Geodynamics Lecture 8 Thermal processes in the lithosphere

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1 Geodynamics Lecture 8 Thermal processes in the lithosphere Lecturer: David Whipp david.whipp@helsinki.fi Geodynamics 2

2 Goals of this lecture Introduce time dependence in the heat transfer equations Describe heat advection and where it is important Provide an overview of the thermal structure in various geodynamic settings 3

3 Time dependent heat transfer In the last lecture, we considered heat conduction and heat production in a steady state, meaning the temperature equations did not depend on time For example, we saw the 1D steady-state heat conduction equation with heat production T = T 0 + q 0 k y H 2k y2 which clearly does not depend on time (no in the equation) In some geologic scenarios, the assumption of steady state is reasonable, but many others require consideration of their time evolution For example, problems involving emplacement of magma require time to consider cooling of the magma body 4

4 Time dependent heat transfer In steady state, the 1D heat conduction equation with heat production is 0=k d2 T dy 2 + H where " is thermal conductivity, # is density and $ is heat production by mass The time-dependent equivalent equation for heat conduction with production = 2 + H where % is heat capacity, a material property (typical values for rock are J kg -1 K -1 ) 5

5 Time dependent heat transfer If we ignore heat production, the equation simplifies = 2 and if we divide both sides by #% then we find the typical form of the time-dependent heat conduction equation = T 2 where & is the thermal diffusivity, & = "/#% (typical value for thermal diffusivity: 10-6 m 2 s -1 ) 6

6 Time dependence Rather than focusing on solving the time-dependent heat conduction equation, we ll look at two examples of transient, or time-dependent, thermal processes: The characteristic timescale of diffusion Thermal evolution of an intrusion 7

7 The characteristic timescale of diffusion Sometimes is it helpful to quickly estimate the time required for a diffusion process to be close to thermal equilibrium For example, if you know the dimensions of an intrusion, you might want to estimate how long it took to cool This can be done using the characteristic time of diffusion l 2 l 2 t eq / t eq = apple 2apple It provides an estimate of when a diffusive process is ~85% complete (85% of the way to thermal equilibrium) Table 3.2, Stüwe,

8 The characteristic timescale of diffusion A pluton is estimated to have cooled over 750 ka What is the approximate diameter of this pluton, assuming cooling was the result of heat conduction? You can ignore the latent heat of crystallisation, fluid circulation, etc. in your estimate 9

9 Thermal evolution of a 1D intrusion 2(km +T=500 C The intrusion is one-dimensional with a defined thickness and infinite length and depth 10

10 Thermal evolution of a 1D intrusion =10(a( =100(a( =1(ka( =10(ka( =100(ka( =1(Ma The intrusion slowly cools over time, in this case ignoring the heat released during solidification of the body 11

11 What is advection, and when does it matter? 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. 12

12 What is advection, and when does it matter? Time-dependent advection and diffusion Fig. 3.13, Stüwe, 2007 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. Advection in the vertical direction at velocity 56 can be represented = When combined with the diffusion equation from last lecture, we find the 1D = apple@ Diffusion Advection 13

13 Peclet number In many geologic settings, the effects of heat advection and diffusion are similar, so it is useful to be able to estimate the relative influence of each process The Peclet number is the ratio of the advective to diffusive thermal parameters, providing a simple estimate of the magnitude of the effect of each process Pe = advective di usive = vl apple = vl c k where 7 is the characteristic length scale of advection Thus, when Pe(<(1 diffusion dominates, when Pe(>(1 advection dominates and when Pe is ~1 their influence is similar 14

Peclet number 10-6 m 2 s -1 is a typical thermal diffusivity for crustal rocks Assuming deformation in most mountainous regions involves only the crust,

14 Peclet number 10-6 m 2 s -1 is a typical thermal diffusivity for crustal rocks Assuming deformation in most mountainous regions involves only the crust, with a typical thickness of 35 km, what is the uplift velocity in an active mountain range above which advection becomes more important than diffusion? 15

15 What is advection, and when does it matter? Advection is particularly relevant in three geodynamic situations Advection by magmas Example: Magmatic intrusion Advection by movement of solid rock Example: Erosion, faulting Advection by fluid circulation Example: Groundwater flow 16

16 Advection by magmas In general, magmatic intrusions are fast enough that they can be considered instantaneous intrusions on geologic time scales Thus, their emplacement is better modeled as an instantaneous heating problem, as we have seen Heat loss during emplacement of the intrusion is considered negligible Rather than modeling advection of heat with the intrusion, diffusive heat loss over time is important 17

17 Advection by movement of solid rock 6 Erosion, hot Constant surface elevation maintained by erosion Geothermal gradient increases due to upward transport of warmer rock Sedimentation, cool Constant surface elevation maintained by sedimentation Geothermal gradient decreases due to downward transport of cooler rock Upward mass transport Downward mass transport Advection of heat by movement of solid rock is common Both erosion (upward advection of rock) and sedimentation (downward advection of rock) can significantly modify the thermal field in the crust 18

18 Advection by movement of solid rock 56(=(0.1(mm/a 56(=(1(mm/a 56(=(5(mm/a 56(=(?0.1(mm/a 56(=(0(mm/a 56(=(?1(mm/a 56(=(?5(mm/a Advection of heat by movement of solid rock is common Both erosion (upward advection of rock) and sedimentation (downward advection of rock) can significantly modify the thermal field in the crust 19

$2 x 10-6 W m "3 Relaxation depth = 30 km Exhumation rate = 1 mm/a 20- - 3o ~x,~ I ]OMo Initial State i 1 ~) @ (~ Steady State \ \%*.$

19 Thermal evolution in response to erosion g to a 60- Surface heat production 2.2 x 10-6 W m "3 Relaxation depth = 30 km Exhumation rate = 1 mm/a o ~x,~ I ]OMo Initial State i 1 (~ Steady State \ \%*. \ \ 10 Ma no erosion of heat (~) 40 Mo producing material ~ \k~ ~ 70- '(DIOMa er si n fhaat X\~\\ Mo producing material \ steady state for no ~ 90- heat production \ 1 O0 - I I I I Temperature [ (3] 40 Ma Mancktelow & Grasemann, 1997 Here is an example of two models of the evolution of a 1D geotherm in response to erosion Both include heat production with an exponential decrease in the concentration of heat-producing elements In one case, the heat-producing elements are eroded, in the other the concentrations do not change with time Both models show a clear departure from the initial thermal solution by 10 Ma, but have not yet reached a new steady state by 40 Ma 20

20 Advection by movement of solid rock For 1D steady-state erosion/sedimentation, we can find an analytical solution to the = T 2 + For the steady state case, A/ =0, so By stating B=56/&(and(E= A/ 6, we can write the equation f 0 (y) = = v which is common differential equation that has the solution f(y) =f(0)e f(y) y 21

21 Advection by movement of solid rock The general solution with the substitutions is As before, this equation can be solved for various boundary conditions. Using A=0 at 6=0 and A=AF at 6=6F, the solution is f(y) =f(0)e Replacing the substituted variables B=56/&(and(E= A/ 6, the complete e v (y=0) 1 e v y y/apple T = T L 1 e v yl/apple This is the equation used for plotting the geotherms for various advection velocities three slides back y 22

22 Steady-state geotherms for different boundary conditions As you can see below, the choice of boundary conditions has important implications for the temperature distribution in the lithosphere A6= =1000 C A6=100=1000 C 10.0 mm/a 10.0 mm/a 1.0 mm/a 1.0 mm/a 0.1 mm/a 0.1 mm/a Fig. 3.14, Stüwe,

23 Application: Interpreting thermochronometer data Thermochronometers are mineral systems that record the time since the mineral sample was at a specific temperature AH= =1000 C For example, the 40 Ar/ 39 Ar system in white mica records the time since ~350 C Fig. 3.14, Stüwe, mm/a 1.0 mm/a 0.1 mm/a Thermochronology is widely applied to study erosion and rock exhumation, but studying rock exhumation requires relating temperature to a depth in the lithosphere If you can model the depth of the temperature of interest, you can use the observed thermochronometer age to determine the average exhumation rate 5y,exhumation(=(depth/age 24

24 Application: Interpreting thermochronometer data Thermochronometers are mineral systems that record the time since the mineral sample was at a specific temperature AH= =1000 C For example, the 40 Ar/ 39 Ar system in white mica records the time since ~350 C Fig. 3.14, Stüwe, mm/a 1.0 mm/a 0.1 mm/a Thermochronology is widely applied to study erosion and rock exhumation, but studying rock exhumation requires relating temperature to a depth in the lithosphere If you can model the depth of the temperature of interest, you can use the observed thermochronometer age to determine the average exhumation rate Predicted 40 Ar/ 39 Ar ages 0.15 Ma 13 Ma 320 Ma 5y,exhumation(=(depth/age 25

25 Advection by fluid circulation The flow of fluids within rock can also transfer heat through advection Consideration of fluid circulation is complicated, as the rock and fluid may be advected with different velocities, requiring a thermal solution that considers the thermal effects of both The general governing equation for fluid advection in = v f c f where S is the rock porosity, 5E is the fluid flux, #E is the fluid density and %E is the fluid heat capacity. The product of S and 5E is the fluid volume transported through the rock per unit time and area. 26

Fluid flow in mountainous regions 2 Slow flow ao Rapid flow 35 C 65 C Forster and Smith, 1989 Here is an example of groundwater flow driven by changes in the

26 Fluid flow in mountainous regions 2 Slow flow ao Rapid flow 35 C 65 C Forster and Smith, 1989 Here is an example of groundwater flow driven by changes in the elevation of the water table in a mountainous region Slow fluid circulation does not significantly perturb the thermal field, but rapid circulation has a major effect 27

27 Thermal structure of various geologic settings Mountainous regions Active tectonic areas Active orogens and foreland basin in extensional and contractional settings Subduction zones 28

28 The effects of mountain topography a A B b c C Fig. 3.45, Stüwe, 2007 Lines a, b and c are isotherms, lines of constant temperature, with Aa(<(Ab(<(Ac At a shallower depth, closer to the surface topography, isotherm a shows perturbation by both the short and long wavelength topography As the depths of the isotherms decrease, they become less sensitive to the shorter wavelength topographic features and show less overall perturbation Isotherm b is heavily perturbed by only long wavelength topography, and isotherm c is only slightly perturbed by the long wavelength topography 29

29 summit valley The effects of mountain topography -z 0 +z valley summit T ho km x u =0 km/my 50 C 100 C u =1 km/my 50 C 100 C Fig. 3.46, Stüwe, 2007 (a) (b) (c) (d) u=1 km/my km km km steady state steady state temporal evolution no erosion with erosion during erosion 8 6my 4my 2my 0my The geothermal gradient beneath a peak is generally shallower than that beneath a valley In the absence of erosion, the geothermal gradient is generally low, pushing the 50 C and 100 C isotherms to significant depths 30

30 summit valley The effects of mountain topography -z 0 +z valley summit T ho km x u =0 km/my 50 C 100 C u =1 km/my u=1 km/my km km km steady state steady state temporal evolution no erosion with erosion during erosion Erosion advects the 50 C and 100 C isotherms upward as the geothermal gradient increases 50 C 100 C Fig. 3.46, Stüwe, 2007 (a) (b) (c) (d) 8 6my 4my 2my 0my Transport of the isotherms to shallower crustal levels increases their perturbation by surface topography At a rate of 1 mm/a, the 100 C isotherm has been advected to close to its steady-state position by 6 Ma 31

31 Thermal field beneath periodic topography V(=(2.5(WW(m?3 ( hr(=(10(km( "(=(2.75(W(m?1 (K?1 ( ^m(=(20(mw(m?2 ( h0(=(4(km( B(=(???(km( a(=(6.5 C(km?1 The equation for 2D steady-state heat conduction beneath periodic topography was presented in the previous lecture on heat conduction 32

Thermal structure in extensional settings Relatively warm Relatively cool Ehlers and Farley, 2003 In active extensional orogens, erosion of the uplifting footwall increases the thermal

32 Thermal structure in extensional settings Relatively warm Relatively cool Ehlers and Farley, 2003 In active extensional orogens, erosion of the uplifting footwall increases the thermal gradient, whereas sedimentation in the neighboring basin decreases the geothermal gradient This combined effect, from slip on the bounding fault can significantly bend shallow crustal isotherms 33

Thermal structure in contractional settings Relatively cool Relatively warm Ehlers and Farley, 2003 In active contractional orogens, the hanging wall of thrusts are relatively warm due to

33 Thermal structure in contractional settings Relatively cool Relatively warm Ehlers and Farley, 2003 In active contractional orogens, the hanging wall of thrusts are relatively warm due to uplift and erosion, with sedimentation cooling the foreland basin region Isotherms in the shallow and even middle crust can be heavily perturbed, even inverting the thermal gradient in places 34

34 3D thermal model of the Nepalese Himalaya Whipp et al., 2007 This is an example where rapid convergence (20 mm/a) is accommodated by a basal thrust fault Slip on this fault and advection of heat bends the isotherms and inverts the thermal gradient locally in the footwall 35

35 Thermal field in subduction zones Subduction zones have a highly deformed thermal structure Advection resulting from the downgoing cold oceanic slab penetrates deeply into the mantle The forearc, on the oceanic side of the volcanic line, is generally cool In the backarc, corner flow in the mantle heats the overlying lithosphere Turcotte and Schubert, 2014 Further inboard, the continental cratonic region shows a typical thermal structure (fairly cool) 36

36 Thermal field in subduction zones Currie and Hyndman, 2006 Figure 4. (a) Heat flow data for the northern Cascadia subduction zone. The white diamond indicates where mantle xenoliths have been recovered. Solid triangles are active arc volcanoes. The eastern limit of the back arc is the Rocky Mountain Trench (RMT). The solid line is the heat flow profile location; dotted lines show the profile data width. (b) Heat flow profile along line A-B. The measured heat flow values (open circles) have been corrected for variations in near-surface heat generation (solid circles) (see text). (c) Back-arc geotherm from surface heat flow (dotted lines are 20% uncertainty) and other thermal constraints. than 900 C. As note somewhat too high b conduction at high tem Moho temperatures le eters. These temperatu temperature for most small amount of water geophysical evidence crust in this region, th mafic and dry. [31] Additional con atures come from seis mic refraction data f especially from the L tently low P n velocitie 1995; Clowes et al. 1995], giving an est 900 C (Figure 4c). T that determined from of the methods. Seis depth resolution but s velocities at k the northern Cascadia are 1 3% slow [e.g., wave velocities that a Grand, 1994; van der al., 2001; van der Lee suggesting mantle te depths greater than 5 perhaps partial melt ar on P wave velocities. S wave velocities like temperatures and the water, other volatiles a Nolet, 1997; Frederik Lee, 2002; Dixon et a [32] Upper mantle several localities in th suites of peridotite xen temperatures of C at km recent study of xeno Surface heat flow data from the northern Cascadia subduction zone show the typical signal Cold forearc, hot backarc, cold craton Steep backarc geotherm, shallow cratonic

37 Recap Time-dependent heat transfer is an important consideration for the thermal evolution of intrusions or time-dependent erosion Similarly, rock and fluid advection can significantly modify the conductive thermal field in regions with rapid erosion/ sedimentation or groundwater flow These processes combine to define the thermal structure in mountainous regions, active orogens and subduction zones 38

38 References Currie, C. A., & Hyndman, R. D. (2006). The thermal structure of subduction zone back arcs. J. Geophys. Res., 111(B8), B doi: /2005jb Ehlers, T. A., & Farley, K. A. (2003). Apatite (U-Th)/He thermochronometry; methods and applications to problems in tectonic and surface processes. Earth and Planetary Science Letters, 206(1-2), Forster, C. B., & Smith, L. (1989). The influence of groundwater flow on thermal regimes in mountainous terrain; a model study. Journal of Geophysical Research, B, Solid Earth and Planets, 94(7), Mancktelow, N. S., & Grasemann, B. (1997). Time-dependent effects of heat advection and topography on cooling histories during erosion. Tectonophysics, 270(3-4), Whipp, D. M., Jr, Ehlers, T. A., Blythe, A. E., Huntington, K. W., Hodges, K. V., & Burbank, D. W. (2007). Plio- Quaternary exhumation history of the central Nepalese Himalaya: 2. Thermo-kinematic and thermochronometer age prediction model. Tectonics, 26. doi: /2006tc

Effects of transient topography and drainage basin evolution on detrital thermochronometer data

UNIVERSITY OF MICHIGAN Effects of transient topography and drainage basin evolution on detrital thermochronometer data Contents Acknowledgments...3 Abstract...4 1. Introduction...5 2. Model setup...6 2.1