Intro to Quantitative Geology

Transcription

1 Introduction to Quantitative Geology Lecture 5 Natural diffusion: Hillslope sediment transport, Earth s thermal field Lecturer: David Whipp david.whipp@helsinki.fi

2 Goals of this lecture Provide a quick introduction to the diffusion process Introduce hillslope diffusive processes (heave/creep, solifluction, rainsplash) Present a short example of heat conduction in the Earth 3

3 Natural diffusion What comes to mind when you think about diffusion? 4

4 Diffusion as a geological process Grain boundary sliding (diffusion creep) 5

5 4 He diffusion Pristine apatite Damaged apatite 4 He produced by radioactive decay may not diffuse equally within a mineral grain 4 He diffusion in the mineral apatite Shuster et al.,

6 Diffusion as a geological process Rain splash results in downhill diffusion of soil/sediment 7

7 Diffusion as a geological process Heat conduction is a diffusive heat transfer process It can be the dominant heat transfer process in tectonically inactive regions (i.e., here) Popov et al.,

8 Diffusion as a geological process Popov et al., 1999 Dominantly conductive heat transfer is typically reflected in a linear relationship between! and " 9

9 Diffusion as a geological process Popov et al., 1999 Dominantly conductive heat transfer is typically reflected in a linear relationship between! and " 10

10 General concepts of diffusion Diffusion is a process resulting in mass transport or mixing as a result of the random motion of diffusing particles Diffusion reduces gradients Net motion of mass or transfer of energy is from regions of high concentration to regions of low concentration This definition is OK for us, but not perfect Hillslope diffusion is a name given to the overall behavior of numerous surface processes that are not themselves diffusion processes based on the definition above 11

11 The diffusion process 12

12 The diffusion process Concentration gradient 13

13 General concepts of diffusion Diffusion is a process resulting in mass transport or mixing as a result of the random motion of diffusing particles Net motion of mass or transfer of energy is from regions of high concentration to regions of low concentration Diffusion reduces concentration gradients This definition is OK for true diffusion processes, but there are also numerous geological processes that are not themselves diffusion processes, but result in diffusion-like behavior Hillslope diffusion is a name given to the overall behavior of various surface processes that transfer mass on hillslopes in a diffusion-like manner 14

14 A more quantitative definition Diffusion occurs when a conservative property moves through space at a rate proportional to a gradient Conservative property: A quantity that must be conserved in the system (e.g., mass, energy, momentum) Rate proportional to a gradient: Movement occurs in direct relationship to the change in concentration Consider a one hot piece of metal that is put in contact with a cold piece of metal. Along the interface the change in temperature will be most rapid when the temperature difference is largest 15

15 A mathematical definition Consider the example to the left of the concentration of some atoms A and B We can think of formulate the diffusion of atoms of A in terms of their flux # across the red line with time q = where $ is a constant called the diffusivity, %A is the concentration of atoms of A, and & is the spatial coordinate From this, we can see the flux of A is directly proportional to the change in concentration %A along an infinitesimal length & (the concentration gradient) 16

16 A mathematical definition If we assume that mass is conserved, we can say that the change in concentration %A in the infinitesimal time ' is a function of the change in the flux of A # across an infinitesimal distance @x What?!? Essentially, all this says is that the concentration of A will change based on the flux across a reference face at position & minus the flux across a reference face at position & + (& 17

17 Let s see if we get it & & + (& q = A @x Based on our two equations for diffusion, how do you expect the concentration of atoms of A %A to change between positions & and & + (&? Think in terms of the mass flux 18

18 Let s see if we get it & & + (& q = A @x What about now? How do you expect the concentration of atoms of A %A to change between positions & and & + (&? Think in terms of the mass flux 19

19 General concepts of diffusion So our definitions of diffusion to this point are OK for true diffusion processes, but there are also numerous geological processes that are not themselves diffusion processes, but result in diffusion-like behaviour Hillslope diffusion is a name given to the overall behaviour of various surface processes that transfer mass on hillslopes in a diffusion-like manner 20

20 Erosional processes Erosional processes are divided between short range (e.g., hillslope) and long range (e.g., fluvial) transport processes 21

21 Hillslope processes Hillslope processes comprise the different types of mass movements that occur on hillslopes Slides refer to cohesive blocks of material moving on a well-defined surface of sliding Flows move entirely by differential shearing within the transported mass with no clear plane at the base of the flow Heave results from disrupting forces acting perpendicular to the ground surface by expansion of the material 22

22 Hillslope processes Hillslope processes comprise the different types of mass movements that occur on hillslopes Slides refer to cohesive blocks of material moving on a well-defined surface of sliding Flows move entirely by differential shearing within the transported mass with no clear plane at the base of the flow Our focus Heave results from disrupting forces acting perpendicular to the ground surface by expansion of the material 23

23 Mass movement processes Creep is almost too slow to monitor Fig. 4.27, Ritter et al.,

24 Heave and creep Creep: The extremely slow movement of material in response to gravity Heave: The vertical movement of unconsolidated particles in response to expansion and contraction, resulting in a net downslope movement on even the slightest slopes Seasonal creep or soil creep is periodically aided by heaving 25

25 Heave and creep Nearly vertical Romney shale displaced by seasonal creep Fig. 4.28, Ritter et al.,

26 Heave and creep Fig. 4.29, Ritter et al.,

27 How does heaving work? Near-surface material moves perpendicular to the surface during expansion (E) Expansion can result from swelling or freezing In theory, particles settle vertically downward during contraction (C) In reality, particle settling is not vertical, but follows a path closer to D Fig. 4.30, Ritter et al., 2002 What influences the rate of downslope material transport by heaving? Slope angle, soil/regolith moisture, particle size/ composition 28

28 How does heaving work? Near-surface material moves perpendicular to the surface during expansion (E) Swelling can result from swelling or freezing In theory, particles settle vertically downward during contraction (C) In reality, particle settling is not vertical, but follows a path closer to D Fig. 4.30, Ritter et al., 2002 Based on this concept, what would you expect to influence the rates of creep? 29

29 How does heaving work? Near-surface material moves perpendicular to the surface during expansion (E) Swelling can result from swelling or freezing In theory, particles settle vertically downward during contraction (C) In reality, particle settling is not vertical, but follows a path closer to D Fig. 4.30, Ritter et al., 2002 Based on this concept, what would you expect to influence the rates of creep? Slope angle, soil/regolith moisture, particle size/ composition 30

30 Mass movement by heaving Creep rates vary with depth and soil/ regolith composition Fig. 4.31, Ritter et al.,

31 Frost creep and solifluction Solifluction occurs in saturated soils, often in periglacial regions In periglacial settings, frost heave leads to expansion of the near-surface material During warm periods, saturated material at the surface flows downslope above the impermeable permafrost beneath Fig b, Ritter et al.,

32 Rain splash Rain splash transport refers to the downslope drift of grains on a sloped surface as a result of displacement by raindrop impacts Although this process can produce significant downslope mass transport, it is generally less significant than heave 33

33 Studying rain splash Experimental setup: Rain drops released from a syringe ~5 m above a dry sand target Drops travel down a pipe to avoid interference by wind Various drop sizes (2-4 mm), sand grain sizes ( mm) and hillslope angles High-speed camera used to capture raindrop impact and sand grain motion Furbish et al.,

34 Studying rain splash Dry sand grains are displaced following raindrop impact Miniature bolide impacts (?) Furbish et al.,

35 Studying rain splash More particles drift downslope as slope angle increase Furbish et al.,

36 Common features What do all of these sediment transport processes have in common? In each case, the rate of transport is strongly dependent on the hillslope angle Steeper slopes result in faster downslope transport In other words, the flux of mass is proportional to the topographic gradient This suggests these erosional processes can be modelled as diffusive 37

37 Heat in the Earth 38

38 Heat transfer in the Earth 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. 39

39 Heat transfer in the Earth 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. 40

40 Heat conduction in the Earth Turcotte and Schubert, 2002 Cooling of a 2-m wide dike following emplacement Time-dependent heat conduction processes are nice examples of thermal diffusion Changes in boundary temperatures take time to propagate 41

41 Heat conduction in the Earth Turcotte and Schubert, 2002 Cooling of a 2-m wide dike following emplacement Time-dependent heat conduction processes are nice examples of thermal diffusion Changes in boundary temperatures take time to propagate 42

42 Heat conduction in the Earth Turcotte Heat and Transfer Schubert, 2002 Cooling of a 2-m wide dike following emplacement Surface temperature changes over the past 500 a Huang et al., 2000 Global Time-dependent heat conduction processes are nice examples of thermal diffusion Temperature profiles at different times during dike solidifica- Temperature relative to present day (K) Northern H emisphere Southern H emisphere Changes in boundary temperatures take time to propagate ountry rock and the solidified magma from Equation (4 139) he temperatureprofiles at several times are given in Figure Use the results of the sudden half-space heating problem, 17), to estimate the time required for dike Intro to solidification Quantitative Geology by b. Howdoesthistimecomparewiththe10.9dayscomputed Year 43

43 Recap Diffusion is a mass transport or mixing process resulting from random motion of diffusing particles Hillslope diffusion occurs as a result of numerous processes, notably heave Heat conduction is an important thermal process where thermal energy diffuses from hot regions to cold regions 44

44 References Allen, P. A. (1997). Earth Surface Processes (1st ed.). Wiley-Blackwell. Furbish, D. J., Hamner, K. K., Schmeeckle, M., Borosund, M. N., & Mudd, S. M. (2007). Rain splash of dry sand revealed by high-speed imaging and sticky paper splash targets. J. Geophys. Res., 112(F1), F doi: /2006JF Huang, S., Pollack, H. N., & Shen, P.-Y. (2000). Temperature trends over the past five centuries reconstructed from borehole temperatures. Nature, 403(6771), doi: / Popov, Y. A., Pevzner, S. L., Pimenov, V. P., & Romushkevich, R. A. (1999). New geothermal data from the Kola superdeep well SG-3. Tectonophysics, 306(3), Ritter, D. F., Kochel, R. C., & Miller, J. R. (2002). Process Geomorphology (4 ed.). MgGraw-Hill Higher Education. Shuster, D. L., Flowers, R. M., & Farley, K. A. (2006). The influence of natural radiation damage on helium diffusion kinetics in apatite. Earth and Planetary Science Letters, 249(3-4), Turcotte, D. L., & Schubert, G. (2002). Geodynamics (2nd ed.). Cambridge, UK: Cambridge University Press. 45