Calculate an equilibrium (i.e., steady-state) geotherm from the one-dimensional

Question

Calculate an equilibrium (i.e., steady-state) geotherm from the one-dimensional heat flow equation given these boundary conditions: partial differential T/partial differential z = 30 degree C/km at z = 0 km and T = 700 degree C at z = 35 km Assume that there is no internal heat generation. Calculate an equilibrium geotherm from the one-dimensional equation given the boundary conditions in Problem 1, but now assume that the internal heat generation is 1 mu W (microwatt) m^3 and the thermal conductivity is 3 W m^-1 degree C^-1. The observed distance from the center of the lithospheric depression due to an island chain and the nearby bulge in the oceanic plate is 375 km. Calculate the depth of the depression.

Explanation / Answer

1)   Here , delta T = (dT/dz) * z

                              =    30 * 35 = 1050 degree celsius

=> equilibrium geotherm = T + delta T

                                          = 700 + 1050

                                          = 1750 degree celsius

2)   equilibrium geotherm from one dimensional equation =   700 + (1 * 10-6) * 109/3

                                                                                           = 1033.33   degree celsius

3) depth of the depression =    375/(9.81 * 8)

                                            = 4.778   km

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