# cooling plate depth vs. age ~120 km. temperature vs. depth vs. timeâ€”erf for...

Post on 19-Dec-2015

214 views

Embed Size (px)

TRANSCRIPT

- 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)