# cooling plate depth vs. age

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Cooling Plate Depth vs. Age ~120 km

Author: shubha

Post on 20-Jan-2016

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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. What about Seafloor Depth due to cooling?. Cooling rocks makes them denser: is the coefficient of thermal expansion (units of inverse temperature) - PowerPoint PPT Presentation

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• Cooling Plate Depth vs. Age~120 km

• Temperature vs. Depth vs. timeErfFor Plates (rocks), cooling skin thickness L=10km x (Age[m.y.])1/2

• 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)

• Plate contraction: average temperature change ~600C between plate & asthenosphereFractional 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

• Isostasy- concept of floatingLithosphere floats on underlying mantle, surface relief is compensated by deeper root

• Plate cooling & depth cartoon

• Plate contraction of 100 m.y. old lithosphereThus, a 100 m.y. old ~100km thick plate will have contracted about 600m vertically due to its coolingBut we see roughly 3km of deepening, not 600m. What gives?

• Balance mass in columnsPredicts 2km subsidencefor 100km-thick lithosphere -- closer, but we see 3km! Whats Missing?Mass in each column is the same

• Can Find Isostatic Effects in Several WaysMass added = mass displacedSame mass in each column of mantle + lithosphere + waterPressure 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)

• Mass added = mass displacedMaybe easiest conceptually, but hardest mathematicallyModel consistent with observations

• (2) Same mass in each columnUsually leads to easier math

• (3) Same mass displaced...If possible to do, is shortest mathmass deficitbalancesmass excess

• (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 compensationBase of Lithosphere is Compensation depthPressure = weight of overburden

• Rheologic implications of isostasyWhat does the existence of isostasy imply about mechanical behaviour of lithosphere & underlying mantle?

If oceanic lithosphere is denser than underlying mantle, why doesnt it just sink???

• Heat Flow qFor rocksThermal conductivity kTypical heatflow ~50mW/m2 [between 30-100mW/m2]

Old unit: 1 heat flow unit = 1cal/cm2-s ~ 42 mW/m2(still in fairly common use, perhaps because Earth surface heatflow is typically of order 1 HFU)Predicted heat flow scales with (age)-1/2

• Heat Flow vs. Distance (N. Atlantic & Pacific)

• Lord Kelvins estimate for age of EarthIf continental heatflow is roughly 0.070W/m2 (70mW/m2),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)