Question

The 'iceberg analogy' for the isostatic equilibrium of the continental crust is quite useful because it draws a parallel between the relative densities of icebergs and seawater, analogous to the relative densities of the continental crust and the mantle. According to the 1-to-8 rule derived from this analogy, for every 1 unit of extra elevation for an iceberg or mountain belt, there needs to be 8 units of total thickness.

Assuming continental crust in isostatic equilibrium, where the average thickness at sea level is about 35 kilometers (1 km = 0.6 miles), calculate the required thickness of the crust to support:

a. A 1-kilometer high mountain belt.
b. A 2-kilometer high mountain belt.
c. A 5-kilometer high mountain belt.
d. None of the above.

Answer 1

To support raised mountain belts in isostatic equilibrium, the crust must thicken according to the 1-to-8 rule from the iceberg analogy. For a 1 km, 2 km, and 5 km high mountain belt, the crustal thickness required would be 43 km, 51 km, and 75 km, respectively, added to the average of 35 km thickness at sea level.

Step-by-step explanation:

The 'iceberg analogy' is a concept used to understand the relationship between the elevation of landforms such as mountain belts and the thickness required of the continental crust to support them, mirroring the way icebergs float on seawater. This analogy states that for every 1 unit of extra elevation, there needs to be 8 units of thickness added to the base. The average thickness of the continental crust at sea level is around 35 kilometers.

1. For a mountain belt 1 kilometer high, the equation would be 35 km + (8x1 km) = 43 kilometers of crustal thickness needed.
2. For a 2-kilometer high mountain belt, the thickness of the crust would be 35 km + (8x2 km) = 51 kilometers.
3. For a 5-kilometer high mountain belt, the required crustal thickness would be 35 km + (8x5 km) = 75 kilometers.

In conclusion, to support an elevated mountain belt in isostatic equilibrium, additional crustal thickness is required. The calculation is based on the 1-to-8 rule derived from the iceberg analogy, where the relative densities of the continental crust and the mantle play a significant role.