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Lithosphere rheology and sedimentary basins
89
Tectonophysics, 226 (1993) 89-95 Elsevier
Science
Publishers
B.V., Amsterdam
Lithosphere
rheology and sedimentary basins
J.P. Vilotte a, J. Melosh b, W. Sassi ’ and G. Ranalli d 0Ecole
Normale Superieure, Departement de Geologie, 24 rue Lhomond, 75231 Paris, France b University of Arizona, Tucson, USA ’ Institut Fratqais du P&role, 1 et 4 Avenue de Bois-Preau, 92600 Rueil-Malmaison, France d Carleton VniversiTy, Ottawa, Canada (Received
November
15, 1992; revised version
Introduction The dynamics of sedimentary basins is reflected in the wide range of observational scales inside sedimentary basins. The advent of high-quality data sets have significantly improved the resolution of the record of near-surface tectonic processes. Crustal thinning, mechanical and thermal subsidence, sediment filling, are involved in extensional basin evolution, and controlled by complex interactions between ductile and brittle modes of deformation of the whole lithosphere. The rate of loading (extension and sediment filling) and the thermal evolution are among the most important controlling parameters. These nonlinear interactions do possess a memory of the evolution history and loading. Quantitative understanding of basin subsidence (and the offlap/onlap stratigraphic patterns of a specific basin) obviously benefits from progress in understanding the geodynamical context (HorvLth, 1993-this issue). In compressional settings, foreland basins result from the flexural lithospheric response to loading. Most of the models proposed so far have considered the lithosphere as a rheological unit and have been based on classical elastic and viscoelastic plate theory. The wavelength and amplitude of the flexural response is not an intrinsic property of the lithosphere but result from the history of the competitive interactions between rate of loading and rate of viscous dissipation 0040-1951/93/$06.00
0 1993 - Elsevier
Science
Publishers
accepted
June 1.5,1993)
(thermally activated). A clear physical description of this flexural mode has not yet been proposed, even though some recent results on the mechanisms of uplift shoulder formation during rifting evolution may be considered (Bassi, 1991; Chery et al., 1992). The geodynamical context of those basins is complex, and the relationship between the transition of extensional and compressional domains is a topic of vigorous research. Current models for extensional and compressional basins are strongly based on a bulk rheological description of the whole lithosphere and on a kinematic description of the deformation mechanisms (Sawyer, 1985; Houseman and England, 1986; Quinlan et al., 1993-this issue). The basin record does reveal to some extend the memory of the deformation history starting from the construction of the internal structure of the basins (i.e. from the processes leading to the formation of rocks: sedimentation, diagenesis, compaction; including possible buildup of fluid overpressures), and the pattern of the large deformations by faulting or folding. To enhance the understanding of the formation and evolution of sedimentary basins it is important to fully address the physical mechanisms operating at different scale in the continental lithosphere. For example, faulting forms a most important expression (at least at the surface) of large scale deformation in the basins. How those basins are related to the faulting process and the fault interactions is an unsolved question. Pull-apart basins are certainly
B.V. All rights reserved
one of the clearest example of basins associated with large transcurrent fault systems, but at smaller scale and in an other gcodynamic context, graben formation raise interesting questions on faulting mechanisms (Melosh and Williams, 1989; Ricke and Mechie, 1989; Cundall, 1991a). The construction of lithospheric strength envelopes (see, e.g., Cloetingh and Banda, 1992) forms an important intermediate step in the characterisation of the complex rheological behaviour of the lithosphere underlying basins; even though it remains a static picture based on quite restrictive assumptions (Rutter and Bodrie, 1991). At low pressure and low temperature, a brittle mode operates mostly by microcrack interactions and growth, frictional-slip plasticity, both expected to be pressure dependent and time independent. At conditions of high pressure and high temperature deformation occurs in a ductile mode involving dislocations climbing, diffusion, grain boundary sliding all expected to be thermally activated, time dependent and probably pressure independent. In between a wide transitional mode operates where these different mechanisms are competing and interacting (Ranalli, 1987; Ranalli and Murphy, 1987; Vilotte, 39891. The mechanical behaviour of a rock is not an intrinsic property but depends on different physical parameters such as pressure, temperature, rate of loading, microstructure (e.g., grain size, shape), fluid content. Crustal and mantle materials are heterogeneous polycrystalline aggregates which exhibit several interacting inelastic mechanisms. Although much progress has been made in the understanding of the different modes of deformation (in terms of governing mechanisms and validity domain), more precise knowledge of rock physical properties and behaviour under arbitrary loading path is required. This is particularly important as recent developments in the numerical modelling of localisation phenomena (De Borst, 1989; Leroy and Ortiz, 1989; Desrue, 1990; Cundall, 1991b; Mandl, 1988, 1991; Sulem et al., 1992; Lyakovsky et al., 1993-this issue) allow the incorporation of heterogeneous materials and fractures in basin modelling. Numerical models of sedimentary basins require a full understanding of the nonlinear litho-
spheric modes of deformation. Of primary importance for the next generation of basin models, will be to address the interaction between those mechanisms and the spectrum of scales intrinsically related to these non-linear processes. In all cases most of the models proposed so far consider the evolution of sedimentary basins as a two-dimensional problem although this is obviously not the case. Proper data allowing a full 3-D characterization of a basin (extension, thinning, sediment sequences, fault geometry) should become more easily available to the academic research community. The brittle mode
The construction of quantitative predictive basin formation models requires full understanding of the processes underlying the development of faulting, the interaction between faulted domains and the fine structure of stress propagation and accumulation in rheologically stratified lithosphere. At low pressure and low temperature, the brittle deformation is characterized, at small scale by micro-decohesions originating from the nucleation, growth and coalescence of surfacic (microcracks mostly of mode I) or volumetric (cavities) discontinuities which may be related with dislocations. Those discontinuities result from the heterogeneity of the internal stresses due to the polyphasic and polycrystalline nature of the lithosphere. At basin scale, faulting and fault interactions are among the main mechanisms involved in the deformation of the uppermost part of the continental lithosphere. The problem of scale is further compounded by the fact that those discontinuities have their own spatial and temporal scaling laws. At the laboratory scale as well as in numerical modelling progress has been made in the understanding of failure in terms of progressive localized damage (Bazan, 1986; Lyakhovsky et al., 1993”this issue). Further research on the mechanisms of growth, interaction and localizatiun of arrays of microcracks, as well as their respective sensitivity to pressure and temperature is important. Understanding physically those processes
LITHOSPHERE RHEOLOGY AND SEDIMENTARY
91
BASlNS
and their implications in terms of bulk properties damage (e.g., elasticity, porosity) is of primary importance not only to characterize the prefailure behaviour of rocks, but also to formulate the physical interactions leading to a macroscopic localized mode in term of smaller-grained variables both in time and space. Recent constitutive models taking into account potential frictional slip systems have been formulated leading to non-associative plasticity. These models are now being steered to applications in sedimentary basins modelling to address the conditions for the formation of localized fault zones and their orientations. ~though those models may be useful in predicting the failure of rock species in laboratory testing conditions, they fail to model the post-failure behaviour due to lack of internal length. With such an approach, localization length and evolution through time can not be predicted. At the scale of seismic resolution, patterns of population of faults in the basins are being regarded critically by geologists and geophysicists. Whether fault propagation and fault interaction are auto-similar processes may have important implications in term of the hierarchy of scales involved in their description. The fractal nature of fault size populations also questions the meaning of average spacing of large faults: what is a large fault? Recent analysis of the spatial distribution of faults suggests fractal scaling laws (Hirata, 1989; Okubo and Aki, 1989; Velde et al., 1990; Marret and Allmendinger, 1991; Walsh et al., 1991). Given the improved quality and availability of seismic data, this type of analysis could be performed routinely. Attempts have been made to describe fault growth and fault structuration as the result of a spatio-temporal nonlinear dynamical evolution of a heterogeneous lithosphere. Such approaches provide a framework in which those different scaling laws can be linked together. Recent developments in physical properties of heterogeneous and random materials coupled to the analysis of complex nonlinear dynamical systems have to be explored. Fault structuration of the continental lithosphere might partly result from the inherited heterogeneities of the lithosphere. Current models describing the growth of faults are empirically based and exist-
ing mechanical models providing a basis to fault growth and interactions are under investigation. At small scales models describing faults as Somigliana dislocations have been proposed but not yet fully explored. As discussed previously, the bulk of the currently used basin models are based on an approximation of the rheological description of the brittle regime invoking homogenized stress and strain fields at the scale of the basin itself. The constitutive behaviour is provided by Byerlee’s empirical friction law. As pointed out above (see also Zoback et al., 1993-this issue) this empirical relation appears to be in good agreement with the observed magnitude of stress at least within the uppermost levels (< 5 km). At higher confining presssure and temperature, very little is known on the validity of such a friction law. Recent observations on fault tips and stress patterns associated with major transcurrent fault systems (Zoback et al., 1993-this issue) do not always agree with Byerlee’s law. How this law should be integrated in the overall description provided by basin formation models characterizing the bulk rheological properties is a first order question. At the scale of the basins, the presence of populations of faults as well as the intrinsic heterogeneity of the structures and the dependence on strain rate requires further attention. This applies in particular in the context of subsidence analysis of syn-rift sequences for the effects of varying rates of fault movement and spatial variations in bulk strains, strain rates and stresses. The ductile mode Initially, the modelling of sedimentary basins evolution has focused on the ductile mode operating in the lower crust and the mantle under restrictive assumptions of homogenei~, steady state and isotropy. Major contributions have been made in the understanding of steady-state creep for polycristalline aggregates by experimental studies, and most of the laboratory data have been extrapolated outside the validity domain of those experiments. This mode of deformation (as for the brittle one) do depend on a number of external and
92
internal parameters such as fluid pressure, chemical effects (associated with those fluids), grain sizes and shapes, as well as on microstructural instabilities like phase change, recrystallization, grain growth which are still poorly known. Furthermore, the ductile behaviour of a polycristalline aggregate depends on its chemical composition and its different stable mineralogic phases. Extrapolation of experimental results both in time and space requires knowledge of the different physical mechanisms of each phase. Evidence from exposed lower crustal rocks and recent seismic reflection studies clearly show that ductile deformation is indeed very heterogeneous and localized. Such a contrast cannot be simply explained by the chemical heterogeneity of the lithospheric materials but must also be related to the deformation mechanisms. The experimental data set deals with a great variety of aggregates, microstructures, and environmental parameters. The data set is, however, limited in the sense that most of those data come mostly from hardening tests and to some extent from creep tests, leading to a limited loading paths and a narrow validity domain in time, pressure and temperature. More experimental data providing a greater variety of loading paths are needed. For monophasic aggregates, steady-state creep with the characteristic power-law relationship between the creep strain rate and the stress is probably the most well known ductile behaviour, even though it only characterize a unidimensional response (in term of stress and strain) and a limited domain of pressure, temperature, strain rate and stress. Recently, the attention has been focused on other crucial effects resulting from transient hardening phenomena which clearly controlled for example the so called power-law breakdown. Those are not yet fully understood at the microscopic levels but do involve long-distance dislocations-dislocations interactions, or short-distance dislocations-obstacles interactions. Such mechanisms are very important and have been extensively studied for other polycristalline materials such as metals. A proper three-dimensional viscous-hardening law has not yet emerged due to the lack of experimental data.
J.P.
VII.0
1-1‘1: tl’
Al
Such a law would be of great interest since it will provide a more realistic description of the stress-strain response with potential implications in terms of localization or instability. Transient hardening effects and their proper modelling in a 3-D constitutive relation for the polycristalline structure of those monophasic aggregates has not yet been explicitly taken into account in the constitutive modelling. Interactions between grains and the influence of internal stresses resulting from deformation incompatibility are to be actively explored to understand the progressive fabrics associated with the deformation. This is of central importance for modelling ductile localization and induced anisotropy. Recent models for polycrystalline aggregates have been proposed for metals and the underlying methodologies should be explored in rock mechanics. Experiments on progressive fabrics during simple shear at high temperature and pressure would be valuable as well as studies of the polyphase nature of rocks and its implications for the overall ductile response. This area of research is of crucial importance in order to understand the competing effects between different dissipation mechanisms and their potential implications for ductile instabilities, localization and progressive fabrics. At larger scale (both in space and time) other complications might arise. It is quite clear that ductile deformation is far from being homogeneous and that shear zones have also their own scaling properties. At which extend localization modes like necking, buckling or shear bands depend on the bulk properties, or heterogeneities (chemical and thermal), or the interface properties has yet to be assessed. The thermal implications of those localization phenomena are of crucial importance in the understanding of decollement, core-complex structures. The strong thermal activation of that mode of deformation imply that the thermo-mechanical coupling has to be incorporated in the modelling. Our inability to describe the ductile behaviour at large scale (taking in to account the chemical and thermal heterogeneities) and the lack of detailed constitutive behaviour at smaller scale may explain why shear bands are still not physically understood.
LITHOSPHERE RHEOLOGY AND SEDIMENTARY
The brittle-ductile
93
BASINS
mode
The brittle-ductile transitional mode of deformation results from the competing effects of different dissipative mechanisms and the chemical heterogeneities of geological materials. This mode of deformation cover a range of pressure and temperature which is quite characteristic of most of the continental crust. Improvements in the understanding of this mode is, therefore, of crucial importance for sedimentary basin models. At intermediate pressure and temperature, microcracks, dislocations glide, grain boundary sliding can be active depending of the chemical composition of individual phases and should be taken into account in modelling. The composite structure of rocks can lead to rather heterogeneous internal stresses. In particular, tensile internal stresses can develop even under high confining pressure or compressive loading. This could have interesting implications for the existence of microcracks and interactions between those microcracks, whereas other ductile mechanisms can lead to potential instabilities. These microcracks are also important for fluid mobility inside crustal levels. At large scale, the relations between localized brittle deformation at the surface and localized ductile deformation in depth are essentially unknown (as more fully discussed in Quinlan et al., 1993~this issue). The link between these two localized modes of deformation should be connected and this obviously forms one of the fundamental issues of sedimentary basin studies. Recently, models which take account of the nonlinear behaviour of lithospheric materials, in both brittle and ductile modes, of the thermomechanical coupling, and of the geometrical non linearities of the deformation, have been succesfully proposed and applied to the evolution of extensional basins (Braun and Beaumont, 1989; Kooi et al., 1992). They do, however, have many intrinsic limitations. Among some of those, the difficulty of taking into account multi-scale processes has to be pointed out. Those different scales can be due to the heterogeneity of the structure or acquire during the evolution by such processes as phase change, shear zone formation
and faulting. A better knowledge of the transition between brittle and ductile mode of deformation is of key importance in this context. Modelling of mechanical
bebaviour:
perspectives
The development of sedimentary basins can now be studied by fully dynamical numerical models that incorporate a wide range of rheological behaviour. These models are generally quasistatic, since inertial forces can be ignored in slow geologic processes, but they must incorporate complex realistic relations that link stress and deformation at a required scale while satisfying the balance principles of the thermo-mechanics. This type of modelling allows the consequences of different assumptions about rheological behaviour and load history to be followed in detail and compared with observations on actual sedimentary basins. The comparison between model results and observations may be used to refine the initial assumptions about rheology and local histories or to acquire new data. The most flexible numerical technique for dealing with both complex geometries and rheologic laws is the finite element method (Zienkiewicz and Taylor, 1991). Developed over the past thirty years mainly by engineers for the simulation of complex structures, this technique allows the incorporation of almost abitrarily complex continuum rheologic laws in a simple manner. The recent development of powerful workstations has now brought finite element modelling into the reach of every university and laboratory. The principal differences between the needs of engineers and geologists for modelling their individual areas of interest is a problem of scale and heterogeneities. Displacement discontinuities at all scales (along arrays of fault, joints, cracks) are of central importance for geologic investigations. The difficulties in adapting finite element methods to the solution of geologic problems derive principally from the need to treat discontinuous motion, and to find a scale at which rheologic laws can be incorporated even statistically. The principal areas of concern for the next generation of sedimentary basin models should include the following:
94
Modelling of brittle behaviour
There are fundemental concerns about the applicability of Mohr-Coulomb (or DruckerPrager) constitutive relations. Brittle flow involves a hierarchy of slip along fractures over a broad range of size scales, and it is unclear wether continuum constitutive models can do justice to this complex situation. New models need to be formulated taking advantage of recent works on random material. Further work modelling the results of sand-box simulations as well as real sedimentary basins may resolve these uncertainties. Modelling of faults
Faults are the most characteristic geologic discontinuity. They are the result of localization and interactions. When they have developed, they often control the behaviour of upper level geologic structures. Good constitutive and numerical models of faults have not yet been formulated, even though some techniques have been proposed to incorporate numerically such discontinuities. There is not yet a generally accepted formulation which may describe fault growth and interaction nor a constitutive relation which incorporate friction laws to describe the fault plane properties. Interactions between faults may be responsible of a variety of basin configurations such as grabens, splays, and pull-apart basins. Effects of heterogeneities on model results
It is a matter of common observation that geologic systems deform in a heterogeneous manner, exhibiting independent rotations of blocks on scales ranging from the grain size in a rock to thousands of kilometers. Many natural systems are also composed of small constituent parts with different rheological properties, as for example interlayed sequences of ductile rocks and brittle rocks, or polyphasic aggregates. Describing the physical and rheological properties of such heterogeneous media is a rather complex problem. Homogenezation procedures have improved but can only be applied to weakly disordered mate-
rial. For highly disordered materials, statistical descriptions of those properties seem to be very attractive but are still in infancy. Thermo-mechanical
behaviour
In the past many models of geologic structures have assigned simple invariant properties to different parts, as for example elastic or plastic behaviour to the upper crust and viscous behaviour to lower layers. The rheological behaviour is controlled by physical variables as pressure, temperature, and strain rate which change with time and place in the evolving basin. An elastic layer might thus become viscous as it warms up during basin evolution or for lower strain rate, a viscous layer might also become elastic as it cools off. Further work should incorporate the full range of possible rheological behaviour and allow transitions. The energy and momentum conservation equations should be coupled and solved simultaneously in future models, and the energy resulting from such phenomena as phase changes or strain heating incorporated in a fundamental way. Localization of deformation
It is well known that increasingly narrow zones of deformation can develop even in initially continuous bodies depending on the detailed structure of the constitutive relations or interface properties. Localization processes do occur in brittle, ductile modes but also in brittle-ductile transitional zones. Methods for detecting those localizations are undergoing active developments. Very few studies have, however, been done for geological materials, and further development is needed to follow such localization phenomena both in terms of constitutive and numerical modelling. One of the main concerns for numerical modelling is the sensitivity of model results to variations in the input parameters, or boundary conditions. Such studies are at present relatively scarce but they are essential in future work if the influence of the various rheological and local history assumptions is to be understood.
LITHOSPHERE
RHEOLOGY
AND
SEDIMENTARY
BASINS
References Bassi, G., 1991. Factors controlling the style of continental rifting: insights from numerical modelling. Earth Planet. Sci. Lett., 105: 430-452. Bazan, Z., 1986. Mechanics of distributed cracking. Appl. Mech. Rev., 39: 675-705. Braun, J. and Beaumont, C., 1989. A physical explanation of the relation between flank uplifts and the breakup unconformity at rifted continental margins. Geology, 17: 760-764. Chery, J., Lucazeau, F., Dagnieres, M. and Vilotte, J.P., 1992. Large uplift of rift flanks: a genetic link with flexural rigidity ? Earth Planet. Sci. Lett., 112: 195-211. Cloetingh, S. and Banda, E., 1992. Mechanical structure of Europe’s lithosphere. In: D. Blundell, R. Freeman and St. Mueller (Editors), A Continent Reveals the European Geotraverse. Cambridge University Press, Cambridge, pp. 80-91. Cundall, P., 1991a. Numerical modelling of jointed and faulted rock. In: H.P. Rossmanith (Editor), Mechanics of Jointed and Faulted Rock. Balkema, Rotterdam, pp. 11-18. Cundall, P., 1991b. Shear band initiation and evolution in frictional materials. In: Mechanics Computing in 1990’s and beyond. Proc. Conf. Structural and Material Mechanics, Columbus, OH, May 1991, 2: 1279-1289. De Borst, R., 1989. Non-linear analysis of frictional materials. Ph.D. Thesis, Delft University, 140 pp. Desrue, J., 1990. Shear band initiation in granular materials. In: F. Darves (Editor), Geomaterials Constitutive Equations and Modelling. Elsevier, Amsterdam, pp. 283-310. Hirata, T., 1988. Fractal dimension of fault systems in Japan: fractal structure in rock fracture at various scales. Pure Appl. Geophys., 131: 157-170. Hot&h, F., 1993. Towards a kinematic model for the formation of the Pannonian Basin. In: S. Cloetingh, W. Sassi and F. HotvLth (Editors), The Origin of Sedimentary Basins: Inferences from Quantitative Modelling and Basin Analysis. Tectonophysics, 226: 333-357. Houseman, G. and England, P., 1986. A dynamic model of lithosphere extension and sedimentary basin formation. J. Geophys. Res., 91: 719-728. Kooi, H., Cloetingh, S. and Burrus, J., 1992. Lithosphere necking and regional isostasy at extensional basins. 1. Subsidence and gravity modeling with an application to the gulf of lions margins (SE France). J. Geophys. Res., 97: 17,553-17,571. Leroy, Y. and Ortiz, M., 1989. Finite element analysis of strain localization in frictional materials. Int. J. Num. Anal. Meth. Geomech., 13: 53-74. Lyakhovsky, V. Podladchikov, V. and Poliakov, A., 1993. Rheological model of fractured solid. In: S. Cloetingh, W. Sassi and F. HorvLth (Editors), The Origin of Sedimentary Basins: Inferences from Quantitative Modelhng and Basin Analysis. Tectonophysics, 226: 187-198. Mandl, G., 1988. Mechanics of Tectonic Faulting. Elsevier, Amsterdam, 407 pp.
95 Mandl, G., 1991. Modelling incipient tectonic faulting in the brittle crust of the earth. In: H.P. Rossmanith (Editor), Mechanics of Jointed and Faulted Rocks. Balkema, Rotterdam, pp. 29-40. Marret, R. and Allmendinger, R.W., 1991. Estimate of strain due to brittle faulting: sampling of fault populations. J. Struct. Geol., 13: 7735-7737. Melosh, J., 1990. Mechanical basis for low-angle normal faulting in the Basin and Range province. Nature, 343: 331-325. Melosh, J. and Williams, C.A., 1989. Mechanics of graben formation in crustal rocks: a finite element analysis. J. Geophys. Res., 94: 13,961-13,973. Okubo, P.G. and Aki, K., 1989. Fractal geometry in the San Andreas fault system. J. Geophys. Res., 92: 345-355. Quinlan, G.D., Walsh, J., Skogseid, J., Sassi, W., Cloetingh, S., Lobkovsky, L.L., Bois, C., Stel, H. and Banda, E., 1993. Relationship between deeper lithospheric processes and near-surface tectonics of basins. In: S. Cloetingh, W. Sassi and F. Hotvlth (Editors): The Origin of Sedimentary Basins: Inferences from Quantitative Modelling and Basin Analysis. Tectonophysics, 226: 217-225. Ranalli, G., 1987. Rheology of the Earth. Allen and Unwin, Boston, 366 pp. Ranalli, G. and Murphy, DC., 1987. Rheological stratification of the lithosphere. Tectonophysics, 132: 281-295. Ricke, M. and Meckie, J., 1989. Finite element modelling of a continental rift structure (Rhinegraben) with a large deformation algorithm. Tectonophysics, 165: 81-90. Rutter, E.H. and Bodrie, K.H., 1991. Lithosphere rheology a note of caution. J. Struct. Geol., 13: 363-367. Sawyer, D.S., 1985. Brittle failure in the upper mantle during extension of continental lithosphere. J. Geophys. Res., 90: 3021-3029. Sulem, J., Vardoulakis, I. and Kessler, N., 1992. Some mechanisms for structure selection and periodicity in geology. J. Struct. Geol. Velde, B., Dubois, J., Touchard, G. and Bradi, A., 1990. Fractal analysis of fractures in rocks: the Cantor’s dust method. Tectonophysics, 179: 345-352. Vilotte, J.-P., 1989. Modelisation thermomecanique de la deformation intracontinentale. These d’etat, Univ. Montpellier. Walsh, J.J., Watterson, J. and Yielding, G., 1991. The importance of small-scale faulting in regional extension. Nature, 351: 391-393. Zienkiewicz, O.C. and Taylor, R.L., 1991. The Finite Element Method. Vol. 2: Solid and Fluid Dynamics and Non-Linearity, 4th ed. McGraw-Hil, London, 807 pp. Zoback, M.D., Stephenson, R.A., Cloetingh, S., Larsen, B.T., Van Hoorn, B., Robinson, A.G., Horvath, F., Puigdefabregas, C. and Ben-Avraham, Z., 1993. Stresses in the lithosphere and basin formation. In: S. Cloetingh, W. Sassi and F. Horvath (Editors), The Origin of Sedimentary Basins: Inferences from Quantitative Modelling and Basin Analysis. Tectonophysics, 226: 1-13.
Tectonophysics, 226 (1993) 89-95 Elsevier
Science
Publishers
B.V., Amsterdam
Lithosphere
rheology and sedimentary basins
J.P. Vilotte a, J. Melosh b, W. Sassi ’ and G. Ranalli d 0Ecole
Normale Superieure, Departement de Geologie, 24 rue Lhomond, 75231 Paris, France b University of Arizona, Tucson, USA ’ Institut Fratqais du P&role, 1 et 4 Avenue de Bois-Preau, 92600 Rueil-Malmaison, France d Carleton VniversiTy, Ottawa, Canada (Received
November
15, 1992; revised version
Introduction The dynamics of sedimentary basins is reflected in the wide range of observational scales inside sedimentary basins. The advent of high-quality data sets have significantly improved the resolution of the record of near-surface tectonic processes. Crustal thinning, mechanical and thermal subsidence, sediment filling, are involved in extensional basin evolution, and controlled by complex interactions between ductile and brittle modes of deformation of the whole lithosphere. The rate of loading (extension and sediment filling) and the thermal evolution are among the most important controlling parameters. These nonlinear interactions do possess a memory of the evolution history and loading. Quantitative understanding of basin subsidence (and the offlap/onlap stratigraphic patterns of a specific basin) obviously benefits from progress in understanding the geodynamical context (HorvLth, 1993-this issue). In compressional settings, foreland basins result from the flexural lithospheric response to loading. Most of the models proposed so far have considered the lithosphere as a rheological unit and have been based on classical elastic and viscoelastic plate theory. The wavelength and amplitude of the flexural response is not an intrinsic property of the lithosphere but result from the history of the competitive interactions between rate of loading and rate of viscous dissipation 0040-1951/93/$06.00
0 1993 - Elsevier
Science
Publishers
accepted
June 1.5,1993)
(thermally activated). A clear physical description of this flexural mode has not yet been proposed, even though some recent results on the mechanisms of uplift shoulder formation during rifting evolution may be considered (Bassi, 1991; Chery et al., 1992). The geodynamical context of those basins is complex, and the relationship between the transition of extensional and compressional domains is a topic of vigorous research. Current models for extensional and compressional basins are strongly based on a bulk rheological description of the whole lithosphere and on a kinematic description of the deformation mechanisms (Sawyer, 1985; Houseman and England, 1986; Quinlan et al., 1993-this issue). The basin record does reveal to some extend the memory of the deformation history starting from the construction of the internal structure of the basins (i.e. from the processes leading to the formation of rocks: sedimentation, diagenesis, compaction; including possible buildup of fluid overpressures), and the pattern of the large deformations by faulting or folding. To enhance the understanding of the formation and evolution of sedimentary basins it is important to fully address the physical mechanisms operating at different scale in the continental lithosphere. For example, faulting forms a most important expression (at least at the surface) of large scale deformation in the basins. How those basins are related to the faulting process and the fault interactions is an unsolved question. Pull-apart basins are certainly
B.V. All rights reserved
one of the clearest example of basins associated with large transcurrent fault systems, but at smaller scale and in an other gcodynamic context, graben formation raise interesting questions on faulting mechanisms (Melosh and Williams, 1989; Ricke and Mechie, 1989; Cundall, 1991a). The construction of lithospheric strength envelopes (see, e.g., Cloetingh and Banda, 1992) forms an important intermediate step in the characterisation of the complex rheological behaviour of the lithosphere underlying basins; even though it remains a static picture based on quite restrictive assumptions (Rutter and Bodrie, 1991). At low pressure and low temperature, a brittle mode operates mostly by microcrack interactions and growth, frictional-slip plasticity, both expected to be pressure dependent and time independent. At conditions of high pressure and high temperature deformation occurs in a ductile mode involving dislocations climbing, diffusion, grain boundary sliding all expected to be thermally activated, time dependent and probably pressure independent. In between a wide transitional mode operates where these different mechanisms are competing and interacting (Ranalli, 1987; Ranalli and Murphy, 1987; Vilotte, 39891. The mechanical behaviour of a rock is not an intrinsic property but depends on different physical parameters such as pressure, temperature, rate of loading, microstructure (e.g., grain size, shape), fluid content. Crustal and mantle materials are heterogeneous polycrystalline aggregates which exhibit several interacting inelastic mechanisms. Although much progress has been made in the understanding of the different modes of deformation (in terms of governing mechanisms and validity domain), more precise knowledge of rock physical properties and behaviour under arbitrary loading path is required. This is particularly important as recent developments in the numerical modelling of localisation phenomena (De Borst, 1989; Leroy and Ortiz, 1989; Desrue, 1990; Cundall, 1991b; Mandl, 1988, 1991; Sulem et al., 1992; Lyakovsky et al., 1993-this issue) allow the incorporation of heterogeneous materials and fractures in basin modelling. Numerical models of sedimentary basins require a full understanding of the nonlinear litho-
spheric modes of deformation. Of primary importance for the next generation of basin models, will be to address the interaction between those mechanisms and the spectrum of scales intrinsically related to these non-linear processes. In all cases most of the models proposed so far consider the evolution of sedimentary basins as a two-dimensional problem although this is obviously not the case. Proper data allowing a full 3-D characterization of a basin (extension, thinning, sediment sequences, fault geometry) should become more easily available to the academic research community. The brittle mode
The construction of quantitative predictive basin formation models requires full understanding of the processes underlying the development of faulting, the interaction between faulted domains and the fine structure of stress propagation and accumulation in rheologically stratified lithosphere. At low pressure and low temperature, the brittle deformation is characterized, at small scale by micro-decohesions originating from the nucleation, growth and coalescence of surfacic (microcracks mostly of mode I) or volumetric (cavities) discontinuities which may be related with dislocations. Those discontinuities result from the heterogeneity of the internal stresses due to the polyphasic and polycrystalline nature of the lithosphere. At basin scale, faulting and fault interactions are among the main mechanisms involved in the deformation of the uppermost part of the continental lithosphere. The problem of scale is further compounded by the fact that those discontinuities have their own spatial and temporal scaling laws. At the laboratory scale as well as in numerical modelling progress has been made in the understanding of failure in terms of progressive localized damage (Bazan, 1986; Lyakhovsky et al., 1993”this issue). Further research on the mechanisms of growth, interaction and localizatiun of arrays of microcracks, as well as their respective sensitivity to pressure and temperature is important. Understanding physically those processes
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and their implications in terms of bulk properties damage (e.g., elasticity, porosity) is of primary importance not only to characterize the prefailure behaviour of rocks, but also to formulate the physical interactions leading to a macroscopic localized mode in term of smaller-grained variables both in time and space. Recent constitutive models taking into account potential frictional slip systems have been formulated leading to non-associative plasticity. These models are now being steered to applications in sedimentary basins modelling to address the conditions for the formation of localized fault zones and their orientations. ~though those models may be useful in predicting the failure of rock species in laboratory testing conditions, they fail to model the post-failure behaviour due to lack of internal length. With such an approach, localization length and evolution through time can not be predicted. At the scale of seismic resolution, patterns of population of faults in the basins are being regarded critically by geologists and geophysicists. Whether fault propagation and fault interaction are auto-similar processes may have important implications in term of the hierarchy of scales involved in their description. The fractal nature of fault size populations also questions the meaning of average spacing of large faults: what is a large fault? Recent analysis of the spatial distribution of faults suggests fractal scaling laws (Hirata, 1989; Okubo and Aki, 1989; Velde et al., 1990; Marret and Allmendinger, 1991; Walsh et al., 1991). Given the improved quality and availability of seismic data, this type of analysis could be performed routinely. Attempts have been made to describe fault growth and fault structuration as the result of a spatio-temporal nonlinear dynamical evolution of a heterogeneous lithosphere. Such approaches provide a framework in which those different scaling laws can be linked together. Recent developments in physical properties of heterogeneous and random materials coupled to the analysis of complex nonlinear dynamical systems have to be explored. Fault structuration of the continental lithosphere might partly result from the inherited heterogeneities of the lithosphere. Current models describing the growth of faults are empirically based and exist-
ing mechanical models providing a basis to fault growth and interactions are under investigation. At small scales models describing faults as Somigliana dislocations have been proposed but not yet fully explored. As discussed previously, the bulk of the currently used basin models are based on an approximation of the rheological description of the brittle regime invoking homogenized stress and strain fields at the scale of the basin itself. The constitutive behaviour is provided by Byerlee’s empirical friction law. As pointed out above (see also Zoback et al., 1993-this issue) this empirical relation appears to be in good agreement with the observed magnitude of stress at least within the uppermost levels (< 5 km). At higher confining presssure and temperature, very little is known on the validity of such a friction law. Recent observations on fault tips and stress patterns associated with major transcurrent fault systems (Zoback et al., 1993-this issue) do not always agree with Byerlee’s law. How this law should be integrated in the overall description provided by basin formation models characterizing the bulk rheological properties is a first order question. At the scale of the basins, the presence of populations of faults as well as the intrinsic heterogeneity of the structures and the dependence on strain rate requires further attention. This applies in particular in the context of subsidence analysis of syn-rift sequences for the effects of varying rates of fault movement and spatial variations in bulk strains, strain rates and stresses. The ductile mode Initially, the modelling of sedimentary basins evolution has focused on the ductile mode operating in the lower crust and the mantle under restrictive assumptions of homogenei~, steady state and isotropy. Major contributions have been made in the understanding of steady-state creep for polycristalline aggregates by experimental studies, and most of the laboratory data have been extrapolated outside the validity domain of those experiments. This mode of deformation (as for the brittle one) do depend on a number of external and
92
internal parameters such as fluid pressure, chemical effects (associated with those fluids), grain sizes and shapes, as well as on microstructural instabilities like phase change, recrystallization, grain growth which are still poorly known. Furthermore, the ductile behaviour of a polycristalline aggregate depends on its chemical composition and its different stable mineralogic phases. Extrapolation of experimental results both in time and space requires knowledge of the different physical mechanisms of each phase. Evidence from exposed lower crustal rocks and recent seismic reflection studies clearly show that ductile deformation is indeed very heterogeneous and localized. Such a contrast cannot be simply explained by the chemical heterogeneity of the lithospheric materials but must also be related to the deformation mechanisms. The experimental data set deals with a great variety of aggregates, microstructures, and environmental parameters. The data set is, however, limited in the sense that most of those data come mostly from hardening tests and to some extent from creep tests, leading to a limited loading paths and a narrow validity domain in time, pressure and temperature. More experimental data providing a greater variety of loading paths are needed. For monophasic aggregates, steady-state creep with the characteristic power-law relationship between the creep strain rate and the stress is probably the most well known ductile behaviour, even though it only characterize a unidimensional response (in term of stress and strain) and a limited domain of pressure, temperature, strain rate and stress. Recently, the attention has been focused on other crucial effects resulting from transient hardening phenomena which clearly controlled for example the so called power-law breakdown. Those are not yet fully understood at the microscopic levels but do involve long-distance dislocations-dislocations interactions, or short-distance dislocations-obstacles interactions. Such mechanisms are very important and have been extensively studied for other polycristalline materials such as metals. A proper three-dimensional viscous-hardening law has not yet emerged due to the lack of experimental data.
J.P.
VII.0
1-1‘1: tl’
Al
Such a law would be of great interest since it will provide a more realistic description of the stress-strain response with potential implications in terms of localization or instability. Transient hardening effects and their proper modelling in a 3-D constitutive relation for the polycristalline structure of those monophasic aggregates has not yet been explicitly taken into account in the constitutive modelling. Interactions between grains and the influence of internal stresses resulting from deformation incompatibility are to be actively explored to understand the progressive fabrics associated with the deformation. This is of central importance for modelling ductile localization and induced anisotropy. Recent models for polycrystalline aggregates have been proposed for metals and the underlying methodologies should be explored in rock mechanics. Experiments on progressive fabrics during simple shear at high temperature and pressure would be valuable as well as studies of the polyphase nature of rocks and its implications for the overall ductile response. This area of research is of crucial importance in order to understand the competing effects between different dissipation mechanisms and their potential implications for ductile instabilities, localization and progressive fabrics. At larger scale (both in space and time) other complications might arise. It is quite clear that ductile deformation is far from being homogeneous and that shear zones have also their own scaling properties. At which extend localization modes like necking, buckling or shear bands depend on the bulk properties, or heterogeneities (chemical and thermal), or the interface properties has yet to be assessed. The thermal implications of those localization phenomena are of crucial importance in the understanding of decollement, core-complex structures. The strong thermal activation of that mode of deformation imply that the thermo-mechanical coupling has to be incorporated in the modelling. Our inability to describe the ductile behaviour at large scale (taking in to account the chemical and thermal heterogeneities) and the lack of detailed constitutive behaviour at smaller scale may explain why shear bands are still not physically understood.
LITHOSPHERE RHEOLOGY AND SEDIMENTARY
The brittle-ductile
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BASINS
mode
The brittle-ductile transitional mode of deformation results from the competing effects of different dissipative mechanisms and the chemical heterogeneities of geological materials. This mode of deformation cover a range of pressure and temperature which is quite characteristic of most of the continental crust. Improvements in the understanding of this mode is, therefore, of crucial importance for sedimentary basin models. At intermediate pressure and temperature, microcracks, dislocations glide, grain boundary sliding can be active depending of the chemical composition of individual phases and should be taken into account in modelling. The composite structure of rocks can lead to rather heterogeneous internal stresses. In particular, tensile internal stresses can develop even under high confining pressure or compressive loading. This could have interesting implications for the existence of microcracks and interactions between those microcracks, whereas other ductile mechanisms can lead to potential instabilities. These microcracks are also important for fluid mobility inside crustal levels. At large scale, the relations between localized brittle deformation at the surface and localized ductile deformation in depth are essentially unknown (as more fully discussed in Quinlan et al., 1993~this issue). The link between these two localized modes of deformation should be connected and this obviously forms one of the fundamental issues of sedimentary basin studies. Recently, models which take account of the nonlinear behaviour of lithospheric materials, in both brittle and ductile modes, of the thermomechanical coupling, and of the geometrical non linearities of the deformation, have been succesfully proposed and applied to the evolution of extensional basins (Braun and Beaumont, 1989; Kooi et al., 1992). They do, however, have many intrinsic limitations. Among some of those, the difficulty of taking into account multi-scale processes has to be pointed out. Those different scales can be due to the heterogeneity of the structure or acquire during the evolution by such processes as phase change, shear zone formation
and faulting. A better knowledge of the transition between brittle and ductile mode of deformation is of key importance in this context. Modelling of mechanical
bebaviour:
perspectives
The development of sedimentary basins can now be studied by fully dynamical numerical models that incorporate a wide range of rheological behaviour. These models are generally quasistatic, since inertial forces can be ignored in slow geologic processes, but they must incorporate complex realistic relations that link stress and deformation at a required scale while satisfying the balance principles of the thermo-mechanics. This type of modelling allows the consequences of different assumptions about rheological behaviour and load history to be followed in detail and compared with observations on actual sedimentary basins. The comparison between model results and observations may be used to refine the initial assumptions about rheology and local histories or to acquire new data. The most flexible numerical technique for dealing with both complex geometries and rheologic laws is the finite element method (Zienkiewicz and Taylor, 1991). Developed over the past thirty years mainly by engineers for the simulation of complex structures, this technique allows the incorporation of almost abitrarily complex continuum rheologic laws in a simple manner. The recent development of powerful workstations has now brought finite element modelling into the reach of every university and laboratory. The principal differences between the needs of engineers and geologists for modelling their individual areas of interest is a problem of scale and heterogeneities. Displacement discontinuities at all scales (along arrays of fault, joints, cracks) are of central importance for geologic investigations. The difficulties in adapting finite element methods to the solution of geologic problems derive principally from the need to treat discontinuous motion, and to find a scale at which rheologic laws can be incorporated even statistically. The principal areas of concern for the next generation of sedimentary basin models should include the following:
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Modelling of brittle behaviour
There are fundemental concerns about the applicability of Mohr-Coulomb (or DruckerPrager) constitutive relations. Brittle flow involves a hierarchy of slip along fractures over a broad range of size scales, and it is unclear wether continuum constitutive models can do justice to this complex situation. New models need to be formulated taking advantage of recent works on random material. Further work modelling the results of sand-box simulations as well as real sedimentary basins may resolve these uncertainties. Modelling of faults
Faults are the most characteristic geologic discontinuity. They are the result of localization and interactions. When they have developed, they often control the behaviour of upper level geologic structures. Good constitutive and numerical models of faults have not yet been formulated, even though some techniques have been proposed to incorporate numerically such discontinuities. There is not yet a generally accepted formulation which may describe fault growth and interaction nor a constitutive relation which incorporate friction laws to describe the fault plane properties. Interactions between faults may be responsible of a variety of basin configurations such as grabens, splays, and pull-apart basins. Effects of heterogeneities on model results
It is a matter of common observation that geologic systems deform in a heterogeneous manner, exhibiting independent rotations of blocks on scales ranging from the grain size in a rock to thousands of kilometers. Many natural systems are also composed of small constituent parts with different rheological properties, as for example interlayed sequences of ductile rocks and brittle rocks, or polyphasic aggregates. Describing the physical and rheological properties of such heterogeneous media is a rather complex problem. Homogenezation procedures have improved but can only be applied to weakly disordered mate-
rial. For highly disordered materials, statistical descriptions of those properties seem to be very attractive but are still in infancy. Thermo-mechanical
behaviour
In the past many models of geologic structures have assigned simple invariant properties to different parts, as for example elastic or plastic behaviour to the upper crust and viscous behaviour to lower layers. The rheological behaviour is controlled by physical variables as pressure, temperature, and strain rate which change with time and place in the evolving basin. An elastic layer might thus become viscous as it warms up during basin evolution or for lower strain rate, a viscous layer might also become elastic as it cools off. Further work should incorporate the full range of possible rheological behaviour and allow transitions. The energy and momentum conservation equations should be coupled and solved simultaneously in future models, and the energy resulting from such phenomena as phase changes or strain heating incorporated in a fundamental way. Localization of deformation
It is well known that increasingly narrow zones of deformation can develop even in initially continuous bodies depending on the detailed structure of the constitutive relations or interface properties. Localization processes do occur in brittle, ductile modes but also in brittle-ductile transitional zones. Methods for detecting those localizations are undergoing active developments. Very few studies have, however, been done for geological materials, and further development is needed to follow such localization phenomena both in terms of constitutive and numerical modelling. One of the main concerns for numerical modelling is the sensitivity of model results to variations in the input parameters, or boundary conditions. Such studies are at present relatively scarce but they are essential in future work if the influence of the various rheological and local history assumptions is to be understood.
LITHOSPHERE
RHEOLOGY
AND
SEDIMENTARY
BASINS
References Bassi, G., 1991. Factors controlling the style of continental rifting: insights from numerical modelling. Earth Planet. Sci. Lett., 105: 430-452. Bazan, Z., 1986. Mechanics of distributed cracking. Appl. Mech. Rev., 39: 675-705. Braun, J. and Beaumont, C., 1989. A physical explanation of the relation between flank uplifts and the breakup unconformity at rifted continental margins. Geology, 17: 760-764. Chery, J., Lucazeau, F., Dagnieres, M. and Vilotte, J.P., 1992. Large uplift of rift flanks: a genetic link with flexural rigidity ? Earth Planet. Sci. Lett., 112: 195-211. Cloetingh, S. and Banda, E., 1992. Mechanical structure of Europe’s lithosphere. In: D. Blundell, R. Freeman and St. Mueller (Editors), A Continent Reveals the European Geotraverse. Cambridge University Press, Cambridge, pp. 80-91. Cundall, P., 1991a. Numerical modelling of jointed and faulted rock. In: H.P. Rossmanith (Editor), Mechanics of Jointed and Faulted Rock. Balkema, Rotterdam, pp. 11-18. Cundall, P., 1991b. Shear band initiation and evolution in frictional materials. In: Mechanics Computing in 1990’s and beyond. Proc. Conf. Structural and Material Mechanics, Columbus, OH, May 1991, 2: 1279-1289. De Borst, R., 1989. Non-linear analysis of frictional materials. Ph.D. Thesis, Delft University, 140 pp. Desrue, J., 1990. Shear band initiation in granular materials. In: F. Darves (Editor), Geomaterials Constitutive Equations and Modelling. Elsevier, Amsterdam, pp. 283-310. Hirata, T., 1988. Fractal dimension of fault systems in Japan: fractal structure in rock fracture at various scales. Pure Appl. Geophys., 131: 157-170. Hot&h, F., 1993. Towards a kinematic model for the formation of the Pannonian Basin. In: S. Cloetingh, W. Sassi and F. HotvLth (Editors), The Origin of Sedimentary Basins: Inferences from Quantitative Modelling and Basin Analysis. Tectonophysics, 226: 333-357. Houseman, G. and England, P., 1986. A dynamic model of lithosphere extension and sedimentary basin formation. J. Geophys. Res., 91: 719-728. Kooi, H., Cloetingh, S. and Burrus, J., 1992. Lithosphere necking and regional isostasy at extensional basins. 1. Subsidence and gravity modeling with an application to the gulf of lions margins (SE France). J. Geophys. Res., 97: 17,553-17,571. Leroy, Y. and Ortiz, M., 1989. Finite element analysis of strain localization in frictional materials. Int. J. Num. Anal. Meth. Geomech., 13: 53-74. Lyakhovsky, V. Podladchikov, V. and Poliakov, A., 1993. Rheological model of fractured solid. In: S. Cloetingh, W. Sassi and F. HorvLth (Editors), The Origin of Sedimentary Basins: Inferences from Quantitative Modelhng and Basin Analysis. Tectonophysics, 226: 187-198. Mandl, G., 1988. Mechanics of Tectonic Faulting. Elsevier, Amsterdam, 407 pp.
95 Mandl, G., 1991. Modelling incipient tectonic faulting in the brittle crust of the earth. In: H.P. Rossmanith (Editor), Mechanics of Jointed and Faulted Rocks. Balkema, Rotterdam, pp. 29-40. Marret, R. and Allmendinger, R.W., 1991. Estimate of strain due to brittle faulting: sampling of fault populations. J. Struct. Geol., 13: 7735-7737. Melosh, J., 1990. Mechanical basis for low-angle normal faulting in the Basin and Range province. Nature, 343: 331-325. Melosh, J. and Williams, C.A., 1989. Mechanics of graben formation in crustal rocks: a finite element analysis. J. Geophys. Res., 94: 13,961-13,973. Okubo, P.G. and Aki, K., 1989. Fractal geometry in the San Andreas fault system. J. Geophys. Res., 92: 345-355. Quinlan, G.D., Walsh, J., Skogseid, J., Sassi, W., Cloetingh, S., Lobkovsky, L.L., Bois, C., Stel, H. and Banda, E., 1993. Relationship between deeper lithospheric processes and near-surface tectonics of basins. In: S. Cloetingh, W. Sassi and F. Hotvlth (Editors): The Origin of Sedimentary Basins: Inferences from Quantitative Modelling and Basin Analysis. Tectonophysics, 226: 217-225. Ranalli, G., 1987. Rheology of the Earth. Allen and Unwin, Boston, 366 pp. Ranalli, G. and Murphy, DC., 1987. Rheological stratification of the lithosphere. Tectonophysics, 132: 281-295. Ricke, M. and Meckie, J., 1989. Finite element modelling of a continental rift structure (Rhinegraben) with a large deformation algorithm. Tectonophysics, 165: 81-90. Rutter, E.H. and Bodrie, K.H., 1991. Lithosphere rheology a note of caution. J. Struct. Geol., 13: 363-367. Sawyer, D.S., 1985. Brittle failure in the upper mantle during extension of continental lithosphere. J. Geophys. Res., 90: 3021-3029. Sulem, J., Vardoulakis, I. and Kessler, N., 1992. Some mechanisms for structure selection and periodicity in geology. J. Struct. Geol. Velde, B., Dubois, J., Touchard, G. and Bradi, A., 1990. Fractal analysis of fractures in rocks: the Cantor’s dust method. Tectonophysics, 179: 345-352. Vilotte, J.-P., 1989. Modelisation thermomecanique de la deformation intracontinentale. These d’etat, Univ. Montpellier. Walsh, J.J., Watterson, J. and Yielding, G., 1991. The importance of small-scale faulting in regional extension. Nature, 351: 391-393. Zienkiewicz, O.C. and Taylor, R.L., 1991. The Finite Element Method. Vol. 2: Solid and Fluid Dynamics and Non-Linearity, 4th ed. McGraw-Hil, London, 807 pp. Zoback, M.D., Stephenson, R.A., Cloetingh, S., Larsen, B.T., Van Hoorn, B., Robinson, A.G., Horvath, F., Puigdefabregas, C. and Ben-Avraham, Z., 1993. Stresses in the lithosphere and basin formation. In: S. Cloetingh, W. Sassi and F. Horvath (Editors), The Origin of Sedimentary Basins: Inferences from Quantitative Modelling and Basin Analysis. Tectonophysics, 226: 1-13.