Basin Research (2008) doi: 10.1111/j.1365-2117.2008.00366.x Pro- vs. retro-foreland basins M. Naylor and H. D. Sinclair School of GeoSciences, Grant Institute, University of Edinburgh, Edinburgh,UK

ABSTRACT Alpine-type mountain belts formed by continental collision are characterised by a strong cross- sectional asymmetry driven by the dominant underthrusting of one plate beneath the other. Such mountain belts are £anked on either side by two peripheral foreland basins, one over the underthrust plate and one over the over-riding plate;these have been termed pro- and retro-foreland basins, respectively.Numerical modelling that incorporates suitable tectonic boundary conditions, and models orogenesis from growth to a steady-state form (i.e. where accretionary in£ux equals erosional out£ux),predicts contrasting basin development to these two end-member basin types.Pro-foreland basins are characterised by: (1) Accelerating tectonic subsidence driven primarily by the translation of the basin ¢ll towards the mountain belt at the convergence rate.(2) Stratigraphic onlap onto the cratonic margin at a rate at least equal to the plate convergence rate. (3) A basin in¢ll that records the most recent development of the mountain belt with a preserved interval determined by the width of the basin divided by the convergence rate. In contrast, retro-foreland basins are relatively stable, are not translated into the mountain belt once steady-state is achieved, and are consequently characterised by: (1) A constant tectonic subsidence rate during growth of the thrust wedge, with zero tectonic subsidence during the steady-state phase (i.e. ongoing accretion-erosion, but constant load). (2) Relativelylittle stratigraphic onlap driven only by the growth of the retro-wedge. (3) Abasin ¢ll that records the entire growth phase of the mountain belt, but only a condensed representation of steady- state conditions. Examples of pro-foreland basins include the Appalachian foredeep, the west Taiwan foreland basin,theNorthAlpineForelandBasin andtheEbroBasin(southernPyrenees).Examples of retro-foreland basins include the SouthWestland Basin (Southern Alps, New Zealand), the Aquitaine Basin (northern Pyrenees), and the Po Basin (southern European Alps).We discuss how this new insight into the variability of collisional foreland basins can be used to better interpret mountain belt evolution and the hydrocarbon potential of these basins types.

INTRODUCTION 100oLbasino300 km depending on the wavelength of iso- static compensation which is a function of the £exural Foreland basins are the sedimentary basins located on rigidity of the lithosphere.The cratonic margin of foreland continental lithosphere at the outer edge of mountain basins may be de¢ned by the point of zero de£ection that belts (cf. Dickinson,1974).They are formed by the regional separates the down£exed basin from the region of fore- isostatic compensation by lithospheric £exure driven by bulge uplift. This is best recorded by marine settings, both the topography and internal density variations of where the palaeocoastline is used as a proxy for this point mountain ranges; additional bending forces on the down- (Crampton & Allen, 1995). In continental basin ¢lls, it is £exed lithosphere may also drive further subsidence (for common for sediment to drape well beyond the point of review see Beaumont, 1981; Jordan, 1981). Foreland basins zero de£ection, and hence DeCelles & Giles (1996) advo- are characterised by a regionally low gravity anomaly that cated the use of ‘forebulge’and ‘backbulge depocenters’. broadly mimics the geometry of the £exural pro¢le of the The ¢rst recognition of the variety of foreland basin underlying lithosphere (Karner & Watts, 1983). This geo- types was by Dickinson (1974) who distinguished retro- metry also results in a marked asymmetry in cross-section arc from peripheral foreland basins. The former develops of foreland basins, with a much deeper orogenic margin during ocean-continent collision associated with the beneath the deformation front of the mountain belt, and growth of a magmatic arc. In this case, the foreland basin a wedge-shaped form that tapers out over the stable cra- evolves on the continental side of the mountain belt as tonic margin of the basin (Allen et al., 1986).Their dimen- seen to the east of the Andes and the Rockies (Jordan, sion perpendicular to the mountain front ranges from 1995). In contrast, peripheral foreland basins develop on both sides of a mountain belt resulting from continent^ Correspondence: M. Naylor, School of GeoSciences, Grant Institute, University of Edinburgh, West Mains Rd, Edinburgh continent collision (for review see Miall,1995); well-docu- EH93JW,UK.E-mail:[email protected] mented examples of peripheral foreland basins include the r 2008 The Authors. Journal compilation r 2008 The Authors 1 M.NaylorandH.D.Sinclair

North Alpine Foreland Basin of western Europe and the evolution of these basins is divided into a growth phase Ganges Basin of northern India. where the topographic mass of the mountain belt Understanding di¡erences in tectonic boundary condi- increases and a steady state phase where the topographic tions for peripheral foreland basin types came from the mass remains constant (Willett & Brandon, 2002). The analysis of doubly vergent thrust wedges where one thrust contrasting tectonic boundary conditions are explored for wedge evolves over the underthrust lithosphere, and the the side of a mountain belt experiencing active under- opposing wedge develops over the overriding plate (Fig.1) thrusting and accretion (pro-side sensu Willett et al., (Willett et al., 1993). Johnson & Beaumont (1995) used a 1993) vs. the side that is being overthrust, and which numerical model to simulate the evolution of peripheral experiences relatively little accretion (retro-side sensu foreland basins on either side of a doubly vergent moun- Willett et al., 1993, Fig.1). By comparing results from these tain belt. In so doing, they introduced the terms pro- and experiments with natural examples, we demonstrate the retro-foreland basins in order to distinguish the basin marked contrast between these basin types, and go on to overlying the underthrust plate from that overlying the provide new predictions for stratal architecture, chronos- overriding plate, respectively (Fig.1); we adopt this termi- tratigraphy and subsidence that discriminate between nology for distinguishing between these peripheral fore- them.We conclude by exploring the implications for inter- land basin types. While the nominal distinction between pretations of tectonics from stratal records, and for hydro- pro- and retro-foreland basins on either side of a moun- carbon prospectivity. tain belt has been recognised in terms of basin setting (e.g. Allen & Allen, 2005), no criteria in terms of basin evo- Background on foreland basins lution, subsidence histories or stratigraphic architecture have yet been provided to distinguish between them.This The primary criteria used to characterise the stratigraphic study focuses on distinguishing peripheral foreland basins in¢ll of foreland basins are thickness, lateral extent, rates using these criteria, but also highlights the potential sig- of subsidence, rates of onlap and broad depositional envir- ni¢cance for retro-arc basin types. onments. Numerical models that combine the tectonics of We use numerical modelling to investigate the strati- the system with algorithms to simulate surface processes graphic record of peripheral foreland basins.The temporal have been used to analyse basin development and predict

(a) Pro-foreland Retro-foreland basin Pro-wedge Retro-wedge basin

Cratonic basin Deformation Deformation Cratonic basin margin front front margin

osphere ing lith Underth errid rust Ov litho sp he re

(b) Load divider H F F E α E h α retro 0 o pro W FA

V

Fig. 1. Cartoon of a steady-state doubly vergent orogen. (a) The pro-foreland basin lies in the £exural depression over the subducting slab which advances towards the orogen at the regional convergence rate, v.The retro-foreland basin lies in the £exural depression above the over-riding slab which is predominantly stationary with respect to the orogen. (b) The mass budget of the wedge system is controlled by the relative rate of the accretionary and erosive £uxes (FA and FE, respectively).The rate of accretion of new material from the downgoing plate is a function of the convergence rate and the thickness of material that is accreted from that plate, h0.The cross- sectional area of the mountain’s topography is described by two triangles of height H and surface taper angles apro and aretro that abut at the load divider.

2 r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x Pro- vs. retro-foreland basins these characteristics for di¡erent boundary conditions and this represents only half the story, lacking a comparative parameter sets. Initially, these models used blocks pro- model for retro-foreland basins. gressively added onto an elastic plate to simulate the pro- Here, we use a numerical model of a mountain belt gressive addition of thrust sheets into a wedge and their whose asymmetry into pro- and retro-sides is de¢ned by £exural response (Beaumont, 1981; Jordan, 1981; Quinlan the asymmetry of underthrusting.We consider the impact & Beaumont, 1984). A signi¢cant advance was provided by of this asymmetry on the stratigraphic development of the a model that coupled the growth of a single, critically ta- opposing peripheral foreland basins, and so provide a new pered thrust wedge to the in¢ll of a foreland basin through model aimed at distinguishing the subsidence and strati- the simulation of erosion and sedimentation by a di¡usion graphic development of pro- vs. retro-foreland basins. algorithm (Flemings & Jordan, 1989; Sinclair et al., 1991). A The model only analyses the main foredeep of foreland more sophisticated surface process model coupled to a basin systems (sensu DeCelles & Giles, 1996), we do not doubly vergent thrust wedge model was used to explore consider the impact upon wedge-top or forebulge sedi- the impact of the asymmetry of orographically enhanced mentation. precipitation over mountain ranges (Johnson & Beau- mont,1995).This important insight into the potential im- pact of orogenic asymmetry on the two neighbouring THE MODEL foreland basins hinted at the prospect of fundamental dif- ferences in basin types. Recent models of thrust wedge We investigate the coupled evolution of the pro- and ret- development have evolved to demonstrate the intimate ro-foreland foreland basins (Fig.1) that bound a collisional coupling between the timescale of deformation on loca- mountain belt. Because there are many regional special lised structures to the surface processes response time cases that can be considered, we choose a parameterisation (Simpson, 2006); this has implications for the link that produces a singular solution which we believe re£ects between propagation of the deformation front, ¢lling of the most general case from which more complicated sys- the basin, and source areas for sediment. tem-speci¢c cases can be considered. The sensitivity of Numerical model developments have evolved in parallel the modeltovaryingthe parameterisationis reserveduntil with improved documentation of a range of basins from the ‘Summary and Discussion’section. around the world. Studies of peripheral foreland basins have The total system area, Asystem above the £exed slabs is been dominated by those developed on the pro-side of a broken down into a topographic component Atopo,and mountain belt due to the improved access to surface expo- the region bounded below the zero de£ection datum and sures of foreland basin sediments that have been accreted above the £exed slabs, A¢ll which comprises the basin in¢ll and deformedwithin the thrustwedge. For example, the no- and the root of the mountain belt.We consider two phases tion that subsidence in foreland basins should accelerate of evolution of the system; (a) its growth phase, where the dAsystem through time was initially tested in the North Alpine Fore- area of the topographic wedge is increasing dt > 0and land Basin (Allen et al., 1986), and by subsequent analyses in (b) its subsequent steady-state phase, where the in£ux of the Ebro Basin of the Pyrenees (Verge¤ s et al., 1998) and in material FA into the topographic wedge is balanced by the dAsystem southeastern Papua New Guinea (Haddad & Watts, 1999). erosional e¥ux FE out of the wedge and dt ¼ 0. This The erosion of a region of forebulge uplift was ¢rst docu- transition occurs as the volume of a mountain belt mented and modelled from the Appalachian and North increases, assuming a constant rate of accretion, because Alpine systems (Quinlan & Beaumont, 1984; Crampton & surface uplift rates progressively decrease, allowing uplift Allen,1995).Comparisons have been made between the pro- and erosion rates to converge (Dahlen & Suppe, 1988). gressive stratigraphic onlap of the outer craton of foreland The model requires the integration of three compo- basins with the time-equivalent activity of the deformation nents: front in the North Alpine and Himalayan systems (Home- (1) A topographic model that describes the cross-sec- wood et al., 1986; Burbank et al., 1996; Sinclair,1997). Finally, tional pro¢le of the mountain belt from which the tectonostratigraphic models for the progressive evolution of topographic load is derived. ‘peripheral’ foreland basins from a deep-water ‘under¢lled’ (2) Tectonic boundary conditions that describe both the stage to a shallow marine to continental ‘¢lled’or ‘over¢lled’ rate of accretion of new material into the system and stage have been provided by the Appalachian, Himalayan the advection of the basins due to the motion of the and North Alpine Foreland Basins (Stockmal et al., 1986; underlying slabs. Sinclair & Allen,1992; Sinclair,1997). (3) A £exural model for the semi-in¢nite slabs that In contrast, retro-foreland basins have been relatively respond to the topographic load. understudied, except where extensive subsurface data exists. Hence, basins like the Aquitaine Basin to the north of the Pyrenees, or the South Alpine foreland basin have had little impact on the development of stratigraphic Topographic model models for peripheral foreland basins. We argue that our mechanical understanding of foreland basins is currently The form of the mean topographic elevation of the doubly based on the model for pro-foreland basin types, but that vergent mountain belt is approximated by two triangles of r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x 3 M.NaylorandH.D.Sinclair

2 the same height, H, abutting back to back (Fig. 2).Thus the Atopo 5 275 km , generating a pro-wedge115km wide and total cross-sectional area of the topographic load is given a retro-wedge 69 km wide. This represents the maximum by: topographic load applied in this study.

Tectonic boundary conditions H2 H2 Atopo ¼ þ ð1Þ 2tanapro 2tanaretro The tectonic boundary conditions are the underlying source of asymmetry (Fig. 1b). The simulated mountain Pro- and retro-wedges accrete material in kinematically belt evolves above the subduction zone as a consequence di¡erent ways (Willett, 1992), which leads to a characteris- of new material being accreted into the system from the tically di¡erent topographic form. The pro-wedge grows down going plate. The slab underlying the pro-foreland by the accretion of material at the toe, which leads to the basin is continually translated towards and down the stress solution corresponding to the minimum taper subduction zone at the regional convergence rate. The angle predicted by critical wedge theory (Davis et al., 1983; pro-foreland stratigraphic model incorporates this by Dahlen et al., 1984). However, the retro-wedge predomi- translating the basin ¢ll along and down the subducting nantly grows by material added at the back of the wedge slab, creating new accommodation space. In contrast, the and has the maximum taper angle predicted by critical retro-foreland basin ¢ll, on the overlying slab, is not trans- wedge theory (Willett, 1992).We apply typical surface an- lated toward the subduction zone. This study uses a con- 1 gles of apro 51.51, aretro 5 2.51 which are at the lower end vergence rate of v 5 5kmMyr typical to a number of of typical wedge angles (e.g. Davis et al., 1983; Ford, 2004) settings (e.g. Beaumont et al., 2000). This velocity repre- to highlight the impact of load distribution. Thus, the sents the rate at which material is translated towards the cross-sectional area of our modelled topography with mountain belt from the far ¢eld. Further, we simulate the the mean elevation at the highest point Hmax 5 3km is case where the basins are instantaneously ¢lled to the level

(a)

δx=0 Pro-side Retro-side H(t) α α pro retro 0 x

w(xpro,t) w(xretro,t)

v Gap between slabs

Load divider

Retroward shift in topography (b) δx to minimise the gap between slabs H(t) α α pro retro 0

v

Load divider

(c) Atopo=Ap+Ar α Ap Ar α H(t) pro retro

A =A /2 half topo Ahalf

l δx Fig. 2. End-member scenarios to balance the topographic load across the slabs. (a) The subducting slab supports the pro-wedge and the over-riding slab supports the retro-wedge.This leads to a discontinuity between the tips of the slabs. (b) The pro- and retro-wedges are shifted with respect to the slabs in order to ensure that the gap between the slabs is minimised. (c) The simpli¢ed model for topographic shift used in Appendix A.

4 r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x Pro- vs. retro-foreland basins of zero de£ection (i.e. approximately sea-level), however, result there is no further increase in the loading on the all of our results are also directly applicable to under- ¢lled slabs once steady-state has been attained. basins. The growth phase of the simulated mountain belt de- Flexure models scribes the period over which thewedge grows from noth- ing to a topographic maximum of 3 km elevation. By A £exure model provide a description for the shape of the assuming a convergence rate and a thickness of material slab which supports the mountain belt and its pro- and retro-foreland basins. The general £exure equation to be accreted into the mountain belt, h0 we can determine the total amount of material that is accreted into the sys- describing the de£ection of an elastic plate assuming no tem after a period of time, t: horizontal compressional force and a hydrostatic restoring force is given by:

Aaccreted ¼ Asystem þ Aloss ¼ vh0t ð2Þ d4wðx; tÞ Which implies that A A .The loss of mass D þ Drgwðx; tÞ¼qðx; tÞð4Þ accreted system dx4 from the system represents the material that is transported out of the mountain belt ^ foreland basin system. It is tri- Where, w(x, t) is the vertical de£ection of point on the vial to incorporate transportation of material out of the slab from the horizontal z 5 0 datum at some time t, D is system, however, this results in an non-unique solution the £exural rigidity parameter and x is the horizontal dis- which requires either calibration to a speci¢c setting or tance from the free end of the slab.The second term repre- full coupling to a surface process model. Because the aim sents the upward hydrostatic restoring force per unit area of this paper is to de¢ne the ¢rst order signal, we take the that results from the replacement of mantle rocks with unique end-member case where the basins are instanta- crustal rocks in a layer of thickness w.Thus,Dr 5 rmantle- neously¢lledand no material escapes the system such that rcrustl and g is the acceleration due to gravity.We use this Aloss 5 0and: term to describe the instantaneous ¢lling of the foreland basins.The applied load, q(x, t) describes the time evolving vertical force per unit length at the position x,derived Asystem ¼ Atopo þ Afill ¼ Aaccreted ¼ vh0t ð3Þ from the topography. During the steady-state phase, Asystem 5 constant and We assume that the system is supported on two semi- thus any additional material accreted is exactly balanced in¢nite plates which represent the subducting and over- by material that is transported out of the system by ero- riding plates (Fig. 1b). Initially, the slabs are unloaded and sion. In practice, A¢ll is calculated from the current topo- £at, thus we ignore system speci¢c pre-orogenic inherited graphic distribution. Therefore to implement this model, stratigraphy. at each model time-step we: (1) increment the topographic We investigate two di¡erent end member solutions to distribution Atopo 5 Atopo1DA, (2) calculate the resulting Eqn. (4). Firstly, we use the end load solution to isolate increase in A¢ll, and (3) calculate the age of the system the ¢rst-order role of the asymmetric tectonic boundary using t 5 (Atopo1A¢ll)/vh0. conditions in pro- and retro-foreland basin evolution. Under this parameterisation, and choosing a value of Secondly, we extend this model by coupling the basins h0 5 5.0 km, material is accreted into the system at a rate together by appropriately partitioning the distributed dA 2 1 of dt ¼ vh0 ¼ 25 km Myr .The sensitivityofthe system topographic load. The distributed load scheme reduces to these choices of parameters is considered in the ‘Sum- to the endload model if the wedge angles are set to mary and Discussion’ section. As a rule of thumb for the apro 5 aretro 5 901. Airy isostatic case, the de£ected area is expected to be approximately ¢ve times the area of the topographic load. 2 End load model Thus, given that Atopo 5 275 km and using the Airy approximation we can predicts the total duration required The end load model assumes that all of the topographic to grow the entire mountain belt system to the elevation of load, q(x) can be reduced to a single line load, Q(t)atthe 3kmis6Atopo/vh0 66 Myr. Further, the total topographic end of the slab such that: load at the end of the growth period is: Qtopo 5 Atopo r g 5 7.28 106 MPa. To the ¢rst order, this approxi- crust qð0Þ¼Q ðtÞ mation provides a reasonable estimate to the £exural case, which also depends on the £exural rigidity of the slabs, that qðx ¼6 0Þ¼0 can be measured directly from the simulation. The £exure of an elastic plate under the in£uence of an In the steady-state phase, we assume that the rate of evolving end load (Turcotte & Schubert, 2001) is described accretion of new material is sustained and that time aver- by: aged in£ux of accreted material into the topographic wedge balances the erosional e¥ux of material out of the no a2ex=a x x wedge such that the mean topography remains constant. wðx; tÞ¼ M0 sin þðaQ ðtÞþM0 cos The £exure model assumes that the £uctuations about this 2D a a time average (Naylor & Sinclair, 2007) are negligible. As a ð5Þ r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x 5 M.NaylorandH.D.Sinclair

Where M0 is a bending moment applied to the end of Therefore, in deriving the coupled £exural history of the the slab. The bending moment a¡ects the static shape of two basins, assumptions need to be made concerning the theslabsandthepositionofthepinchoutpoint,however, position of the topographic load with respect to the two our ¢rst-order conclusions are insensitive to its precise slabs.We investigate two end-member scenarios that vary choice of value when it is taken to be a constant, so we set the position of the topographic maximum with respect to it to M0 5 0.This reduces Eqn. (5) to: the underlying slabs; (i) allowing an open gap between the underthrust and over-riding slabs where each wedge is a3ex=a x supported solely on its corresponding slab (Fig. 2a) and, wðx; tÞ¼ Q ðtÞ cos ð6Þ 2D a (ii) the topography is shifted retrowards minimising the gap between the two £exed slabs (Fig. 2b). Where D ¼ ET 3=12ðl u2Þis the £exural rigidity with e The size ofthe gapbetween the slabs in the¢rstscenar- E the Young’s modulus, T the e¡ective thickness of the e io (Fig. 2a) is a function of the asymmetry of the distribu- elastic plate and u is Poisson’s ratio.When the topography ted loads of the two thrust wedges, i.e. a more broadly is modelled as an end-load, the ¢ll between the slab and distributed pro-wedge load vs. the narrower, but steeper the z 5 0 datum (the elevation of the stable cratonic plate) retro-wedge load. can be dealt with analytically via the density contrast in the In order to test the plausibility of the scenario (ii), the £exural parameter retroward topographic shift minimising the gap between the slabs, we consider a simple analytic model that 4D 1=4 a ¼ ¼ 76 km: assumes the di¡erential load is solely derived from the gðÞrmantle rfill wedges (Fig. 2c).This allows us to testwhether the magni- In order to focus on the ¢rst-order signal related to tec- tude of the retroward shift of topography lies within a geo- tonic asymmetry and topographic form, we assume that logically plausible range. In this analytic model, the both slabs have the same material properties E 5 70 GPa, horizontal separation between the ridge crest and the slab ends is a function of the height of the wedge and the wedge Te 5 20 km, u 5 0.25 which are typical values for a young mountain belt (Allen & Allen, 2005); therefore taper angles (Appendix A), D 5 5 1022 Nm. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! For the end load model we assume that the topo- 1 1 1 1 graphic load is distributed evenly across the pro- and ret- dx ¼ H þ ro-slabs.Thus the applied topographic load, to each slab, tan apro 2tanapro tan apro tan aretro increases linearly from Q(t 5 0)5 0toQ¢nal 5 Qtopo/2 ð7Þ 5 3.64 106 MPa. The total rate of accretion of dQ For wedge angles in this study (apro 51.51, aretro 5 2.51) material provides a loading rate of dt ¼ 0:5rcrust dA 5 1 the separation is given by dx 5 4.03H.Thus, for our exam- g dt ¼ 3:31 10 MPa Myr for the whole system of topography and ¢ll material. ple of a mountain with mean topography at the highest A major limitation of the end load model is that it can- point of H 5 3 km, Eqn. (7) provides an initial estimate not simulate onlap driven by changing the distribution of of the separation required between the convergence point topography as the pinchout point is analytically ¢xed. For of the underlying slabs and the surface drainage divide this we require the distributed load model. of 12.1km, which is geologically reasonable. Both of the scenarios predict a Bouguer gravity anomaly low on the pro-side of the topographic high, with the Distributed load model greatest o¡set occurring with the greatest asymmetries in The distributed load model takes into account the distri- wedge taper angles. bution of the thrust wedge topographic load.We apply a1D The case for the shifted topography is supported by (i) solution to Eqn. (4) for a distributed load of arbitrary the fact that there is no mechanical reason to expect the cross-section resting on a thin semi-in¢nite elastic plate pro- and retro-wedges to be solely supported on their that £oats on a £uid substratum. The method approxi- respective slabs, (ii) computational models of orogenesis mates the continuous distribution, q(x) by a distributed generally demonstrate a retro-ward shift in the topo- series of line loads. The impulsive response to each line graphic maximum with respect to the subduction point load is summed to determine the total £exure of the slab (Willett et al., 1993; Naylor et al., 2005). (Garfunkel & Greiling, 2002). For consistency with the end-load model, we again assume that the total area bounded by the £exed slab and RESULTS the zero de£ection datum is always ¢lled,i.e.instantaneous ¢lling of the basin to the surface of the stable cratonic plate In this section, we contrast the evolution of the pro- and on geological timescales. As for the end load model, we retro-foreland basin model results in terms of stratigra- implement this using the density contrast term. phy,subsidence, basin geometry and rates of thrust defor- The geometrical relation between the topographic mation. Case1, the end load model, provides the ¢rst order maximum and the slabs is not well constrained (Fig.1b). e¡ects associated with the asymmetric tectonic boundary

6 r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x Pro- vs. retro-foreland basins conditions. Case 2, the distributed load model, highlights material being transported across a basin-wide bypass sur- the important second-order e¡ects associated with expli- face. Thus, we expect the subsidence history of the retro- citly describing the thrust wedge as a distributed load.The foreland basin to provide a good record of the entire simulated basins record only the foredeep depocenter growth phase, provided there was adequate sediment sup- (DeCelles & Giles, 1996) and does not consider sediment ply. As a consequence of the end load model, there is no accumulated in wedge-top, forebulge or backbulge set- onlap in the retro-side units at the basin margin (Fig. 3b tings. and d).

Case 1: end load model Total subsidence histories Stratigraphic evolution Predicted total subsidence histories of wells placed within The stratigraphic evolution of the pro- and retro-foreland the pro- and retro-foreland basins are plotted in Fig. 4. basins is summarised in Fig. 3. The retro-foreland basin shows constant, linear subsi- The translation of the basin in¢ll towards the subduc- dence during the growth phase (Fig. 4a), with stratigraphic tion zone for the pro-foreland basin can be seen in both thickness increasing towards the orogen. During the stea- Fig. 3a and c, which leads to onlap at the basin margin. dy-state phase, the subsidence histories that were locked Because the basin ¢ll is uniformly translated towards the in during the growth phase simply age with no further sub- orogen, the maximum residence time of any unit within sidence thus, a deceleration in subsidence through time. In the foredeep depocenter of the pro-foreland basin is given contrast, the pro-foreland basin records a partial history of by the basin width divided by the convergence rate. The recent basin evolution. It shows the ‘classic’acceleration of true width of the basin is poorly represented in the end- subsidence rates driven by basin translation following the load model (Fig. 3) as the distributed topography is absent. £exural pro¢le of the downgoing slab (Fig. 4b). In a foreland basin of width 60 km and regional conver- Consider the subsidence histories of the pro- and ret- gence rate of 5 km Myr1, the turnover of the basin in¢ll ro-foreland basins some time after steady-state has been would be at least12 Myr. attained (Fig. 4c). In this example, the lag between the last In contrast, the retro-foreland basin stores a complete recorded subsidence in the retro-foreland basin and cur- record of the growth phase (Fig. 3b and d). A retro-fore- rent time delimits the duration of the steady-state phase. land basin that is nearly full at the end of the growth phase There exists a contrast between short-duration, convex- has little space available for new sediment deposition once upwards basin subsidence curves in pro-foreland basins steady-state has been attained, with the majority of new and long-duration, concave-upward subsidence curves in

(a)Pro−side during growth phase (b) Retro −side during growth phase

well well 0 v 0 Pinned Onlap No onlap 5 5

10 10 Depth [km] Each well records a total history Depth [km] of the growth phase 15 v 15

200 150 100 50 0 0 50 100 150 200 x [km] x [km]

(c) Pro−side during steady state (d) Retro−side during steady state Bypass surface 0 v 0 Pinned Onlap 5 5

10 10 Stratigraphic history locked in Depth [km]

Depth [km] during growth phase 15 v 15

200 150 100 50 0 0 50 100 150 200 x [km] x [km] Fig. 3. Stratigraphic pro¢les for a pro- and retro-foreland basin modelled using an endload, applied at x 5 0, during (a) and (b) the growth phase and (c) and (d) the steady-state phase.The stratigraphic horizons are spaced at 3.55Myr intervals.The total duration for each run is 71Myr. Awell drilled in the retro-side basin records the entire growth phase. Awell drilled in the pro-side only records a stratigraphic record related to the recent advection of the basin. r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x 7 M.NaylorandH.D.Sinclair

(a) Retro−side subsidence (Growth phase) (b) Pro−side subsidence

0 0 90km 2 2 Growth phase 90km Steady state phase 60km 4 4 30km Towards 6 60km 6 Towards forebulge forebulge Depth (km) Depth (km) 30km 8 8 Wells towards forebulge record a shorter history 10 10 70 60 50 40 30 20 10 0 20 15 10 5 0 Age (Ma) Age (Ma)

(c) Growth phase Steady-state phase 0

2 90km

4 Pro 60km 6 Depth (km) Retro 8

10 30km

110 100 90 80 70 60 50 40 30 20 10 0 Age (Ma) Fig. 4. Graphs of the subsidence histories recorded in wells located 30 km, 60 km and 90 km away from the endload. (a) The retro-side wells all record a complete history of the growth phase of the mountain-belt.There are no steady-state curves as no new accommodation space is created during the steady-state phase. (b) The pro-side wells only record a modern subset of the entire history as the oldest parts of the basin are being continually destroyed as they are accreted into the mountain belt.The growth phase shows greater acceleration of subsidence rates with due to the extra £exural component of subsidence. (c) A sample scenario of how the pro- foreland and retro-foreland subsidence curves relate to each other.The pro-side wells only record a partial history of the modern basin evolution. In contrast, the retro-side wells only record the growth phase and then steadily age with no further subsidence. retro-foreland basins. A transition from the growth phase (that de¢nes the position of the deformation front). During to a steady-state phase driven by the asymptotic conver- the growth phase, the evolving distributed load introduces gence of uplift and erosion rates would be characterised an extra £exural component that drives onlap in both the by a more gradual and smoother retro-foreland subsi- pro- and retro-foreland basins.This induced onlap bythe en- dence curve than is suggested in Fig. 4c. croachment of the thrust load for the retro-foreland basin is an important correction to the end load model. During Case 2: distributed load model growth of the system, the regional convergence drives the progressive accretion of new material into the thrust wedges, The end load model demonstrates the ¢rst order signal de- evolving the distributed load; at steady state, this accretion rived from the asymmetric tectonic boundary conditions merely maintains a stable load distribution. Consequently, that require no assumptions about the topographic load during growth, the time averaged rate of migration of the distribution.We now use a distributed load model to inves- pro-foreland cratonic basin margin is greater than the regio- tigate the second-order overprinting associated with the nal convergence rate and equals it at steady state. In contrast spatial distribution of mountain belt topography and the the onlap rate of the cratonic margin of the retro-foreland de¢nition of the basin margin by the deformation front. basin is signi¢cantly less than the regional convergence rate The cross-sectional evolution of the mountain belt for during growth, and negligible at steady state. the open gap (Fig. 2a) and closed gap (Fig. 2b) loading schemes is shown in Fig. 5.The depth of the slab pro¢les is clearly sensitive to relatively subtle changes in the posi- Deformation fronts tion of the topographic load. However, the basic basin evo- The deformation fronts are de¢ned to be the point where lution signal remains clear. the wedge tips intersect the top of the basin succession (Fig.5). As the wedges grow,the deformation fronts propa- gate out across the basins (red lines in Fig. 5 show the Onlap of cratonic margin paleo-deformation front positions). Because the wedges The position of both basin margins is now controlled by both must be the same height where they meet (at the load divi- the £exural parameter and the form of the distributed load der), the relative taper angles of the wedges controls the

8 r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x Pro- vs. retro-foreland basins

δx=0 δx α α α α pro retro pro retro

v v Load divider Load divider (a) Open gap (d) Closed gap

17.8Myr 17.8Myr 0 0

Depth [km] 5 5 −200 −1000 100 200 −200 −1000 100 200

(b) 35.5Myr (e) 35.5Myr

0 0

5 5 Depth [km]

10 10

−200 −1000 100 200 −200 –1000 100 200

(c) 71.0Myr (f) 71.0Myr

0 0

5 5

10 10 Depth [km]

15 15

20 20 −200 −1000 100 200 −200 −100 0 100 200 x [km] x [km] Fig. 5. Stratigraphic evolution of pro- and retro-foreland basins coupled by a topographic wedge load. (a^c) Show the time evolution for the open gap model where the pro-wedge is supported on the subducting slab and the retro-wedge is supported on the over-riding plate. (d^f) Show the time evolution for the closed gap model where the topographic load is shifted laterally in order to close the gap between the subducting and over-riding plates.The stratigraphic horizons are projected under the mountain belt as greydashed lines to highlight the contrast between the basins; such stratigraphy is of course deformed as the basin is consumed at the deformation fronts. The evolution of the paleo-deformation front positions are shown in red (online).

relative rates at which the deformation fronts propagate change in the length of the base of the wedge, out in order to accommodate the accretion of new material. As a kinematic consequence of how material is accreted 2 2 pro H retro H into mountain belts, the mean surface slope angle of the Atopo ¼ > Atopo ¼ 2tanapro 2tanaretro retro-wedge is generally steeper than that of the pro- ð8Þ pro dH 1 retro dH 1 wedge (Willett et al., 1993).Thus, geometrically,the topo- vDF ¼ > vDF ¼ graphic load of the retro-wedge is more compact than the dt tan apro dt tan aretro pro-wedge load and more mass is stored in the pro-wedge Thus, the rate at which the retro-wedge deformation retro than the retro-wedge. Further, the rate at which the defor- front propagates out, vDF is slower than the pro-wedge pro mation fronts propagate out across the basin are directly deformation front vDF (Fig.6a and b)providedaretro4apro. related to their taper angles. We can compare the rate at The rate at which material crosses the deformation which the wedges grow using the cross-sectional areas of fronts can be used to estimate the amounts of tectonic each wedge and noting that they must have the same deformation, i.e. thrusting.The mean rate atwhich material height, H (Fig. 2c).The rate of propagation of each defor- is accretedatthe pro-side deformationfront is the sum of mation front relative to the load divider is then the rate of the rate at which the deformation front migrates out and r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x 9 M.NaylorandH.D.Sinclair

(a) Time evolution of the fronts (b) Time evolution of the fronts with open gap with closed gap Pro Retro Pro Retro Steady state Steady state 70 70 Growth Growth 60 60 50 50 40 40 30 30

Model time (Myr) 20 20 Model time (Myr) 10 pro 10 pro X retro retro pro pro retro retro X DF X X X X X X 0 PP DF PP 0 PP DF DF PP −200 −100 0 100 200 −200 −100 0 100 200 Absolute position of fronts (km) Absolute position of fronts (km)

(c) Time evolution of basin width (d) Time evolution of basin width with open gap with closed gap

Steady state Steady state 70 70 Growth Growth 60 60 50 50 Pro Pro 40 Retro 40 Retro 30 30

Model time (Myr) 20 20 Model time (Myr) 10 10 0 0 70 80 90 100 110 70 80 90 100 110 Basin Width (km) Basin Width (km) Fig. 6. Graphs showing the geometric evolution of the pro- and retro-foreland basin margins (solid lines for pro-foreland basin margins and dashed lines for the retro-foreland basin margins). (a and b) Show the absolute positions of the basin margins for the open gap and closed gap experiments, respectively.The outermost lines are the basin pinchout points, xPP and the innermost lines are the deformation fronts, xDF. (c and d) Show the resulting evolution of the basin widths. Notice that the retro-foreland basins (dashed lines) are wider than the pro-foreland basins (solid lines) and that closing the gap between the slabs minimises this di¡erence. the convergence rate atwhich thebasin¢llis translatedto- terises retro-wedges, more of the £exural depression is wards the mountain belt. Because the retro-side basin ¢ll ¢lled with sediment rather than deformed wedge, hence is not translated and the retro-side deformation front pro- the basins are wider (Fig.6c and d). Because the retro-fore- pagates out at a slower rate than its counterpart on the land basin is wider, so it is also deeper at the deformation pro-side; the rate of structural deformation (i.e. accretion) front than the pro-foreland basin.This holds for both to- of the basin margin is signi¢cantly lower on the retro-side pographic load distribution scenarios (Fig. 5). than the pro-side. The width of both basins decreases as the mountain belt grows, primarily due to the deformation front propagating out faster than the pinchout point (Fig.6).Because the rate Basin width and depth at which the deformation fronts and basin margins propa- In contrast to the deformation fronts, the position of the gate out decrease as the mountain belt grows, the width of basin margins is more strongly controlled by the £exural the basins stabilises with time. parameter than the topographic load, and so if we assume constant £exural rigidities, the retro-foreland basin is Chronostratigraphy of basin ¢ll wider than the pro-foreland basin. This is a result of the degree to which the thrust wedge occupies the £exural Chronostratigraphic plots are key to understanding the de£ection vs. the sediment in¢ll; with lower taper thrust temporal development of a basin, and are simply plotted wedges, often characterised by a salt detachment, the as time against the distribution of sedimentation and ero- wedge can propagate to occupy a large portion of the £ex- sion (Wheeler, 1964). In foreland basins, it is usual to plot ural depression (Ford, 2004), and so the foreland basins are the spatial development of the stratigraphy with reference relatively narrow. With steeper taper angles, as charac- to a stable cratonic foreland. However, when considering

10 r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x Pro- vs. retro-foreland basins the synchronous development of two opposing foreland EXAMPLES basins, it is interesting to note that these cannot be plotted on the same ¢gure, as the cratonic forelands are moving Pro-foreland basins relative to one another i.e. there is no ¢xed reference point. The onlap of the cratonic margin of pro-foreland basins The reference frame for Fig. 6 is x 5 0theregionwherethe has been documented from the Palaeozoic Appalachian slabs meet. The reference frame for the chronostrati- foreland basin (Quinlan & Beaumont, 1984; Tankard, graphic fronts in Fig. 7 is a ¢xed point on each of their 1986) the Cretaceous strata of the North Slope foreland respective plates. As the pro-foreland basin sits on the basin, Alaska (Bird & Molenaar,1992) and from numerous down going plate but is moving relative to it, the chronos- Tertiary examples such as the Pyrenees (Verge¤ s etal., 1998), tratigraphic reference frame changes with respect to plate Alps (Sinclair,1997) and Taiwan (Lin etal., 2003). As such it convergence rate as well as the growth of the foreland basin is a well known attribute of these basin types. As outlined during the growth phase (for an expansion on this refer- in the model, such dramatic onlap is driven by the advec- ence frame problem see Appendix B). tion of the pro-foreland basin ¢ll into the deforming Given the di⁄culty of reference frames in these set- thrustwedge.A further outcome of this is that these basin tings, we will consider the two basins separately,as if being types typically only preserve a stratigraphic studied on an individual basis. The contrasting character record of the more recent stages of orogenesis; the earlier of the pro- and retro-chronostratigraphic plots (Fig. 7) basin ¢ll being accreted into the thrust wedge, and com- can be summarised in terms of the temporal preservation monly eroded. This is why there is a lack of stratigraphy of stratigraphy,and the rate of migration over the foreland. older than 16 Ma in the south Himalayan foreland basin Pro-foreland basins only preserve the most recent record oftheGangeticPlainswhencollisionstarted 50 Ma of basin development, the rest being accreted into the (Burbank et al., 1996; Najman et al.,2001).Similarly,there thrust belt. The age of the oldest sediments found at the is only a partial preservation of the Eocene/Oligocene his- bottom of the basin ¢ll at the deformation front equates tory of the North Alpine Foreland Basin in the folds and to the width of the basin times the rate of convergence. In thrusts of the Helvetic domain of the Swiss Alps (Home- contrast, retro-foreland basins preserve a much fuller his- wood et al., 1986). tory of mountain belt growth and steady state, as there is Subsidence histories of foreland basins in general little destruction of the basin through accretion. However, are thought to be characterised by accelerating subsidence the transition from growth to steady state should be through time (Miall, 1995; Allen & Allen, 2005). We recorded by a reduction in sediment accumulation rates, view this as a unique characteristic of pro-foreland as there is no longer a tectonic driver of subsidence.There basins supported by a range of examples including New are only subtle di¡erences between the open and closed Guinea/Timor Trough (Haddad & Watts, 1999), western gap experiments. Ta iw a n ( L i n et al., 2003), Ebro Basin, Pyrenees (Verge¤ s The onlap of the outer margin of a pro-foreland basin is et al., 1998), and the North Alpine Foreland Basin (Allen driven by both the growth of the mountain belt, and the un- et al., 1986). As demonstrated in the modelling experi- derthrusting of the plate at the convergence rate. Hence, ments, this pattern is dominated by subsidence induced during growth, the onlap rate combines these factors, but by the progressive underthrusting of the slab beneath during steady state it should equate to the convergence rate the mountain belt with a secondary component driven (Fig.7). In contrast, the progressive onlap of the retro-fore- by any growth in the size of the topographic load. land basin can only be driven by the growth of the mountain The former control does not occur in retro-foreland belt, and so during steady-state onlap should cease. basins.

(a) Chronostratigram with open gap (b) Chronostratigram with closed gap Pro Retro Pro Retro

Steady state Steady state 70 70 Growth Growth 60 Deformation 60 fronts 50 50

40 40

30 30 Pinchout

Model time (Myr) 20 points Model time (Myr) 20 10 10

0 0 −600 −500 −400 −300 −200 −100 0 100 200 −600 −500 −400 −300 −200 −100 0 100 200 Position of chronostrat fronts (km) Position of chronostrat fronts (km) Fig. 7. Chronostratigraphic plots summarise the temporal preservation of stratigraphy,and the rate of basin migration over the foreland.The pro- and retro-chronostratigraphic plots are constructed relative to their respective stable cratons. r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x 11 M.NaylorandH.D.Sinclair

Retro-foreland foreland basins short-lived, accelerating record during early Eocene time. Additionally,in comparing the Aquitaine to the Ebro Basin Detailed documentation of retro-foreland basins is less (its pro-foreland counterpart), the amount of basin short- common than for their pro-foreland counterparts. The ening is markedly di¡erent with approximately 60 km Aquitaine Basin to the north of the Pyrenees in southern shortening of the Ebro Basin (Verge¤ s, 1999) to o10 km in France (Fig. 8) is on the retro-side of the mountain belt the Aquitaine basin (Desegaulx & Brunet, 1990). (Sinclairet al., 2005) and has been thoroughly documented Another well documented example of a retro-foreland due to the long history of hydrocarbon exploration and foreland basin is the South Westland Basin to the west of production (Bourrouilh et al., 1995). In contrast to the the Southern Alps, New Zealand (Kamp et al., 1992; pro-foreland basins described above, the Aquitaine Basin Sircombe & Kamp, 1998). This Pliocene basin is located forms a wedge of sedimentary in¢ll 4^6 km thick, that immediately west of the steep retro-wedge dominated by tapers over a distance of approximately 140 km away from the Alpine Fault (Beaumont et al., 1996) and contains a full the Pyrenees, and contains a full stratigraphic record of stratigraphic record of Southern Alps orogenesis. The pre- and syn-orogenic sedimentation (Desegaulx et al., shortening of the Australian plate adjacent to the basin is 1991) (Fig. 8). The Upper Cretaceous to Oligocene units small (from 2 to 12km), and is accommodated on steep all thin onto the European craton with a wedge-shaped ar- basement faults rather than thin-skinned deformation; chitecture that are vertically superimposed i.e. they exhibit again attributes typical of retro-wedge deformation fronts. little, if any, onlap. Additionally, the tectonic subsidence Tectonic subsidence within the basin accelerated at histories oftheAquitaineBasin(Fig.8c)recorda minorac- 5^6Ma, and either remained steady or decelerated since celeration in subsidence at around the onset of Pyrenean that time as predicted above for retro-foreland basins. orogenesis ( 60 Ma), followed by a deceleration to zero Similar examples of decelerating subsidence histories since then (Desegaulxetal.,1991).The pre-orogenic subsi- are documented for the Miocene history of theTertiary dence of the Aquitaine Basin records the remnant thermal Piedmont basin, which from Oligocene through early subsidence tothe thinnedlithosphere.Incontrast,the tec- Miocene timeswas part of the western Po Basin compres- tonic subsidence of a restored stratigraphic succession sional system (Carrapa et al., 2003). Hence, this basin rem- from the South Pyrenean Fold and thrust belt records a nant records the retro-foreland basin of the southern

(a) (c)

(b)

Fig. 8. The Pyrenees mountain belt as a type example of a systemwith a pro-foreland (Ebro Basin) and retro-foreland (Aquitaine Basin) foreland basin that can be compared in terms of their stratigraphic in¢ll and tectonic subsidence histories. (a) Summary cross-section of the Pyrenean mountain belt formed by the Iberian plate of Spain subducting beneath the European Plate of south-western France.This section is constrained by the ECORS deep seismic section (Choukroune, 1989), other geophysical measurements (Pous et al., 1995) and surface geology (Munoz,1992). (b) Close-up of the stratigraphy of the Ebro (Verge¤ s, 1999) and Aquitaine Basins (Desegaulx et al., 1991). (c) Subsidence plots from two wells located near to the deformation front in the Aquitaine Basin (Desegaulx & Brunet, 1990) and from structurally restored stratigraphic pro¢les from the central South Pyrenean fold and thrust belt (Verge¤ s,1999). Note that the Ebro Basin contains a limited section of stratigraphy dominated by Upper Eocene strata; the subsidence plots through this record a rapid phase of accelerating subsidence at this time. In contrast, the Aquitaine Basin contains a much broader chronostratigraphic range, and shows only minor tectonic subsidence during the early stages of orogenesis, but this decreases to zero.These contrasts match predictions made for pro-foreland vs. retro-foreland foreland basin development, respectively.

12 r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x Pro- vs. retro-foreland basins

French Alps, although this is complicated by Apennine Onlap is driven by both the outward propagation of the deformation and loading from the south. pinchout point by an increasingly distributed load and any The full stratigraphic record of orogenesis, the rela- relative motion between stable craton and the mountain tively insigni¢cant record of progressive basin onlap, and belt that translates the basin ¢ll; out of these two mechan- the linear to decelerating subsidence histories of these ba- isms it is the regional convergence that predominantly sins ¢t the modelled predictions, and contrast with their drives onlap. The mobile pro-foreland basin records on- pro-foreland counterparts. lapping stratigraphy and the oldest sediments in the basin can be found beneath the deformation front with an age approximated by the width of the basin divided by the re- SUMMARYAND DISCUSSION gional convergence rate (Fig. 9b, Appendix B, eqn (B1)). Young sediments continue to onlap in the steady state While the chosen boundary conditions that determine phase while convergence is sustained. In contrast, the old- slab behaviour beneath mountain belts are vital to under- est sediments in the retro-foreland basin date from the in- standing orogenesis,the predictions for the di¡erentiation itiation of growth of the mountain belt (eqn (B3)) and this of pro- and retro-foreland basins require only an asymme- basin records little onlap. As steady state is attained, the try of underthrusting and consequent thrust accretion. retro-foreland basin becomes ¢lled and dormant with a The generic ¢rst-order signal is summarised in Fig. 9. bypass surface. A collisional mountain belt is generally bounded by two Owing to the long-term translation of the mobile pro- basins, a relatively mobile pro-basin above the subducting foreland basin towards the mountain belt at the far ¢eld slab and a relatively stable retro-basin above the over-rid- convergence rate, the pro-foreland basin records acceler- ing slab (Figs 8a and 9a).The rate of growth of the moun- ating subsidence (Fig.9c). In contrast, the retro-basin re- tainbelt is primarilycontrolledbythe net rate ofaccretion cords decelerating subsidence in the time period that of new material (Eqn. (2)).Thus the system will grow faster relates to the transition from growth to steady state. when accreting thicker material and for faster convergence We can relate surface uplift to the increasing topo- rates.Varying the rate of accretion also has other implica- graphic mass by di¡erentiating Eqn. (1), tions because it controls the rate at which the pro-foreland basin ¢ll is carried towards the mountain belt. Increasing dA dH topo ¼ KH the convergence rate increases the contrast between the dt dt pro- and retro-foreland basins; it increases the rate of tec- Where tonic deformation at the pro-deformation front which in- creasing the thickness of the accreted layer would not. 1 1 However, increasing h promotes longer thrust sheets (Platt, K ¼ þ : tan a tan a 1988;Naylor& Sinclair, 2007).Varying accreted thickness can pro retro be taken intoR account by generalising Eqn. (2) From this, using the rate of accretion (2)and dropping the to Aaccreted ¼ vhðtÞdt. Such changes in thickness may proportion of material that is accreted into the topography occur because of inherited rheology or a progressive transi- (which is approximately 1/6), we can rearrange for the sur- tion from thin skinned to thick-skinned tectonics.The im- face uplift rate, pact of increasing the thickness of the accreted layer is to increase the rate of accretionwith time, delaying the conver- dH vh0 gence of uplift and erosion rates. However, such variations dt KH only transiently modify the behaviour we have documented Increasing either wedge angle decreases K and increases in this paper rather than negating it. the surface uplift rate required to accommodate a given The relative rates of migration of the deformation in£ux of material. Further, this equation reinforces the fronts relative to the load divide are purely a function of relationship that the mean surface uplift rate will decrease as the wedge angles, assuming critical wedge theory. Rear- a mountain belts increase in size unless the rate of accretion ranging Eqn. (8), of new material also increases.While this e¡ect is not impor- tant for the ¢rst-order signal documented in this paper, it vpro Apro tan a does become important when explicitly coupling such DF ¼ ¼ retro vretro Aretro tan a systems to a surface process model (e.g. Whipple & Meade, DF pro 2006) to investigate sediment sourcing and supply.Thus, the The pro- and retro- wedge angles, we chose are at the height of the mountain belt at steady state is also dependent lower end of the range of observed angles.This a¡ects the upon the wedge angles (Dahlen & Suppe,1988). physical geometry, but it is the ratio of these angles that By studying the ¢rst-order e¡ects that are distinguish- controls the relative asymmetry in the propagation rates. able between pro- and retro-foreland basins we have made Increasing the wedge angles makes the mountain belt nar- a number of assumptions in the modelling approach that rower, tending the system towards the endload model, and need further quali¢cation. The predicted evolution of the contains less mass for the same maximum height at the orogenic and cratonic basin margins for both basin types is divide and is bounded by shallower basins. depicted as the intercept of the deformation front and the r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x 13 M.NaylorandH.D.Sinclair

(a) Pro-foreland Retro-foreland basin Pro-wedge Retro-wedge basin

osphere U g lith ndert ridin hrus ver t lith O osp he re

-oldest strata in foredeep = -oldest strata in foredeep = basin width/convergence rate onset of orogenesis

(b) - Chronostratigraphy

Onlap Condensed interval due to bypass Steady-state

Time Unconformable gap Time

Growth

Pre-orogenic craton stratigraphy Onset of Pre-orogenic craton stratigraphy orogenesis Distance Distance

(c) - Tectonic subsidence

Onset of Growth Steady Onset of Growth Steady orogenesis state orogenesis state

Depth

Depth

Time Time Fig. 9. Summary ¢gure contrasting the basin characteristics of Pro-foreland (left-hand side) and Retro-foreland (right-hand side) foreland basins. (a) The Pro-foreland foreland basin exhibits dramatic basin onlap of the cratonic margin, at a rate greater or equal to the plate convergence rate dependent upon whether the thrust wedge is in a growth or steady-state phase, respectively; in contrast the Retro-foreland basin records little onlap except in the early stage of growth.This contrasting onlap pattern is clearly seen in the chronostratigraphic equivalent, (b) which also illustrates the relatively limited chronostratigraphic interval preserved in the pro- foreland basin relative to the retro-foreland basin. Note that the reference frame for both chronostratigraphic ¢gures are their respective cratonic plates (cf. Appendix B and Fig.10), and not an absolute frame.The degree to which foreland basin deposits are accreted and preserved in the thrustwedges also contrasts markedly due to the ongoing advection of the pro-foreland basin’s succession into the pro- wedge, in contrast to the retro-foreland basin succession which will only be accreted during growth of the mountain belt. Hence, the oldest deposits preserved in the foredeep of the pro-foreland basin equal the width of the basin divided by the convergence rate. In contrast, the oldest strata preserved in the foredeep of the retro-foreland basin record the initiation of orogenesis.The tectonically driven subsidence of the two basins also contrasts, (c) The pro-foreland basin records accelerated subsidence over a relatively short interval of orogenesis. In contrast, the retro-foreland basin records the full history of the basin with initial uniform subsidence during growth of the mountain belt, and hence of the retro-thrust wedge, followed by zero subsidence during steady-state when the retro- wedge no longer accretes new material. During this latter stage, the retro-foreland basin record a condensed stratigraphic succession which is likelyto be dominated bybypass of the sediment generated in the mountain belt and exported farther a¢eld.

14 r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x Pro- vs. retro-foreland basins basin ¢ll, and the stable craton and the basin ¢ll, respec- the stratigraphy is preserved in the accreted thrust units of tively.Naturally, the way in which sediment supply is mod- the pro-wedge of the mountain belt (e.g. Homewood et al., elled determines these parameters. For this exercise, we 1986; Lihou & Allen, 1996). Similarly, it is the retro-fore- have assumed that all accommodation space in the basins land basin that should hold a record of the transition from are ¢lled to a reference base-level (the z 5 0 datum). Clearly, growth of the mountain belt to steady-state; the subsi- these geometries will di¡er for under or over¢lled basin dence histories should record this transition as a cessation successions (Covey, 1986; Jordan, 1995). Consequently, it is of tectonic subsidence, and so the stratigraphy should essential that the nature of the stratigraphy used to approx- reveal increased condensation. In contrast, the most imate the cratonic basin margin is clearly documented in recent history of orogenesis will always be preserved in terms of the facies (Sinclair, 1997); i.e. whether they record the pro-foreland basin. coastal, deep-water or fully continental settings. The distinction between linear basin subsidence Critical to understanding output from numerical mod- induced by the growth of the thrust wedge and accelerat- els is determining the role of the boundary conditions; in ing subsidence generated by the advection of the basin this case the laws that determine the behaviour of the down and towards the mountain belt implies that subsi- downgoing tectonic slab and its impact on the growth of dence histories may be inverted to distinguish these the doubly vergent thrust wedge. Understanding the nat- controls. The question of whether an overthrust plate has ure of the coupling between the two slabs is a complicated been actively subducted is usually investigated using issue and depends upon the nature and maturity of the geophysical imaging (Van der Voo et al., 1999). We now orogen. For example, we applied the same £exural rigidity consider basin subsidence records as a valuable additional to both slabs, even though there is no requirement that the tool to answering this question. £exural rigidities should be the same. Such variations will The recognition that peripheral foreland basins can be modify the curvature of the slabs that bound the basins separated into two end-member models with distinct and change the topographic shift required to close the subsidence histories and stratigraphic architectures also gap between the slabs. Because the shift in the topography has signi¢cant implications for hydrocarbon prospectivity. did not have a major e¡ect on the ¢rst order signal, we ex- The subsidence history of a sedimentary basin is the pri- pect our conclusions to be robust to reasonable contrasts mary control on the maturation history of hydrocarbons in elastic thickness between the two slabs. (Allen & Allen, 2005). Despite the presence of excellent In small, collisional orogens (e.g. Pyrenees, Olympics, structural traps on the edge of many foreland basins, Taiwan) with little evidence of crustal melting, the discussion source rocks are commonly ‘overcooked’ due to the rapid of a physical coupling is justi¢ed,as the surface geology reveals subsidence near the deformation front; this is particularly discrete faulted contacts between rocks accreted from the problematic for pro-foreland basins, with the notable downgoing slab vs. those accreted from the overlying slab exception of the Zagros thrust belt (Koop & Stoneley, (Munoz,1992; Willett et al., 2003). Mountain belts with signif- 1982). The problem of overcooked source rocks is icant crustal melting of the root demonstrate the juxtaposition enhanced in post-orogenic settings when the basin is of crustal melt with mantle melt and the nature of the contact inverted in response to the reduction of the orogenic load. becomes less obvious. For very large orogens where their In examples such as the North Alpine Foreland Basin, the height is limited by the rheology of a £owing lower crust and succession has been eroded and exhumed by over 1km in mantle as recorded through volcanism (e.g. Himalaya/Tibet the last 5 Myr in response to the cessation of deformation and Andes) the slabs are clearly decoupled. Examples such as and increased erosion rates in the mountain belt (Ceder- the Southern Alps, New Zealand provide a case of strong bom et al., 2004). Retro-foreland basins may also contain thrust wedge asymmetry (Kamp & Tippett, 1993), but with signi¢cant hydrocarbon reserves such as the Aquitaine continuous deformation of the mantle lithosphere,i.e.without Basin (Bourrouilh et al., 1995). Hence, understanding the a dominant subducting slab (Molnar et al., 1999). Thus, while geodynamic context of a foreland basin in terms of it being the separation of pro- and retro-wedges in settings such as a retro- or pro-foreland basin aids prediction of source the Southern Alps has been strongly advocated (Beaumont rock maturation, and potentially reservoir architecture. etal.,1996),the deep structure that determines this asymmetry Finally,such a clear distinction between peripheral fore- is debated. land basin types based on the asymmetry of the tectonic forcing raises the question ofwhether this has implications WIDER IMPLICATIONS for understanding retro-arc foreland basins (Jordan, 1995).Toa¢rst order,the boundaryconditions that charac- Enhanced understanding of the coupling between the terise continent/continent collision appear similar to growth of mountain belts and the development of their as- ocean/continent collision, i.e. the underthrusting or sub- sociated foreland basins enables more sophisticated inter- duction of one lithosphere beneath another. Based on this, pretation of foreland basin stratigraphy. Importantly, in it is tempting to suggest that the model predictions for ret- order to gain insight into the growth phase of a mountain ro-foreland foreland basins should be similar to those for belt, it is clear that the best preserved records are at the retro-arc foreland basins. However, there are some clear base of the retro-foreland basin. It is possible to recon- di¡erences that may play a signi¢cant role in distinguish- struct this record from the pro-foreland basin, but only if ing the controls on these basin types.The marked density r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x 15 M.NaylorandH.D.Sinclair contrast between oceanic and continental lithosphere is a Ingersoll for discussions on terminology.M.N. was funded strong driver of subduction leading to steeper subduction byEPSRCgrantGR/T11753/01as part of theNANIAproject. angles (Royden, 1993), enhanced melting (Pearce & Peate, 1995),andgreater impact on mantle circulation and hence, dynamic topography (Burgess et al.,1997). Enhanced melt- REFERENCES ing a¡ects rheology, and hence the mechanical growth of Allen P.A. Allen J.R. the mountain belt (Willett et al.,1993), and dynamic subsi- , & , (2005) Basin Analysis, 2nd edn. Black- dence due to mantle £ow is superimposed on the isostatic well Publishing, Oxford. ALLEN, P.A., HOMEWOOD,P.&WILLIAMS, G.D., eds. (1986) signal, greatly enhancing the wavelength of subsidence of Foreland Basins: An Introduction. Foreland Basins. International the retro-arc basin (Burgess et al., 1997). Therefore, we Association of Sedimentologists. Blackwell Scienti¢c Publica- believe that retro-foreland and retro-arc foreland basins tions, Oxford. should be di¡erentiated and that more work is needed to Beaumont, C. (1981) Foreland Basins. Geophys. J. R. Astronom. determine their contrasting characteristics. Soc., 65, 291^329. Beaumont, C., Kamp, P.J.J., Hamilton, J. & Fullsack, P. (1996) The continental collision zone, South Island, New CONCLUSIONS Zealand: comparison of geodynamical models and observa- tions. J. Geophys. Res.-Solid Earth, 101,3333^3359. In this paper, we have described how the asymmetrical for- Beaumont, C., Munoz, J.A., Hamilton, J. & Fullsack, P. cing of orogenic systems by the underthrusting of one (2000) Factors controlling the alpine evolution of the Central plate relative to the other results in contrasting foreland Pyrenees inferredfrom acomparison ofobservations andgeo- basins. Speci¢cally, dynamical models. J. Geophys. Res.-Solid Earth, 105, 8121^8145. Subsidence histories of pro-foreland basins comprise a BIRD,K.J.&MOLENAAR,M.C.,eds.(1992)The North Slope Fore- linear component driven by thrust wedge growth, and an land Basin, Alaska. Foreland Basins and Fold Belts. American accelerating component driven by the advection of the basin Association of Petroleum Geologists Memoirs,Tulsa. Bourrouilh R. Richert J.P. Zolnai G. towards the thrust wedge. In contrast, retro-foreland basins , , , & , (1995) The North Pyrenean Aquitaine Basin, France ^ evolution and hydrocar- only subside in response to the growth of the thrust wedge, bons. AAPGBull., 79,831^853. and hence are linear during the growth phase, and have no Burbank, D.W., Beck, R.A. & Mulder, T., eds. (1996) The Himala- tectonic driver during steady-state. On a plot of subsidence yan Foreland Basin. TheTectonic Evolution of Asia Cambridge through time, pro-foreland basin subsidence will be convex- University Press. upward, whereas retro-foreland basins are concave (Fig.9c). Burgess, P.M., Gurnis, M. & Moresi, L. (1997) Formation of Pro-foreland basins are characterised by a basin ¢ll that sequences in the cratonic interior of North America by inter- records only the recent history of the mountain belt; the action between mantle, eustatic, and stratigraphic processes. recorded interval is given by the width of the basin divided Geol. Soc. Am. Bull., 109, 1515^1535. by the plate convergence rate. In contrast, retro-foreland Carrapa, B., Bertotti, G. & Krijgsman,W. (2003) Subsidence, basins preserve the full stratigraphic record of mountain stress regime and rotation(s) of a tectonically active sedimen- growth, but only a condensed record of steady-state devel- tary basin within the Western Alpine Orogen: the tertiary Piedmont Basin (Alpine Domain, NW Italy). In:TracingTectonic opment of a mountain belt (Fig.9b). Deformation Using the Sedimentary Record (Ed. byT. McCann & Pro-foreland basins record basin onlap of the cratonic A. Saintot). 208, 205^227.The Geological Society of London, margin equal to the rate of plate convergence plus a com- London. ponent driven byoutwardgrowth of the thrustwedge.Ret- Cederbom, C.E., Sinclair, H.D., Schlunegger, F. & Rahn, ro-foreland basins record a relatively small amount of M.K. (2004) Climate-induced rebound and exhumation of the onlap driven solely by thrust wedge growth. During stea- European Alps. Geology, 32(8), 709^712, doi: 10.1130/G20491.1. dy-state (i.e. with no growth), retro-foreland basins record Choukroune, P. (1989) The Ecors Pyrenean deep seismic pro- little or no onlap, whereas pro-foreland basins record on- ¢le re£ection data and the overall structure of an Orogenic lap equal to plate convergence rate (Fig.9b). Belt.Tectonics, 8, 23^39. Covey M. These conclusions are supported by ¢eld examples. , (1986) The evolution of Foreland Basins to steady Classic examples of pro-foreland basins include the Appa- state: evidence from the Western Taiwan Foreland Basin. In: Foreland Basins (Ed. by P.A. Allen & P. Homewood), Spec. Publ. lachian foredeep, the Himalayan foredeep, the North Int. Assoc. Sedimentol. 77^90. Blackwell, Oxford. Alpine Foreland Basin, the Ebro Basin (south Pyrenees) Crampton, S.L. & Allen, P.A. (1995) Recognition of forebulge and the west Taiwan basin. Examples of retro-foreland unconformities associated with early-stage Foreland Basin basins include the South Westland Basin (New Zealand), development ^ example from the North Alpine Foreland Ba- The Po Basin (southern European Alps) and the Aquitaine sin. AAPGBull., 79, 1495^1514. Basin (north Pyrenees). Dahlen, F.A. & Suppe, J. (1988) Mechanics, growth and erosion of Mountain Belts. In: Processes in Continental Lithospheric Defor- mation (Ed. by S.P. Clark, B.C. Burch¢el & J. Suppe), Geol. Soc. ACKNOWLEDGEMENTS Amer.Spec. Pap 218, 161^178. Dahlen, F.A., Suppe, J. & Davis, D. (1984) Mechanics of Fold- We would like to thank Brian Horton, Guy Simpson and and-Thrust Belts and Accretionary Wedges ^ cohesive cou- an anonymous reviewer for constructive reviews and Ray lomb theory. J. Geophys. Res., 89,87^101.

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Davis, D., Suppe, J. & Dahlen, F.A. (1983) Mechanics of Fold- Lin, A.T.,Watt s , A.B. & Hesselbo, S.P. (2003) Cenozoic strati- and-Thrust Belts and Accretionary Wedges. J. Geophys. Res., graphy and subsidence history of the South China Sea Margin 88, 1153^1172. in theTaiwan region.Basin Res., 15,453^478,doi:10.1046/j.1365- DeCelles, P.G. & Giles, K.A. (1996) Foreland Basin systems. 2117.2003.00215.x. Basin Res., 8, 105^123, doi: 10.1046/j.1365-2117.1996.01491.x. Miall, A.D. (1995) Collision-Relate Foreland Basins. Blackwell Desegaulx, P. & Brunet, M.F. (1990) Tectonic subsidence of Science, Oxford. the Aquitaine Basin since cretaceous times. Bull.Soc.Geol. Molnar, P., Anderson, H.J., Audoine, E., Eberhart-Phil- France, 6, 295^306. lips, D., Gledhill, K.R., Klosko, E.R., McEvilly, T.V. , Desegaulx, P., Kooi, H. & Cloetingh, S. (1991) Conse- Okaya, D., Savage, M.K., Stern,T. & Wu, F.T. (1999) Conti- quences of Foreland Basin development on thinned continen- nous deformation versus faulting through the continental tal lithosphere ^ application to the Aquitaine Basin (SW lithosphere of New Zealand. Science, 286, 516^519. France). Earth Planet. Sci. Lett., 106,116^132. Munoz, J.A. (1992) Evolution of a continental collision belt: Dickinson, W.R . (1974) Plate tectonics and sedimentation. In: ECORS-Pyrenees crustal balanced cross-section. In: Thrust Tectonics and Sedimentation (Ed. by W.R. Dickinson), Spec. Publ. Tectonics (Ed. by K. McClay). 17, 235^246. Chapman & Hall, 22,1^27.Society ofEconomicPaleontologists andMineralogists, London. Los Angeles. Najman, Y. , Pringle, M., Godin, L. & Oliver, G. (2001) Dat- Flemings, P.B. & Jordan,T. E . (1989) A synthetic stratigraphic ing of the oldest continental sediments from the Himalayan model of Foreland Basin development. J. Geophys. Res.-Solid Foreland Basin. Nature, 410, 194^197, doi: 10.1038/35065577.. Earth Planets, 94,3851^3866. Naylor, M. & Sinclair, H.D. (2007) Punctuated thrust defor- Fo rd, M. (2004) Depositional wedge tops: interaction between mation in the context of doubly Vergent Thrust Wedges: im- low basal friction external Orogenic wedges and £exural fore- plications for the localization of uplift and exhumation. land basins. Basin Res., 16, 361^375, doi: 10.1111/j.1365 - Geology, 35, 559^562, doi: 10.1130/G23448A.1. 2117.2004.00236.x. Naylor, M., Sinclair, H.D.,Willett, S.D. & Cowie, P.A. (2005) Garfunkel, Z. & Greiling, R.O. (2002) The implications of A discrete element model for Orogenesis and Accretionary Foreland Basins for the causative tectonic loads. EGU Stephan Wedge growth. J. Geophys. Res., 110, doi: 10.1029/2003JB002940. Mueller Spec. Publ. Ser., 1,3^16. Pearce, J.A. & Peate, D.W. (1995) Tectonic implications of the Haddad, D. & Watt s , A.B. (1999) Subsidence history, gravity composition of volcanic arc magmas. Ann. Rev. Earth Planet. anomalies, and £exure of the Northeast Australian Margin in Sci., 23, 251^285, doi: 10.1146/annurev.ea.23.050195.001343. Papua New Guinea.Tectonics, 18,827^842. Platt, J.P. (1988) The mechanics of frontal imbrication ^ a 1st- Homewood, P., Allen, P.A. & Williams, G.D. (1986) Dy- order analysis. Geol. Rundschau, 77, 577^589. namics of the Molasse Basin of Western Switzerland. In: Fore- Pous, J., Munoz, J.A., Ledo, J.J. & Liesa, M. (1995) Partial melt- land Basins (Ed. by P.A. Allen & P. Homewood). 8,199^219. ing of subducted continental lower crust in the Pyrenees. International Association of Sedimentologists, Blackwell J. Geol. Soc., 152, 217^220. Scienti¢c Publications, Oxford. Quinlan, G.M. & Beaumont, C.(1984) Appalachian thrusting, Johnson, D.D. & Beaumont, C. (1995) Preliminary results lithospheric £exure, and the paleozoic stratigraphy of the east- from a planform kinematic model of Orogen evolution, surface ern interior of North-America. Can. J. Earth Sci., 21,973^996. processes and the development of Clastic Foreland Basin Royden, L.H. (1993) Evolution of retreating subduction bound- Stratigraphy. In: Stratigraphic Evolution of Foreland Basins aries formed during continental collision.Tectonics, 12, 629^638. (Ed. by S.L. Dorobek & G.M. Ross), Spec. Publ. 52, 3^24. Simpson, G.H.D. (2006) Modelling interactions between Fold- Society of Economic Paleontologists and Mineralogists, Thrust Belt deformation, Foreland £exure and surface mass Los Angeles. transport. Basin Res., 18, 125^143, doi: 10.1111/j.1365- Jordan, T.A. (1995) Retro-arc foreland and related basins. In: 2117.2006.00287.x. Tectonics of Sedimentary Basins (Ed. by C.J. Busby & R.V.Inger- Sinclair, H.D. (1997) Tectonostratigraphic model for under- soll), 331^363. Blackwell Science, Oxford. ¢lled peripheral Foreland Basins: an Alpine perspective. Geol. Jordan, T. E . (1981) Thrust loads and Foreland Basin evolution, Soc. Am. Bull., 109, 324^346. Cretaceous,Western United-States. AAPGBull., 65, 2506^2520. Sinclair, H.D. & Allen, P.A. (1992) Vertical versus horizontal Kamp, P.J.J., Green, P.F. & Ti p p ett, J.M. (1992) Tectonic archi- motions in the Alpine Orogenic Wedge: stratigraphic response tecture of the Mountain Front-Foreland Basin transition, in the Foreland Basin. Basin Res., 4,215^232. South Island, New Zealand, assessed by ¢ssion track analysis. Sinclair, H.D., Coakley, B.J., Allen, P.A. & Watt s , A.B. Tectonics, 11,98^113. (1991) Simulation of Foreland Basin stratigraphy using a di¡u- Kamp, P.J.J. & Ti p p ett, J.M. (1993) Dynamics of Paci¢c Plate sion-model of Mountain Belt uplift and erosion ^ an example Crust in the South Island (New-Zealand) zone of oblique con- from the Central Alps, Switzerland.Tectonics, 10, 599^620. tinent-continent convergence. J. Geophys. Res.-Solid Earth, 98, Sinclair, H.D., Gibson, M., Naylor, M. & Morris, R.G.(2005) 16105^16118. Asymmetric growth of the Pyrenees revealed through measure- Karner, G.D. & Watt s , A.B. (1983) Gravity-anomalies and £ex- ment and modeling of Orogenic £uxes. Am.J.Sci., 305, 369^406. ure of the lithosphere at mountain ranges. J. Geophys. Res., 88, Sircombe, K.N. & Kamp, P.J.J. (1998) The South Westland 449^477. Basin: seismic stratigraphy, basin geometry and evolution of a Koop, W.J. & Stoneley, R. (1982) Subsidence history of the Foreland Basin within the Southern Alps Collision Zone, New Middle-East Zagros Basin, Permian to recent. Philos.Trans. R. Zealand.Te c t o n o p h y s i c s , 300, 359^387. Soc. Lond. Ser. A-Math. Phys. Eng. Sci., 305, 149^168. Stockmal, G.S., Beaumont, C. & Boutilier, R. (1986) Geo- Lihou, J.C. & Allen, P.A. (1996) Importance of inherited rift dynamic models of convergent margin tectonics ^ transition margin structures in the Early North Alpine Foreland Basin, from rifted margin to Overthrust Belt and consequences for Switzerland. Basin Res., 8,425^442. 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2 Ta n k a r d, A.J. (1986) On the depositional response to thrusting l tan apro and lithospheric £exure: examples from the Appalachian and Ahalf ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Rocky Mountain Basins. In: Foreland Basins (Ed. by P.A. Allen 2A 1 1 1 & P. Homewood). 8, 369^392. International Association of Se- ) l ¼ half ¼ H þ dimentologists, Blackwell Scienti¢c Publications, Oxford. tan apro 2tanapro tan apro tan aretro Tu r c o t t e , D.L. & Schubert, G. (2001) Section 3^17.In: Geody- namics Ed.by127.Cambridge,CambridgeUniversityPress. The total width of the pro-wedge is L 5 H/tanapro, Va n d e r Vo o, R., Spakman,W. & Bijwaard, H. (1999) Tethyan which is greater than l. Therefore the approximate hori- subducted slabs under India. Earth Planet. Sci. Lett., 171,7^20. zontal separation dx between the ridge crest and the con- Verge¤s, J. (1999) Estudi Geologic Del Vessant Sud Del Pirineu tact between the slabs, to minimise the gap between the Oriental I Central. In: Evolucio Cinematica En 3d (Ed. by Col- slabs, is given by: Leccio MonografiesTecniques, 7,194. Institut Cartogra¢c H dx ¼ L l ¼ l de Catalunya, Barcelona. tan a Verge¤s J. Marzo M. Santaeula'ria T. Serra-Kiel J. pro , , , , , , , , sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! Burbank, D.W., Munoz, J.A. & Gime¤nez-Montsant, J. 1 1 1 1 ¼ H þ (1998) Quanti¢ed vertical motions and tectonic evolution of tan a 2tana tan a tan a the SE Pyrenean Foreland Basin. In: Cenozoic Foreland Basins pro pro pro retro of Western Europe (Ed. by A. Mascle, C. Puigdefa' bregas, H.P. Luterbacher & M. Ferna' ndez), Spec. Publ. 134, 107^134. Geolo- gical Society of London. APPENDIX B: FRAMES OF REFERENCE Wh eeler, H.E. (1964) Baselevel, lithosphere surface, and time- The position of the pro-deformation front and pro-fore- stratigraphy. Geol. Soc. Am. Bull., 75,599^610. land basin margin in a chronostratigraphic diagram (black Whipple, K.X. & Meade, B.J. (2006) Orogen response to lines in Fig. 10) are di¡erent from those in the absolute changes in climatic and tectonic forcing. Earth Planet. Sci. Lett., 243, 218^228, doi: 10.1016/j.epsl.2005.12.022. frame of reference (red lines in Fig. 10). In fact, the posi- Willett S.D. tions of the pro-side chronostratigraphic fronts, , (1992) Kinematics and dynamic growth and pro change of a Coulomb Wedge. In: Thrust Tectonics (Ed. by XChronostratare in a di¡erent frame of reference to the ret- retro K. McClay), pp.19^31. Chapman & Hall, London. ro-side chronostratigraphic fronts, XChronostrat.Thisisbe- Willett, S.D., Beaumont, C.& Fullsack, P. (1993) Mechani- cause the pro-side chronostratigraphic fronts are cal model for the tectonics of doubly Vergent Compressional Orogens. Geology, 21, 371^374. pro retro X absolute X chronostrat Willett, S.D. & Brandon, M.T. (2002) On steady states in Mountain Belts. Geology, 30, 175^178, doi: 10.1130/0091- 7613(2002)030h0175:OSSIMBi2.0.CO;2. Willett, S.D., Fisher, D., Fuller, C., En-Chao,Y. & Lu, C.Y. (2003) Erosion rates and orogenic-wedge kinematics inTaiwan 70 inferred from ¢ssion-track thermochronometry. Geology, 31, +vt 945^948, doi: 10.1130/G19702.1. 60

Manuscript received 24 September 2007; Manuscript accepted 7 50 May 2008. 40

Model time (Myr) 30 pro APPENDIX A X chronostrat 20 The basis for this analysis is illustrated in Fig. 2c.This ¢rst order analysis assumes that the gap between the slabs is 10 minimised when the topography is shifted such that half 0 of the total topographic area is supported by each slab. Given the total topographic area, we can calculate half −500 −400 −300 −200 −100 0 100 200 of that value: Position of chronostrat fronts (km) Fig. 10. Demonstration of how the evolution of the basin margins H2 H2 as measured relative to a point on the stable craton can be A ¼ þ topo 2tana 2tana transformed into a stationary frame of reference, relative to the pro retro centre of the mountain belt.The black lines show the position of 2 H 1 1 the pro- and retro-deformation fronts and basin margins relative Ahalf ¼ Atopo=2 ¼ þ 4 tan apro tan aretro to their respective stable cratons, as measured by the stratigraphic record.The red lines show the position of the pro-side deformation front and basin margin relative to the core of the mountain belt. Because the pro-wedge has a larger area than the retro- The conversion between the two requires knowledge of the total wedge, we equate half of the total area to a triangle with amount of shortening that has occurred between the pro-side base length l and slope angle apro: craton and the mountain belt. See online version for colour ¢gure.

18 r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x Pro- vs. retro-foreland basins

3 measured with respect to a stable point on the pro-side Dr 5 rmantle rcrust 5 600kg m Density contrast craton while the retro-side chronostratigraphic fronts are 4D 1=4 measuredwith respect to a stable point on the retro-side cra- a ¼ ¼ 76 km Flexural parameter ton.Because the pro-side craton is moving towards the retro- gðrmantle rfilliÞ side craton at the regional convergence rate, the pro- and ret- ro-chronostratigraphic diagrams must be in a di¡erent frame M0 5 0 Applied end bend- of reference.This is not the case in the absolute frame of re- ing moment pro retro w(x, t)De£ectionofslab ference, XAbsolute and XAbsolute.Thus the mapping between the absolute frame and the chronostratigraphic frame is: q(x) Distributed load

pro pro XChronostratðtÞ¼XAbsolute ðtÞþvt Tectonic boundary conditions retro retro ðB1Þ 1 XChronostratðtÞ¼XAbsolute ðtÞ v 5 5.0 mm yr Regional convergence rate Assuming that the rate atwhich the position of the de- h0 5 5.0 km Accreted layer thickness (Implicit assumption that the retro-side layer formation front, XDF and basin margin pinchout point, thicknessisthesame.) XM migrate are small with respect to the regional conver- gence rate, the stratigraphic duration of the pro-foreland basin record and the depositional age of the sediments at Wedge and basin geometry the bottom of a well at its deformation front are coincident apro 51.51 The angle which the and given by the distance between its basin margins di- pro-wedges make wrt vided by the convergence rate: to the horizontal XM XDF aretro 5 2.51 The angle which the tprobasin ðB2Þ v retro-wedges make The age of the deepest sediments youngs towards the wrt to the horizontal 3 cratonic basin margin, re£ected in the onlapping stratigra- rtopo 5 r¢ll 5 rcrust 5 2700 kg m Assume that the den- phy.In contrast, the duration of the record held in the ret- sity of the upper crustal ro-foreland basin is given by the duration of the growth material is invariant. phase which can be calculated by determining how long it Hmax 5 3 km Height of drainage took to grow the entire system to steady-state: divide at end of the Asystem growth phase tretrobasin ðB3Þ vh0 H2 H2 Area under topo- Atopo ¼ þ The age of the deepest sediments is given by the total 2tanapro 2tanaretro graphic wedge duration because growth of the system started.These old- A Area above slabs and est sediments are spread across the entire retro-foreland ¢ll beneath zero de£ec- basin, except in the small region of onlap associated with tion datum, comprises the migration of the pinchout point. foreland basins and root of mountain belt Parameter List Asystem 5 Atopo1A¢ll Total cross-sectional Flexural parameters area of the simulated mountain belt E 5 70 GPa Young’s modulus Aaccreted The total amount of u 5 0.25 Poisson’s ratio material accreted from the underthrust plate Te 5 20 km Elastic thickness Flexural rigidity XM Position of basin margin X Position of deforma- D ¼ ET 3=12ð1 u2Þ¼5 1022 Nm DF e tion front 2 g 5 9.8 m s Acceleration due to tpro-basin Duration of pro-fore- gravity land basin record 3 rmantle 5 3300 kg m Mantle density tretro-basin Duration of retro- 3 rcrust 5 2700 kg m Crustal density foreland basin record

r 2008 The Authors. Journal compilation r 2008 The Authors, Basin Research, 10.1111/j.1365 -2117.2008.00366.x 19