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Chapter2: Lithospheric Mechanics

Chapter2: Lithospheric Mechanics This presentation contains illustrations from Allen and Allen (2005 ) and Press et al. (2004). Physical State of the Lithosphere. Key Concepts Surface Forces Local Isostasy Flexural isostasy Thermal conductivity Thermal Expansion

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Chapter2: Lithospheric Mechanics

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  1. Chapter2: Lithospheric Mechanics This presentation contains illustrations from Allen and Allen (2005 ) and Press et al. (2004)

  2. Physical State of the Lithosphere Key Concepts • Surface Forces • Local Isostasy • Flexural isostasy • Thermal conductivity • Thermal Expansion • Heat transfer: A special case • Rock Rheology (2.3) • Relevant mantle rheological behavior • Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening

  3. Key Concepts Lithostatic stress(CA), deviatoric stress(TA), uniaxial stress, plane stress bulk modulus(MB),flexural rigidity(JTB) thermal conductivity(AD), geotherm(SE) Geoid(HF), Bouguer anomalies(TJH) Isostasy(CJ) diffusion and dislocation creep(AL), Byerlee’s Law(CP) (one per student --- e-mail me your answer written in PowerPoint slide– one illustration and two sentences … worth 1 point for final, due Tuesday 12, September – e-mail to me)

  4. Surface (not surficial!) forces in geology We measure these forces of gravity and reaction to gravity not in terms of Newtons but by using the concept of stress, in Newtons per meter square, or Pascals. (See structural geology notes). What is atmospheric pressure? What is the hydrostatic state of stress?

  5. Lithostatic stress 1 cu. meter of water weighs 1000 kg x 10m/s2 or 10000 Newtons (N) 1 cu meter creates 10000N/m2 (Pa) of pressure at its bas 10 meters of water depth produces 100000 Pa (1 atm) of 0.1 MPa, that is every 10 m you dive down, pressure  increases  by 1 atm.  1000 vertically stacked 1-m-cubes of water weigh 10 million Newtons  1000 m (1 km) of stacked 1-m-cubes of water create 10 million Pascals (Pa) or 10 MPa at its base

  6. Lithostatic stress • If the above is true, then under 1 km of  mud (2200 kg/m3) there should be about 22 MPa of pressure then under 30 km of granite (2670 kg/m3) there should be 801 MPa, or .8 GPa The rule to convert density into MPa of pressure per km is to take the density of the material in g/cc, move the decimal point over one space and change the units to MPa Other useful conversions to know are: To get MPa from psi mutliply Pounds/sq in by 0.689 x 10 ^-2 To get psi from MPa multiply MPa by 145.05 To convert  to MegaPascals.... Divide by 1000000 Pa per 1 MPa

  7. Lithostatic stress • If you think you understand the previous slide, then answer the following question: On Planet Zog the average density of the 10 km-thick crust is 2500 kg m^-3 . Acceleration due to gravity is 3.2 m s^-2 . What is the pressure at the base of the crust?   A. 80 MegaPascals   B. 80 Newtons   C. 800 Newtons   D. 3 GigaPascals   E. 30 Gigapascals   F. None of the above

  8. Lithostatic stress is responsible for the increase of pressure with overall depth in the earth but it is the differential stress that creates the faults and folds.

  9. What is the vertical lithostatic stress gradient in granitic crust? What is the vertical stress gradient in the first 2 km of the ocean?

  10. Faults can develop: (Side view) (Side View) (Bird’s Eye View)

  11. Brittle faults can develop: (Side view) (Side View) (Bird’s Eye View)

  12. Sea of Galilea Dead Sea

  13. What is the direction of directed pressure (maximum principal stress direction)? How many orientations of faults can be generated for the same directed pressure direction??

  14. Physical State of the Lithosphere Key Concepts • Surface Forces • Local Isostasy • Flexural isostasy • Thermal conductivity • Thermal Expansion • Heat transfer: A special case • Rock Rheology • Relevant mantle rheological behavior • Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening

  15. Surface Forces (Pressure)- LOCAL ISOSTASY Depth of compensation

  16. Isostasy or Archimedes’ Principle states that the crust, mantle can float above the underlying material If the crust and mantle float then there exists a depth at which pressuer above and pressure below are equal. This surface is known as the compensation depth

  17. General recommendations for local isostatic calculations (1) Define a surface of compensation (2) Define a reference column of crust and mantle (3) Compare the weight of the reference column with the unknown (4) Simplify algebra in terms of two unknowns (4) Keep physical units the same See syllabus (Tuesday, 19 September) for elaborated examples

  18. Isostasy homework due Thursday, 21 2006 • Derive the relation between basin-floor depth and Moho depth. • Assuming that underneath Lake Baikal the continental crust and mantle is homogeneous, calculate the expected thickness of continental crust. • Same for the continental shelf of the Gulf of Mexico • Show all your work –type it up and e-mail it to me

  19. Physical State of the Lithosphere Key Concepts • Surface Forces • Local Isostasy • Flexural isostasy • Thermal conductivity • Thermal Expansion • Heat transfer: A special case • Rock Rheology • Relevant mantle rheological behavior • Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening

  20. Flexure of the lithosphere • The outer skin of the earth down to depths where the temperature is cool enough and rock properties permit the earth can be visualized to be effectively elastic (e.g., rubber ball) over long periods of time, i.e., hundreds of millions of years.

  21. A conclusion is that mountain belts will not sag over time but will maintain their mechanical strength indefinitely for practical purposes. A measure of the strength of the crust is how much it bends to a given load. This value is known as the flexural rigidity (D – units of Nm) Nm is equivalent to about 34 km of elastic thickness (Te) or moderately strong elastic lithosphere

  22. One view on flexure in basins • Use local isostasy as a reference • Assume stationary conditions • Deviation from this reference is a measure of internal strength balanced against an applied load

  23. Measure of elasticity But, if we use the other extreme case …. the case of a weight that is very wide… (i.e. > 1000 km)…..????? When it is very wide the condition reaches that of local isostasy and all the weight pushing down is balanced by the reaction of the mantle pushing up. If the load is exceptionally narrow and small then the lithosphere will appear (infinitely) very strong because it does not give way at all to the load!

  24. =

  25. + =

  26. + =

  27. + =

  28. + + + + + + + + + + + + + + + + + =

  29. Finite (reasonable and not extreme) geological load versus infinite (very wide) load

  30. Maximum depth of subsidence of the base of the crust in the case that the load is very wide and that hydrostatic compensation is local… i.e. some the elastic lithosphere has no internal strength. Now compare the case where the load is relatively narrow….

  31. Point load versus infinite (very wide) load

  32. Now compare the case where the load is relatively narrow and the strength of the lithosphere becomes apparent…. Point load versus infinite (very wide) load

  33. = -( Strength of elastic lithosphere) (weight)

  34. Downward directed invisible load creates space that fills with water and adds more vertical load Use reference at infinity (very far away) and pressure at level of compensation. At level of compensation pressures are in equilibrium. Level of compensation g(h.rhom + hw. rhow + w .rhom)

  35. (At infinity) g(h.rhom + hw. rhow + w .rhom) = (Under load) qa (Point load) + g(w.rhow + hw.rhow + h.rhom)-internal resistance to bending

  36. g(h.rhom + hw. rhow + w .rhom) = qa (Point load) + g(w+hw) rhow + h.rhom) – internal resistance to bending If there is internal strength in the lithosphere, then hw will not be as deep as it should be because the oceanic lithosphere resists!

  37. (Under load) (At infinity) qa (Point load) + g( (w+hw).rhow + h.rhom) – internal resistance to bending g(h.rhom + hw. rhow + w .rhom) = internal resistance to bending + g (rhom-rhow) w = qa (Point load) “Equation 2.28” Equation 2.28

  38. Physical State of the Lithosphere Key Concepts • Surface Forces • Local Isostasy • Flexural isostasy • Thermal conductivity • Thermal Expansion • Heat transfer: A special case • Rock Rheology • Relevant mantle rheological behavior - Rheology of continental crust • Elastic-perfectly plastic • Strain hardening and strain softening

  39. Thermal conductivity measures how well… for a given temperature gradient, conductive heat transfers moves through rock. Heat moves from higher temperature to areas of lower temperature. Halite: 7 kW/m/ºK Shale: 3 kW /m/ºK

  40. Thermal conductivity • The efficiency of that transfer is the thermal conductivity. So, for a given temperature gradient – dT/dz (continental or oceanicgeotherms) the amount of heat being passed across any given portion of the earth’s surface (heat flux-Q) per unit time will depend on the coefficient of thermal conductivity (K). Fourier’s Law: Q for continents is ~ 60 mW/m^2 or 60W/1000 m^2 Q for continents is ~ 80 mW/m^2

  41. Geotherm Temperature variation with depth in solid crust indicates how much heat is flows from the mantle, and how much heat is generated within the crust. Q- heat flow K- conductivity A- internal heat generation Z -depth

  42. Geotherm Temperature oceanic z continent

  43. Heat Production versus depth Heat production at surface (Hs )is maximum H eat production = Hs exp (-z/ar)

  44. Heat production Z Depth(km)

  45. Geotherms Surface heat flow observations indicate that heat flow increases linearly with the heat production of surface rocks. This is mathematically accomplished by assuming that heat production decreases with depth in an exponential manner. ar is the depth at which heat production is halved A0 is the surface heat production

  46. Global heat production • Continental surface heat flow comes about 50% from the mantle (U,K,Th) and about 50% from radioactive sources. • Heat flow was x2 what it is now, about 3 billion years ago • Oceanic heat flow largely depends on thermal age of the lithosphere and not on the radioactivity

  47. Sampling thermal conductivity On board R/V Joides Resolution, Leg 150 New Jersey Margin, US Atlantic Coast, B. Hoppie (right) (MNSU, Mankato), C. Fulthorpe(left) (UT Austin)

  48. Thermal conductivity • We can measure thermal conductivity with respect to standards as you can see in this overhead of a thermal conductivity measurements on board Leg ODP 150 New Jersey Margin in the summer of 1993. People are (L toR) Bryce Hoppie and Craig Fulthorpe. These needles contain heaters and temperature sensors. These needles measure the speed at which the temperature changes over time to calculate the conductivity of the material into which they are inserted.

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