G e o s c i e n c e s 4 4 0 / 5 4 0 : G E O D Y N A M I C S F a l l 2 0 0 9 P r o b l e m S e t I V Gravity and geoid These problems are due in class Wednesday, 11 November 2009 4.1a Turcotte & Schubert Problem 5-4, p. 204 4.1b Turcotte & Schubert Problem 5-5, p. 205 4.1c Turcotte & Schubert Problem 5-20, p. 212 (these are all 2nd edition page numbers) 4.2 Problem: How does the geoid anomaly across the continent/ocean lithospheric boundary change for various depths of isostatic compensation D? Note: Use the Excel spreadsheet Isostatic_geoid.xls, which you can download from the software link page on the class website. There's no tutorial for this program; it's hardly worth one. This problem asks you to calculate how much the geoid anomaly across the boundary of the continental and oceanic lithosphere changes if a significant portion of the isostatic compensation between the two partly occurs within the deeper part of the continental lithosphere. The scenario: standard oceanic lithosphere, as shown in the Excel file (left box), is balanced by Airy compensation of a 30-km thick sea-level continental crust of density 2800 km/m3 with normal mantle of density 3300 kg/m3 down to 300 km (middle box). The equations are near Turcotte & Schubert p. 220. a) Let's postulate that the sea-level continental crust is actually 40 km thick, and the extra buoyancy is compensated by slightly higher density in the whole continental lithosphere down to 300 km. Use Isobal to figure out what density is needed for the mantle lithosphere to balance the oceanic lithosphere. Then, in the Excel spreadsheet, find what geoid anomaly would result. Is your answer consistent with the geoid anomaly shown by Turcotte & Schubert for the continental margin of eastern North America ? b) Another scenario: 30 km thick continental crust with density 2850 km/m^3, and a lower density for the mantle lithosphere to compensate. Is this anomaly consistent with the observed difference from continent to ocean used by Turcotte & Schubert? 4.3 Problem: Using the lithospheric flexure you studied in Problem II, model the geoid and free-air gravity signature on a profile perpendicular to the Hawaiian island chain through Oahu. The data you need is in Figure 1 and 2, which are included as separate pdf files. These are research problems. There’s a skeletal tutorial with this problem set. a) Inspect: Look at the bathymetry and geoid maps of Figure 1. Comment on what similarities and differences you note between the two maps. Do they share the same failures of symmetry across the Hawaiian chain, and later be prepared to offer ideas of why or why not? b) Flexure: Revisit your calculations in Problem II, using a broken-plate model in FLEX, and a 3-box load model based on figure 2A). Using the same mechanical parameters as in Problem IIGeos 440/540: Geodynamics Problem Set IV, Fall 2009 Page 2 with a base level of 5500 m below sea level, sea water density 1035 kg/m3, and an infill density of 2800 kg/m3, confirm or adjust your estimate of the flexural parameter α based on the distance from the center of the profile to the forebulge. c) Model: For use in geoid99, construct a 2-dimensional model of the structure of the Hawaiian lithosphere <your_name>.ge2 whose geometry is consistent with your flexural model. For this model, include the Extend the nodes on left and right end of profile to 1000 km from the center. Use 6.5 km thickness for the oceanic crust and crustal density 2800 kg/m3. The mantle density should be 3300 kg/m3. How deep does this put the Moho under Oahu? Now execute the geoid99 program, make any adjustments you want to the input file, and screen-capture or otherwise display the results to turn in with your narrative and your .ge2 file. d) Compare: How well does your model fit with Figure 2B)? Go back to a) and complete the line of thought. e) Introspect: What, if anything, have you learned from this