lithospheric geotherms and strength.

Transcription

1 Toasting the Jelly Sandwich: The effect of shear heating on lithospheric geotherms and strength. Ebbe H. Hartz Physics of Geological Processes, University of Oslo, 316 Oslo, Norway Aker Exploration, Badehusgate 39 A, P.O. Box 589 Strømsteinen, NO 43 Stavanger, Norway Yuri Y. Podladchikov Physics of Geological Processes, University of Oslo, 316 Oslo, Norway ABSTRACT We refine conventional continental-scale geodynamic model by including conversion of mechanical work done by deformation into heat. The intensity of the shear heating is extracted from the Brace-Goetze strength envelope without any additional model parameters or assumptions. Incorporation of this, certainly present, heating rate into a model may result in up to tenfold stress reduction, which is exceeding the effects of variation of common parameters within their uncertainties limits. Shear heating while lithospheric thickening at high integrated strength solve the puzzle of the hereunto-missing heat source recorded by metamorphism, magmatism and heat flow in mountain building. However, the mechanism is self-limiting as the rising temperature reduces stress and thus the rate of heat production. Thus this is a self-regulating mechanism maintaining a moderate integrated lithospheric strength equal to results of model-independent force balanced calculations, and surface heat flow measurements. Keywords: Shear-heating, lithosphere, strength, geotherm, rheology, heat-flow. Page 1 of 15

2 DYNAMIC VERSUS STATIC MODELS OF LITHOSPHERIC STRENGTH AND TEMPERATURE The lithosphere encases the convecting, fluid-like silicate earth. It can be strong enough to resist deformation for billions of years, but also undergo short phases (tens of million years) of rapid deformation. Mechanical strength and temperature are key controls on lithospheric deformation, and magmatism. Lithospheric strength estimates from laboratory deformation experiments (Brace and Kohlstedt, 198) or inferred from natural observations (Jeffreys, 197) are commonly summarized in a global, 1D model, the Brace-Goetze lithosphere or strength envelope (Molnar, 1992). This model incorporates both brittle rock strength, increasing with pressure (depth), and viscous rock strength, which is a function of rock properties, strain rate and temperature, and generally decreases with depth (Fig. 1). Rocks are assumed to fail by the weaker of the two criteria resulting in a branched strength envelope with a strong, brittle (seismogenic) upper crust, and dry rock in the lower crust/upper mantle, separated by a weak ductile middle crust (Buck, 1991) (Carter and Tsenn, 1987) (Burov and Watts, 26): the jelly sandwich (Jackson, 22). These, traditional, one-dimensional mechanical models of lithospheric strength (the Brace- Goetze lithosphere) ignore the thermal effects of deformation (Molnar, 1992). In such models orogenic thickening would stretch the geotherm and thus cause a decay in the geothermal gradient. However, high surface heat flow and magmatism show that thick orogens are hotter that the stable continental lithosphere at a given depth (Chapman and Furlong, 1992) (Pollack et al., 1993). Had it not been for this orogenic heat Earth s lithosphere would be ~2 times too strong to deform under tectonic forces, and orogenic processes would be violent and short-lived, affecting only narrow sutures between Page 2 of 15

3 colliding plates (Hyndman et al., 25). Orogenic heat has been attributed to pre or non- orogenic processes such as the rise of hot astenospheric material following delamination and sinking of relatively colder, denser lithosphere from an orogenic root (Hyndman et al., 25), or shortlived tectonic wedges of highly radiogenic material (Jamieson et al., 1998). Other explanations invoke shear heating by viscous deformation in two or three- dimensional finite difference/element models of a complexly deforming lithosphere (Regenauer-Lieb et al., 21; Roselle and Engi, 22; Burg and Gerya, 25; Doglioni et al., 25; Kaus and Podlachikov, 26; Regenauer-Lieb et al., 26). Here we consider the effects on a lithospheric scale of shear heating in a deforming continent, using a comparatively simple 1D approach. Shear heating intensity (W*m -3 ) is equal to strength (differential stress to be more precise) times strain rate, thus having units Pa* s -1 (Stüwe, 22). Multiplying the Brace-Goetze lithospheric strength envelope by the strain rate used to produce it, therefore quantifies shear heating intensity throughout the lithosphere (Fig. 1b, upper scale). In comparison to the above-cited studies, this method is general and easy to implement. It furthermore includes dissipation for both brittle and viscous irreversible deformation, and works for both lithospheric thickening and thinning. In addition the approach allows calculations of both lithospheric strength and shear heating rate to be easily compared to model-independent force balanced calculations and measurements of surface heat flow. We use this facility to explore temperature and strength of a thickening lithosphere, composed of a wet quartz upper crust ( 3 km initial depth) (Carter and Tsenn, 1987), dry mafic granulite lower crust (3 4 km initial depth) (Wilks and Carter, 199), and dry dunite mantle (below 4 km initial depth) (Chopra and Page 3 of 15

4 Paterson, 1984). Other modeling properties and numerical methods are given in the supplementary material. Traditionally, the Brace-Goetze strength envelope is taken to be static (e.g. Molnar, 1992). Instead, our computer code LiToastPhere allows rock units to thicken or thin according to ambient strain rates, as described in the methods section below. Stresses and thus shear heating in extensional settings is roughly a third of compressional setting. Thus here we focus on a compressional scenario, in which the crust thickens from 4 to 85 km with a strain rate of 3*1 15, as has happened during the India Asia collision. We compare results with and without shear heating, and three different modes of viscous deformation and strain rates. For comparisons, we present an example of the effects of shear heating in an extending lithosphere in the supplementary material. SHEAR HEATING AND STRENGTH DECAY IN DYNAMIC COMPRESSIONAL MODELS WITH POWER LAW CREEP In our first example the lithosphere is thickened, neglecting, as is conventional, the effects of shear heating. Then, rocks in the lower crust and upper mantle retain their low initial temperature during thickening (Fig. 1a), and stress remains almost constant within creeping sections (Fig. 1b). In contrast differential stresses increase within brittle parts of the rock column due to their downward displacement (rising pressure) (Fig. 1b, blue lines). If rocks near the Moho deform under a differential stress of 2.5*1 9 Pa (25 Kbar) at a strain rate of 3*1 15 s -1 (Fig. 1b, lower scale), as in conventional models (e.g. Jackson, 22)(Fig. 1b, the black line), the neglected corresponding rate of shear heating is 7.5*1 6 W*m -3 (Fig. 1b, upper scale). This is an order of magnitude greater than the radiogenic heat production in highly radiogenic rocks (Turcotte and Schubert, 22), and would rise Page 4 of 15

5 the maximum temperature increase of 755 K per 1% strain in rock with a lower crustal density (33 kg*m -3 ) and heat capacity (1 J*kg -1 *k -1 ) if deformation was fast enough that the heat was contained. At realistic strain rates the actual rise in temperature will be lower due to conduction of heat during shearing and thermal weakening of the rocks suppressing the actual heat production. As a result, a two-way, thermomechanically coupled model predicts a temperature rise of ~1 K with respect to the case without shear heating for 1% strain (Fig. 1a, 2a). Such a rise would cause the strength of the upper mantle to drop by a factor ten (Fig. 1b, 2b). SHEAR HEATING AND STRENGTH DECAY IN MODELS WITH HIGH STRESS CREEP The magnitude of shear heating in our first compressional example is tied with the 25 Kbar stress inherent to the common, simplified Brace-Goetze strength envelope, in which power law creep is the only mode of viscous, compressional deformation (Fig. 1b). This is inappropriate for deep Earth/high stress (Tsenn and Carter, 1987), where the weaker, non-exponential Dorn or Peierls creep law should be used (Brace and Kohlstedt, 198; Molnar, 1992; Stüwe, 22; Goetze, 1978; Tsenn and Carter, 1987). Use of the Dorn creep law (Goetze, 1978) in the Brace-Goetze strength envelope for stresses above 6 Kbar, gives a substantial reduction of the initial lithospheric strength (Fig. 3b, lower scale): initial upper mantle strength is 11 Kbar, rather than 25 Kbar, and the corresponding shear heating is 3*1 6 W*m -3 rather than 7.5*1 6 W*m -3 (Fig. 3b, upper scale). Nevertheless, once thermomechanical feedbacks have been taken into account, the temperature and strength profiles predicted with and without the Dorn creep law are indistinguishable after the Page 5 of 15

6 lithosphere is thickened illustrating how shear heating overshadows all other modeling parameters (Figs. 1ab and 3ab). SHEAR HEATING AND STRENGTH DECAY IN MODELS WITH VARIABLE STRAIN RATE Conventional models of lithospheric deformation assume a constant strain rate throughout the lithosphere, with strong and weak rocks deforming at the same rate. The typical strain rate in these models of 1 15 s -1 is many orders of magnitude too slow for high strain zones, for example along detachment faults, and too fast for rigid blocks between these zones (Stüwe, 22). To test the effect of a variable strain rate we have modeled deformation of a lithosphere with strong upper crust, lower crust and mantle, deforming ten times slower (strain rate 1 15 s -1 ) than the weak middle crust (strain rate 1 14 s -1 ), while keeping the overall thickening rate of the crust the same as in previous models. The resulting stresses are more evenly distributed throughout the lithosphere (Fig. 3c), and stress and strain rate patterns agree well with fully dynamic models in which two strong layers (i.e., upper crust and upper mantle), bend up and down rather than thicken to accommodate overall shortening (Schmalholz et al., 25). For lower strain rates of 1 15 s -1, our earlier estimate of shear heating in the upper mantle (strength 1.5 Kbar), is reduced to 1 6 W*m -3. The corresponding rise in temperature could be as much as 315 K per 1% strain, but in our model, the upper mantle is thickened by only 33% during 9 My of deformation. With two-way, thermomechanical coupling, this gives an estimated temperature rise of only 5 K. Meanwhile, higher strain rates of 1 14 s -1 in the middle crust do not contribute significantly to shear heating due to weakness of the rocks (Figs. 2cd, 3c). Overall, this Page 6 of 15

7 geologically more realistic model shows less shear heat production than equivalent models with uniform strain rate (Figs. 2d, 3d) and thus present strongest upper mantle of all shear heated scenarios discussed here (Figs. 2c, 3c). Generally earthquakes in the deep crust or upper mantle are considered as brittle or Byerlee type failure. In our first model, neglecting shear heating (Fig. 1b), such earthquakes would occur near Moho of a thickened orogen, as predicted by e.g., Jackson (22). In contrast none of the shear heating models, present such high stresses at depth (e.g., Figure 2b,d). Conversely one could argue that this is an artifact of all deformations being modeled as pure shear thickening at modest strain rates. Earthquakes in contrast occur along faults, which are local high strain zones. Thus potentially, brittle failure could occur by rapidly raising the strain rate in a narrow zone. We test this hypothesis by raising the strain rate exponent 1% every.1 second, in an m-scale subhorizontal simple shear zone. Initially the differential stresses in the shear zone, rise proportional to the increase in strain rate. As both strain rate and stresses increases, the subsequent shear heating becomes intense, thereby weakening the rocks, so that stresses decrease despite the continuous rise in strain rate. In the example presented in Figure 3 differential stresses peak at ~35 Kbar, utilizing a strain rate of 1 1 /s (Fig. 3a,c). By then shear heating is intense (1 8 W*m -3 ), causing frictional melting within.1 second (Fig. 3d). Shear heating thus provide a plausible alternative to traditional models of deep brittle earthquakes neglecting the effect of thermomechanical feedback (Kelemen and Hirth, 27), through a positive feedback between shear heating and raising strain rates at stresses below brittle failure. INTEGRATED LITHOSPHERIC STRENGTH COMPARED TO FORCE - BALANCED MODELS Page 7 of 15

8 Notably, all our shear heated models yield integrated lithospheric strengths of ~1 13 Pa*m after 1% thickening, regardless of the highly different assumptions of strain rate, and creep laws. This balance occurs because high strength models also produce more shear heat (Figs. 1,2,3). Thus within 3% strain the integrated lithospheric strength is balanced at a steady-stateof ca Pa*m (e.g., Figures 1b, 2b). This contrasts models neglecting shear heating, in which compression without shear heating result in continues rise in lithosphere strength, reaching ~1 14 Pa*m by the end of the numeric experiment (Fig. 1b, blue line). Interestingly the forces in an orogen can be calculated using only gravity, and without any rheological or thermal input (Jeffreys, 197; Molnar and Lyon-Caen, 1989) and caps the strength integrated over depth in the Brace-Goetze envelope at 1 13 Pa*m, or an average of 1 Kbar strength over 1 km depth (Stüwe, 22). Thus only models with shear-heating return realistic estimates of long term quasi steady-statelithospheric strength (Fig. 2d). THE EFFECT OF SHEAR HEATING ON SURFACE HEAT FLOW Another important difference between lithospheric deformation models with and without shear heating is the predicted surface heat flow. In stable continents, the average surface heat flow is.7 W*m -2, with approximately equal contributions from conduction of astenospheric heat, and radiogenic heat from within the lithosphere (Turcotte and Schubert, 22). In the model without shear heating, surface heat flow drops from~.7 to ~.5 W*m -2 due to stretching of the geotherm during lithosphere thickening (Fig. 4). Instead, shear heating elevates the surface heat flow: multiplying a lithospheric stress of 1 13 Pa*m by a strain rate of 3*1 15 s -1, we obtain a depth-integrated shear heat intensity of.3 W*m -2. However shear heating is faster than the conduction of heat toward the Page 8 of 15

9 Earth s surface. Accounting for this, our models with shear heating yield a transient surface heat flow rise to ~.8 W*m -2 (Fig. 4) This finding may go toward resolving the puzzle of orogenic heat (Hyndman et al., 25), and where the heat source is in orogenic (Barrovian) metamorphism (Jamieson et al., 1998), and support results from more complex finite element models (Burg and Gerya, 25). Common orogenic processes cool the lithosphere. For example melting of rocks absorb heat and crustal thickening and thrusting stretch or stack the geotherm. Yet magmatism inverted metamorphic gradients, and a high surface heat flow (.7.9 W*m -2 ) is common in orogens (Chapman and Furlong, 1992; Pollack et al., 1993; Beaumont et al., 21). It has been proposed that this extra orogenic heat is inherited from the pre-orogenic setting, caused by the rise of hot astenosphere following delamination of the lower lithosphere, the result of enhanced heat transport due to circulating fluids, or an increase in radiogenic heat production below mountain belts (Hyndman et al., 25; Jamieson et al., 1998; Jiménez-Munt and Platt, 26). Acknowledging the potential role of these processes we note that even our most conservative estimates of shear heating of.3 W*m -2 during mountain building match the missing orogenic heat. CONCLUSIONS We have devised a simple, easily reproducible and universally applicable method to modify the Brace-Goetze strength envelope to calculate shear heating. Using this simple 1D method and despite our use of minimum estimates of strain rate and stress, we have shown that shear heating represent a first order control on the distribution of strength and temperature in Earth s lithosphere, and therefore has a dramatic effect on patterns of Page 9 of 15

10 deformation particularly during continental collision. While others utilize to Brace-Goetze strength envelope to explore two to threefold variations in strength dependent on choice of creep law (Tsenn and Carter, 1987), rocks parameters (Buck, 1991), wetness of rocks (Burov and Watts, 26; Jackson, 22; Afonso and Ranalli, 24), rheological strain- softening (Huismans and Beaumont, 23), or strain rate (Cloetingh and Burov, 1996), our calculations indicate that shear heating can change strength in the deep earth by as much as a factor ten, and in some important cases conclusions of strength models directly reverse when shear heating is considered. Lithosphere deformation models without shear heating have yielded estimates of total lithospheric strength that are 5 2 times higher (Jackson, 22; Hyndman et al., 25) than force balanced calculations (Stüwe, 22). These strength estimates have been presented as evidence for extreme stresses and brittle earthquakes in deep orogenic roots (Jackson, 22). Shear heating and thermomechanical coupling in our models yields steady-statelithospheric strengths that are close to force balanced estimates, and well below those needed for brittle earthquakes in deep orogenic roots. Furthermore shear heating causes a rise in modeled surface heat flow, similar to measured data. The effects of shear heating on lithospheric deformation are profound, and no geodynamic model is complete without it. ACKNOWLEDGMENTS Research is funded by the Norwegian Science Council through the Petromaks program and a Centre of excellence grant to Physics of Geological Processes. N. Hovius, S. Medvedev, S. Bræck and E. Jettestuen are thanked for discussions, and S. Schmalholz, T. Gerya and C. Doglioni are thanked for constructive comments. Page 1 of 15

11 228 REFERENCES CITED Afonso, J.C., and Ranalli, G., 24, Crustal and mantle strengths in continental lithosphere: Is the jelly sandwich obsolute?: Tectonophysics, v. 394, p , doi: 1.116/j.tecto Beaumont, C., Jamieson, R.A., Nguyen, M.H., and Lee, B., 21, Himalayan tectonics explained by extrusion of a low-viscosity crustal channel coupled to focussed surface denudation: Nature, v. 414, p , doi: 1.138/414738a. Brace, W.F., and Kohlstedt, D.L., 198, Limits on Lithospheric stress imposed by laboratory experiments: Journal of Geophysical Research-Solid Earth, v. 85, p Buck, W.R., 1991, Modes of continental lithospheric extension: Journal of Geophysical Research-Solid Earth, v. 96, p Burg, J.P., and Gerya, T.V., 25, The role of viscous heating in Barovian metamorphism of collisional orogens: Thermomechanical models and application to the Lepontine Dome in the central Alps: Journal of Metamorphic Geology, v. 23, p , doi: /j x. Burov, E.B., and Watts, A.B., 26, The long-term strength of continental lithosphere: jelly sandwich or Crème brûèe?: GSA Today, v. 16, p. 4 1, doi: 1.113/ (26)16<4:TLTSOC>2..CO;2. Carter, L.M., and Tsenn, M.C., 1987, Flow properties of continental lithosphere: Tectonophysics, v. 136, p , doi: 1.116/4-1951(87) Page 11 of 15

12 Chapman, D.S., and Furlong, K.P., 1992, Thermal state of the continental crust, in Fountain, D.M., Arculus, R.J., and Kay, R.W., eds., Continental lower crust: Development in geotectonics, Volume 23: Amsterdam, Elsevier, p Chopra, P.N., and Paterson, M.S., 1981, The experimental deformation of dunite: Tectonophysics, v. 78, p , doi: 1.116/4-1951(81)924-X. Cloetingh, S., and Burov, E.B., 1996, Thermomechanical structure of European continental lithosphere: Constraints from rheology profiles and EET estimates: Geophysical Journal International, v. 124, p , doi: /j X.1996.tb5633.x. Doglioni, C., Green, D., and Mongelli, F., (25): On the shallow origin of hotspots and the westward drift of the lithosphere: in Plates, Plumes and Paradigms, G.R. Foulger, J.H. Natland, D.C. Presnall, and D.L. Anderson (Eds), GSA Sp. Paper 388, Goetze, C., 1978, The mechanism of creep in olivine: Philosophical Transactions of the Royal Society of London: Series A, v. 288, p , doi: 1.198/rsta Huismans, R.S., and Beaumont, C., 23, Symmetric and asymmetric lithosphere extension: Relative effects of frictional-plastic and viscous strain softening: Journal of Geophysical Research-Solid Earth, v. 18, p Hyndman, R.D., Currie, C.A., and Mazzotti, S.P., 25, Subduction zone backarcs, mobile belts, and orogenic heat: GSA Today, v. 15, p Jackson, J., 22, Strength of the continental lithosphere: Time to abandon the jelly sandwich?: GSA Today, v. 12, p. 4 9, doi: 1.113/ (22)12<4:SOTCLT>2..CO;2. Jamieson, R.A., Beaumont, C., Fullsack, P., and Lee, B., 1998, Barrovian regional metamorphism: Where s the heat? in P.,T., and P., O.B., eds., What Controls Page 12 of 15

13 Metamorphism and Metamorphic Reactions? Volume 138, Geological Society London Special Publication, p Jeffreys, H., 197, The Earth: Cambridge, University press, 3 p. Jiménez-Munt, I., and Platt, J.P., 26, Influence of mantle dynamics on the topographic evolution of the Tibetan Plateau: Results from numerical modelling: Tectonics, v. 25, p. doi:1.129/26tc1963. Kaus, B.J.P., and Podlachikov, Y.Y., 26, Initiation of localized shear zones in viscoelastioplastic rocks: Journal of Geophysical Research-Solid Earth, v. 111, p Kelemen, P.B., and Hirth, G., 27, A periodic shear-heating mechanism for intermediate- depth earthqaukes in the mantle: Nature, v. 446, p , doi: 1.138/nature5717. Molnar, P., 1992, Brace-Goetze strength profiles, The partitioning of strike-slip and thrust faulting at zones of oblique convergence, and the stress-heat flow paradox of the San Andreas fault, in Evans, B., and Wong, T.-F., eds., Fault mechanics and transport properties of rocks: A Festschrift in honor of W.F. Brace: London, Academic Press, p Molnar, P., and Lyon-Caen, H., 1989, Some simple physical aspects of the support, structure and evolution of mountain belts: Geol. Soc. Am. special paper, v. 218, p Pollack, H.N., Hurter, S.J., and Johnson, J.R., 1993, Heat flow from the Earth s interior: Analysis of the global data set: Reviews of Geophysics, v. 31, p , doi: 1.129/93RG1249. Page 13 of 15

14 Regenauer-Lieb, K., Weinberg, R.F., and Rosenbaum, G., 26, The effect of energy feedbacks on continental strength: Nature, v. 442, p. 67 7, doi: 1.138/nature4868. Regenauer-Lieb, K., Yuen, D.A., and Branlund, J., 21, The initiation of subduction: Criticality by addition of water?: Science, v. 294, p , doi: /science Roselle, G.T., and Engi, M., 22, Ultra high pressure (UHP) terrains: Lessons from thermal modeling: American Journal of Science, v. 32, p , doi: /ajs Schmalholz, S.M., Podladchikov, Y.Y., and Jamtveit, B., 25, Structural softening of the lithosphere: Terra Nova, v. 17, p , doi: /j x. Stüwe, K., 22, Geodynamic of the Lithosphere: An introduction: Berlin, Springer, 449 p. Tsenn, M.C., and Carter, N.L., 1987, Upper limits of power law creep of rocks: Tectonophysics, v. 136, p. 1 26, doi: 1.116/4-1951(87) Turcotte, D.L., and Schubert, G., 22, Geodynamics: Cambridge, Cambridge University Press, 456 p. Wilks, K.R., and Carter, L.M., 199, Rheology of some lower crustal rocks: Tectonophysics, v. 182, p , doi: 1.116/4-1951(9) FIGURE TEXT Figure 1., Lithospheric temperature and strength profiles with and without shear heating. (a) geotherm and (b) Brace-Goetze strength envelope before and after thickening an isostatically balanced three-layer (wet quartz, dry mafic granulite (crust) and dry dunite (mantle) lithosphere for 9 million years, so that Moho deepens from 4 to 8 km depth. Page 14 of 15

15 Shear heating reduce the strength by a factor 1, which is well above all traditional modeling variables. Figure 2., Temperature (a,c), strength and shear heating (b,d) plotted against time for a lithosphere thickened to twice its original thickness. The panels to the left show the dramatic effect of shear heating when standard power law rheologies and constant strain rate ( ) are implied. The panels to the right illustrate the more stable scenario implementing Dorn creep at high stresses, and concentration deformation in the weak middle crust. Shear heating balance the lithospheric strength by thermal weakening, so that after thickening rocks has about the same strength regardless of initial assumptions. Figure 3., Profiles of temperature, strength, and shear heating at variable modes of lithospheric deformation. (a) Geotherm, (b,c) Brace-Goetze strength and (d) shear heating profiles before and after thickening the same lithosphere as in Figure 1. The two models both include shear heating and high stress creep laws for stresses above 6 Kbar, but (a) applies constant strain rate, and (b) infers variable strain rate, and a simple shear (fault) zone just below Moho at 8 km depth. Notice how the variable strain rate has little effect on the strength (b,c) but a large effect on the shear heating (d) and thus temperature (a). Figure 4., Surface heat flow in models with and without heat flow (power law rheology)( Fig. 1). Notice that only when shear heating is included the heat flow rise, as observed in nature. 1 GSA Data Repository item 28xxx, outlines numerical methods, and present a case showing the effect of shear heating in an extending lithosphere. It is available online at or on request from editing@geosociety.org or Documents Secretary, GSA, P.O. Box 914, Boulder, CO 831, USA. Page 15 of 15

16 2 a Shear heat (W*m-3) *1-6. b Strainrate (ε) = 3*1-15 Byerlee or brittle failure Depth (km) No shear heating Initial conditions Shear heating Moho Power law Shear heating No shear heating Temperature ( o C) Strength( σ, Kbar)

17 oc a Depth (km) Temperature Temperature Depth (km) Kbar 4 σ 1 Power Law Creep 1 Constant strain rate 2 m.y m.y. 6 d Power Law/ Dorn Creep Variable strain rate 2 m.y W*m-3 b 8 3 shear heating 6 Kbar m.y. σ W*m-3 shear heating 1 oc c

18 Depth (km) Variable strain rate Constant strain rate Initial conditions Shear heat (W*m -3 ) *1-6 a. b Strainrate (ε) c d. Strainrate (ε) (intial depth) Brittle failure for compression Dorn creep = 3*1-15 No shear heating Temperature ( o C) Strength ( σ, Kbar) Shear-strain rate (γ) =1-1 for.1 second Strength ( σ, Kbar) Shear heat (W*m -3 ) 1 2 3*1-6 _ Variable strain rate _ Constant strain rate Before thickening Shear heat = 1 8 W*m -3 After thickening

19 Surface heat flow (W*m-2).8.6 with shearheat without shearheat.4 2 Time (m.y.) 6 8

20 TABLE 1, DATE REPOSITORY, ROCK PARAMETERS USED yhartz & PODLADCHIKOV Parameter Unit Wet quartz granulite Dry dunite Activation energy (E) (J mol -1 ) Pre-exponent constant (A) (MPa -n * s - ) Power law exponent (n) Density (r) (Kg*m -3 ) Heat capacity ( c p ) (W*m -1* K -1 ) Radiogenic heat production (Q) (W*m -3 ) 1E-6 1E-7 1E-7 Thermal conduction coeficient (W/m/K) Initial depth (km) Reference for E,A and n Carter & Tsenn Wilks & Carter Chopra & Paterson (1987) (199) (1982)