1. Cooling Plate Depth vs. Age ~120 km

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

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 300°C temperature change)

4. Plate contraction: average temperature change ~600°C 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

5. Isostasy- concept of ‘floating’ Lithosphere ‘floats’ on underlying mantle, surface relief is compensated by deeper root…

6. Plate cooling & depth cartoon

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?

8. Balance mass in columns… Predicts 2km subsidence for 100km-thick lithosphere -- closer, but we see 3km! What’s Missing? Mass in each column is the same

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’)

10. Mass added = mass displaced Maybe easiest conceptually, but hardest mathematically Model consistent with observations…

11. (2) Same mass in each column Usually leads to easier math

12. (3) Same mass displaced... If possible to do, is shortest math mass deficit balances mass excess

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

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 doesn’t it just sink???

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

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

17. Lord Kelvin’s 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…)