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Geology 438 – Problems for 3/22/04

1. Here's one we started in class: start with 35 km thick continental crust in isostatic equilibrium with the surface at 500 meters above sea level. The average crustal density is 2750 kg/m³ , the mantle density is 3250 kg/m³ mantle and the compensation depth is100 km below sea level. Suppose we magically erode (or blast away) 20% of the crust.

• What is the new elevation of the surface?
• How much basalt (3000 kg/m³) do you have to flood into the hole before the surface is back to sea level?
  

2. Here's a situation like the Bolivian Altiplano, which rises above the descending Nazca plate: assume 4km of elevation above sea level (2670 kg/m³), 52 km of 2670 kg/m³ crust, 15 km of 2819 kg/m³ lower crust, and mantle (3200 kg/m³) down to a compensation level 125 km below sea level. Assume 100% Airy compensation and calculate how much erosion will be needed to erode the surface to sea level. Express your answer in kilometers and percent erosion, and think about the rocks.

3. Suppose a 10 km thick thrust sheet of the same density as the crust is emplaced on normal continental crust which is 35 km thick with an elevation of 50 meters above sea level. Assuming Airy isostacy, what is the new elevation of the surface?

A couple GravCadW problems:

4. Imagine you are working in a groundwater system where the general depth to bedrock (2.75 g/cm³) is 125 meters. The average density of the sediments in the basin is 2100 kg/m³. Suppose an apparent divide in groundwater flow causes you to suspect a local bedrock high in the basin. The bedrock high is 1000 meters wide, very long, and sticks up into the sediments. Suppose you think the top of the bedrock high must be about 45 meters below the surface.

• Use GravcadW to show what the expected anomaly looks like.
• What station spacing would you propose for a gravity survey, and why?
• What must the precision of your measurements be to measure the anomaly from the proposed bedrock high?

5. The Mission fault separates Precambrian Belt Supergroup (2.95 g/cm³) from Tertiary valley fill (2200 kg/m³). The fault dips west at about 60^o near the surface. Suppose there is some question about the subsurface dip of the fault for the upper 20 kilometers of crust. One person suspects the fault changes to a 30^o dip at 10 kilometers below the surface, another thinks it is 60^o all the way to twenty kilometers. Will a gravity survey allow you distinguish between these two models? Use GravcadW to present your case in a sound, well-reasoned couple of paragraphs. Think of a clever, informative, and convincing way to illustrate your answer.

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