Assignment: Isostasy Name
The rigid outer layer of the Earth, the lithosphere, floats on a softer, plastic layer known as the asthenosphere, analogous to how an ice cube floats in water. Geologists use the term isostasy to refer to a state of equilibrium between the lithospheric plates and the underlying asthenosphere. The lithospheric plates adjust vertically so that there is a balance between the buoyant force pushing the lithosphere up and the gravitational force pulling the lithosphere down. Isostasy is based upon Archimedes' principle - that a floating object displaces its own weight of fluid. The height of a floating object depends on its thickness and density.
The following exercise explores how density and thickness affect the elevation of floating objects using the following buoyancy equation.
(densityblock / densityliquid) = (heightroot /heightblock) rearranging gives → heightroot = heightblock X (densityblock / densityliquid)
apparent elevation = heightblock - heightroot
Record what happens to the height of the block root when the density and height of the block changes in the table below. Use this information to calculate the apparent elevation (the "crown"). Density of the mantle ("liquid") is 3.3.
|
Block density
|
heightblock
|
heightroot
|
apparent elevation
|
|
2.7
|
40
|
|
|
|
3.0
|
40
|
|
|
|
3.0
|
8
|
|
|
|
2.7
|
60
|
|
|
|
2.7
|
55
|
|
|
|
2.7
|
50
|
|
|
|
2.7
|
45
|
|
|
To answer the questions below, you may find it useful to sketch out a block diagram on graph paper based on the data in the table.
1) The lithosphere is composed of crust plus the upper part of the mantle. Two types of crust exist, oceanic and continental. Oceanic crust has a density of 3.0 g/cm3 and an average thickness of 8km. In contrast, continental crust has a density of 2.7 g/cm3 and an average thickness of 40km.
What is the apparent elevation of a 40km high block with a density of 2.7 g/cm3? What is the apparent elevation of an 8km high block with a density of 3.0 g/cm3?
2) What happens to the block when the density of the block increases, but height stays the same? How does this impact the apparent elevation (the part of the block above the equilibrium line)?
3) What happens when the height of the block increases, but density stays the same? Compare the calculated results for any two rows with same density. What % of the height increase goes to the root versus the crown?
4) What happens to apparent elevation as the height of the block is reduced, as if by erosion? How does the magnitude of elevation change compare to the amount of material removed? What is going on?