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Continental Geotherms |
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We derive here the equation for the steady state crustal geotherm. For a steady state geotherm we get that ∂T/∂t=0 and uz =0 (no convection in the lithosphere and no erosion or sedimentation); therefore: |
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This is a second order differential equation. They are solved using two boundary conditions. For example we may know the temperature at the surface let's say: T=To at z=0; and that the surface heat flow -Qo at z=0 (<0 because heat flows upward). Assuming that A is constant with depth, the first integration gives: |
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The second boundary condition implies that at z=0: |
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therefore C1 = Qo/k, and... |
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After a second integration we get: |
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and since T=To at z=0 (boundary condition 1)... |
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