Piggyback basin development above a thin-skinned thrust belt with two detachment levels as a function of interactions between tectonic and superficial mass transfer: the case of the Subandean Zone (Bolivia)

Tectonophysics 320 (2000) 45–67 www.elsevier.com/locate/tecto

Piggyback basin development above a thin-skinned thrust belt with two detachment levels as a function of interactions between tectonic and superficial mass transfer: the case of the Subandean Zone (Bolivia) P. Leturmy a, *,1, J.L. Mugnier a, P. Vinour a, P. Baby b, B. Colletta c, E. Chabron a a ESA CNRS 5025, Laboratoire de Ge´odynamique des Chaıˆnes Alpines, 15 rue Maurice Gignoux, 38031 Grenoble Cedex, France b ORSTOM, San Ignacio 805 y Humboldt, Apartado 17.11.6596, Quito, Ecuador c Institut Franc¸ais du Pe´trole, Rueil Malmaison, France Received 29 January 1999; accepted for publication 10 January 2000

Abstract The Subandean fold and thrust belt of Bolivia is characterised by two major detachment levels and large piggyback basins. ‘Sand-box’ and numerical models have been used to study sedimentation and erosion control on thrust belt evolution and to study the retroactive effects of tectonics on piggyback development in thin-skinned thrust belts with two detachment levels. Analogue models show that surface processes play a dominant role in controlling wedge evolutions: erosion promotes fault reactivation and tectonic delamination (passive roof duplex) while sedimentation promotes forward shifting of the frontal thrust and consequently piggyback basin development. Numerical models were used to understand the development of the Subandean fold and thrust belt of Bolivia. Numerical experiments show that the simultaneity of basement tilting and high sedimentation rates promotes the formation of a stable tectonic wedge. Outer and inner faults are alternately active during the beginning of deformation, a kinematic evolution that favours the development of piggyback basins between. The step-by-step history of the thrust belt predicts that each change in tectonic location is recorded with large unconformities in basins, but these unconformities are not well preserved from progressive erosion in the final geometry. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Bolivian Subandean Zone; duplex; piggyback basin; superficial processes; syn-sedimentary tectonics

1. Introduction Piggyback basins that develop above moving thrust sheets (Ori and Friend, 1984) constitute a record of tectonic activity and express mass transfer * Corresponding author. E-mail address: [email protected] (P. Leturmy) 1 Present address: De´partement des sciences de la Terre, Universite´ de Cergy-Pontoise, avenue du Parc, 8 Le Campus, Bat I, 95031 Cergy-pontoise Cedex, France.

by erosion/sedimentation. Surface processes are of great importance in the evolution of a thrust wedge when considered on a large scale (Barr and Dahlen, 1989; Beaumont et al., 1992; Willet, 1992). In the first part of this paper, the authors used analogue models to study the role of erosion/sediment processes on the kinematic evolution of a thrust belt at a smaller scale: do erosion and sedimentation control the sequence of thrust development in a thin-skinned thrust belt, and what is the retrocontrol of tectonics on piggyback basin develop-

0040-1951/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S0 04 0 - 1 95 1 ( 0 0 ) 00 0 2 3- 8

46

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

ment? This analogue approach consists of ‘sandbox’ models that have been scaled to obtain realistic mechanical behaviour compared to nature. Even though erosion/sedimentation processes are only crudely simulated in these models, they allow recognition of the impact of these processes on deformation style and propagation. Experimental conditions and final geometry of these modelling systems were presented in a previous short paper (Mugnier et al., 1997), and the present paper describes the evolutionary path during experiments and discusses how superficial conditions have to be introduced in a mechanical approach. In the second part, numerical experiments are used to study piggyback basin development. A numerical method, that only assessed the case of a single detachment level (Chalaron et al., 1995a) has been improved to study the case of piggyback basins that have developed above several detachment levels. Parameter values of these experiments have been estimated from the case of the eastern part of the Andean chain. This zone consists of a thin-skinned thrust belt, with several detachment levels, that developed synchronously with syn-orogenic sedimentation located either in a flexural trough (Flemmings and Jordan, 1989) or in large deep piggyback basins (Beer et al., 1990; Baby et al., 1995). This study recognises piggyback basins stages and interprets the organisation of sedimentary formations as a record of tectonic events. Numerical models provide a better simulation of the syn-tectonic erosion/sedimentation processes than analogue models since a physical law ( linear diffusion) is used to calculate the mass transfer along the surface of the thrust wedge, and a better description of a peculiar thrust belt is obtained by a trial-and-error fit of its geometry. The basic aim is not to reconstruct the exact geometry of the Subandean structure but to investigate interactions between sedimentary processes and tectonic movements and to understand piggyback basin development. For this purpose, the effects of parameter variations in the models are tested to identify those that control structural evolution. 2. Geological setting The Subandean Zone of Bolivia is a foreland fold and thrust belt (Oller, 1986; Roeder, 1988;

Sheffel, 1988; Baby et al., 1989, 1992), which forms the external zone of the Andean chain ( Fig. 1). This 140–150 km wide zone is bounded to the east by the present foreland basin (Chaco Plain and Beni Plain) and to the west by the CFP (‘Cabalgamiento Frontal Principal’), which separates the Subandean Zone from the Interandean Zone and Eastern Cordillera. Deposits involved in deformation consist of a nearly continuous Ordovician to Mesozoic series, overlain by Neogene sediments. This was relatively undeformed prior to 6 Ma, (Baby et al., 1995): a few anticlines only began growing in the Subandean zone, whereas thrust tectonics mainly occurred in the Eastern Cordillera from 21 to 9 Ma (Herail et al., 1996). Similar values have been computed in Northern Bolivia (Baby et al., 1997). After 6 Ma, structures are fault-propagation-folds, duplexes and back thrusts in the internal part of the Subandean Zone, and fault bend folds in the external part ( Fig. 2). Anticlines are separated by synclines more than 25 km wide, where more than 6000 m thick tertiary deposits have been preserved. Growth strata above fold structures in the Southern Subandean Zone show that strong sedimentation is synchronous with deformation, and the piggyback basins are separated from the foreland by very low ridges. An unconformity in the Tertiary sediments is inferred in the western basin of the Subandean Zone of North Bolivia (Fig. 2B). This may have been induced by deformation and could also mark the beginning of the piggyback basin stage. The average shortening velocity calculated from balanced-cross-sections is about 7 mm/yr in southern Bolivia ( Vinour, 1995). The variation from north to south in the thickness and lithology of the series leads to some differences in deformation style (Baby et al., 1989, 1995). In the northern part of the Bolivian Subandean Zone, two major detachments are observed, respectively, in the Ordovician formation and in the Devonian black shales (Baby et al., 1995). In the southern part, the basal detachment is located at the base of the Silurian formation, and several other detachments are located in the Devonian shales (Baby et al., 1992). The dip of the basal detachment slope is about 5° in the north, while it is only 2° in the south (Baby et al.,

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

47

Fig. 1. Tectonic and geological provinces map of Bolivia (from YPFB — ORSTOM convention, Baby et al., 1995). The Subandean zone represents the most external deformed part of the chain. AA∞ and BB∞ lines refer to the cross-sections on Fig. 2.

1989). The topographic slope of the Subandean belt varies from 1.4–1.7° in the north to 0.6–1.3° in the south.

3. Sandbox experiments Analogue sandbox experiments were performed to investigate the interaction between sedimentation, erosion and deformation. These experiments were performed at the IFP (Institut Franc¸ais du Pe´trole) by P. Vinour, P. Baby and B. Colletta.

3.1. Methodology, experimental set-up and scaling of the analogue models Modelling was performed in a normal gravity field with the ‘Structurator’ sandbox of the IFP. The small apparatus fits within the investigation field of an X-ray tomograph (medical scanner) located in this Institute (Colletta et al., 1991). Tomography is used to visualise cross-sections of the deformed model. Three sections (tomographic sections A, B, C on Fig. 3) were scanned at regular time steps. The central section B is shown (Fig. 4) because it is the least influenced by edge effects.

48

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

Fig. 2. Balanced cross-section of the Subandean Zone of Bolivia. See location in Fig. 1.

Fig. 3. Schematic diagram of the experimental apparatus. Three tomographic sections were performed for each of the steps presented on Fig. 4A–C to check the influence of borders on deformation location. Only the central section (tomographic section B) is shown.

49

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67 Table 1 Scales and velocities in analoguemodels andin theSubandean zone Parameter

‘Standard’ experiment

‘Syn-orogenic’ experiment

Erosion of the ‘synorogenic’ experiment

Equivalent of analogue models in nature

Subandean wedge

Mean thickness of the lower sand layer Mean thickness of the silicone layer Mean thickness of the upper sand layer Tilting velocity Initial length Shortening velocity Final shortening Superficial conditions

6 mm 2 mm 7 mm 5.7∞/h 29.1 cm 4 mm/h 8.43 cm No erosion — no sedimentation

6 mm 2 mm 7 mm 5.7∞/h 28.5 cm 4 mm/h 7.5 cm No erosion sedimentation

6 mm 2 mm 7 mm 5.7∞/h 28.7 cm 4 mm/h 7.8 cm Erosion sedimentation

3150 m 1000 m 3680 m 0.34°/ Myr 150 km 7 mm/yr 42 km

Basal friction (glass micro beds) Internal friction (sand)

0.36 0.58

0.36 0.58

0.36 0.58

0.36 0.58

2400 m 600 m 3200–4800 0.34°/ Myr 100–200 km 4–7 mm/yr >40 km Weak erosion strong sedimentation ? ?

The rectangular apparatus consists of a rigid basal plate bordered with three fixed walls and one moving wall. A motor pushes this wall at a velocity varying between 0.1 and 1000 mm/h. Another motor lifts and tilts the basal plate. The two moving plates provide a means of shortening the model and simulating basement tilting. The domain analysed with the scanner (hashed domain of Fig. 3) does not include the zones where the side walls influence the development of the shortening structures. X-ray tomography was applied at regular steps of shortening during each experiment in order to visualise different layers that have different radiological densities. Furthermore, deformation in the shear zone creates a local dilatancy zone, and this induces a decrease in density making it possible to recognise faults with the X-ray method. Scaling laws for brittle/ductile experiments have already been published and tested (Mulugeta, 1988; Cobbold et al., 1989), and the approach discussed by Richard (1991) is applied ( Table 1). The key parameter in scaling analogue models is the ratio between viscosity of rocks and viscosity of silicone. Considering a viscosity of about 1019 Pa for sedimentary rocks (van Keken et al., 1983), the ratio for viscosity is then 7.5×10−16. The scale ratio between our models and natural examples are, respectively, 2×10−6 for length (1 cm in the experiments represents 5 km in nature), 4×10−10 for time (1 h of experiment time

represents about 285 000 yr), and 5×103 for shortening velocity (an experimental displacement rate of 4 mm/h represents a shortening rate of 7 mm/yr in an orogenic belt). 3.1.1. Initial condition and simulation of sedimentation and erosion In its initial state, the model is composed of three layers of granular material and one layer of viscous material. From bottom to top, the materials include one glass micro bead layer for the basal de´collement, one sand layer for the lower competent series, one layer of silicone for an intermediate de´collement, and one sand layer for the upper competent series. This succession is analogous to the Silurian black-shales, Silurian/Devonian sandstones, Devonian shales and Carboniferous/ Mesozoic sandstones that form the sediment pile of the southern part of the Subandean zone of Bolivia. Sand exhibits Coulomb behaviour (Byerlee, 1978) and is used to simulate brittle rocks. In this material, rupture appears along a shear plane comparable to a fault plane. Silicone putty (SMG 36 from Dow Corning) is a viscous material used to simulate de´collement levels characterised by a weak strength. It exhibits Newtonian behaviour with the range of strain rates used in the modelling system used here (see below). Its characteristics include a density of 0.965, a radiological density

50

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

A Fig. 4. Scanner view of the geometry of the experiments performed with tilting of the basement (see text for the experimental conditions and description of the major points of the evolution). (A) Experiment performed without erosion and without sedimentation. (B) Experiment performed without erosion and with sedimentation. (C ) Experiment performed with erosion and with sedimentation.

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

B Fig. 4. (continued )

51

52

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

C Fig. 4. (continued )

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

of +100 HU, and a dynamic viscosity of 5×104 Pa. Sedimentation is reproduced by the deposition of pyrex and sand layers. These two materials were superimposed in alternating layers because they have approximately the same brittle behaviour but a different radiological density which differentiates them on the tomographic images. Sedimentation rate in the continental foreland basin is mainly controlled by basement subsidence, and the following process is used to simulate basin filling: (1) the flexure of the foreland lithosphere has a long wavelength and is reproduced by tilting the rigid basal plate; (2) the altitude of the top of the fill is the altitude of the external lateral border of the model. The scaling of the sedimentation rate obeys the same equations as the scaling of a shortening velocity (Richard, 1991), and a 0.5 mm/h sedimentation rate in the model represents a natural sedimentation rate of 0.87 mm/yr. Erosion is simulated by removal, at regular intervals, of the materials forming the relief above a defined altitude, which is 0.5 mm above the sedimentation level in the experiment with erosion and sedimentation. 3.1.2. Reproducibility of results Numerous experiments have been performed since the initial presentation (Colletta et al., 1991) of the sandbox model at the Institut Franc¸ais du Pe´trole (IFP). Their reproducibility depends on the construction precision of the layered sequence: initial thickness irregularities promote the nucleation of ramps and could affect the reproducibility. Therefore, the influence of subtle undulations ( less than 0.5 mm) that may occur in the silicone layer is always analysed. If the cylindricity of the structures is preserved above non-cylindrical irregularities, their effect is negligible and the result considered reliable. This test is easily performed as the deformation box is longer along the strike direction than along the shortening direction and as the X-ray scanner gives a continuous 3-D view with a precision better than 0.3 mm. 3.2. Results Three experiments were performed to investigate erosion, sedimentation and tectonic inter-

53

actions: one experiment was conducted with basement tilting, without erosion and without sedimentation; one with basement tilting, with sedimentation and without erosion and one with erosion, with sedimentation and with basement tilting. The progressive deformation and the final geometry of the three models are recorded and can be compared. 3.2.1. Duplex development In the final geometry of the three experiments, the two sand layers are always deformed differently. The shear zones (dilatancy zones) that cross the sand layers are narrower in the lower level than in the upper level, though the materials are identical. In the upper level, in the early stages of deformation, the dilatancy zone correlates to the limbs of detachment folds, before development of narrower and more intensively deformed shear zones. The lower sand layer accommodates the shortening with the formation of a duplex in which the number of horses varies between six and eight. This structure is linked to the two superimposed de´collements. Growth of new horses in the duplex is forward, but reactivation occurs frequently in the internal part of the structure. The duplex stack geometries are not exactly the same from one experiment to the next, because it is difficult to reproduce exactly the same initial geometry each time, and because deformation in the uppermost level is accommodated differently for each experiment. 3.2.2. ‘Standard’ experiment (Fig. 4A) As mentioned before, a duplex is formed in the lowermost brittle layer. In the first stage, the duplex deformation is accommodated with a passive roof backthrust at the base of the uppermost sand level. After 3.6 cm of shortening, deformation is also accommodated with symmetrical folds above thrusts in the upper sand level. The first structure is a vertically propagating ‘pop-up’, that is locked when the structural thickness above the de´collement is nearly twice the stratigraphic thickness; then, another structure forms forwards. In the final geometry, for 7.6 cm of shortening, three folds are well developed. The final geometry pres-

54

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

ents regularly spaced anticlines. Shortening is accommodated by a duplex in the lowermost brittle layer and by three regularly spaced pop up structures and a passive backthrust in the uppermost layer. 3.2.3. ‘Syn-orogenic wedge-shaped basin’ experiment (Fig. 4B) In this second experiment, syn-orogenic sedimentation is added to fill the basin, the subsidence of which is controlled by the tilting of the basement. Sedimentation is added manually and regularly to fill holes. As in the first experiment, deformation in the lowermost sand layer is accommodated by a duplex. In the uppermost layer, the first stage is characterised by a passive backthrust, which rapidly becomes inactive after 1.3 cm of shortening. Deformation is then accommodated by thrust structures. For about 5.2 cm of shortening and 1.4° of basement tilting, the deformation propagates forwards to the edge of the syn-tectonic sediments where a pop-up forms. This structure is superimposed on an irregularity of the initial geometry. The lateral extension of the pop-up and its cylindricity show that its development is independent of the initial undulation. Moreover, its location, close to the external border of the model, suggests that it is only the size of the sandbox that prevents a greater external propagation of the de´collement. After this stage, simultaneous sedimentation and thrusting promote the fault-propagation-fold process in the hanging wall of the external sheet of the duplex ( Tondji Biyo, 1993). This fault-propagation-fold process is reflected in an out-of-sequence thrusting in the shortened belt. During the last part of the experiment, a rise in the external structure and an out-of-sequence reactivation above the external sheet of the duplex take place alternately. In the final geometry, shortening is accommodated in the lowermost layer by a duplex and in the uppermost layer by three irregularly spaced thrusts. 3.2.4. ‘Erosion of the syn-orogenic wedge-shaped’ experiment (Fig. 4C) The third experiment is similar to the second, except that erosion is also simulated. This erosion

is applied in a regular way, removing all topographical features above a fixed altitude. In this experiment, lowermost layers accommodate shortening with a duplex, whereas the superficial layers accommodate shortening with one thrust above the duplex (occurring at 1.3 cm of shortening) and two backthrusts located above the duplex (occurring at 2.7 and 3.5 cm of shortening). The uppermost structures are eroded, and the unique structure observed at the end of the experiment is a passive roof duplex. Numerous reactivations in the duplex cause a complex geometry of the thrust sheets. 3.3. Summary: the role of superficial mass transport in the thrust wedge equilibrium 3.3.1. Mechanics of the thrust wedge The mechanics of the fold and thrust belt has been described by the use of the wedge theory (Chapple, 1978). Initial work assumed plastic behaviour, but further studies have been performed (Davis et al., 1983; Malavieille, 1984; Zhao et al., 1986; Lallemand et al., 1994; Williams et al., 1994) and show that the critical wedge-shaped geometry of a thrust belt is a useful concept whatever the inferred rheology. The analytical work of Davis et al. (1983) and Dahlen et al. (1984) popularised the Coulombwedge theory and gives a framework for the presentation of the wedge theory, which has already been tested by analogue modelling (Liu et al., 1992; Storti and McClay, 1995; Gutscher et al., 1996). Physical parameters (density, r, cohesion, C , internal friction coefficient, m, basal friction 0 coefficient, m and the pore fluid ratio in the wedge, b l) and geometrical parameters (dip of the basal detachment, b) define a range of stable surface slopes (a) ( Fig. 5, adapted from Davis et al., 1983) of a shortened Coulomb wedge. Three cases are found: (1) the wedge is undercritical and thrusts are active to thicken the wedge until it reaches the lower critical condition for the stability of the wedge; (2) the tectonic prism is in the stable domain and moves above the basal detachment; and (3) the wedge is over the upper critical profile. Superficial mass transport affects the surface

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

55

Fig. 5. Equilibrium Coulomb wedge theory. The physical parameters of the wedge (density, cohesion, internal and basal friction angle, fluid pressure/lithostatic pressure ratio) and the geometrical parameters (topographical slopes, basal de´collement slope) govern the stress field within the wedge. When the entire wedge is on the verge of failure, a critical profile is predicted (Dahlen et al., 1984).

slope of the growing wedge and therefore the thrust system development. The respective influences (Fig. 6) of internal thickening (arrow 1a), of

Fig. 6. Conceptual graphic showing the effects of changes along the boundaries (topographical slope and basal de´collement dip) of a Coulomb wedge. The arrows reflect respectively the following evolutions: 1a: thickening increases the surface slope, and transforms an undercritical wedge into a stable wedge; 1b: tilting of the whole wedge decreases the surface slope and increases the basal dip by the same value; therefore it has little effect on the stability of the wedge; 2a: basement tilt increases the basal slope, whereas sedimentation maintains the surface slope at zero; these two phenomena change an undercritical wedge into a stable wedge; 2b: development of local relief above the frontal ramp momentarily induces a surface slope that dips toward hinterland and locks the displacement along the basal de´collement; 3: erosion decreases the surface slope and changes a stable wedge into an undercritical wedge.

basement tilting (arrow 1b), of sedimentation (arrow 2a), of the local topographical bump (arrow 2b) and of erosion (arrow 3) are symbolised in an (a, b) graph. 3.3.2. Evolutionary path of analogue models For the analogue models described above, the strain velocity in the viscous silicone layer controls the shear stress along the basal surface, the nucleation of ramps, the propagation of de´collement along the weak layers and the partitioning of displacement within the thrust system. Furthermore, the superimposition of two weak layers induces a more complex deformation pattern than an ideal critical wedge. None the less, the graph in Fig. 6 still accurately describes the interplay of the different phenomena. Evolution of the ‘standard’ model (Fig. 4A) is as follows: in the first stage of deformation, the topographical slope of the wedge is lower than the minimum critical slope, the back-thrust and duplex are then active to thicken its internal part and increase the surface slope. When the structural thickness has increased, the high shear stress along the de´collement induces a high strain velocity in the viscous layer that propagates deformation toward the external zones (arrow 1a on Fig. 6). The simultaneous tilting does not significantly affect this evolution, as it simultaneously decreases a and increases b, an (a, b) evolution rather parallel to the curve that limits the domain of stability (arrow 1b on Fig. 6). Tilting of the base-

56

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

ment and deposition of orogenic sediments in the second experiment ( Fig. 4B) thicken the wedge and increase the dip of the basal de´collement. When the taper of the wedge reaches the stable domain thanks to the syn-orogenic sediment wedge (arrow 2a on Fig. 6), de´collement propagates below this wedge, and structures appear in the more external part of the model. The development of a local relief above a ramp induces a surface slope dipping towards the back-stop (arrow 2b on Fig. 6). Displacement along the basal de´collement stops if the backward slope is large enough. Such a slope toward hinterland only appears momentarily, as sedimentation fills the basin behind the anticline. Therefore, the wedge alternates between an undercritical state and a stable state, and there is a succession of out-of-sequence thrusting and frontal displacement (Chalaron et al., 1995b).

Erosion prevents (Fig. 4C ) the wedge from reaching the minimum critical equilibrium in its internal part (arrow 3 on Fig. 6): in spite of the formation of the duplex and the activation of the back-thrusts, the structural thickness is constant, due to removal of material by erosion. In this case, deformation does not propagate towards the foreland, and a large syncline forms in front of the external part of the duplex. 3.3.3. Thrust system as a function of sedimentation and erosion Analogue models (Baby et al., 1995; Storti and McClay, 1995; Mugnier et al., 1997) suggest rules that link the thrust system geometry to conditions of subsidence, sedimentation and erosion. When the subsidence is controlled by the progressive increase of basement dip during tectonic move-

Fig. 7. Comparison of the final geometry of the experiments performed with erosion and sedimentation: (A) the syn-orogenic wedgeshaped basin is controlled by tilting the basement; (B) the pre-orogenic wedge-shaped sediments with no basement tilting and a regular sedimentation rate (from Baby et al., 1995).

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

ments, the wedge-shaped syn-tectonic sediments ( Fig. 7A) are a factor favouring forward tectonic propagation. This propagation occurs by a forward shift of the deformation front and delineates a piggyback basin. In the case of a pre-orogenic wedge-shaped-sediment pile, an initial horizontal surface may allow the de´collement to propagate below the pre-orogenic wedge (Fig. 7B) at the beginning of the shortening event, leading to an early development of a piggyback basin. In this case, equilibrium conditions of the wedge are preserved and movement along the external part of the de´collement occurs even when erosion affects the relief above the duplex. Constant subsidence does not influence propagation but creates available space to catch sediments either in the foreland basin or in the piggyback basin ( Fig. 7B). In the case where tectonics plays a dominant role compared to superficial processes, the wedge develops with a regular prograde sequence. In the case where superficial processes are significant with respect to tectonic movements, the wedge does not develop so regularly because of the change created in the topographical slope and in the thickness of the sedimentary pile. A numerical approach has been developed and used to apply these basic rules to complex thrust systems.

4. Numerical modelling Numerical development has been performed to obtain a better understanding of the deformation of a wedge subjected to varying conditions applied along its boundaries. This is used to study the evolution of the Subandean thrust system of North Bolivia (Fig. 2B). 4.1. Method The method already developed by Chalaron et al. (1995b) is briefly presented below, and the new developments are highlighted. This model is based on: 1. the incorporation of discontinuities in the critical wedge model; 2. a kinematic forward model of serial cross-

57

sections describing the displacement of sheets above flat and ramp thrusts; 3. tilting of the basement beneath the basal de´collement; 4. a linear diffusion model that simulates superficial transport (erosion, sedimentation). 4.1.1. Equilibrium of any thrust wedge Any portion of a thrust wedge, defined by its geometrical and mechanical parameters, can be compared with the critically tapered wedge solution. For this purpose, the following procedure is used. To determine the ratio of shear and normal stresses along the basal plane, the critically tapered wedge equation is transformed into a ‘frictional function’ (Chalaron et al., 1995b): m

(a, b, H, l, S , w) 0 (a+b) (1+(1−l)K )+Q(S /rgr) cot w−b 0 , = 1−l (1)

bc

where g is the acceleration of gravity, r, C and w 0 are, respectively, the density, cohesion and internal friction angle of the sediments in the wedge, m is b the coefficient of friction along the basal surface, l is the ratio of fluid pressure to lithostatic stress (P /s ), a is the local topographical slope, b is the f n dip of the basal de´collement, H is the thickness, and r and (a+b) are the cylindrical co-ordinates for the studied portion of the wedge. K and Q are two mathematical coefficients [ from eqs. (18a) and (18b) of Dahlen et al., 1984]. The value of the ‘frictional function’ is compared with the friction coefficient of the basal plane ( m ) to determine where slippage is likely to b occur. This method is similar to that of Liu and Ranalli (1992). For a critically tapered wedge, m b equals m . If m >m , fractures occur in the wedge, bc b bc but shear stress along the de´collement does not exceed the basal friction. This portion of the wedge is undercritical, and there is no slippage beneath it. It is located in the left-lower domain in an (a, b) plot (Fig. 6). If m
58

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

4.1.2. Discontinuities in the critical wedge model A prismatic shape is predicted when every point of a given wedge is on the verge of failure (Dahlen et al., 1984), whereas both in nature and in sandbox models (Mulugeta, 1988), prismatic shapes are obtained by displacement along thrusts. In order to approach this discontinuous brittle behaviour, the present study simulates the deformation of the wedge by confining displacement along several discrete faults. If the parameter values are chosen to match specific conditions, such as those studied by Huyghe and Mugnier (1992) or Chalaron et al. (1995b), the stress field calculated in a homogeneous material can none the less be applied to a material with localised anisotropic zones (Chalaron et al., 1995b). 4.1.3. Forward kinematic modelling Forward kinematic modelling methods (Platt, 1988, 1990; Endignoux and Mugnier, 1990) allow the evolution of a thrust system to be described. Discontinuities are pre-defined in the initial geometry. The sheets are deformed during displacement using a simple vertical shear method (Jones and Linsser, 1986). The amount of displacement at each increment is equal to the size of the cells to match nodes. The frictional function along the basal surface is calculated to locate the tip of the basal de´collement (between the most internal part of the undercritical domain and the stable domain of the wedge), and displacement occurs along the outermost ramp branched on the part of the de´collement where slippage occurs (Chalaron et al., 1995b). This code has been modified to study structures as complex as the Subandean thrust wedge of north Bolivia, where active ramps transfer displacement from one detachment level to an upper detachment and delineate duplexes. Furthermore, it has been assumed that displacement along ramps of the duplex does not exceed the length underneath the duplex, i.e. the duplex forms an antiformal stack (Boyer and Elliott, 1982). 4.1.4. Basement tilting An elastic flexural model can be used to describe the geometry of the continental lithosphere as being bent with a wavelength of several hundred

kilometres ( Turcotte and Schubert, 1982; Karner and Watts, 1983). Given the size of the studied wedge, it is considered, as a first approximation, that the effects of the lithospheric flexure induce a tilt of the basement beneath the wedge. The kinematics of the basement is therefore defined by one parameter, which is the rotation velocity around an axis situated on the external border of the model. 4.1.5. Superficial short range transport Two- and three-dimensional models have already been proposed to take into account erosion and sedimentation during thrust tectonics (Moretti and Turcotte, 1985; Flemming and Jordan, 1989; Beaumont et al., 1988, Beaumont et al., 1992; Hardy et al., 1998). Todten (1976) proposed that erosion is mainly controlled by local slope. The cumulative effects of surface transport are represented as a linear downslope diffusion of the material volume. If Ks is the transport coefficient (in m2/yr), the horizontal flux, s, is related to the local slope, Vh, by: s=−KsVh.

(2)

The diffusion equation is a good approximation for hillslope erosion but is less correct for competent layers resistant to erosion. Beaumont et al. (1992) presented a study of superficial transport based on several algorithms. The diffusion algorithm used in this study (Chalaron et al., 1995a,b) basically represents the cumulative effects of processes (soil creep, rainsplash, earthflows, landslides and rockfalls) that remove materials from hill and mountain sides and transport them to the valleys (Carson and Kirkby, 1972) along which they need to be relayed by long-range fluvial transport (Beaumont et al., 1992). None the less, hillslope erosion is the less effective phenomenon in the succession of processes involved in erosion and controls the solid discharge in the rivers (Souriau, 1995). Although, on short time scales, the distribution of mass movement of the hillslope processes is quite different, on the long time scale, used in the model, mass is distributed over a short distance, and this depends on the local slope. This law does not allow the orogen shape to be reproduced, but it is useful for examining the limits of

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

elevation (Leturmy et al., 1995) and of the general surface slope as a function of tectonic uplift and is used to illustrate the effects of erosion and sedimentation controlling tectonic activity. This study focuses on ramp anticlines and piggyback basins, and the iterative use of the 3D-diffusion model gives a first-order solution for the syntectonic superficial transport in these restricted areas.

59

4.2. Application of the model: estimation of parameter values

account in the numerical experiments and demarcate the 13 pre-defined discontinuities of the initial state of the model ( Fig. 8A). They are located between the CFP to the east and Snia Chine to the west on Fig. 2. Five of them constitute the internal antiformal stack, three others form the duplex under the Liquimuni anticline, and five are emergent thrusts. Because the three most external thrusts are active only during the latest period of deformation and post-date sediment deposits in piggyback basins, they are not modelled.

4.2.1. Initial state geometry In North Bolivia, structures are almost cylindrical. Therefore, a 2-D approach has been used along a cross-section perpendicular to the trend of the belt. Balanced cross-sections ( Fig. 2B) based on seismic lines, field data, and drilling data (Baby et al., 1995) and restoration techniques give the initial geometry of the different sheets comprising the wedge. This part of the Bolivian Subandean Zone is characterised by three main de´collement levels leading to the formation of two duplexes: one in deep formations (Ordovician and Silurian) beneath the internal part of the Subandean Zone, and the other in intermediate levels (Devonian to Cretaceous), beneath the Liquimuni anticline. Most of the ramps in the duplexes dip toward hinterland, but forward dipping thrusts have also been found in exploratory holes. To restrict the modelling complexity and to focus the work on the piggyback basins (in grey on Fig. 8), only 13 thrust sheets are taken into

4.2.2. Mechanical parameters The density of sediments varies, from drilling data, between 2500 kg/m3 for the Tertiary syntectonic sediments, and 2650 kg/m3 for the Palaeozoic formations. This latter value is used. Cohesion for the rocks of the thrust wedge is in the range of 5–20 MPa for sedimentary rocks (Dahlen et al., 1984). For a thick wedge (h= 15 km), the variation in the slope value is around 0.5° for a cohesion parameter varying between 5 and 20 MPa ( Fig. 9A), whereas the variation in the slope is more than 2° for a thin wedge (h= 2.5 km). In the Subandean belt of Bolivia, there are no data with which to estimate the cohesion. An arbitrary cohesion value of 5 MPa has been taken, a choice that has little influence on the modelling process because the thickness of the Subandean belt of north Bolivia varies from 10 to 15 km. The three parameters (m, m , l) have been b considered as a function, F, of the topographical

Fig. 8. Initial condition used in the numerical model, and obtained by restoration of the balanced cross-section of the Subandean Zone of North Bolivia.

60

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

Fig. 9. (A) Topographical slope of a wedge in the stable domain as a function of wedge cohesion and thickness. The slope is plotted on the y-axis, the cohesion on the x-axis and each curve is calculated for different wedge thicknesses and constant mechanical parameters (r=2650 kg/m3, m=0.85, m =0.7, l=0.6, b=5°). (B) Estimated solution of mechanical parameters (l, m, m ) for a critical b b wedge defined by a 1.5° topographical slope and a 5° basal de´collement dip (r=2650 kg/m3; C =5 MPa). l, m, m are, respectively, 0 b the fluid pressure to lithostatic stress ratio, the coefficient of friction along the basal de´collement and the internal coefficient of friction. The grey plane is the domain for l=0.6 and its intersection with the gridded surface gives the ( m, m ) values to reach a critical wedge b with a 1.5° topographical slope and a 5° basal de´collement.

slope and basal de´collement dip, from the analytical solutions of Dahlen et al. (1984). The set of solutions of ( m,m , l)=F (a, b) depicts a surface b in a ( m, m , l) space. The sets of l, m and m used b b to model the Subandean belt of north Bolivia (mean topographical slope estimated at 1.5° and a basal de´collement dip estimated at 5°) are shown by a net on Fig. 9B. Similarly, a set of solutions has been determined for the cross-section of the southern part of the Subandean belt characterised by a topographical slope that ranges between 0.6 and 1.3° and a basement slope close to 2°. The tapers of the southern and northern Subandean belts of Bolivia are clearly different, and their mechanical parameters are also different. These differences could be linked to the lithology of basal de´collement levels that are formed in the south by the Silurian blackshales and in the northern part by the Ordovician arenaceous lutites. Alternatively, Williams et al. (1994) studied the Andean mountain belt and found that the Subandean belt represents the frictional toe of a brittle–ductile critical taper wedge. They proposed a basal coefficient of friction, m =0.6, an internal b coefficient of friction m=0.84, and a fluid pressure

ratio, l=0.5. This small value of m is assumed to b be related to a fluid pressure ratio along the de´collement higher than the fluid pressure ratio in the wedge ( Williams et al., 1994). A variation in fluid pressure from south to north cannot be excluded as the taper of the wedge differs considerably from north to south. The experiments described in this study were performed with the following mechanical parameter values: r=2650 kg/m3, C =5 MPa, m=0.85, m =0.7, 0 b l=0.6.

4.2.3. Shortening and tilting velocity The tilting of the basement coeval with the sedimentation is evaluated from the geometry of the sedimentary sequences in the foreland basin and from the restoration of syntectonic basins. The difference between the dip of the basal de´collement on the restored cross-section at 10 Ma and the present dip of the basal de´collement is 3.4°. Therefore, a tilting velocity close to 0.34°/Ma has been calculated. The total amount of shortening is close to 40 km for the 13 internal sheets, and the shortening velocity close to 7 mm/yr. The 40 km shortening has been divided into 80 steps:

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

each step is then related to a shortening of 500 m that occurs in 71 500 yr. 4.2.4. Transport coefficient The respective influence of time-dependent parameters has been studied in the case of a simple tectonic system consisting of a single ramp anticline (Leturmy et al., 1995). It is found that Ks is not an intrinsic physical characteristic, but rather includes a characteristic length scale ( Turcotte, 1992). This scaling effect agrees with the selfsimilarity properties of topography. Therefore, care has to be taken that the size of cells used to describe the whole structure influences the value of the transport coefficient. Different values for the transport coefficient (Ks) have been tested, and those that induce basins filled with more than 6000 m of syntectonic sediments are retained. Leturmy et al. (1995) have found a transport coefficient of 60–100 m2/yr for a single anticline studied with 250 m size cells. Therefore, the lowest tested value is 100 m2/yr. As analogue models suggest that the Subandean zone corresponds to a tectonic wedge where sedimentation is the dominant factor, i.e. part of the sediment volume comes from outside the wedge, two types of experiments were performed: one assuming no input of sediments at the boundary of the model, and one assuming a sediment input deduced from Eq. (2) applied to a topography with a slope close to that of Eastern Cordillera. 4.3. Results: influence of variations in timedependent parameters In the following paragraph, some of the experiments conducted will be presented. Mechanical parameters are constant, and time-dependent parameters (tilting velocity and transport coefficient) vary. 4.3.1. Model with no superficial transport (Fig. 10A) This experiment is performed with no superficial processes and a regular tilting of the basement (0.34°/Ma). The final geometry (Fig. 10A) is characterised by the presence of two large synforms. The internal synform is located ahead of the deep

61

duplex and is limited forwards by the development of a relief above the intermediate duplex. The second synform is located ahead of the intermediate duplex, and is limited forwards by the frontal anticline. 4.3.2. Model with low superficial erosion transport efficiency (Ks=100 m2/yr, Fig. 10B) A value of Ks=100 m2/yr reduces the height of relief and fills the synforms compared to the previous experiment. The addition of sedimentation processes changes the thrust sequence: after 30 steps of shortening (2.14 Ma), a large piggyback basin forms and thrusts above a more external basin formed at the beginning of the experiment. The final geometry shows a topographical slope of 2.6° and two basins: the internal basin is filled with 4000 m of sediments, and the external basin is thinner (2000 m of sediments). 4.3.3. Model with high superficial erosion transport efficiency (Ks=500 m2/yr, Fig. 10C) In this experiment (Fig. 10C ), the thrust sequence diagram shows in a first stage that the wedge oscillates near the lower boundary of the stable domain during the 35 first steps (near 2.5 Ma); the most internal sheet and the detachment are alternately active. Then, sheets number 6, 5, 3 and 1 are active in a retrograde thrust sequence. None the less, out-of-sequence thrust reactivation represents 8.8% of total shortening. The final geometry is characterised by two large piggyback basins filled with 4300 m of sediments for the internal one and 6000 m for the external one, and the topographical slope is 1.4°. 4.3.4. Model with high superficial erosion transport efficiency, and sediments coming from an internal part of the chain (Fig. 10D and E) Two experimental runs were performed with two different Ks values of 500 and 1000 m2/yr. At the rear of the model, a virtual topography was added to simulate sediments coming from an inner part of the chain. For a Ks value of 500 m2/yr ( Fig. 10D), the virtual topography at the rear is 1.7°; The propagation sequence is not strongly influenced by the sediment influx from the internal part of the chain.

62

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

Only a few details differentiate this experiment from the previous experiment with the same Ks value and no virtual topography (out-of-sequence reactivations represent only 3.75% of the total shortening in this case). There are also two piggyback basins of similar sedimentary thickness (4100 m in the internal one and 6100 m in the external one). The foreland basin is more extensive than in the other experiments, but its thickness is still lower than in the natural basin. In the second case, Ks is 1000 m2/yr (Fig. 10E), and the virtual topography slope is 3°. From the beginning of deformation until 2.85 Ma, the wedge oscillates around the minimum critical taper. After 2.85 Ma (40 steps of deformation), the superficial processes and sediment influx strongly modify the thrust sequence: the backward sequence is reduced, thrust 1 is more active, and the intermediate thrust moves later. Three piggyback basins are observed. The two most internal ones in the final state form only one basin until an intermediate ramp anticline separates them. The foreland basin is well developed, but the topographical slope of 2.3° is too high compared to that of the natural wedge. 4.3.5. Model with a high superficial transport efficiency, no sediments coming from the internal part of the chain and no tilting of the basement (Fig. 10F) This experiment was performed with a Ks value of 500 m2/yr. The thrust sequence shows that the internal sheet moves during 50 steps (3.5 Ma). After this stage, a forward sequence occurs with some out-of-sequence reactivations (7.5% of the shortening). The final geometry (Fig. 10F ) is characterised by many basins. In the 50 first steps, only

63

two basins are present: a piggyback basin moved on the back of the internal sheet and a foreland basin. After 3.5 Ma, the piggyback basin separates into two basins with intermediate thrust activation, and a part of the foreland basin is incorporated into the thrust belt. The lack of tilting of the basement promotes a higher sedimentation rate in the foreland basin and inhibits sedimentation in the piggyback basins. 4.3.6. Summary A high rate of sediment removal associated with a progressive basement tilting allows a stable wedge to develop. This induces oscillation of the wedge around the lower critical profile during the first half of each run, and only the external and the internal thrusts are active. During the second part of the runs, other thrusts are active in a retrograde sequence. However, a small rate of sediment removal activates the external and internal sheets for almost the entire experiment. The presence of two major de´collement levels and a third minor level is of great importance in the location of piggyback basins because they produce duplexes. These structures deform the above-thrust sheets and produce bumps that form the piggyback basin borders. The addition of sediments from an inner part of the chain changes the morphology of the wedge (increases the topographical slope) but does not significantly affect the thrust sequence for at least half of the experiments. The influence of those sediments is only visible for a high Ks value (experiment with Ks=1000 m2/yr). In this case, deformation accommodates the change in sediment volume only after 40 steps of deformation, showing

Fig. 10. Final cross-sections with thrust numbers and synorogenic sediments in grey. Thrust propagation sequences of the experiments are shown on the right; the number of the active thrust sheet is presented along the vertical axes; time (number of increment of shortening) is along the horizontal axes. Results of the calculation are plotted for every increment, the horizontal line refers to a permanent displacement along a single ramp, and the ‘teeth’ pattern refers to the out-of-sequence reactivation. In the thrust sequences, movement of the basal sheets forming the duplex is not shown. Common parameters are: r=2650 kg/m3, C =5 MPa, m=0.85, 0 m =0.7, l=0.6, shortening velocity=7 mm/yr. (A) Experiment carried out with a tilting velocity=0.34°/Ma and without superficial b processes. (B) Experiment carried out with a tilting velocity=0.34°/ Ma and Ks=100 m2/yr. (C ) Experiment carried out with a tilting velocity=0.34°/Ma and Ks=500 m2/yr. (D) Experiment carried out with a tilting velocity=0.34°/ Ma and Ks=500 m2/yr; a topography at the back of the model is added to simulate sediments coming from the internal part of the chain. ( E ) Experiment carried out with a tilting velocity=0.34°/Ma and Ks=1000 m2/yr; a topography at the back of the model is added to simulate sediments coming from the internal part of the chain. (F ) Experiment carried out with no basement tilting and Ks=500 m2/yr.

64

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

that changes in the morphology need to be very large to influence deformation. These numerical runs show that sediment volume is less important than the geometry and the volume of hollows to fill.

4.4. Results: the best fit The best fit between the final geometry of the runs ( Fig. 10) and the target geometry of the Subandean belt (Fig. 8) is obtained for a high value of Ks (500 m2/yr). With this value, the two internal basins are almost the same size as the Subandean basins, but there is less sediment in the external part of the model than in the real foreland basin ( Fig. 11). This experiment is also in accord with the Rock-Eval analysis on Permian rocks (Moretti et al., 1996) of the El Pelado anticline of the northern cross-section ( Fig. 2A). These rocks show an immature pattern, indicating that the anticline has never been buried under Tertiary sediments. In numerical experiments, the internal sheet (number one) is the equivalent of El Pelado anticline and has been active since the beginning of deformation. The two piggyback basins have distinct evolutionary features ( Fig. 11B). The external one evolves as a piggyback basin until 18 km of shortening. Due to the oscillation of the wedge around the lower critical limit (see the propagation sequence on Fig. 10D), the basin is alternately displaced with the active sheet when the external sheet propagates and not displaced when only the internal sheet moves. During the rest of the experiment, a retrograde thrust sequence occurs. This basin is no longer displaced, and sediments are deposited over the external sheets. The internal basin, from the beginning to 50 steps of shortening (25 km of shortening during the oscillation of the wedge around its minimum critical taper), follows the same evolution as the more external basin. During the backward sequence (between 25 and 31 km of shortening), it is passively moved above a flat, and from 62 steps of shortening until finally, it is located above an active duplex ( Fig. 11B). The width of the basin reduces continually during its evolution.

Deposition is represented ( Fig. 11B) with a time line every 10 steps (715 000 yr). After 50 steps of shortening, previous onlaps in the external part of the basin have been eroded after being uplifted above the ramp (Leturmy et al., 1995). In the internal part, sediments prograde towards the inner part of the basin, and some onlaps are preserved from erosion. During the backward sequence, the evolution of the basin changes considerably: it is alternately folded and displaced by the growing duplex. Toplaps and unconformities record this phenomenon, whereas erosion still affects the outer part of the basin.

5. Conclusion By simulating the evolution of a thin-skinned thrust belt with two detachment levels, like the belt of the Bolivian Subandean Zone, the following conclusions can be made, concerning the role of erosion/sedimentation processes in the geometry and kinematics of structures. 5.1. Interactions between tectonics and superficial mass transfer Analogue models show that superficial processes influence the nucleation of new faults and the partitioning of displacement along the fault system. Analogue and numerical approaches show that the evolution of a thrust belt considered on a large scale is controlled by the growth of a shortened wedge. The change imposed along its upper boundary by surface transport influences the propagation of de´collement along weak layers and partitioning of displacement along the fault system. It is concluded that erosion restrains the forward propagation of the thrust system while high sedimentation rates associated with basement subsidence promote the formation of a wedge-shaped syn-orogenic. This induces a forward shift of the front, which is followed by out-of-sequence reactivations. The efficiency of the surface transport smoothes the topography by erosion of the antiforms and sedimentation in depressions. The efficiency rate influences the tectonic distribution until

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

65

Fig. 11. (A) Detailed evolution of the numerical experiment C on Fig. 10, corresponding to the four second-order sequences of the fault propagation sequence. Parameters used: r=2650 kg/m3, C =5 MPa, m=0.85, m =0.7, l=0.6, V/Ks=500 m2/yr, tilting veloc0 b ity=0.34°/Ma. a: during the 50 first steps of shortening, the inner and outer faults are alternately activated. b, c, and d show a backward sequence with respective activation of thrusts 6, 3, and 1. (B) Evolution of the internal piggyback basin during the experiment detailed in (A) and Fig. 10C. Sediments record changes in the thrust sequence: discontinuities develop above previous folded sediments but are progressively eroded.

a stage where all the depressions are filled, and the culminations are nearly hidden. As erosion mainly restrains the forward propagation of the thrust in the upper level, development of a passive roof duplex is favoured in the lower levels. 5.2. Piggyback basin development On a large scale, piggyback basin development is promoted by an increase in the foreland basin cone angle or by the presence of a pre-orogenic wedge inducing forward propagation of deformation far into the foreland. On a smaller scale,

piggyback development is also promoted by the presence of hollows due to two independent anticlines or the presence of a duplex stack that deforms upper tectonic sheets. The origin of the sediments in the piggyback basins does not influence the interaction between sedimentation and tectonics: a wedge eroded to fill its own basins follows almost the same evolution as a less eroded wedge, whose basins are partly filled with sediments coming from an internal part of the chain. In piggyback basins, numerical experiments show that sediments record changes in the tectonic activity location. Each change in

66

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67

the thrust sequence is recorded in the basin by unconformities that cover previous folded sediments and by a shift in the deposition centre. 5.3. Piggyback basins of the Subandean zone This study suggests that the Tertiary sediments presently located above the Subandean thrust belt of North Bolivia were deposited in a piggyback basin separated from the foreland by a weakly eroded topography. The cause of this early piggyback basin development is the wedge-shaped Silurian–Ordovician rocks amplified by basement tilting and a high rate of sedimentation, which make it close to the minimum critical taper. In the Subandean belt of Southern Bolivia, the initial wedge is gentler, and a weaker basal friction is inferred. None the less, an increase in the taper due to the flexure beneath the wedge-shaped foreland sediments could control the development of piggyback basins.

Acknowledgements This study was supported by a research agreement between Insitut franc¸ais du Pe´trole, ORSTOM and Grenoble University. We thank Dr Gutscher and an anonymous reviewer for their critical reviews and suggestions, and Ph. Rochat for helpful discussions during this study.

References Baby, P., He´rail, G., Lopez, J.M., Lopez, O., Oller, J., Pareja, J., Sempere, T., Tufino, D., 1989. Structure de la Zone Subandine de Bolivie: influence de la ge´ome´trie des se´ries se´dimentaires ante´oroge´niques sur la propagation des chevauchements. C. R. Acad. Sci. 309, 1717–1722. Baby, P., He´rail, G., Salinas, R., Sempere, T., 1992. Geometric and kinematic evolution of passive roof duplexes deduced from cross section balancing: example from the foreland thrust system of the southern bolivian Subandean Zone. Tectonics 11, 523–536. Baby, P., Colletta, B., Zubietta, D., 1995. Etude ge´ome´trique et expe´rimentale d’un bassin transporte´: exemple du synclinorium de l’Alto Beni (Andes centrales). Bull. Soc. Ge´ol. Fr. 166, 797–811. Baby, P., Rochat, P., Mascle, G., Herail, G., 1997. Neogene

shortening contribution to crustal thickening in the back arc of central Andes. Geology 25, 883–886. Barr, T.D., Dahlen, F.D.A., 1989. Brittle frictional Mountain Building. 2. Thermal structure and heat budget. J. Geophys. Res. 94, 3923–3947. Beaumont, C., Quinlan, G.M., Hamilton, J., 1988. Orogeny and stratigraphy: Numerical models of the Paleozoic in the eastern interior of North America. Tectonics 7, 389–416. Beaumont, C., Fullsack, P., Hamilton, J., 1992. Erosional control on active orogens thrust and nappes tectonics. In: McClay, K. ( Ed.), Thrust Tectonics. Chapman & Hall, London, pp. 1–18. Beer, J.A., Allmendinger, R.W., Figueroa, D.A., Jordan, T.E., 1990. Seismic stratigraphy of a Neogene piggyback basin, Argentina. Am. Assoc. Pet. Geol. Bull. 74, 1183–1202. Boyer, S., Elliot, D., 1982. Thrust systems. Am. Assoc. Pet. Geol. Bull. 66, 1196–1230. Byerlee, J., 1978. Friction of rocks. Pure Appl. Geophys. 116, 615–626. Carson, M.A., Kirkby, M.J., 1972. Hillslope Forms and Processes. Cambridge University, New York, 475 pp. Chalaron, E., Mugnier, J.L., Mascle, G., Perrin, F., 1995a. L’e´volution des bassins transporte´s d’un syste`me chevauchant: un exemple d’interactions entre la tectonique l’e´rosion et la se´dimentation. Acte du colloque ge´oprospective UNESCO, Paris, April, pp. 219–238. Chalaron, E., Mugnier, J.L., Mascle, G., 1995b. Control of thrust tectonics in the Himalayan foothills: a view from a numerical model. Tectonophysics 248, 139–163. Chapple, W.M., 1978. Mechanics of thin-skinned fold-andthrust belts. Geol. Soc. Am. Bull. 89, 1189–1198. Cobbold, P.R., Rossello, E., Vendeville, B., 1989. Some experiments on interacting sedimentation and deformation above salt horizons. Bull. Soc. Ge´ol. Fr. 8, 453–460. Colletta, B., Letouzey, J., Pinedo, R., Ballard, J.F., Bale, P., 1991. Computed X-ray tomography analysis of sandbox models: Examples of thin-skined systems. Geology 19, 1063–1067. Dahlen, F.A., Suppe, J., Davis, D., 1984. Mechanics of fold and thrust belts and accretionary wedges: cohesive Coulomb theory. J. Geophys. Res. 89, 10087–10101. Davis, D., Suppe, J., Dahlen, F.A., 1983. Mechanics of foldand-thrust-belts and accretionary wedges. J. Geophys. Res. 88, 1153–1172. Endignoux, L., Mugnier, J.L., 1990. The use of forward kinematic model in the construction of balanced cross sections. Tectonics 9, 1249–1262. Flemming, P.B., Jordan, E.T., 1989. A synthetic stratigraphic model of foreland basin development. J. Geophys. Res. 94, 3851–3866. Gutscher, M.A., Kukowski, N., Malavieille, J., Lallemand, S., 1996. Cyclical behavior of thrust wedges. Insight from high basal friction sandbox experiments. Geology 24, 135–138. Hardy, S., Duncan, C., Masek, J., Brown, D., 1998. Minimum work, fault activity and the growth of critical wedges in fold and thrust belts. Basin Res. 10, 365–373. Herail, G., Oller, J., Baby, P., Bonhomme, M., Soler, P., 1996.

P. Leturmy et al. / Tectonophysics 320 (2000) 45–67 Strike slip faulting and related basins in the Cenozoic evolution of the southern branch of the Bolivian Orocline. Tectonophysics 259, 201–212. Huyghe, P., Mugnier, J.L., 1992. Short-cut geometry during structural inversions: competition between faulting and reactivation. Bull. Soc. Ge´ol. Fr. 163, 691–700. Jones, P.B., Linsser, H., 1986. Computer synthesis of balanced crossed sections by forward modelling (abstract). Am. Assoc. Pet. Geol. Bull. 70, 605. Karner, G.D., Watts, A.B., 1983. Gravity anomalies and flexure of the lithosphere. J. Geophys. Res. 93, 1049–1061. Lallemand, S., Schnu¨rle, P., Malavieille, J., 1994. Coulomb theory applied to accretionary and non accretionary wedges: Possible causes for tectonic erosion and/or frontal accretion. J. Geophys. Res. 99, 12033–12055. Leturmy, P., Mugnier, J.L., Chalaron, E., 1995. Erosion et se´dimentation au voisinage d’un anticlinal de rampe: apport d’un mode`le nume´rique. Bull. Soc. Ge´ol. Fr. 6, 783–795. Liu, J.Y., Ranalli, G., 1992. Stresses in an overthrust sheet and propagation of thrusting: an airy stress function solution. Tectonics 11, 549–559. Liu, H., McClay, K.R., Powell, D., 1992. Physical models of thrust wedges. In: McClay, K. (Ed.), Thrust Tectonics. Chapman & Hall, London, pp. 71–81. Malavieille, J., 1984. Mode´lisation expe´rimentale des chevauchements imbrique´s: application aux chaıˆnes de montagnes. Bull. Soc. Ge´ol. Fr. 26, 129–138. Moretti, I., Turcotte, D.L., 1985. A numerical model for erosion, sedimentation, and flexure with application to New Caledonia. J. Geodyn. 3, 155–168. Moretti, I., Baby, P., Mendez, E., Zubietta, D., 1996. Hydrocarbon generation in relation to thrusting in the Subandean Zone from 18°–22° S, Bolivia. Petrol. Geosci. 2, 17–22. Mugnier, J.L., Baby, P., Colletta, B., Vinour, P., Bale, P., Leturmy, P., 1997. Thrust geometry controlled by erosion and sedimentation: A view from analogue models. Geology 5, 427–430. Mulugeta, G., 1988. Modelling the geometry of Coulomb thrust wedges. J. Struct. Geol. 10, 847–859. Oller, J., 1986. Consideraciones generales sobre la geologia de la Faja Subandina norte. Thesis, Universitad mayor de San Andreas, La Paz, 120 pp. Ori, G., Friend, P., 1984. Sedimentary basins, formed and carried piggy-back on active thrust sheets. Geology 12, 475–478.

67

Platt, J.P., 1988. The mechanics of frontal imbrication: a first order analysis. Geol. Rundsch. 77, 577–589. Platt, J.P., 1990. Thrust mechanics in highly over pressured accretionary wedges. J. Geophys. Res. 95, 9025–9034. Richard, P., 1991. Experiments on faulting in a two-layer cover sequence overlying a reactivated basement fault with oblique-slip. J. Struct. Geol. 13, 459–469. Roeder, D., 1988. Andean age structure of Eastern Cordillera (province of La Paz, Bolivia). Tectonics 5, 23–29. Sheffel, B., 1988. Structural constraints on crustal shortening in the Bolivian Andes. Ph.D. thesis, Massachusetts Institute of Technology, 170 pp. Souriau, M., 1995. Les processus d’e´rosion me´canique a` l’inte´rieur des grands bassins fluviaux. Bull. Soc. Ge´ol. Fr. 6, 763–781. Storti, F., McClay, K., 1995. Influence of syntectonic sedimentation on thrust wedges in analogue models. Geology 23, 999–1002. Todten, H., 1976. A mathematical model to describe surface erosion caused by overland flow. In: Ahnert, F.Z. ( Ed.), Quantitative Slope Model, Geomorphol. Suppl. 25. 89–105. Tondji Biyo, J.J., 1993. Chevauchements et bassins compressifs. Influence de l’e´rosion et de la se´dimentation. Mode´lisations analogiques et exemples naturels. The`se Doctorale, Rennes. Turcotte, D.L., Schubert, G., 1982. Geodynamics, Appplication of Continuum Physics to Geological Problems. Wiley, New York, 450 pp. Turcotte, D.L., 1992. Fractals and Chaos in Geology and Geophysics. Cambridge University Press, Cambridge. 221 pp. van Keken, P.E., Spiers, C.J., Berg, A.P., Muysert, E.J., 1993. The effective viscosity of rocksalt: implementation of steadystate creep laws in numerical models of salt diapirism. Tectonophysics 124, 325–358. Vinour, P., 1995. Influence de la se´dimentation et de l’e´rosion sur la propagation des chevauchements d’avant-chaıˆne: e´tude re´gionale (sud Bolivie) et expe´rimentale. Unpublished DEA memory, Universite´ J. Fourier, Grenoble, 80 p. Willet, S.D., 1992. Dynamic and kinematic growth and change of a Coulomb wedge. In: McClay, K. ( Ed.), Thrust Tectonics. Chapman & Hall, London, pp. 19–31. Williams, C.A., Conners, C., Dahlen, F.A., Price, E.J., Suppe, J., 1994. Effect of the brittle–ductile transition on the topography of compressive mountain belts on Earth and Venus. J. Geophys. Res. 99, 19947–19974. Zhao, W.L., Davis, D.M., Dahlen, F., Suppe, J., 1986. Origin of convex accretionary wedges: evidence from Barbados. J. Geophys. Res. 91, 10246–10258.