Dynamique et regime thermique des chaines de
montagnes – application aux Andes Centrales

Equilibre des contraintes à l’aplomb d’une zone de subduction

Subduction zones display a wide range of tectonic features correlated to different stress patterns. Although the main characteristics of subductions are similar anywhere with burial of mainly oceanic material beneath oceanic or continental plates, their surface morphological and tectonic expressions vary widely from intensely compressive to extensive through intermediate settings. The intraplate stress field has been intensively discussed and is still the focus of many studies. Although worldwide data have been collected, the data base remains geographically uneven and of variable quality (Mueller et al., 1997). The stress fields within cratons are mainly neutral or compressive. But it is fairly common to see combined extensional and compressional settings in convergent systems (either in collisions or in subductions). The Aegean sea and the Lau Basin (Tonga-Kermadec trench) display strong extensional patterns, the Japan sea and Italy show coeval extensional and compressional features, while the Andes mainly undergo compression with some areas of neutral/extensional regimes. Moreover, changes in the tectonic regime occur through time : for instance the Aegean formerly underwent compression (e.g. Jolivet & Faccenna, 2000), and the Basin and Range evolved from the Laramide compression to the present day fast extension (Atwater, 1970). This capability of swapping between two tectonic regimes suggests that the physical processes ruling deformation only slightly differ from one geodynamic setting to another. As a consequence, the associated topography can be of various types. In the Andes, the orogenic belt shows different shapes, including high plateaus. In several cases, extension can occur next to the trench, leading to back-arc basins (Japan sea, Lau basin, Aegean sea…). Topography is the consequence of stresses applied to tectonic plates and of their evolution with time. All stresses in Earth are the consequences of lateral variations in the internal density. The habit in the geological literature is to interpret loosely the driving forces, ridge-push and slab pull as boundary forces (Forsyth & Uyeda, 1977 ; Richardson et al., 1979) although it is well-known that the ridge-push is, for instance, a force distributed all along the aging lithosphere and not localized at ridges (e.g. Turcotte and Schubert, 1982). These forces are resisted mostly by a basal shear traction on the mantle. Other forces seem to be of lower importance although they may locally dominate the stress field. Among them, interplate friction, trench suction and driving shear from the convecting mantle can be outlined. Various models aimed to constrain the magnitude of the global driving forces by  lancing the net torques applied to each plate. This approach generally points at ridge push and slab pull as the main driving forces (Stefanick & Jurdy, 1992 ; Richardson, 1992 ; Meijer & Wortel, 1992). Unfortunately, the solution suffers from non-uniqueness as the same kinematics can be obtained by different combinations of forces. For instance, ridge push alone or slab pull alone can both explain the motion of a plate away from a spreading ridge toward subduction. In principle, tectonic stresses should help to discriminate which forces are acting : ridge push drives a plate in compression while slab pull induces extension. However stress data is scarce away from plate boundaries where it would have the most significant discriminating capability. The role of crustal or lithospheric density variations has been emphasized by many authors (Artyushkov, 1973 ; England & McKenzie, 1982, 1983 ; Houseman & England, 1993, Fleitout & Froidevaux, 1983 ; Bai Wuming et al., 1992). The importance of the local density structure has been illustrated by models using the thin viscous sheet approximation which is valid at long wavelengths. The thin sheet approximation has been used to model the Andes in Wdowinski et al. (1989). In their paper, the Andean topography is the consequence of a basal shear induced by corner-flow circulation while the internal sources of stresses due to crustal thickening were neglected. In our paper we propose another mechanism for mountain building near active plate margins where the traction by the subducting plate under the overriding one is balanced by internal stresses due to crustal thickening. We first address the problem by using simple cases to decipher which forces can be responsible for various topographic responses. Then, we use the topography of the Andes to quantify the stresses acting on the western South American margin, and probe the results by producing a time-marching model of the Andes. 

The model

Thin viscous sheet approximation

The derivation of the thin viscous sheet model for the lithosphere has been discussed in details in various papers dealing with continental deformation (e.g. England & McKenzie, 1982, 1983 ; Wdowinski et al., 1989). This approximation has also been used to understand the coupling between lithosphere and mantle convection (Lemery et al., 2000). It is based on the vertical integration of the Navier-Stokes equations coupled with mass conservation. 

EQUILIBRE DES CONTRAINTES à L’APLOMB D’UNE ZONE DE SUBDUCTION

THE MODEL

In this paper, we only briefly discuss the assumptions of this approach. The lithosphere is stiff enough with respect to the underlying mantle so that the vertical variations of the horizontal velocity can be neglected. The lithosphere is also thin enough with respect to the scale of the deformations under consideration that the horizontal gradients of the stresses are negligible with respect to the vertical gradients (Fleitout & Froidevaux, 1982). In the lithosphere we define èxéëê , ì™éëê and í to be the total stress tensor, the deviatoric stress tensor and the pressure, respectively (î or ï stand for ð or ñ as we only derive a two-dimensional model), èFéëêóò–ìPéëê<ô%í)õPéëê¿ö (2.2.1) We assume that the lithosphere behaves like an incompressible viscous fluid with ì™émêóòE÷iøTùúé ù ðêšû ùúê ù ðégüþý (2.2.2) where the viscosity ÷ can be constant, laterally variable or even some non-linear function of the stress tensor. The variable ú é represents either the horizontal velocity ú or the vertical velocity ÿ. Within the thin sheet approximations, the vertical equilibrium simply becomes the topography (Fig. 2.2.2b), the deviatoric stress decreases (Fig. 2.2.2a).