Lecture 6 Isostasy , mountains, and the asthenosphere

1. Lecture 6Isostasy, mountains, and the asthenosphere

2. Earth elevation is bimodal Elevation km

3. Lhasa, Tibet 3.7 km in elevation

6. 200-300 My Great unconformity 1.4 Gy Sandia Mountains New Mexico, USA

7. PRESSURE = FORCE per UNIT AREA P = Force/Area Force = mass x acceleration F = m x a kg x m/s2 Your weight is a force weight = F = m x g g is gravity 9.8 m/s2

8. Your weight is due to the gravitational force of the Earth acting on your body What is gravitational force?

9. Mass of Earth 5.97x1024 kg Gravitational acceleration 9.8 m/s2 Mass of ninja kg MEmninja = mninja a = mninja g F = G R2 Weight of ninja Gravitational constant 6.67x10-11 m3kg-1s-2 Radius of Earth 6370 km R ME g = G R2 Stick ninja from http://quotes-pictures.feedio.net/how-to-draw-stick-ninja/fc00.deviantart.net*fs71*f*2011*176*5*6*stick_figure_ninja_by_irkeninvaderkit-d3k07vm.png/

10. How does gravitational acceleration g change with elevation? R ME g = G R2 Stick ninja from http://quotes-pictures.feedio.net/how-to-draw-stick-ninja/fc00.deviantart.net*fs71*f*2011*176*5*6*stick_figure_ninja_by_irkeninvaderkit-d3k07vm.png/

14. There is only a small increase in gravitational acceleration … which can be accounted for by the airplane just being closer to the mountain

15. gA~ gB MA ~ MB Total mass beneath the mountain and the plains are equal MA MB gB = G gA = G R2 R2 B. Mountain A. Plains

16. There must be lateral variations in density rin the Earth And high elevations underlain by thick low density crustal root crust Low r mantle High r Note that one could have lateral variations in crustal density, but for now, let’s ignore that

17. Let’s come back to pressure

18. What is the pressure beneath a column of rock, water, etc? d P = mass x g / area = mg/d2 M = density x volume = ρ V Volume = h x d x d P = (ρ h d2) g / d2 P = r g h d Weight of column of rock h Density of water = 1000 kg/m3 Density of granite = 2700 kg/m3 Density of mantle = 3300 kg/m3

19. Continental Crust made up of granitic rocks Density = 2700 kg/m3

20. Mantle made of olivine-rich rock called peridotite Density = 3300 kg/m3

21. Let’s consider a continent “floating” at the surface of the Earth Analogy is a rubber duck Why does a rubber duck float? What happens if you push the rubber duck deep beneath the surface?

22. Let’s push the rubber duck (continental crust) deep beneath the water (mantle)…. rcrust < rmantle mantle hR ht crust Pcrust < Pmantle

23. Let’s push the rubber duck (continental crust) deep beneath the water (mantle)…. rcrust < rmantle mantle hR ht crust Pcrust < Pmantle Pressures at the depth equivalent to the base of the crust are not equal, thus, there is a buoyancy force acting on the crust to cause it to rise upwards The crust will be forced to rise towards the surface until lateral pressure differences disappear, e.g., Pcrust= Pmantle.

24. he ht hR crust mantle Compensation depth rcrustght = rmantleghr Pmantle Pcrust = At equilibrium: This is ISOSTASY ISO = same STASY = not moving, static

25. he ht hR crust mantle Compensation depth rcrustght = rmantleghr Pmantle Pcrust = At equilibrium: Elevation of the continent can thus be determined he = (rmantle-rcrust) ht / rmantle

26. ISOSTASY

27. Tip of the iceberg….

28. Continents ride high because they are buoyant (low density and thick)

29. Continents are “floating” on a fluid mantle The underlying mantle must be able to flow (even though the mantle is solid)

30. Earth loses its heat by convection