Geosciences 440/540 Fall 2009 GEODYNAMICS Problem Set I These problems are due in class Wednesday 09 September 2009 1.1 Turcotte & Schubert isostasy problems, all represent practice in elementary algebra or arithmetic: Problem 2-2, (p. 75), Problem 2-6, (p. 76), and Problem 2-7 (p. 78). Don't use IsoBal for these. Answers in back of book, more or less. For these and subsequent problems, please show your work. For the next two multi-part problems, you will need to run the ancient microcomputer program IsoBal (hey, it works, if you’re lucky). This problem set is accompanied by a tutorial handout on how to use IsoBal. The handout and the program are available from the Problems page you are looking at now. From that page: For Macintosh computers: “Secret DOS version with a dosbox around it. Click Boxer link, go found where your Mac put it, and double-click boxer_0.71.dmg to open the .dmg file. You will (should) see a folder open up containing Boxer.app. Make yourself a folder for all this DOSish stuff, and put Boxer.app into it. Double click Boxer so your system knows it is there, then click on IsoBal and drag it into your DOS folder. It's a good idea to keep all your program output there also.” For Windows computers: “DOS version. Double click the Isobal link, make yourself a folder, and put ISOBAL.COM in there together with any results you want to keep. Windows will complain every time you quit IsoBal, but no harm done.” For any future problem sets that use DOS code, you only need to toss it into your own folder. If you’re using U of A computers, get yourself a cheap USB flash drive (memory stick, thumb drive, whatever). 1.2 Ocean ridge problems: isostasy is very important in ocean basin morphology. a) Imagine a 5.2 km deep ocean basin filled with sea water of density 1035 kg/m3, and underlain by oceanic crust , with density 2850 kg/m3. What would be the oceanic crustal thickness needed for local isostatic compensation relative to a standard reference crust that has zero elevation, 30 km total thickness (0-10 km depth with density 2670 kg/m3, 10-20 km depth with density 2870 kg/m3, 20-30 km depth with density 2950 kg/m3), and a standard mantle density of 3300 kg/m3? (This is IsoBal’s automatic standard column.) b) Calculate the mean density of the standard crust. What conclusion do you draw from its similarity to the oceanic density about the relative importance of crustal density versus crustal thickness in maintaining isostatic elevation differences between oceanic and continental crust? c) Now take an ocean underlain by crust and lithosphere as in part a) and fill it with sediment having a density of 2450 kg/m3 while maintaining isostatic equilibrium. How much can be deposited before the top of the sediment pile reaches sea level? Isn't that an awful lot? Specify where on Earth this process is actually taking place. d) Now consider the lithospheric column under a mid-ocean ridge with water depth of 2.5 km and the same crustal thickness and density as in part a) (Fig. 4-44). What mantle density under the ridge is required for isotatic balance with the old oceanic lithosphere (part a) for a compensation depth of 100 km? If the appropriate coefficient of thermal expansion !0 is 3.0x10-5, what is the average temperature surplus of the hot mantle under the ridge (Turcotte & Schubert, Eqn. 4-205, p. 175)? Discuss why this temperature is reasonable.Geos 440/540 Problem Set I, Fall 2009 Page 2 of 2 1.3 Colorado Plateau problems: the Colorado Plateau is underlain by 40 to 50 km-thick ancient continental crust that was at sea level in Cretaceous and now has an average elevation of around 2 km. Let us explore what this implies. a) First, try a Cretaceous Colorado Plateau column at sea level (elevation of first layer z = 0) which has 1km of sediments with density 2450 kg/m3 lying on 3 crustal layers each 13 km thick, but with the same densities as the standard column, and a mantle density of 3300 kg/m3. Does it balance? If not, can you bring it into balance by letting the program vary the thickness of the crustal layers while keeping the total crustal thickness constant at 40 km? b) To see why part a) should have consistently frustrated you, try a sea level-elevation column with a 1 km sediment layer as above, a single 39 km thick crustal layer, and make the program find the right density to balance. Is it clear now where the problem arose? Would a thicker crust make the problem better or worse? c) O.K., let's blame the mantle. Using a compensation depth of 100 km, find the mantle density that will balance the sea-level Colorado Plateau crust of part a) against the standard. What is the magnitude of the density contrast between this old Colorado Plateau mantle and the standard mantle? Do the same calculation for a compensation depth of 200 km. Is this within the range of normal mantle densities? d) Now for the uplift. Using the structure you found for part c) as a starting point, uplift the crust to an elevation of 2 km (first z = -2.0) and recalculate the mantle density for both of the compensation depths. As in problem 1.2.d, calculate the temperature change in the mantle of the uplifted case relative to the sea-level case (thermal expansion coefficient 3.0x10-5 as before) that would be necessary to cause the uplift for 100 and 200 km compensation depths. In terms of the melting properties of the upper mantle, this thermal explanation for uplift of the Colorado Plateau doesn’t work at all for 100 km depth, and is marginal for 200 km. Explain