For the following exercises, assume a Young’s modulus of 7 x 1010 Pa, Poisson’s ratio of 0.25, acceleration due to gravity of 9.81 ms-2, a density of the mantle of 3300 kgm-3, a density of crust (loads) of 2700 kgm-3, a density of sea water of 1035 kgm-3, and a density of sedimentary basin fill of 2400 kgm-3.
For each problem include a diagram setting up the problem (5 points), the equations that you will use (5 points), and then solve the equations (10 points). You may use a spreadsheet to conduct the calculations. Print or draft the deflected crustal profile for each question (10 points).
1. Calculate the maximum deflection beneath and width of a water-filled basin surrounding an infinite line of volcanoes on an infinite (i.e., unbroken plate) with an effective elastic thickness of 20 km. The line of volcanoes constitutes a 5 km high and 50 km wide load. Use the equations for line loading from lecture 2 to calculate wo and xo.
2. Next consider a broad mountain belt that can be characterized by 5 blocks, each 20 km wide that decrease in height from the hinterland to the foreland from 5 to 1 km. Assume that these sit on an infinite plate with an effective elastic thickness of 40 km. Calculate the total subsidence in a filled sedimentary basin directly in front of the shortest block. Calculate the basin width from the front of the shortest block to the zero deflection point. You will have to use the distributed line loading approach discussed in lecture 2.
