cooling plate depth vs. age ~120 km. temperature vs. depth vs. time—erf for...

Download Cooling Plate Depth vs. Age ~120 km. Temperature vs. Depth vs. time—Erf For Plates (rocks), cooling skin thickness L=10km x (Age[m.y.]) 1/2

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  • Slide 1
  • Cooling Plate Depth vs. Age ~120 km
  • Slide 2
  • Temperature vs. Depth vs. timeErf For Plates (rocks), cooling skin thickness L=10km x (Age[m.y.]) 1/2
  • Slide 3
  • What about Seafloor Depth due to cooling? Cooling rocks makes them denser: is the coefficient of thermal expansion (units of inverse temperature) Cooling rocks makes them contract (which is why they become denser): For rocks, typically ~3x10 -5 C -1 (e.g. ~1% volume change per 300C temperature change)
  • Slide 4
  • Plate contraction: average temperature change ~600C between plate & asthenosphere Fractional density change between lith (cold plate) & asth: Contraction: Thus, a 100 m.y. old ~100km thick plate will have contracted about 600m vertically due to its cooling
  • Slide 5
  • Isostasy- concept of floating Lithosphere floats on underlying mantle, surface relief is compensated by deeper root
  • Slide 6
  • Plate cooling & depth cartoon
  • Slide 7
  • Plate contraction of 100 m.y. old lithosphere Thus, a 100 m.y. old ~100km thick plate will have contracted about 600m vertically due to its cooling But we see roughly 3km of deepening, not 600m. What gives?
  • Slide 8
  • Balance mass in columns Predicts 2km subsidence for 100km-thick lithosphere -- closer, but we see 3km! Whats Missing? Mass in each column is the same
  • Slide 9
  • Can Find Isostatic Effects in Several Ways (1)Mass added = mass displaced (2)Same mass in each column of mantle + lithosphere + water (3)Pressure at depth of compensation is uniform (similar idea to idea that mass of each column is the same same overburden implies same pressure at the depth of compensation)
  • Slide 10
  • Mass added = mass displaced Maybe easiest conceptually, but hardest mathematically Model consistent with observations
  • Slide 11
  • (2) Same mass in each column Usually leads to easier math
  • Slide 12
  • (3) Same mass displaced... If possible to do, is shortest math mass deficit balances mass excess
  • Slide 13
  • (4) Same pressure at depth of compensation (same math as for equal mass in columns, except for extra g in all terms) Equal pressure at the depth of isostatic compensation Base of Lithosphere is Compensation depth Pressure = weight of overburden
  • Slide 14
  • Rheologic implications of isostasy (1)What does the existence of isostasy imply about mechanical behaviour of lithosphere & underlying mantle? (2)If oceanic lithosphere is denser than underlying mantle, why doesnt it just sink???
  • Slide 15
  • Heat Flow q For rocks Thermal conductivity k Typical heatflow ~50mW/m 2 [between 30-100mW/m 2 ] Old unit: 1 heat flow unit = 1cal/cm 2 -s ~ 42 mW/m 2 (still in fairly common use, perhaps because Earth surface heatflow is typically of order 1 HFU) Predicted heat flow scales with (age) -1/2
  • Slide 16
  • Heat Flow vs. Distance (N. Atlantic & Pacific)
  • Slide 17
  • Lord Kelvins estimate for age of Earth If continental heatflow is roughly 0.070W/m 2 (70mW/m 2 ), Then this expression would suggest an age of the continents (=Earth) of ~45Ma. We now know Earth is ~4.55Ga old (1000 times older) Because Kelvin neglected ? (As a sidenote, Kelvin independently determined the age of the sun by assuming its energy source was the energy released by gravitational collapse and also came up with ~40 Ma. The agreement between these two independent (mis-) estimates of the age of the solar system is what made him so certain he was right)

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