Introduction to Geophysics relating gravity and isostasy name: _________________________ For each topographic profile complete the following: i) Fill in the missing segment of Moho assuming Airy isostatic equilibrium ii) Draw a Bouguer gravity profile over the feature iii) Draw the free-air gravity profile over the feature As in previous gravity exercises, the vertical scale is arbitrary. However, the three plots should be consistent. ρ 3 ρ 3 Assume crust = 2.7 Mg/m and mantle = 3.3 Mg/m . Extra copies of worksheet available from course website. Plateau Rift free-air free-air technically, it is: Bouguer Bouguer crust crust mantle mantle about 7 times as big as surface topography Basalt filled rift free-air Bouguer No topography. Free-air and Bouguer are the same! ρ 3 basalt = 2.9 Mg/m crust mantle Introduction to Geophysics relating gravity and isostasy 1) In many places in the world we find high plateaus that are slowly eroded by surface weathering. As rock is removed from the surface, the mean elevation of the area goes down. Yet often the elevation of the highest peaks increases at the same time, without any additional tectonic events. Use isostatic arguments, and pictures as needed, to explain how this happens. As mass is eroded away from the plain, the mean elevation drops. However with this mass removed, isostatic (buoyant) forces can lift the entire crustal block. Places that avoid extensive errosion are actually raised up. An aside: Because the crust can be buoyed up like an ice cream push-up, it is not uncommon for mountains to erode 10's of km of material, though the elevation may decrease by just a few km's. 2) Consider a wide plain with a mean elevation of 500 m. The region is shortened due to a nearby convergent margin. Shallow thrust faulting places an extra 2000 m of material on top of the crust. Assuming Airy isostatic equilirium, what would you expect to be the new elevation of the plain? Assume the crust is of uniform density and the 7-to-1 rule applies. before 2000 m of material is loaded on top of the crust. This load will cause the crust to sink somewhat. (If penguins stand on an iceberg, it sinks a little to compensate). By the 7-to-1 rule, for every additional meter of topography, 7 meters will be after used to increase the "root". Only 1/8th of the material will add to the elevation. 1/8 of 2000 m is 250 m. The new elevation is 750 m. 3) The Moho beneath Antarctica is about 40 km deep. About 2 km of ice sit on top of the crust. If the the ice sheet were thickened to 4 km, roughly how deep would you expect the Moho to be? You can use the 7-to-1 rule but remember, ice has a density of ~1, compared to crust which has density of ~2.7. There are several ways to approach this problem. Here is one: As in problem 2, much of the added 2 km will be offset by a sinking of the crust. If the load were an additional 2 km of crust material, the Moho would be depressed by 1750 m and the new elevation would be 250 m higher (see problem 2). However, the load is ice in this case. 2 km of ice is equivalent to adding only [ 2 km *(1 Mg/m3)/(2.7 Mg/m3) ] of crust. That is, the mass of 2 km of ice is the same as the mass of 0.74 km of crust. Instead of depressing the Moho by 1750 m, the ice load will only depress it by (0.74 km/2.0 km)*1750 m, or 647.5 m. The new Moho depth is 40.6475 km, or about 40.65 km. Introduction to Geophysics relating gravity and isostasy Addendum and further explanation of problems The following concept caused people considerable difficulty in problems 2 and 3 of the homework. You are likely to see it again ... Consider a section of crust in isostatic equilibrium (A). A load is added to it, perhaps more crust, an ice sheet or even a sea (B). The whole section must sink to reach equilibrium (C). An alternative situation exists wherein, at the exact same time the new load is placed on the crust, a massive unexplained amount of new material is added to the bottom (D). This material on the bottom just happens to be the right amount to support the new load on top of the crust without sinking at all. Situation D is in isostatic equilibrium. However, it is geologically implausable and it requires massive tectonic events not considered in the problem. D is an easier situation to solve for than C. However, it is improbable and not the geologic situation we are considering. I would recommend carefully reviewing the solutions to worksheet problems number 2 and 3 before the first exam if this was an issue for you. isostatic equilibrium. isostatic orig. crust + equilibrium. new load + isostatic Not in isostatic unexplained (huge) equilibrium. equilibrium. orig. crust + mass added to new load base of crust AB CD new load new load new load orig. crust orig. crust orig. crust orig. crust ??? not to scale unexplained new crust.