Our predicted propagation rates during development

of the AFTB and K values contain information about thepotential range of power law exponents that may beapplicable to the AFTB. First, as m and n increase in ourmodels, K must decrease to produce equivalent wedgegeometries [e.g., Sklar and Dietrich, 1998; Whipple andTucker, 1999]. Regardless of this decrease in K, the re-sponse time of the wedge also decreases as the result ofincreasing m and n (Figure 14) [Whipple and Tucker, 1999].We can partially constrain potential m and n values byincluding qualitative observations of relative rock erodibil-ities exposed during different deformation stages. Deforma-tion within the Cordillera Principal exposed sandstones,

mudstones, and platform carbonates during the first stageof deformation. These rocks likely have the highest erod-ibility during the three stages of deformation. Extensiveexposure of metamorphic basement in the Cordillera Frontalduring the second stage of deformation likely representedthe least erodible rocks during wedge growth. Finally,incorporation of foreland basin sediments into the Precor-dillera during the last deformation stage likely wouldincrease the effective value of K within the entire wedge.While K convolves many factors including rock typeclimate, and/or degree of fracturing or foliation in the rocks[Whipple et al., 2000], Stock and Montgomery [1999] foundthat bulk lithologic type was the first order control on theirdetermined values of K. Therefore we expect the value of Kto decrease, and slightly increase between the first andsecond and second and third stages of deformation, respec-tively. When 1/3 � m � 0.4 and 2/3 � n � 1, K valuesundergo the qualitatively predicted transition during thedeformation history of the wedge. However, when m =5/4, n = 5/2, rock erodibility continually decreases, contraryto our qualitative observations. Our determination of prop-agation rates shows that when m and n are large, the shorterresponse time of the wedge moves its geometry closer to itstime-invariant form at the end of each deformation phase. Inthis case, progressively lower values of K are required toartificially maintain high propagation rates throughout thefollowing phase of the wedge’s history. The continualdecrease in K observed in our models when m = 5/4 andn = 5/2 indicate that these values force the wedge toundergo these unrealistic decreases in K over its history.

7. Conclusions

[42] We developed a semianalytical model that couplesthe accretion of foreland material to a critically growingorogenic wedge that undergoes erosion. The wedge isrequired to be in its critical state during growth, grows byaddition of material from the foreland, and is limited byfluvial bedrock incision. We used this model to examine thepotential interaction between rates of foreland accretion ofmaterial into the wedge, erosional removal of material, andwedge widths and propagation rates over time. We made thefollowing conclusions based on our model results:[43] 1. The bedrock power law exponents m and n exert

first-order controls on the response time of the wedge and itsgeometry through time. High values of m and n (m = 5/4, n =5/2) cause the wedge to rapidly adjust to changes in erosionalor accretion rates, ormechanicalwedge parameters. However,wedge geometry is generally insensitive to these erosionaland accretionary parameters when these exponents are high.Low values (m = 1/3, n = 2/3) allow a range of interactionbetween erosion, accretion of material, and wedge propa-gation rates and width over time. Commensurate changes inK with m and n may partially offset this effect; however,lack of knowledge about scaling laws between these vari-ables makes it difficult to evaluate such changes on wedgedevelopment. In any case, currently employed coupledthermomechanical-erosional models often use power lawexponent values of m = 1, n = 1 to simulate erosion [e.g.,Willett, 1999; Beaumont et al., 2000]. Our results indicatethat these power law exponents play an important role indetermining wedge geometry, and so their restriction to


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these fixed, and perhaps unrealistic values, may complicatethe assessment of the role of erosion relative to other (i.e.,rheology) factors.[44] 2. When the bedrock power law exponents are low,

decreased erodibility (K) due to dry climates and/or ero-sionally competent rock types, and/or increased forelandaccretion fluxes (vT) result in higher wedge propagationrates and ultimately wider wedges than their higher K andvT counterparts. The time between commencement of de-formation and full erosional evacuation of accreted materialincreases as K decreases and vT increases. For the range inK found in nature, a variety of wedge growth conditions ispossible. Importantly, this study is the first to document thisbehavior for a realistic range in K inferred for various rocktypes and climatic conditions.[45] 3. Increasing sole-out depth of the basal decollement

decreases wedge propagation rates and increases wedgeresponse time. Wedges with deeper sole-out depths areultimately wider than those with shallow sole-out depths.[46] 4. As the Hubbert-Rubey fluid pressure ratio within

the wedge and along the basal decollement is increased,wedge width and response time increase. High wedgepropagation rates correspond to high fluid pressure ratios.[47] 5. Low friction basal decollements generally lead to

higher propagation rates than when friction is low. Wedgeresponse time and wedge width increase with decreasingbasal friction.[48] To test our formulation, we modeled the development

of the Aconcagua fold-and-thrust belt in western Argentina.[49] 6. Using field data to constrain the growth history of

the wedge, we solved for the unknown bedrock erodibilityconstant (K) and compared this to previous publishedestimates within similar rock types. When m = 0.4, n = 1,K is within the range of these independently determinedestimates for rock types that might be expected to havesimilar erodiblities to those exposed in the AFTB. Thus ourresults are the first to determine the erodibility valuesrequired to produce an observed wedge growth historyand to quantitatively test these models by comparing thesevalues to those determined independently.[50] 7. As m and n increase, correspondence between

qualitatively determined relative rock erodibilities and thosedetermined in our analysis decreases. Therefore we considerit likely that erosional processes are best represented in thiswedge by low to moderate power law exponents (1/3 � m �0.4, 2/3 � n � 1).

Appendix A: Detailed Model Formulation

[51] Our model of orogenic wedge growth assumes thatthe wedge accumulates mass by incorporating only materialof the foreland into the wedge, loses mass by erosion andtransport of material to the foreland, and changes its cross-sectional area so as to maintain a mechanical balancebetween tectonic and body stresses during its development.Importantly, we assume that the cross-sectional areachanges continuously with time as material is accreted tothe wedge. However, the process of accretion usually takesplace by the periodic migration of deformation toward theforeland on discrete faults. Therefore our model serves as anapproximation for this accretion process over longer (>1Myr)timescales. This simple model can be cast in terms of the

mass flux entering the wedge due to frontal accretion andleaving the wedge due to erosion, and the change in volumeof the wedge. In the case that the density of material does notchange as material is incorporated into the wedge, the massbalance of the wedge may be treated as a volume balance:

dA

dt¼ Fa � Fe ðA1Þ

where dA/dt is the rate of change of the cross-sectional areaof the wedge, and Fa and Fe are the volume fluxes added toand removed from the wedge by frontal accretion anderosion per unit width (hereafter simply referred to asvolume flux), respectively. Where the volume fluxes relatedto these two factors can be quantified, changes in wedgegeometry may be investigated.[52] In all cases, an orogenic wedge grows by incorporat-

ing sections of the foreland as it converges with the advanc-ing wedge. The higher parts of the orogen act as a rigidbackstop against which material added to the wedge from theforeland accumulates [e.g., DeCelles and Mitra, 1995](Figure 1). Under these conditions, the volume flux ofmaterial entering thewedge is [DeCelles andDeCelles, 2001]

Fa ¼ vT ðA2Þ

where v is the convergence velocity of the foreland withrespect to the wedge, and T is the thickness of the accretedforeland layer [DeCelles and DeCelles, 2001].[53] The material entering the wedge by frontal accretion

is at least partially removed by erosion. Following the workof others [e.g., Whipple et al., 1999; Whipple and Tucker,1999, 2002; Whipple, 2001], we consider the relief andslopes traversing the orogenic wedge to be limited by therate of fluvial incision into bedrock. This rate is thought tobe a power function of the channel slope (S), the catchmentarea (A; a proxy for discharge, [Howard et al., 1994]), and aconstant (K) that represents the effects of rock erodibilityand climate [Howard and Kerby, 1983; Howard et al., 1994;Stock and Montgomery, 1999]:

dz

dtb¼ �KAmSn ðA3Þ

where the subscript b indicates that this material is erodedfrom the portion of the wedge above the foreland. Here, thepower law exponents (m, n) represent the processes acting toerode the channel bed. In addition, rock type and climate arecaptured in theK parameter [Howard et al., 1994]. To expressA in terms of the downstream profile position (x) we relate thesource area to the upstream profile length [Hack, 1957]:

A ¼ kaxh ðA4Þ

where ka and h are constants that depend on the catchmentgeometry. By combining equations A3 and A4, we expressthe rate of change of the channel elevation in terms of thedownstream profile distance, x:

dz

dtb¼ �Kkma x

hmSn ðA5Þ


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[54] Finally, the volume flux of material eroded from thewedge (Fe) is determined by integrating equation (A5) withrespect to space:

Fe ¼ �Z W

0

dz

dtbdx ¼ Kkax

hmþ1ð Þ

hmþ 1Sn��W

0

ðA6Þ

where W is the width of the orogenic wedge (Figure 1).[55] Finally, we estimate how the difference between the

eroded and accreted flux is expressed in the change inwedge geometry. In particular, we investigate the rates ofchange of the dip of the basal decollement, surface slope,and wedge width. For clarity, we treat the rate of change inthe orogenic wedge area (dA/dt) as the sum of the rate ofchange of the portion below (dA/dtb) and above (dA/dta) theforeland surface:

dA

dt¼ dA

dt

� �a

þ dA

dt

� �b

ðA7Þ

[56] DeCelles and DeCelles [2001] noted that dA/dtb isgeometrically related to the rate of change of the fault dipand wedge width by

dA

dt

� �b

¼ W tan bdW

dtþ W 2

2 cos2 bdbdt

� �ðA8Þ

where b is the average basal fault dip of the wedge(Figure 1). As material is accreted to the wedge, thisaverage decollement angle may decrease as deformation istaken up on structures within the foreland that widen thewedge. Conversely, in the case that erosion removes largeamounts of material from the wedge, structures within thewedge may be reactivated while those at its forelandperiphery may cease to accommodate convergence. Thismay result in an effective contraction in the wedge’s arealextent. Both the fault dip and the wedge width may bevaried independently; however, many studies suggest thatthe basal decollement flattens as its strength becomesindependent of the applied normal traction [Davis et al.,1983]. If the decollement depth exceeds that at whichquartz and feldspar deform plastically due to increasedtemperature (typically between 12 and 16 km [Brace andKohlstedt, 1980]), the model requirements of the wedgedeforming as a brittle, elastic material may be violated. Werelate b to W by assuming that the wedge soles out at adepth D below the foreland surface. Furthermore, becausematerial only enters the wedge by frontal accretion, we setthe rigid backstop at the location where the basaldecollement intersects the brittle-plastic transition. Underthese circumstances, the wedge width and its rate ofchange over time may be related to the fault dip as

W ¼ D cot b ðA9aÞ

dW

dt¼ �D csc2 b

dbdt

ðA9bÞ

[57] Substituting equations (A9a) and (A9b) into equation(A8), we can express the change in the lower portion of thewedge solely in terms of b and its rate of change:

dA

dt

� �b

¼ �D2 csc2 b2

dbdt

ðA10Þ

[58] The section of the orogenic wedge that lies above theforeland surface is a function of W, and the wedge’stopographic slope (a). As with the lower portion of thewedge, we express the change in area of this upper sectionas

dA

dt

� �a

¼ W tanadW

dtþ W 2

2 cosadadt

ðA11Þ

Substituting the expression for the wedge width as afunction of fault dip (equation (A9a)) into this equationyields

dA

dt

� �a

¼ � D2 tanasin b cos b

dbdt

þ D2 cot2 b2 cos2 a

dadt

ðA12Þ

According to equations (A10) and (A12), the rate ofchange of the area of the orogenic wedge depends on thesole-out depth, the surface and fault angles, and the rateof change of these angles. In our model, we relate thesurface slope and its rate of change to the decollementgeometry using the critical Coulomb wedge (CCW)theory [Davis et al., 1983; Dahlen et al., 1984; Dahlen,1984]. In this formulation, body forces due to lithostaticloading increase with surface slope and fault dip. Thetheory predicts that the orogenic wedge is in mechanicalequilibrium when the resolved tractions along the faultsurface are equal to the failure limit along the surface asdefined by the Coulomb Failure Criterion [Davis et al.,1983; Dahlen, 1984]. The relationship between thesurface slope and fault dip at this critical condition isexpressed most simply as [Dahlen, 1984]

aþ b ¼ yb � yo ðA13Þ

[59] For subaerial orogenic wedges, yb and yo depend onthe internal angle of friction of the wedge (f), the internalangle of friction of the fault plane (fb), the Hubbert-Rubeyfluid pressure ratio within the orogenic wedge (l) and alongits basal decollement (lb), and the surface slope (a).Complete expressions for these parameters are given byDahlen [1984]. Hereafter, we denote the relation betweensurface slope and critical fault dip as

a ¼ f b;y;yb;l;lbð Þ ðA14Þ

and for a fixed set of mechanical wedge parameters, a =f (b). Importantly, equation (A14) is meant only to representthe relationship between a and b explicitly predicted by thecritical Coulomb wedge theory [Davis et al., 1983] and arenot necessarily meant to imply that a is controlled by b. TheCCW theory predicts that in cases where a < f(b) and a >


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f(b), the orogenic wedge will undergo internal deformationthat acts to increase the surface slope, and extension withinthe wedge reduces the surface slope, respectively, until a =f(b) [Davis et al., 1983]. In our model, we assume thatmechanical adjustments within the wedge that maintain thesurface slope and fault dip at their critical angles occurrapidly relative to the rates of accretion of material into anderosion from the wedge. In these cases, the orogenic wedgegrows and shrinks in its critical state such that the relationbetween the surface slope and fault dip (equation (A13)) ismaintained at all times.[60] The rate of change of the surface slope is dependent

on the rate of change of the fault dip and a function, g(b):

dadt

¼ g b;y;yb;l;lbð Þ dbdt

ðA15Þ

This allows us to express the change in total area of thewedge (equations (A10) and (A12)) solely terms of thedepth to the brittle-plastic transition, and the fault dip and itsrate of change:

dA

dt¼ db

dt

�D2 tan f bð Þsin b cos b

�þD2 cot2 bg bð Þ

2 cos2 f bð Þ � D2 csc2 b2

�ðA16Þ

[61] The characteristics of the wedge geometry canbe linked to frontal accretion of the foreland and surficialerosion processes of the orogen by combining equations (A2),(A6), and (A16) using equation (A1). First, we note thatif the wedge is growing critically in its mechanicallystable configuration and the basal decollement is planar,the surface slope does not vary as a function of distancealong the wedge. If this slope is limited by fluvialbedrock incision, S in equation (A6) is invariant withposition along the wedge and may be removed from theintegration. In addition, we note that S = tan(a) =tan( f(b)). Combining these equations and rearranging tosolve for the rate of change of the fault dip angle, wefind that

dbdt

¼ �D2 tanasin b cos b

þ D2 cot2 bg bð Þ2 cos2 f bð Þ � D2 csc2 b

2

� ��1

� vT � KkahmD hmþ1ð Þ cot hmþ1ð Þ bSn

hmþ 1

� �ðA17Þ

[62] Using this expression with equation (A9b), the rateof change of the wedge width may also be computed. Inaddition, where an initial wedge geometry is prescribed,integration of equation (A17) with respect to time yieldsthe temporal history of the change in basal decollementdip, which may in turn be converted into changes in W(equation (A9b)) over time. Because the wedge starts andgrows in its mechanically critical state, initial conditions mustconsist of a stable orogenic wedge geometry in which a =f(b).[63] We chose a numerical solution method to determine

two of the parameters in our model. First, we solve for g(b)at a given value of b by calculating the change in a thatresults from a small (1 � 10�5 degrees) increment in the

value of b. The resulting change in a was normalized bythis increment to determine the change in a resulting from aunit change in b. When this value is scaled by db/dt, g(b)db/dt is approximated. Second, we chose to integrateequation (A17) numerically when calculating the temporaldevelopment of the modeled wedge. We used a simple, first-order explicit integration scheme with �t = 1000 years inthe models. To assess the accuracy of our solutions, weperformed several trials on rapidly changing wedge geom-etries in which the time step was reduced by an order ofmagnitude and found no significant difference between themodel results. Therefore this explicit integration methodprovides reliable results within the range of model param-eters investigated.

Appendix B: Wedge Parameter Estimates

[64] In this appendix, we present our estimations of theorogenic wedge parameters (m, mub, l, lb) and erosionparameters (K, ka, h). We have no direct measures of thefluid pressures or friction coefficients within or along thewedge and wedge base, respectively; however, measure-ments of the current and initial geometry of the wedgepartially constrain these parameters. To estimate the wedgewidths over time, we used the propagation rates of Ramos etal. [2002] of 2.5, 13.3, and 9.1 mm/yr over the last 15–9,9–6, and 5–2 Myr, respectively, to compute 103.8 km ofwidening over the history of the wedge. We subtracted thisfrom the currently observed 175 km wedge width to obtainan initial width of 71.2 km. On the basis of regional crosssections through the AFTB [Giambiagi and Ramos, 2002],we assumed that the flattening depth of the wedge wasaround 20 km throughout most of its deformation history.Using this depth, the initial fault angle (bo) was likelyaround 13.6. This range agrees well with restored sectionsof the westernmost AFTB, which estimate the average faultdip to be 5 [Giambiagi and Ramos, 2002].[65] When the Hubbert-Rubey fluid pressure ratio within

the wedge and along the basal decollement are equal anda = 0�, b is primarily dependent on m and mb [Davis et al.,1983]. We assumed that the basal decollement obeyedByerlee’s friction law during deformation (mb = 0.85). Inaddition, we assumed that the fluid pressure within thewedge and along the decollement are equal. Finally, weconsidered the surface of the AFTB to have no topographyprior to 20 Ma. Under these assumptions, we computed m tobe 0.982 when the initial fault dip was 13.6�. The highercoefficient of friction values within the wedge relative toByerlee’s law likely reflects the contribution of cohesion tothe strength of the wedge [Dahlen et al., 1984]. Using theseestimates of m and mb with the current wedge geometry, weestimated pore fluid pressures within the wedge to be l =lb = 0.7. These pore fluid pressures agree well withestimates for the Himalaya and Taiwan (l = lb = 0.76and l = lb = 0.675, respectively) [Davis et al., 1983].Because we have no direct evidence for or estimates ofchanges in m, mb, l, and lb over time, we assume that theyremained constant over the lifetime of the orogen.[66] Geomorphic parameters were constrained by DEM

analysis and estimation of unit erodibility exposed in theAFTB wedge. We used the Hydro1K digital elevationmodel (DEM) and flow direction grids to constrain ka and


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h. A number of combinations of ka and h yield similar root-mean-square (RMS) misfits between values measured inthe Hydro1K DEM and predicted by equation (A4). Weselected the combination ka = 4, h = 1.4. Similar RMSvalues were obtained by increasing h; however, best fitvalues for ka rapidly became unreasonably small (ka < 0.1)with larger h values.

Notation

a surface slope of the wedge [L/L].b fault decollement angle [L/L].D depth to the decollement at wedge backstop [L].Aa area of wedge above horizontal datum (foreland

elevation) [L2].Ab area of wedge below horizontal datum (foreland

elevation) [L2].z elevation above sea level [m].v convergence velocity of the foreland with respect to

the rear of the wedge [L/t].T thickness of accreted foreland material [L].K coefficient of erosion [L1–2m/t].m area exponent, erosion rule.n slope exponent, erosion rule.ka area-length coefficient [L2-h].h exponent in area-length relationship (reciprocal of

Hack’s exponent).f (b) function relating wedge surface slope to decollement

angle at Coulomb failure limit.g(b) function relating rate of change in surface slope to

rate of change in decollement angle at Coulombfailure limit.

[67] Acknowledgments. G.H. acknowledges funding from theAlexander von Humboldt Foundation and the DAAD IQN program forsupporting his research at Potsdam University. We greatly acknowledge thecareful reviews of Brian Horton and Jean Braun, and an anonymousreviewer, which improved the quality of the manuscript.

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��G. E. Hilley, Department of Earth and Planetary Science, 377 McCone

Hall, University of California, Berkeley, CA 94720-4767, USA. ([email protected])V. A. Ramos, Departmento de Geologıa, Laboratorio de Tectonica

Andina, Universidad de Buenos Aires, Cuidad Universitaria, Pabellon II,1428 Buenos Aires, Argentina.M. R. Strecker, Institut fur Geowissenschaften, Universitat Potsdam,

Postfach 601533, D-14415 Potsdam, Germany.


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growth and erosion of fold-and-thrust belts with an application to the aconcagua fold...

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