Tectonophysics 526–529 (2012) 16–23

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Tectonophysics

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Varying mechanical coupling along the Andean margin: Implications for trenchcurvature, shortening and topography

G. Iaffaldano a,⁎, E. Di Giuseppe b,c, F. Corbi b, F. Funiciello b, C. Faccenna b, H.-P. Bunge d

a Research School of Earth Sciences, The Australian National University, Australiab Dipartimento di Scienze Geologiche, Università “Roma TRE”, Italyc Laboratoire FAST, CNRS/UPMC/Université Paris Sud, Franced Sektion Geophysik, LMU Munich, Germany

⁎ Corresponding author. Tel.: +61261253424.E-mail address: giampiero.iaffaldano@anu.edu.au (G

0040-1951/$ – see front matter © 2011 Elsevier B.V. Alldoi:10.1016/j.tecto.2011.09.014

a b s t r a c t

a r t i c l e i n f o

Article history:Received 24 March 2011Received in revised form 8 August 2011Accepted 22 September 2011Available online 1 October 2011

Keywords:Laboratory modelsTrench curvatureOverriding plate shorteningTopographyAndean margin

Convergent margins often exhibit spatial and temporal correlations between trench curvature, overridingplate shortening and topography uplift that provide insights into the dynamics of subduction. The Andeansystem, where the Nazca plate plunges beneath continental South America, is commonly regarded as the ar-chetype of this class of tectonics systems. There is distinctive evidence that the degree of mechanical couplingbetween converging plates, i.e. the amount of resistive force mutually transmitted in the direction opposite totheir motions, may be at the present-day significantly higher along the central Andean margin compared tothe northern and southern limbs. However quantitative estimates of such resistance are still missing andwould be desirable. Here we present laboratory models of subduction performed to investigate quantitativelyhow strong lateral coupling variations need to be to result in trench curvature, tectonic shortening and dis-tribution of topography comparable to estimates from the Andean margin. The analogue of a two-layersNewtonian lithosphere/upper mantle system is established in a silicone putty/glucose syrup tank-modelwhere lateral coupling variations along the interface between subducting and overriding plates are pre-im-posed. Despite the simplicity of our setup, we estimate that coupling in the central margin as large as 20%of the driving force is sufficient to significantly inhibit the ability of the experimental overriding plate toslide above the subducting one. As a consequence, the central margin deforms and shortens more than else-where while the trench remains stationary, as opposed to the advancing lateral limbs. This causes the marginto evolve into a peculiar shape similar to the present-day trench of the Andean system.

. Iaffaldano).

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© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Subduction is a central process in plate tectonics (Morgan, 1968),whereby cold lithospheric plates sink into Earth's mantle along con-vergent margins, primarily driven by their weight (McKenzie,1969). The balance of forces determines the evolving curvature ofconvergent margins (e.g. Morra et al., 2006), but a mere parameteri-zation of the sole buoyancy term, or slab-pull, often fails to explaineven the observed temporal variations of convergence rates. This in-dicates that other forces, presumably of resistive nature, may at dif-ferent times contribute more significantly to the momentumbalance, and therefore to the shape of trenches.

A prime example of active subduction and evolving curvature isthe Andean margin, where the present-day simple geometry (Fig. 1)possibly allows identifying the current major controls on the dynamicsmore easily than elsewhere. The Andean trench extends from north tosouth formore than40° in latitude and features a pronounced curvature

that makes South America convex towards the Nazca plate. Paleomag-netic and geodetic data indicate that such shape is progressively ac-quired through crustal rotations that are clockwise to the south andcounter-clockwise to the north of the Bolivian Orocline (Fig. 1)(Allmendinger et al., 2005). Constraints on the temporal evolutionof the curvature available from paleomagnetic studies of the Andeanforeland indicate that north of the Bolivian Orocline rotations predate~15Ma and become progressively younger as one moves northward(Rousse et al., 2003). Similarly, to the south Maffione et al. (2009) con-cluded that significant clockwise rotation occurred since 30–40 Ma.Other studies, however, propose that most of the curvature developedin the Eocene-Oligocene (e.g. Arriagada et al., 2008; Roperch et al.,2011).

Deformation along the Andean margin has been documented tooccur since around 100 Ma. Typically three major phases are identi-fied: the Peruvian, the Incaic and the Quechuan phases (see Cobboldet al., 2007 for a comprehensive review). Compression has beenwidespread during all phases, while some extension has occurred atthe Oligocene–Miocene boundary (e.g. Jordan et al., 2001). It is onlysince the recent Quechuan phase, however, that crustal thickeninghas been predominant. Estimates of paleo-elevation from botanical

Fig. 1. Tectonic setting of the Andean margin. Continental topography is in gray color-scale. Arrow indicates average NZ/SA convergence direction since 40 Ma. Thickness ofthe NZ/SA margin varies with the observed amount of sediments above the trench(data from the National Geophysical Data Center – NOAA). Other plate margins are inthin black. AN – Antarctica.

17G. Iaffaldano et al. / Tectonophysics 526–529 (2012) 16–23

(e.g. Gregory-Wodzicki, 2000) and more recently from carbonatedata (e.g. Ghosh et al., 2006) provide additional constraints to oroge-ny in the Andes. In fact there is much consensus that the developmentof the present-day height and inland extension of the central plateautook place mostly in the Neogene. Naturally, this has focused muchinterest on what are the peculiar characteristics of the convergentmargin since then, rather than what are the previously-accrued de-formation and inherited structures. Constraints on paleo-elevationhave prompted the community to agree that indeed most of thetrench curvature developed because the central Andes experiencedmore crustal shortening in late Cenozoic compared to elsewherealong the margin, as originally proposed by Isacks (1988).

Despite this advance, what geological process may simultaneouslyexplain curvature of the margin, crustal shortening and topographyuplift in the Andes still stands today as a most intriguing question,to which various authors have proposed different answers. Russoand Silver (1996) linked deformation and shortening to mantle flowbeneath the Nazca slab. Specifically, they resorted to shear-wavesplitting observations and proposed that flow stagnation beneaththe central Nazca slab does not allow the latter to roll back as muchas it does in the northern and southern margin. Schellart et al.(2007) revisited this proposition, arguing that plate width also con-tributes to the curvature of the margin. The impact of propertiesand characteristics of the overriding plate on trench deformationhas in the past also been explored by taking advantage of analogand numerical models of subduction (e.g. Heuret et al., 2007;Marques and Cobbold, 2006; Mart et al., 2005). On a more fundamen-tal level, these studies relate trench deformation to variations of platecoupling – that is, the amount of resistive force that plates mutuallyexert upon each other in the direction opposite to their motions. A

variety of evidence supports the emplacement of such variationsalong the Nazca/South America margin in late Cenozoic, but we stilllack a precise estimate of the coupling recently emplaced. Theamount of sediments entering the trench has been widely recognizedwith the potential to lubricate the inter-plate area, effectively reduc-ing the coefficient of friction (Kopf and Brown, 2003). In fact, climate-controlled sediment starvation of the central Andean margin (Fig. 1)is thought to increase friction and therefore mechanical coupling(Lamb and Davies, 2003), focusing in the central margin the stressesnecessary to foster shortening and sustain uplift of the high Andeanplateau. In addition, Iaffaldano et al. (2006); Iaffaldano and Bunge(2009) proposed that the gravitational collapse associated with the de-veloping topographic volume of the central Andesmay locally offset thehorizontal deviatoric stress by ~50 MPa compared to the northern andsouthern margin. Such collapse is indeed capable of deflecting the sub-ducting plate downwards along the trench (Iaffaldano and Bunge,2008), as evident from sound and gravity surveys.

In this study we take advantage of laboratory models of subduc-tion (e.g. Funiciello et al., 2003) to test how strong lateral gradientsof plate coupling need to be in order to generate trench curvature,upper-plate shortening and possibly uplift in amounts comparableto estimates available for the Andean system. We present a selectionof end-member cases where pre-imposed plate coupling is systemat-ically varied by means of different materials placed along the inter-face of the model plates. Results are compared to previouslypublished field data. It is admittedly difficult to control a priori the de-gree of plate coupling in analog models, and typically only a prelimi-nary qualitative ranking of coupling is possible. We propose a simplemethod that takes advantage of kinematic measurements in analogmodels of subduction to estimate a posteriori plate coupling, relativeto the driving force.

2. Laboratory models

Our laboratory models reproduce oceanic/continental subductionas a viscous, two-layered system (Fig. 2). The overriding and subduct-ing plates are simulated by means of two types of silicon putty, fea-turing different values of density (i.e. ρs, ρop) and viscosity (i.e. ηs,ηop) (see Table 1 for details). Plates lay initially flat on a layer oflow-viscosity glucose syrup simulating the upper mantle (Fig. 2).Models are carried out at room temperature and we have verified thatthe regime of plates and mantle are purely Newtonian (see Funicielloet al., 2003 for details on the rheology). The model parameters havebeen properly scaled to the reality (e.g. Funiciello et al., 2003;Weijermars and Schmeling, 1986) as follows: 1 cm in the laboratorycorresponds to 60 km in nature (length-scale factor Hl=1.7·10−7).Similarly, 60 s in the laboratory correspond to 1 Myr (time-scale fac-tor Ht=1.9·10−12). Plates are 1 cm thick and 30 cm wide, whereasthemodel mantle is 11 cm deep (Fig. 2). These lengths are equivalentto a plate thickness of 60 km, a plate width of 1800 km and a mantleas deep as the 660-km transition zone. It is worth noting that themodel mantle is some 10 cm wider than the plates, therefore anytoroidal flow that will be excited at the plate edges during the exper-iment should not affect significantly the dynamics (Funiciello et al.,2004).

In our models we let two pistons drive the subducting and over-riding plates. In each model, the subducting plate lays on one sideof the tank, attached to piston A. The overriding unit lies on the op-posite side attached to piston B, overlapping by ~2 cm on top of thesubducting plate (Fig. 2). In order for subduction to operate sponta-neously, we initially drive the oceanic plate towards the overridingplate through piston A at a velocity as low as va=1.6×10−3 cm/s –equivalent to va=0.6 cm/yr – and stop piston A only when the slabstarts sinking into themodel mantle under its ownweight. Once sub-duction proceeds naturally under the effect of negative buoyancy, welet piston B drive continuously the overriding plate at a velocity vb in

Fig. 2. Schematics of the 3D model set-up used in this study. In order to test the effect of lateral variations of plate coupling on the curvature of the trench, we perform a first modelwhere we cover left and right portions of the subducting plate with lubricating paste, leaving its central portion clean (see white labels on the subducting plate. White dashed seg-ments indicated transition between areas with/without lubricant). As subduction goes on in our models, plates experience persistent lateral variations in coupling due to the pres-ence of lubricant along the lateral edges of their interface, and the absence of the same in the central interface. Results from this set-up are compared to a second model, where nopaste is used. Rather we lubricate the entire interface uniformly with a layer of glucose syrup, to obtain low coupling everywhere between plates.

18 G. Iaffaldano et al. / Tectonophysics 526–529 (2012) 16–23

range (8.3–27.5)×10−3 cm/s – equivalent to (3–10) cm/yr. This ac-counts for the effect of ocean basin opening on the overriding plate.Models have been documented by taking pictures from the topside.At the same moments, we have also employed a laser-scanning de-vice to digitally acquire the image and monitor the evolution ofplate relief during the process. Furthermore, we detected and mea-sured shortening of plates by means of 2×2 cm2 black squarespainted on top of both plates, as well as a lateral ruler with the pre-cision of 1 mm. All model parameters are listed in Table 1.

We run two subduction experiments where conditions of me-chanical coupling between plates significantly vary from one another.In one model the central portion of the margin is more stronglycoupled compared to the rest (we refer to this model as mod. 1). Spe-cifically, we implement strong lateral variations of mechanicalcoupling by distributing lubricant paste (petroleum jelly) along the

Table 1Values of parameters from laboratory models and from nature.

Parameter Notation Laboratory Units Nature Units

Bodyforce

g, gravitational acceleration 9.81 m/s2 9.81 m/s2

Thickness hs, hop, subducting andoverriding plate

0.01 m 60×103 m

H, upper mantle 0.11 m 66×104 mWidth ws, wop, subducting and

overriding plate0.30 m 18×105 m

Density ρs, subducting plate 1510 kg/m3 3300 kg/m3

ρop, overriding plate 1380 kg/m3 kg/m3

ρM, upper mantle 1430 kg/m3 3220 kg/m3

Viscosity ηs, subducting plate 3.7×105 Pa⋅s 1022–1024

Pa⋅s

ηop, overriding plate 3.0×105 Pa⋅s 1022–1024

Pa⋅s

ηM, upper mantle 82 Pa⋅s 1019–1021

Pa⋅s

Velocity va, piston A 1.6×10−3 cm/s 0.6 cm/yrvB, piston B (8.3–

27.5)×10−3cm/s 3–10 cm/yr

Length-scale factor, Hl 1.7×10−7

Length-scale factor, Ht 1.9×10−12

lateral edges of the subducting plate. Each lubricated segment isabout 1/4 of the total plate width (Fig. 2) and equivalent to~500 km in nature, while the central portion of the plate interface isleft without any lubricant. In the second model we instead maintainplate coupling uniformly low along the entire interface by leaving achannel of glucose syrup between the overriding and the subductingplates (we refer to this model as mod. 2).

Previous studies tested the rheological properties of petroleumjelly (e.g. Chang et al., 2003) and found its behaviour to be quite com-plex, because different factors (e.g. temperature, surface roughness,etc.) have the potential to influence the effective viscosity. Withinthe context of analog subduction models, petroleum jelly is oftenemployed as lubricant at the interface between model plates (e.g.Heuret et al., 2007). However, quantifying its contribution to platecoupling in a systematic way remains elusive because it requiresknowledge of the stresses inside the model plates, which are arguablyunfeasible to measure. For these reasons, we can only rely on previ-ous studies (e.g. Funiciello et al., 2003, Heuret et al., 2007) and pre-liminary rank the degree of coupling along the central margin inmod. 1 as high, while coupling along the lateral edges is ranked asmoderate. By comparison, the uniform coupling in mod. 2 is rankedas low. A more formal analysis of our results made a posteriori revealsquantitatively the relative importance of mechanical coupling withrespect to the driving force in each model (see next section).

3. Experimental results and estimates a posteriori of plate coupling

Results from our laboratory models are reported in Figs. 3 and 4.Panels A–D show the subducting system from a topside view at fourdifferent moments, from subduction initiation to the end of themodel. Figs. 3E and 4E summarize the temporal evolution of thelower half-trench shape in each model, imaged through the laser-scanning device. A comparison between Figs. 3E and 4E shows thatlateral variations of plate coupling are indeed capable of inducing sig-nificant curvature of the trench, which evolves into a pronounced arcduring the final 20–30 min of mod. 1. Based on the time-scale factorof our models, this is equivalent to 20–30 Myr and is thus compatiblewith estimates from paleomagnetic rotations along the Andean belt

19G. Iaffaldano et al. / Tectonophysics 526–529 (2012) 16–23

(Allmendinger et al., 2005 and references therein). Furthermore, notethe development of topography on the overriding plate correspond-ing to the strongly coupled central margin (Fig. 3B–D). We arguethat the high degree of coupling efficiently works against the overrid-ing plate motion so that deformation and local bulging occur. At theend of mod. 1 we observe a relief as high as 1.5–2 mm (Fig. 3C-D),equivalent in nature to about 8–12 km. Such relief will also enforce,although minimally, the degree of coupling between convergingplates by providing an additional offset to the horizontal deviatoricstress. Considering that erosive processes are not implemented inthis type of laboratory models and that no internal faults are availableto distribute the topography laterally rather than vertically, we arguethat the topographic volume obtained falls within an acceptablerange compared to the high Andean plateau. On the contrary, mod.2 (Fig. 4) shows that the trench maintains the original straight profileduring the entire duration of the process, and no topography de-velops on the overriding plate when the margin features low, uniformmechanical coupling (Fig. 4A–D).

The qualitative ranking of the coupling degree in our models maybe replaced by a quantitative estimate, which would be desirable togain novel insights into the relative importance of trench resistancewith respect to the driving force in the real case. We show in the fol-lowing that such estimate in our models may be obtained a posteriorifrom kinematic measurements. Fig. 5 shows a sketch of the sole over-riding plate. We initially assume an ideal, perfectly rigid plate movingon top of a Newtonian fluid. The plate has total length L, while thick-ness is assumed to be negligible with respect to L. We will also as-sume the plate infinitely long in the third dimension, so that we canapproach the problem in two dimensions. For convenience we willassume at all times the mid-point along the plate length as origin ofthe reference frame, x=0. −L

2;þL2= ���represents the domain of var-

iability for x.Let

→D be the total force applied at x=-L/2, driving the plate on the

right-hand side. This force accounts for the effect of opening of oceanbasins on the side opposite of subduction in the reality. Let also

→R be

the resistive force on the left-hand side at x=L/2, oriented as→D but

acting in the opposite direction. This force accounts for the resistancein place within the brittle interface between converging plates, butneglects the contribution to momentum from bending of the subduct-ing plate.

→VR is the total viscous resistance from the fluid underneath.

This force will be distributed along the plate base and will act as soonas the plate begins to move. It is therefore also oriented as the otherforces. It is reasonable to assume R≤D, where capital letters identifythe magnitude of the corresponding vector. By comparing the orien-tation of forces with our laboratory models and in reality, it is clearthat the model trench is located on the left-hand side of the plate (tin Fig. 5). As the plate is sufficiently thin, it is reasonable to assumethat all forces lie on the same imaginary plane, and that spinningabout any axes is prevented from occurring. This eliminates theneed to solve the equation of moment, or torque; therefore the dy-namics of the rigid plate is fully described by the sole momentumequation for the centre of mass. When the plate achieves a steady mo-tion, the momentum balance is

→Dþ→

VR þ→R ¼ 0 ð1Þ

Fig. 3. Trench evolution of laboratory model 1: (A–D) snapshots of the process. Elapsedtime from model start is in the upper-right corner. The subducting plate moves towardthe overriding one from left to right. The upper half of each panel is a picture of theplates, where 2×2 cm2 squares are outlined to detect deformation. The lower half isa laser-scanned image of plate relief (offset from the beginning of the model) acquiredat the same moment: red represents bulging upwards, blue is bulging downwards.Note that the model plates are manually attached to the pistons, therefore the periph-eral regions naturally bulge upwards or downwards, and are thus detected as anoma-lous. (E) Evolution of half-trench through time, as detected through the laser-scannedimages. Red on white is the portion of trench with no lubricant paste, hence featuringhigh coupling. Blue on gray is one of the lateral edges with lubricant paste, thus featur-ing average coupling (see text for details).

20 G. Iaffaldano et al. / Tectonophysics 526–529 (2012) 16–23

Eq. (1) corresponds in our case to one scalar equation along the di-rection of all forces

D ¼ Rþ VR ð2Þ

If the motion of the rigid plate is the only process exciting flowwithin the Newtonian fluid beneath, the strain rate s will be propor-tional to the velocity of the plate vp. Therefore VR becomes

VR ¼ μ·s·Σ ¼ μ·vpH

·Σ ¼ μ·ΣH

� �·vp ¼ α·vp ð3Þ

Where μ is the viscosity of the Newtonian fluid beneath the plate,H is its height, and Σ is the surface of the plate base. The coefficient αcontains the aspect ratio of the problem and has dimension of a vis-cosity times length. Eq. (2) therefore becomes

D ¼ Rþ α·vp ð4Þ

Because the plate is assumed perfectly rigid, vp in Eq. (4) describesthe motion of any portion of the plate. In the more realistic case of adeformable plate the velocity can no longer be described by one sin-gle scalar value, but will vary along the plate length due to its defor-mation and compression. In other words a field v(x) is required.Consequently, the strain rate will also vary along the plate base andthe viscous resistance VR will be proportional, through the viscosity,to the surface integral of the strain rate. The momentum equation inthis case may be solved numerically, particularly because of the com-pressibility of the plate. We would like, however, to retain the abilityto relate driving and resisting forces through the kinematics in a sim-ple fashion, as in the rigid case. We therefore propose to take into ac-count deformation in our models by perturbing the velocity solutionof the perfectly rigid case, rather than by solving numerically the mo-mentum equation for the compressible case. In other words, we at-tempt including the complexity arising from deformability directlyinto the kinematics rather than into the dynamics. Of course this isno exact solution to the problem, but it provides a first-order estimateof the resistance relative to the driving force, which would otherwiseremain elusive.

If RbD, the plate will experience non-uniform compression alongthe x axis and the trench velocity vt will be smaller than the velocityelsewhere within the plate. It is straightforward to imagine that forsmall values of R relative to D, the plate portion at the driving endwill still keep behaving as if rigid and therefore move at velocityequal to vp. As R increases toward values comparable to D, compres-sion and thickening of the plate will occur. Eventually, when R=D,the plate will shrink about its centre, with trench and driving endsconverging toward the centre at equal maximum velocity. The fol-lowing equation will be then valid

v x¼ þL2;R ¼ D

�¼ vt¼ �vp¼ �v x¼ �L

2;R ¼ D�.�.�

ð5Þ

It is convenient at this point to switch to a new reference framewhere y ¼ 2x

L= varies within the range [−1;1]. We can reasonablyapproximate the velocity at any position along the plate, for anyvalue of resistance R∈ [0;D], with the general formula

v y;Rð Þ ¼ vp·f y;Rð Þ ð6Þ

Fig. 4. Trench evolution of laboratory model 2: (A–D) analog subduction featuring uni-formly low mechanical coupling along the plate interface, obtained with lubricatingsyrup. (E) Evolution of half-trench through time in green. Images are equivalent tothe ones in Fig. 3.

0 0.1 0.2 0.3 0.40.5

0.6

0.7

0.8

0.9

1

Rt + Rd = 1

0

0

10

10

20

20

30

30

Elapsed time (Minutes)

Equivalent time (Myr)

0 0

1 60

2 120

3 180

4 240

5 300

Mo

del

sh

ort

enin

g (

cm)

Eq

uiv

alen

t sh

ort

enin

g (

km)

Low coupling (Mod. 2)Moderate coupling (Mod. 1)High coupling (Mod. 1)

A

B

Fig. 6. (A) Shortening of the overriding plate since subduction initiation in each of ourmodels. Shortening is measured from the progressive deformation of 2×2 cm2 squaresoutlined on the overriding plates, error-bars are also shown. Measures in model 1 wereconducted distinctively across portions of the margin with (blue dots) and without(red dots) lubricant paste. Green dots are from model 2. Shortening increases withthe increasing degree of mechanical coupling between converging plates. Equivalentvalues of elapsed time and shortening are reported on the left- and top- side of thepanel; for model 1 they compare well with available observations along the Andeanbelt. (B) Rate of trench-advancement (Rt) versus rate of horizontal deformation inthe overriding-plate (Rd) from our models, reported as fraction of the piston velocitydriving the overriding plate. Error-bars are also shown.

V R

Fig. 5. Sketch of the experimental overriding plate on top of a Newtonian upper mantle.The reference frame used is also shown.

21G. Iaffaldano et al. / Tectonophysics 526–529 (2012) 16–23

Where f(y,R) is a bilinear function that satisfies the followingthree conditions

f y;R ¼ 0ð Þ ¼ 1 for all values of y∈ −1; 1½ � ð7Þ

f y ¼ 1;R ¼ Dð Þ¼ �1 ð8Þ

f y ¼ � 1;Rð Þ ¼ 1 for all values of R∈ 0;D½ � ð9Þ

Eq. (7) indicates that the plate behaves as if rigid when no resis-tance is applied. It undergoes no compression and therefore the ve-locity is constant throughout the plate, as found from Eq. (4).Eq. (8) follows from Eq. (5). Eq. (9) indicates that the driving endmay be assumed to have velocity always equal to the case of perfectrigidity. Note that f(y,R) is required to be bilinear in accord with ourlaboratory conditions, where the Newtonian upper plate deforms lin-early with the applied force (linearity with respect to R), and defor-mation is isotropic within the plate (linearity with respect to y).Note furthermore that f(y,R) is unique, given the constraints fromEqs. (7)–(9). In fact there is only one linear function passing by twogiven points. The uniqueness of f(y,R) is easily demonstrable byextending this notion into two dimensions.

In order to find the explicit expression of f(y,R) we first write a lin-ear function of the sole variable R satisfying Eq. (7) for y=1 andEq. (8). We then use the result in conjunction with Eq. (9) to findthe linear dependence from y. The result is

f y;Rð Þ ¼ 1− RD−y⋅ R

Dð10Þ

Substituting Eq. (10) and Eq. (6) into Eq. (5) it follows that

vtvp

¼ v y ¼ 1;Rð Þv y¼ �1;Rð Þ ¼

f y ¼ 1;Rð Þf y¼ �1;Rð Þ ¼ 1−2·

RD

for R∈ 0;D½ � ð11Þ

Eq. (11) shows that the ratio between trench-velocity and over-riding-plate velocity is directly related to the ratio between drivingand resisting forces, R and D. Therefore the latter ratio may be esti-mated a posteriori from kinematic measurements in analog modelsof subduction.

4. Discussion

In the ideal case of perfectly rigid plates, the shape of the trenchwould be prevented from undergoing any temporal variations, as me-chanical coupling would only affect the rate of convergence betweensubducting and overriding units. In the more realistic case of deform-able plates it is therefore natural to relate trench curvature to defor-mation, occurring particularly in the overriding plate. The horizontaldeformation measured in our models allows us to compute theamount of shortening from subduction initiation. It is worth remind-ing at this point that deformation in our models is purely viscous, be-cause the silicon putty employed is Newtonian at room temperature.Previous studies featuring a brittle layer on top of viscous model

plates recognized the latter with the ability to affect the resultingmorphology (e.g. Davy and Cobbold, 1991). Our setup may thereforeappear as a simplification, however we point out that the inclusion ofa brittle layer in our models would have at the same time made the aposteriori estimate of plate coupling significantly more complex. Weregard this to be an acceptable compromise in favour of gaining theability to estimate coupling in a simple fashion from kinematicmeasurements.

We collectively report estimates of shortening from both modelsin Fig. 6A. We find that the high degree of mechanical coupling inthe central margin of mod. 1 causes the upper plate to shorten~4 cm by the time significant curvature and topography have devel-oped (Fig. 6A – red dots). According to the characteristic length-scale factor of our models, this is equivalent to more than 240 km inreality. On the other hand, since the lateral edges of the upper platefeature a moderate degree of coupling, they only experience~2.5 cm of shortening, equivalent to less than 180 km (Fig. 6A –

blue dots). We note that the equivalent shortening values comparewell to field estimates along the Andean belt. In fact, it has been esti-mated that ~300 km of shortening are required to account for the to-pographic volume of the central Andes, but only ~150 km are neededin the northern and southern limbs (Hindle et al., 2005; Kley andMonaldi, 1998). In comparison, very little shortening is detected in

22 G. Iaffaldano et al. / Tectonophysics 526–529 (2012) 16–23

model 2, where the margin features uniform low coupling (Fig. 6A –

green dots).This may be conveniently put in the framework of rates of hori-

zontal deformation (Rd) and trench-advancement (Rt) (Fig. 6B). Inthe presence of low mechanical coupling the upper plate deformsand shortens very slowly, because most of the driving velocity is trans-ferred into advancement of the trench (Fig. 6B– greendot). As the degreeof coupling along the plate-interface increases, trench-advancement isprogressively compromised in favour of upper-plate shortening undercompressive deformation (Fig. 6B – red and blue dots). After a finitetime interval, different amounts of trench-advancement along differentlycoupled portions of the trench will determine the latter to assume itspronounced curvature. Generally, for small amounts of deformationthat the upper plate undergoes, the corresponding volume change willbe small and virtually undetectable, implying Rd+Rt=1 at all times.Within the accuracy of our estimates, this applies to all cases but one,where mechanical coupling is the highest (red dot in Fig. 6B). In thiscase the trench advances even less than what would be predictedbased on the measured rate of horizontal deformation, implying thepresence of additional deformation undetected along the horizontal,that instead concentrates along vertical planes and gives rise to topogra-phy of the upper plate (central margin in Fig. 3B–D).

Note that Rt is nothing but the ratio of trench-velocity and platevelocity. We therefore use kinematic measurements in conjunctionwith in Eq. (11) to estimate the importance of the resisting couplingrelative to the driving force (R/D) in our models (Fig. 7). The centralmargin of mod. 1, which we had initially ranked with high coupling,in fact experiences a resisting force of ~21% of the driving force. In-stead, resistance along the lateral edges in the same model is ~11%of the driving force. The convergent margin in mod. 2 experiences aresisting force as low as ~2% of the driving one. From this, and onthe base of the agreement between equivalent and observed shorten-ings, we conclude that plate coupling along the central Andean mar-gin needs to be as large as 20% of the driving force to result in thecurvature and deformation of the trench that are observed.

5. Conclusions

To summarize, we performed laboratory models of subductionaimed at gaining quantitative insight into the role of lateral variationsof mechanical coupling emplaced along the Andean margin. In ourmodels we have systematically varied the mechanical coupling be-tween converging plates from low to high based on a preliminary

Fig. 7. Trench-velocity (in bold black line, units relative to plate velocity) as a function ofthe magnitude of the resisting force (units relative to the driving force). Bold colorsegments dots on the vertical axis represent the ratios between trench- and plate-velocitymeasured in the laboratory. Bold color segments on the horizontal axis are thecorresponding ranges of resistance (units relative to the driving force) in place along thetrench of our analog models.

ranking. We tested the impact of coupling gradients on trench curva-ture, shortening and overriding-plate topography. Two end-memberscenarios, where (i) low mechanical coupling implies little deforma-tion and shortening of the overriding unit while (ii) high couplingwill force the latter to shorten and eventually bulge upwards morethan elsewhere, may be conveniently described in terms of trench-advancement and horizontal-deformation rates. A comparison of ex-perimental results with the reality may not be straightforward,because we lack a proper scaling rule for temperature-dependentproperties of the subduction system. Despite this major oversimplifi-cation, we attempt to compare experimental results with previouslypublished field observations from the Andean system and find signif-icant similarities in shortening rates, temporal evolution of the curva-ture and the development of topography.

Furthermore, we proposed a method to estimate a posteriori theamount of plate coupling – relative to the driving force – emplacedalong the plate interface in our models. From these estimates we con-clude that resistive coupling along the central Andean margin needsto be as high as 20% to simultaneously result in the peculiar curvatureof the trench, shortening and topography of the upper plate. Whileseveral studies have previously showed that shortening, curvatureand topography of the upper plate are indeed related to lateral varia-tions ofmechanical coupling (e.g. Boutelier andOncken, 2010;Marquesand Cobbold, 2002), our results take a step further in providing novelquantitative information on the relative importance of driving andresisting forces emplaced along the Andean system. The presence ofthe overriding plate and its degree of coupling with the undergoingslab determine the evolution of convergent systems perhaps morethan previously thought.

To our best knowledge, it remains debated why shortening andorogeny in the Andes occurred mostly during the Cenozoic (Lamband Davies, 2003; Montgomery et al., 2001), when subduction hasbeen active since the late Jurassic (Mueller et al., 2008). Similarly, itis not straightforward to assess what curvature the margin featuredat the time when significant shortening began. Lateral and temporalvariations of inter-plate friction and local deviatoric stress may im-pact the total inter-plate strength and mechanical coupling possiblyto the same order of magnitude. However, it remains admittedly dif-ficult to distinguish whether and when these mechanisms have beenindependently active, because potential feedbacks between themmake the interpretation of the geologic record more challenging.

Acknowledgments

This studywas funded by theVigoni Project. G.I. thanks Brian Kennettfor providing useful comments to the manuscript. E.D.G., F.C., and F.F.have been supported by the EURYI (European Young Investigators)Awards Scheme (Eurohorcs/ESF including funds the National ResearchCouncil of Italy; resp. F.F.). We thank Peter Cobbold, Laurent Hussonand two anonymous reviewers for their comments.

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