Ductile deformation of rocks within a closed system: Effects of compatibility of deformation geometries on strainrate and rheology.

The dynamic nature of the earth is apparent in the deformation of the lithosphere. Studies on rock deformation are carried out in very different scales ranging from lattice processes in rock forming minerals to the scale of lithospheric plates and involve several approaches: 1) The mechanical approach taken by experimentalists relates, crudely speaking, stress to strain/strainrate under specific boundary conditions. 2) The geometric/kinematic approach based on theoretical considerations is commonly used among field geologists to explain movement of particles and flow in naturally deformed rocks. For the optimistic user of available data sets. all relevant parameters of rock deformation might be constraint in a specific volume of rock. However, interrelations between two neighbouring rock volumes that deform under differently defined conditions are rarely considered. This project is dedicated to the interaction between adjacent volumes of rocks. Thereby, our basic assumption is compatibility of different deformation geometries in adjacent "blocks" which are not separated by discontinuities (faults). This is a commonlv observed scenario in naturally deformed rocks and shall be termed a "closed system" in the following text. Theoretical models show that different deformation geometries result in different strain rates. In other words, pure shear is more effective for the accumulation of finite strain than simple shear. General shear, the simultaneous combination of simple and pure shear deformation, is in between in its effectivity. To avoid discontinuities within a "closed system", the plane of contact between two blocks must be of equal dimension (length in the 2D space, area in the 3D space). All variables relevant for deformation are no longer independent and therwith, there is a limited amount of possible deformation geometries to accommodate bulk deformation in both blocks. An enormous potential to explain structural associations and microstructures lies in the consequent use of this "closed system". The practical access to the problem includes three subtopics: 1. Theoretical modelling of the "closed system" using combinations of different deformation geometries. The effect on strain rates, differential stress and other parameters will be studied. The geometric models will largely follow the theoretical work of Tikoff and Fossen (1993), Fossen and Tikoff (1993) and Tikoff and Teyssier (1994). Amount of noncoaxiality (kinematic vorticity) within the closed system may be modelled using algorithms published by Tikoff and Fossen (1993, 1995) and Wallis (1992, 1995). The relations between flow geometries and variables included in the constitutional flow laws can be evaluated following work of Weijermars (1991) and series of papers dealing with flow properties of rocks (e.g., Carter and Tsenn, 1987, Kohlstedt et al., 1995; Wenk (ed.) 1985; Barber and Meredith (eds.), 1990). 2. In order to test the reliability of results from theoretical considerations, two field examples have been chosen. Because of the large numbers of variables involved, a simple, well constraint geology is required. One field example is dedicated to outcrop scale variations in deformation geometry (vorticity) and the relationships to active deformation mechanisms. Promising results have been obtained from a reconnaissance study within a granitic lithology in an extensional regime in the Eastern Desert of Egypt (Bregar et al., 1996). We intend to continue our study in this area. The second example is dedicated to orogen scale tectonics. For several reasons we have chosen the large scale thrust zone (Main Central Thrust: MCT) in the central Himalayas to relate geometry of thrusting with extensional deformation in the hangingwall. Firstly there is an excellent database on the kinematic, thermal and chronolooical evolution of this deformation zone. Secondly a preliminary study on vorticity along the MCT has been already carried out in co-operation with Dr. Grasemann (Wien). 3. Since we are firmly convinced that basic science should not only be published for the scientific community but must be transparent to the general public, a public relation work is planned to improve acceptance and motivate young people. We intend a CD-ROM production on this aspect of mountain building including an audio-visual computer animation of the model and documentation of the field work. This task will be done in cooperation with Klaus Rüscher Videoproduction. The proposed project would be carried out in cooperation with Ch. Teyssier (University of Minnesota), B. Grasemann (Universität Wien) and K. Stüwe (University of Monash). Ch. Teyssier would contribute with his experience in kinematic and geometric modelling, B. Grasemann would help in model designs and cooperate in the the work along the MCT in the Himalayas. K. Stüwe contributes with his experience on stress variations in fault zones and their petrological relevance.

Theoretical Aspects of "Closed System Deformation" include interrelations between flow geometry, strain and stress during coherent deformation. We argue that within two coherently deformed rock units with different amount of shear strain fabrics do not evolve independently. Enhanced shear deformation has to be accommodated by enhanced bulk strain and consequently by enhanced strain rate. This in turn goes along with enhanced differential stresses within the highly sheared rock unit. Knowing the flow geometry and the stress and strain relations within a defined block, the relevant quantities can be modelled in the adjacent block with different flow geometry. We modelled these relationships and applied the theoretical results for a high deformation zone that exhibits variable flow geometry. Results show exponential relations between flow geometry and differential stress. Hence, in zones of coherent deformation, stress distribution can be predicted. Within naturally observed examples the predicted variation of differential stress with changing deformation geometry (vorticity) may not fit field and laboratory data. This is interpreted to reflect change of material properties during progressive deformation, strain-softening respectively strain-hardening. We use these relations and suggest a new tool to quantify flow properties (i.e. the stress exponent) in ductile deformed rocks. In an orogen scale (Himalayas), the interrelations between non-coaxial deformation with adjacent, coherently deformed rock units is studied. Models of "Closed System Deformation" suggest that deformation along the Main Central Thrust Zone (MCTZ) has to induce deformation within hangingwall units and coeval extension along the South Tibetan Detachment Zone (STDZ). In order to test this scenario, a section across the High Himalayan Crystalline Wedge between MCTZ and STDZ has been studied. Coeval activity of MCTZ and STDZ together with extrusion and cooling of the High Himalayan Crystalline Wedge (HHC) at ca. 13 million years (Ma) is constraint by 40Ar/ 39Ar data on muscovite. Thereby rocks had been exhumed to mid-crustal levels and fabrics had been statically annealed. Central portions of the HHC suffered major coaxial deformation as predicted by the theoretical model. The pressure-temperature history related to this tectonic event includes starting conditions during onset of exhumation of ca. 7-8 kbar and ca.600C. The cooling history varies within the High Himalayan Crystalline Wedge with almost isothermal decompression within marginal portions (stability of kyanite) and thermal equilibration in the stability field of sillimanite in the core. This is explained by the three-dimensional cooling geometry including lateral cooling along MCTZ and STDZ. Final cooling of the HHC occurred significantly later. Fission Track data on apatite constrain surprisingly late cooling and final exhumation of rocks between ca. 0,3 and 1,4 Ma. This event is correlated with late out-of- sequence thrusting when the present, steep relief developed within the HHC. Highly dynamic fabrics associated with high fluid flow (hot brines) evolved. The variation of cooling ages within the Himalayan Crystalline Wedge is used to reconstruct relative vertical motion of rocks.