Geology 101 Lab 7: Isostasy Laboratory

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1 Name TA Name Geology 101 Lab 7: Isostasy Laboratory To what thickness can sediments accumulate on the earth s surface, and what controls this thickness? How deeply can the continents be eroded? These are two of the most important questions in the earth sciences, and their answer reveals a great deal about how our planet operates. The purpose of this laboratory is to experimentally answer these questions by conducting a simple analogue laboratory experiment, and then to apply the laboratory results to the earth using a simple mathematical formula which you derive. I. Background data and principles: You need only four pieces of information: 1. Law of Isostasy: A body floats when it displaces a mass of fluid equal to its own mass. 2. Density of water = 1 g/cm 3, sediments = 2.4 g/cm 3, continental crust = 2.8 g/cm 3, uppermost mantle = 3.17 g/cm Average depth of oceans below sea level = 5.5 km 4. Average height of Tibetan Plateau = 5 km. II. Experiment: Equipment: water, 4 wood blocks, 2 plexiglass containers Experiment with the wood blocks to determine how much sediment can be deposited in a dry ocean. The tall edges of your experimental apparatus extend up to sea level, and the low edges represent the base of the dry ocean or the top of the fluid mantle. In reality, the bottom of the ocean is the top of the oceanic lithosphere (the rigid uppermost part of the mantle and oceanic crust), and the fluid mantle (asthenosphere) lies some 100 km below. However, loads greater than a few hundred kilometers easily deform the lithosphere and effectively float on the fluid part of the mantle as if the lithosphere were not present. You can think of the

2 lithosphere as an elastic sheet stretched out on top of the water. The sheet will deform and, except for very small loads, will not affect the floating equilibrium. The lithosphere is not present in this experiment. The wood floats in the asthenosphere (water) with no intervening lithosphere. Fill the experiment box to the lower rim with water. The water represents the fluid (hot) mantle. Add the first block. The block is just the thickness of the dry ocean, but adding this block does not fill the dry ocean. Why? What fraction of the wood block lies below the water surface? How many blocks can you add before the dry ocean is filled to the height of the tall edges of your box? When the sediments reach sea level, deposition will normally stop. Why? Why can you fill the oceans with sediment several times rather than just once?

3 III. Analysis: Generalize your lab analysis so that you can make application to the earth 1. Calculate the density of the wood block using the principle of isostasy: a. Draw a diagram depicting the wood block, the depth of it submergence, and the height of the block above the water table. b. Measure the fraction of the wood block submerged in water. c. Isostasy states that the block floats when it displaces its own mass in water. Write a formula expressing isostasy that relates the submerged thickness of the block, h s, the total thickness of the block, h, the density of water, ρ f, and the density of wood (sediment), ρ s. d. Use your formula to calculate the density of the wood block from the known density of water.

4 2. Rework your formula so that the total thickness of the sediment pile is related to the sediment thickness floating above the mantle fluid. E.g. substitute h s = h - h a in the formula you deduced above. 3. Check your formula to verify that the total thickness of wood blocks when you filled your ocean with wood is ~3h a as you measured it. 4. Use your formula to calculate the thickness of sediment that can be deposited in a dry ocean 3.76 km deep if the density of the fluid mantle is 3.17 g/cm 3 and the density of compacted sediments is 2.4 g/cm Why is the depth of the dry ocean less than the average depth of the world s water-filled oceans (~5.5 km)?

5 6. Use your formula to calculate the depth of water-filled oceans given that the air-filled depth is 3.76 km. E.g., use ρ w = 1.0 g/ cm 3 rather than ρ s = 2.4 g/cm Now use your formula to calculate how deeply the earth s crust will be excavated when the 5 km high Tibetan Plateau is eroded to sea level. Assume a crustal density of 2.8 g/cm 3. You should predict over 40 km of excavation.

6 8. Temperature increases with depth into the earth s crust at about 20 C/km (e.g., the geothermal gradient is usually ~20 C/km). If the geothermal gradient is 20 C/km and the surface temperature is 20 C, what will be the temperature at 16 km and 40 km depth? 9. Would organic matter at 340 C be cooked? 10. Could this produce oil and gas? 11. Would rocks at 820 C be metamorphosed? 12. Could erosion of former Tibetan Plateaus be the reason metamorphic rocks are exposed at the earth s surface? By the way, the deepest well drilled by humankind to date is a Russian scientific drill hole in the Kola Peninsula which took over 10 years to drill and reached a depth of about 15 km.

7 IV. Discussion Comment briefly on what you have learned in this laboratory. Could you have applied your experimental results to the earth without using your simple formula? How severely impacted would a society be if no one in that society could use formula and manipulate symbolic expressions of any kind? How does this apply to individuals in modern society? The fact that the earth is a rotating fluid with a thin cold skin is of the greatest importance. How would the earth be different if it developed a very thick and rigid lithosphere similar to that on the moon? Could sediments accumulate to as great a thickness or erosion occur to such great depths? What do you suppose is the fundamental cause of the difference in elevation of the ocean bottom and the continental land surface. Can continents be thought of as icebergs floating in the fluid mantle?