lecture 6 isostasy mountains and the asthenosphere n.
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Lecture 6 Isostasy , mountains, and the asthenosphere. Earth elevation is bimodal. Elevation km. Lhasa, Tibet 3.7 km in elevation. 200-300 My. Great unconformity. 1.4 Gy. Sandia Mountains New Mexico, USA. PRESSURE = FORCE per UNIT AREA P = Force/Area Force = mass x acceleration

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slide6

200-300 My

Great unconformity

1.4 Gy

Sandia Mountains

New Mexico, USA

slide7

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

slide8

Your weight is due to the gravitational force of the Earth acting on your body

What is gravitational force?

slide9

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/

slide10

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/

slide14

There is only a small increase in gravitational acceleration

… which can be accounted for by the airplane just being closer to the mountain

slide15

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

slide16

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

slide18

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

slide21

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?

slide22

Let’s push the rubber duck (continental crust) deep beneath the water (mantle)….

rcrust < rmantle

mantle

hR

ht

crust

Pcrust <

Pmantle

slide23

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.

slide24

he

ht

hR

crust

mantle

Compensation depth

rcrustght = rmantleghr

Pmantle

Pcrust =

At equilibrium:

This is ISOSTASY

ISO = same

STASY = not moving, static

slide25

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

slide29

Continents are “floating” on a fluid mantle

The underlying mantle must be able to flow

(even though the mantle is solid)