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Geodynamics Lecture 7 Heat conduction and production Lecturer: David Whipp [email protected] ! 23.9.2014 Geodynamics www.helsinki.fi/yliopisto 1 Goals of this lecture • Gain a conceptual and mathematical understanding of heat conduction ! • Learn the concepts of radiogenic heat production in the Earth ! • View the effects of heat conduction and production on the thermal field in the crust 2 Why talk about heat transfer? Grand Prismatic Spring,Yellowstone National Park, U.S. Image: http://en.wikipedia.org The dynamics of the Earth are dominantly controlled by gravitational and thermal processes. In fact, you could argue that thermal processes have the largest impact. Why? 3 Why now? www.usgs.gov Faulting Folding Many rock properties are largely a function of temperature. Faulting and brittle deformation may occur near the surface, but folding and ductile flow are dominant at depth. 4 The effects of partial melting on rock strength udio L. Rosenberg, Sergei Medvedev, and Mark R. Handy • Partial melting dramatically decreases rock strength ! • Only about 7% melt is required for to decrease rock strength by 80-90% Rosenberg et al., 2007 5 Heat transfer in the lithosphere • Conduction: The diffusive transfer of heat by kinetic atomic or molecular interactions within the material. Also known as thermal diffusion. ! • Advection: The transfer of heat by physical movement of molecules or atoms within a material. A type of convection, mostly applied to heat transfer in solid materials. ! • Production: Not really a heat transfer process, but rather a source of heat. Sources in the lithosphere include radioactive decay, friction in deforming rock or chemical reactions such as phase transitions. 6 Heat transfer in the lithosphere • Conduction: The diffusive transfer of heat by kinetic atomic or molecular interactions within the material. Also known as thermal diffusion. ! Focus in this lecture • Advection: The transfer of heat by physical movement of molecules or atoms within a material. A type of convection, mostly applied to heat transfer in solid materials. ! • Production: Not really a heat transfer process, but rather a source of heat. Sources in the lithosphere include radioactive decay, friction in deforming rock or chemical reactions such as phase transitions. 7 Basic ideas of heat conduction • The conduction of heat in solids is a diffusion process, and well described by Fourier’s laws, the basic mathematical relationships describing diffusion ! • Fourier’s first law states that the flux of heat in a material 𝑞 is directly proportional to the temperature gradient ! • What would this relationship look as an equation? 8 Basic ideas of heat conduction • The conduction of heat in solids is a diffusion process, and well described by Fourier’s laws, the basic mathematical relationships describing diffusion ! • Fourier’s first law states that the flux of heat in a material 𝑞 is directly proportional to the temperature gradient ! • What would this relationship look as an equation? 9 Fourier’s first law • In 1D, the mathematical translation of “Heat flux 𝑞 is directly proportional to the thermal gradient in a material” is ! q= dT k dy • Here, 𝑇 represents temperature and 𝑦 represents spatial position, depth in the Earth in this case • Thus, 𝑑𝑇/𝑑𝑦 is the change in temperature with distance, the thermal gradient • The proportionality constant 𝑘 is known as the thermal conductivity 10 Fourier’s first law • In 1D, the mathematical translation of “Heat flux 𝑞 is directly proportional to the thermal gradient in a material” is ! • q= dT k dy Why is there a negative sign? 11 What is thermal conductivity? • The mathematical translation of “Heat flux 𝑞 is directly proportional to the thermal gradient in a material” is Sandstone q= dT k dy • • Thermal conductivity is a proportionality factor • Thermal conductivity of most crustal rocks is 2-3 W m-‐1 K-‐1 As you can easily see, rocks with a “high” thermal conductivity will produce a large heat flow, whereas rocks with a “low” thermal conductivity will have near zero heat flow Salt Stüwe, 2007 12 Global heat flow map http://www.cbe.cornell.edu 13 Global heat flow map Global average: 87 mW m-2 Continents: 65 ± 1.6 mW m-2 Oceans: 101 ± 2.2 mW m-2 http://www.cbe.cornell.edu Here we can clearly see the connection between geodynamic setting and heat flow 14 Radiogenic heat production • Radiogenic heat production, 𝐴 or 𝐻, results from the decay of radioactive elements in the Earth, mainly 238U, 235U, 232Th and 40K. 𝐴 is generally used for volumetric heat production and 𝐻 for heat production by mass. • These elements occur in the mantle, but are concentrated in 248 Heat Transfer the crust, where radiogenic heating can be significant • Table Typicalheat Concentrations of the Heat-Producing Elements The4.3 surface flow in continental regions is ~65inmW m-2 Several Rock Types and Average Concentrations in Chondritic and ~37 mW m-2 isthefrom radiogenic heat production (57%) Meteorites Type Rock Reference undepleted (fertile) mantle “Depleted” peridotites Tholeiitic basalt Granite Shale Average continental crust Chondritic meteorites U (ppm) Concentration Th (ppm) K (%) 0.031 0.001 0.07 4.7 3.7 1.42 0.008 0.124 0.004 0.19 20 12 5.6 0.029 0.031 0.003 0.088 4.2 2.7 1.43 0.056 Turcotte and Schubert, 2014 15 Radiogenic heat production • Radiogenic heat production, 𝐴 or 𝐻, results from the decay of radioactive elements in the Earth, mainly 238U, 235U, 232Th and 40K. 𝐴 is generally used for volumetric heat production and 𝐻 for heat production by mass. • These elements occur in the mantle, but are concentrated in 248 Heat Transfer the crust, where radiogenic heating can be significant • Table Typicalheat Concentrations of the Heat-Producing Elements The4.3 surface flow in continental regions is ~65inmW m-2 Several Rock Types and Average Concentrations in Chondritic and ~37 mW m-2 isthefrom radiogenic heat production (57%) Meteorites Type Rock Reference undepleted (fertile) mantle “Depleted” peridotites Tholeiitic basalt Granite Shale Average continental crust Chondritic meteorites U (ppm) Concentration Th (ppm) K (%) 0.031 0.001 0.07 4.7 3.7 1.42 0.008 0.124 0.004 0.19 20 12 5.6 0.029 0.031 0.003 0.088 4.2 2.7 1.43 0.056 Turcotte and Schubert, 2014 16 Radiogenic heat production Heat production Rock type By mass, 𝐻 [W kg Reference undepleated (fer/le) mantle 7.39E-12 2.44E-08 0.024 "Depleated" perido/tes 3.08E-13 1.02E-09 0.001 Tholeii/c basalt 1.49E-11 4.41E-08 0.044 Granite 1.14E-09 3.01E-06 3.008 Shale 7.74E-10 1.86E-06 1.857 Average con/nental crust 3.37E-10 9.26E-07 0.927 Chondri/c meteorites 3.50E-12 1.15E-08 0.012 By volume, 𝐴 By volume, 𝐴 [W m [µW m Calculated from Turcotte and Schubert, 2014 17 Radiogenic heat production Heat production Rock type By mass, 𝐻 [W kg Reference undepleated (fer/le) mantle 7.39E-12 2.44E-08 0.024 "Depleated" perido/tes 3.08E-13 1.02E-09 0.001 Tholeii/c basalt 1.49E-11 4.41E-08 0.044 Granite 1.14E-09 3.01E-06 3.008 Shale 7.74E-10 1.86E-06 1.857 Average con/nental crust 3.37E-10 9.26E-07 0.927 Chondri/c meteorites 3.50E-12 1.15E-08 0.012 By volume, 𝐴 By volume, 𝐴 [W m [µW m Calculated from Turcotte and Schubert, 2014 • Typical heat production values for upper crustal rocks are 2-3 µW m-3, but the crustal average is <1 µW m-3 • What does this suggest, and why might this occur? 18 Radiogenic heat production Stüwe, 2007 • 𝐻 Because radiogenic heat production is the result of radioactive decay, the parent isotope concentrations have continually decreased throughout Earth’s history • Today, the total amount of radiogenic heat is about half of what was produced in the ArcheanS at ~3 Ga Crustal heat production over time 19 Radiogenic heat production Stüwe, 2007 • 𝐻 Because radiogenic heat production is the result of radioactive decay, the parent isotope concentrations have continually decreased throughout Earth’s history • Today, the total amount of radiogenic heat is about half of what was produced in the ArcheanS at ~3 Ga Crustal heat production over time 20 LETTER RESEARCH LETTER doi:10.1038/nature13728 Spreading continents kick-started plate tectonics Patrice F. Rey1, Nicolas Coltice2,3 & Nicolas Flament1 Temperature (K) Continent c d e Depth (km) b Depth (km) Depth (km) Aa that of present-day tectonic forces driving orogenesis1. To explore the Stresses acting on cold, thick and negatively buoyant oceanic litho- 2,000 0 1,000 0 sphere are thought to be crucial to the initiation of subduction and tectonic impact of a thick and buoyant continent surrounded by a stag1,2 the operation of plate tectonics , which characterizes the present- nant lithospheric lid, we produced a series of two-dimensional thermo200 was hotter mechanical 1,820 K numerical models of the top 700 km of the Earth, using day geodynamics of the Earth. Because the Earth’s interior 293 K in the Archaean eon, the oceanic crust may have been thicker, thereby temperature-dependent densities and visco-plastic rheologies that depend making the oceanic lithosphere more buoyant than 400 at present3, and on temperature, melt fraction and depletion, stress and strain rate (see whether subduction and plate tectonics occurred during this time is Methods). The initial temperature field is the horizontally averaged tem400 km 600 ambiguous, both in the geological record and in geodynamic models4. perature profile of a stagnant-lid convection calculation for a mantle Here we show that because the oceanic crust was thick and buoyant5, ,200 K hotter than at present (Fig. 1A, a and Extended Data Fig. 2). The lateral temperature gradients ensures that no convective stresses(g cm–3) early continents may have produced intra-lithospheric gravitational absence ofB a Deviatoric Reference density stress (MPa) stresses large enough to drive their gravitational spreading, to initi- act on the lid, allowing100 us to isolate dynamic effects2.8 of the3.0 continent. 300 the 500 3.2 3.4 0 0 ate subduction at their margins and to trigger episodes of subduc- A buoyant and stiff continent 225 km thick (strongly depleted mantle Basaltic crust tion. Our model predicts the co-occurrence of deep to progressively root 170 km thick overlain by felsic crust 40 km thick; see Fig. 1B, a) is shallower mafic volcanics and arc magmatism within continents in inserted within the lid, on the left side of the domain to exploit the symCrust 40 40 a self-consistent geodynamic framework, explaining the enigmatic metry of the problem (Fig. 1A, a). A mafic crust 15 km thick covers the multimodal volcanism and tectonic record of Archaean cratons6. More- whole system (Fig. 1A, a), consistent with the common occurrence of Strongly over, our model predicts a petrological stratification and tectonic struc- thick greenstone80 covers on continents, as well as80 thick basaltic crust on 3 depleted ture of the sub-continental lithospheric mantle, two predictions that the oceanic lid . are consistent with xenolith5 and seismic studies, respectively, and conOur numerical solutions show that the presence oflithospheric a buoyant conDepletion sistent with the existence of a mid-lithospheric seismic discontinuity7. tinent imparts 120 a horizontal force large enough120 to induce mantle a long period The slow gravitational collapse of early continents could have kick- (,50–150 Myr) of slow collapse of the whole continental lithosphere Strain rate started transient episodes of plate tectonics until, as the Earth’s inte- (Fig. 1 and Extended Fig. 3), in agreement with the dynamics of 160 Data –15 –1 10 19 s rior cooled and oceanic lithosphere became heavier, plate tectonics spreading for gravity currents . Hence, a continent of larger volume leads 225 became self-sustaining. to larger gravitational power and faster collapse. BecauseAsthenosphere of lateral spreadPresent-day plate tectonics is primarily driven by the negative buoy- ing of the b continent, the100 adjacent 3.2 3.4 2.8pushed 3.0 under 300lithospheric 500 lid is slowly 0 b and Extended Data Fig. 3A,0a). For gravitational ancy of cold subducting plates. Petrological and geochemical proxies of its margin (Fig. 1A, Basaltic crust subduction preserved in early continents point to subduction-like pro- stress lower than the yield stress of the oceanic lid, thickening of the margin cesses already operating before 3 billion years (Gyr) ago8,9 and perhaps of the lid is slow, and viscous drips (that is, Rayleigh–Taylor instabilities) 40 40 Lithospheric as early as 4.1 Gyr ago10. However, they are not unequivocal, and geo- detach from its base (Extended Data Fig. 3A, a and b). These instabilities, 20 mantle of dynamic modelling suggests that the thicker basaltic crust produced by typical of stagnant-lid convection , mitigate the thermal thickening partial melting of a hotter Archaean or Hadean mantle would have had the lid. 80 80 3,4 increased lithospheric buoyancy and inhibited subduction . Mantle conWhen gravitational stresses overcome the yield stress of the lithospheric vection under a stagnant lid with extensive volcanism could therefore lid, subduction is initiated (Fig. 1A, b and c). Depending on the half-width have preceded the onset of subduction11. In this scenario, it is classically of the continent120 and its density contrast with the120 adjacent oceanic lid (that Strain rate assumed that the transition from stagnant-lid regime to mobile-lid regime is, its gravitational power) three situations can arise: first, subduction Asthenosphere –15 s–1 10 and the onset of plate tectonics require that convective stresses overcame initiates and stalls (Extended Data Fig. 3b); second, 160the slab detaches and 160 21 the strength of the stagnant lid12 at some stage in the Archaean. the lid stabilizes (Fig. 1A, d and e and Extended Data Fig. 3c); or third, On the modern Earth, gravitational stresses due to continental buoyancy recurrent detachment of the slab continues until recycling of the oceanic can contribute to the initiation of subduction2,13. The role of continental lid is completed, followed by stabilization (Extended Data Fig. 3d). When LETTER doi:10.1038/nature13728 Spreading continents kick-started plate tectonics Patrice F. Rey1, Nicolas Coltice2,3 & Nicolas Flament1 Temperature (K) Continent Depth (km) Aa that of present-day tectonic forces driving orogenesis1. To explore the Stresses acting on cold, thick and negatively buoyant oceanic litho- 2,000 0 1,000 0 sphere are thought to be crucial to the initiation of subduction and tectonic impact of a thick and buoyant continent surrounded by a stag1,2 the operation of plate tectonics , which characterizes the present- nant lithospheric lid, we produced a series of two-dimensional thermo200 was hotter mechanical 1,820 K numerical models of the top 700 km of the Earth, using day geodynamics of the Earth. Because the Earth’s interior 293 K in the Archaean eon, the oceanic crust may have been thicker, thereby temperature-dependent densities and visco-plastic rheologies that depend making the oceanic lithosphere more buoyant than 400 at present3, and on temperature, melt fraction and depletion, stress and strain rate (see whether subduction and plate tectonics occurred during this time is Methods). The initial temperature field is the horizontally averaged tem400 km 600 ambiguous, both in the geological record and in geodynamic models4. perature profile of a stagnant-lid convection calculation for a mantle Here we show that because the oceanic crust was thick and buoyant5, ,200 K hotter than at present (Fig. 1A, a and Extended Data Fig. 2). The lateral temperature gradients ensures that no convective stresses(g cm–3) early continents may have produced intra-lithospheric gravitational absence ofB a Deviatoric Reference density stress (MPa) stresses large enough to drive their gravitational spreading, to initi- act on the lid, allowing100 us to isolate dynamic effects2.8 of the3.0 continent. 300 the 500 3.2 3.4 0 0 ate subduction at their margins and to trigger episodes of subduc- A buoyant and stiff continent 225 km thick (strongly depleted mantle Basaltic crust tion. Our model predicts the co-occurrence of deep to progressively root 170 km thick overlain by felsic crust 40 km thick; see Fig. 1B, a) is shallower mafic volcanics and arc magmatism within continents in inserted within the lid, on the left side of the domain to exploit the symCrust 40 40 a self-consistent geodynamic framework, explaining the enigmatic metry of the problem (Fig. 1A, a). A mafic crust 15 km thick covers the multimodal volcanism and tectonic record of Archaean cratons6. More- whole system (Fig. 1A, a), consistent with the common occurrence of Strongly over, our model predicts a petrological stratification and tectonic struc- thick greenstone80 covers on continents, as well as80 thick basaltic crust on 3 depleted ture of the sub-continental lithospheric mantle, two predictions that the oceanic lid . are consistent with xenolith5 and seismic studies, respectively, and conOur numerical solutions show that the presence oflithospheric a buoyant conDepletion sistent with the existence of a mid-lithospheric seismic discontinuity7. tinent imparts 120 a horizontal force large enough120 to induce mantle a long period The slow gravitational collapse of early continents could have kick- (,50–150 Myr) of slow collapse of the whole continental lithosphere Strain rate started transient episodes of plate tectonics until, as the Earth’s inte- (Fig. 1 and Extended Fig. 3), in agreement with the dynamics of 160 Data –15 –1 10 19 s rior cooled and oceanic lithosphere became heavier, plate tectonics spreading for gravity currents . Hence, a continent of larger volume leads 225 became self-sustaining. to larger gravitational power and faster collapse. BecauseAsthenosphere of lateral spreadPresent-day plate tectonics is primarily driven by the negative buoy- ing of the b continent, the100 adjacent 3.2 3.4 2.8pushed 3.0 under 300lithospheric 500 lid is slowly 0 b and Extended Data Fig. 3A,0a). For gravitational ancy of cold subducting plates. Petrological and geochemical proxies of its margin (Fig. 1A, Basaltic crust subduction preserved in early continents point to subduction-like pro- stress lower than the yield stress of the oceanic lid, thickening of the margin cesses already operating before 3 billion years (Gyr) ago8,9 and perhaps of the lid is slow, and viscous drips (that is, Rayleigh–Taylor instabilities) 40 40 Lithospheric as early as 4.1 Gyr ago10. However, they are not unequivocal, and geo- detach from its base (Extended Data Fig. 3A, a and b). These instabilities, 20 mantle of dynamic modelling suggests that the thicker basaltic crust produced by typical of stagnant-lid convection , mitigate the thermal thickening partial melting of a hotter Archaean or Hadean mantle would have had the lid. 80 80 3,4 increased lithospheric buoyancy and inhibited subduction . Mantle conWhen gravitational stresses overcome the yield stress of the lithospheric vection under a stagnant lid with extensive volcanism could therefore lid, subduction is initiated (Fig. 1A, b and c). Depending on the half-width have preceded the onset of subduction11. In this scenario, it is classically of the continent120 and its density contrast with the120 adjacent oceanic lid (that Strain rate assumed that the transition from stagnant-lid regime to mobile-lid regime is, its gravitational power) three situations can arise: first, subduction Asthenosphere –15 s–1 10 and the onset of plate tectonics require that convective stresses overcame initiates and stalls (Extended Data Fig. 3b); second, 160the slab detaches and 160 22 the strength of the stagnant lid12 at some stage in the Archaean. the lid stabilizes (Fig. 1A, d and e and Extended Data Fig. 3c); or third, On the modern Earth, gravitational stresses due to continental buoyancy recurrent detachment of the slab continues until recycling of the oceanic can contribute to the initiation of subduction2,13. The role of continental lid is completed, followed by stabilization (Extended Data Fig. 3d). When b d Larger horizontal stresses force subduction of buoyant oceanic lithosphere Slab detaches, margin stabilizes e Depth (km) c Depth (km) Continent weakens, spreads laterally 1D steady-state heat conduction + production • Consider the heat flux across a slab of thickness 𝛿𝑦 • The net heat flux is simply the heat flux out minus the heat flux in, or • Fig. 4.5, Turcotte and Schubert, 2014 q(y + y) q(y) Using Taylor series expansion and Fourier’s first law, it can be shown that ✓ ◆ dq d dT q(y + k y) q(y) = y dy = y dy dy ✓ 2 ◆ d T = y k 2 dy for constant thermal conductivity 𝑘 23 1D steady-state heat conduction + production Fig. 4.5, Turcotte and Schubert, 2014 • If we assume the only source of changing the heat flux in the slab is radiogenic heat, we can say ✓ 2 ◆ d T ⇢H y = y k dy 2 or 2 d T k 2 + ⇢H = 0 dy where 𝜌 is rock density • Assuming 𝑇 = 𝑇0 and 𝑞 = 𝑞0 at 𝑦 = 0, the solution is q0 T = T0 + y k ⇢H 2 y 2k With this equation, we can plot a geotherm, or change in temperature with depth 24 Heat conduction in the mantle? ! ! q0 T = T0 + y k ⇢H 2 y 2k • 70 mW m-2 is a reasonable average heat flow value observed at the surface • If we assume a surface temperature 𝑇0 = 0°C, rock density 𝜌 = 3300 kg m-3, 𝐻 = 7.38 ⨉ 10-12 W kg-1 and 𝑘 = 4 W m-1 K-1, what is the predicted temperature at 100 km depth? • • Does this seem reasonable? What about at 200 km depth? 25 Heat conduction in the mantle? Fig. 4.8, Turcotte and Schubert, 2014 Clearly, heat flow in the mantle is not strictly conductive! 26 Geotherms in the continental crust With a 40-km-thick crust, you can see that heat production can increase the Moho temperature considerably ! ! Note, that this model has a constant heat flow basal boundary condition 𝑘 = 2.75 W m-‐1 K-‐1 𝑞m = 20 mW m-‐2 ymax = 40 km 27 Geotherms in the continental crust Why might this matter? The approximate depth at which crustal rocks transition from brittle deformation to ductile deformation corresponds roughly to the 300°C isotherm in the crust ! Based on the models here, that depth could vary from ~15-40 km (!), which has serious implications for how the crust deforms 𝑘 = 2.75 W m-‐1 K-‐1 𝑞m = 20 mW m-‐2 ymax = 40 km 28 Distribution of heat producing elements Heat production Rock type By mass, 𝐻 [W kg Reference undepleated (fer/le) mantle 7.39E-12 2.44E-08 0.024 "Depleated" perido/tes 3.08E-13 1.02E-09 0.001 Tholeii/c basalt 1.49E-11 4.41E-08 0.044 Granite 1.14E-09 3.01E-06 3.008 Shale 7.74E-10 1.86E-06 1.857 Average con/nental crust 3.37E-10 9.26E-07 0.927 Chondri/c meteorites 3.50E-12 1.15E-08 0.012 • By volume, 𝐴 By volume, 𝐴 [W m [µW m As we’ve seen, however, the concentration of heat-producing elements is not constant in the crust, but decreases with depth 29 Geotherms in the continental crust ! melting of crust 𝐴 = 2.5 𝜇W m-‐3 𝑘 = 2.75 W m-‐1 K-‐1 𝑞m = 20 mW m-‐2 ymax = 40 km Onset of partial As before, changing the concentration of heatproducing elements shows us something important about how we might expect the crust to deform ! Here, we might predict partial (to complete) melting of the crust and very weak rocks if we don’t consider decreasing heat production 30 Geotherms in thick continental crust ! melting of crust 𝐴 = 2.5 𝜇W m-‐3 𝑘 = 2.75 W m-‐1 K-‐1 𝑞m = 20 mW m-‐2 ymax = 80 km Onset of partial The crust beneath the Tibetan Plateau is thought to be 70-80 km thick resulting from extensive shortening during orogenesis, and it is likely that this over-thickened crust is partially molten at depth as a result of radiogenic heat ! How might this affect the plateau topography? 31 Geodynamic implications • We’ve now see that radiogenic heat production can significantly influence the subsurface thermal field, particularly in the crust • • This may influence geodynamic behavior of the deforming crust by affecting the depth of the transition from brittle to ductile deformation, or the potential for partial melting of the crust Another important influence on the crustal thermal field is topography at the Earth’s surface • Why might topography matter? 32 Thermal field beneath periodic topography • In our calculations of temperatures in the Earth thus far, we’ve assumed a known surface temperature 𝑇0 at 𝑦 = 0 • Atmospheric temperatures decrease with elevation following an atmospheric lapse rate 𝛽 (typical value: 𝛽 = 6.5°C km-1) • Combined, this suggests surface temperatures should vary with elevation in mountainous regions, an effect we can simulate • Importantly, this is clearly a 2D problem 33 Thermal field beneath periodic topography • To do this, we compensate for the temperature variations with elevation by scaling the temperature by 𝛥𝑇 at 𝑦 = 0, yielding ⌘ qm y ⇢H0 h2r ⇣ 2⇡x 2⇡y/ y/hr T (x, y) = T0 + + 1 e + T cos e k k with ✓ ◆ qm ⇢H0 hr T = h0 k k where 𝑇0 is the surface temperature a sea level in nature, 𝑞m is the mantle heat flux, 𝑘 is thermal conductivity, 𝜌 is density, 𝐻0 is the surface heat production value, ℎr is the e-folding depth for heat production, 𝜆 is the wavelength of the 34 topography and ℎ0 is the amplitude Thermal field beneath periodic topography 𝐴 = 2.5 𝜇W m-‐3 ℎr = 10 km 𝑘 = 2.75 W m-‐1 K-‐1 𝑞m = 20 mW m-‐2 ℎ0 = 4 km 𝜆 = ??? km 𝛽 = 6.5°C km-‐1 35 Thermal field beneath periodic topography 𝐴 = 2.5 𝜇W m-‐3 ℎr = 10 km 𝑘 = 2.75 W m-‐1 K-‐1 𝑞m = 20 mW m-‐2 ℎ0 = 4 km 𝜆 = ??? km 𝛽 = 6.5°C km-‐1 36 Thermal field beneath topography • Topography can influence the geometry of the thermal field beneath it, particularly as the relief and wavelength grow • The depth of the perturbation is related to the wavelength, with longer wavelengths affecting deeper crustal levels ! • This has important implications for data that depend on the thermal structure of mountainous regions, such as lowtemperature thermochronology data 37 Recap • Heat conduction, or diffusion, is the process by which molecular or elemental interactions transfer energy to neighboring particles ! • Heat conduction is dominantly controlled by rock material properties, such as the thermal conductivity or radiogenic heat production ! • The thermal field in the crust plays an important role in determining how the crust deforms 38 References Rey, P. F., Coltice, N., & Flament, N. (2015). Spreading continents kick-started plate tectonics. Nature, 513(7518), 405–408. doi:10.1038/nature13728 ! Rosenberg, C. L., Medvedev, S. & Handy, M. (2007) Effects of melting on faulting and continental deformation. In: The Dynamics of Fault Zones, edited by M. R. Handy, G. Hirth, N. Hovius. Dahlem Workshop Report 95, The MIT Press, Cambridge, Mass., USA, 357-401. 39