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Thermal and Mechanical Processes

# The role of Gravity

The internal Gravitational Force that acts in collision zones is a result of lateral variation in density, which produces variations in Gravitational Potential Energy. The following information will firstly explain where the Gravitational force comes from (lateral variations in density which leads to variations in Gravitational Potential Energy) and then specifically the role this gravitational force has in collision zones.

## Lateral Variation in Density (different densities at the same height)

To understand how we get lateral density variation it helps to look at the theory of isostatic equilibrium (Greek for “equal standing”). Isostatic equilibrium states that at or below a depth known as the compensation level the pressure is hydrostatic. This means that if you take cross sections with the same area from any line along or below the compensation level stretching up to a height at or above the highest surface relief the weight of the vertical material will be the same. Figure 1 shows cross sections in isostatic equilibrium. #### Figure 4.1: Isostatic equilibrium.

As a result of isostatic adjustments high mountain belts and plateaus are commonly underlain by thicker crust that extends deeper into the mantle than do areas of low elevation. Isostasy controls the surface elevation. In collision zones to maintain Istostatic equilibrium the surface elevation must increase

Isostatic equilibrium is maintained in this picture but you can see that the thickness of the crust and lithospheric mantle varies. For example the crust may have a density of 2700 kgm-3 and the Lithosphere a density of 3330 kgm-3 . Looking at figure 1 you can see that you would have material with density 2700 kgm-3 next to material with a density of  3300 kgm-3 .(therefore lateral variation in density).

## Gravitational Potential Energy

Gravitational potential energy is given by the integration of (or the area under the curve) p.g.z, where

p = density in kgm-3
g = gravitational acceleration, 9.81ms-2
z = Height

## The Gravitational force

The gravitational force is calculated by the difference between the GPE of two columns such as the ones pictured in figure 1. The difference in GPE between two areas can be calculated using the following formula

# - If the gravitational force (Fg) is negative then Fg will drive extension and if the gravitational force (Fg) is positive then Fg will drive extension.

Figure 2 shows two lithospheric columns in isostatic equilibrium. The gravitational potential energy of column C is greater  than the gravitational potential energy of column B. To find out the gravitational force that column B and C apply to each other you subtract the GPE of C from the GPE of  B. This will produce a negative result because GPE of C is greater than that of column B. A negative Gravitational force (Fg) will produce an extensional force. ## Collision zones and the Gravitational force

* When collision produces Mountain belts or uplift, gravitational potential energy is being growing in the uplifted area.

* In the Figure 2 column C could be the area that has been uplifted during collision and column B the undeformed lithosphere.  As you can see the uplifted column C has a higher GPE.

* As the Mountain belt grows the difference between the Gravitational Potential Energy of the Mountain belt and the undeformed area grows.

* As the difference in GPE grows the Gravitational force will become a higher and higher negative number.

* This negative gravitational force as described above produces a force that drives extension.

* This gravitational force must be less that the tectonic driving force and Lithospheric strength to maintain crustal thickening. (the tectonic forces and the Lithospheric strength are the forces that allow the Mountain belt to be built, the gravitational force opposes these forces)

* Eventually the gravitational force will become equal to the tectonic driving force. The Gravitational force produced by the difference in GPE will balance the force applied due to the collision of the plates.

* Therefore the height of a Mountain Range is restricted by the force of the collisional tectonic driving force and by the plates densities (a denser material needs a larger force to be elevated a set height).

* When the tectonic driving force is balanced by the gravitational force the crustal thickening will extend laterally (forms plateau).

*  If the collision tectonic driving force was to reduce or cease the gravitational force would be greater, therefore the Mountain belt would experience extensional collapse.   ## Gravitational Collapse

There are two main modes of Gravitational collapse:

1) Fixed boundary divergent collapse, where the lithosphere surrounding the unlifted area is fixed. The gravitational potential energy is transferred from the uplifted area to the lowlands. In collision zones where Mountain building has occurred this would involve lateral growth of the Mountain belt (the surrounding        lithosphere thickens).

2) Free boundary divergent collapse, where the surrounding lithosphere is not fixed. Thickened crust thinned without gravitational potential energy transfer into the surrounding area.

Thermal and Mechanical Consequences