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In the thermal model of the oceanic lithosphere, temperature distribution in the interior is given by:

(T-Ts)/(Tm-Ts) = erf (Z/2 ?(Kt) )

where Ts is the surface temperature, Tm is the temperature in the deep mantle, and erf is the error function defined by:

erf(y) = (2/ ?( pi))   Integral from 0 to y of  e-x^2   dx

Z is depth, K is thermal diffusivity and t is the age of the ocean floor.


1) What is the heat conduction equation? Show that T defined above satisfies the heat conduction equation.

2) Derive formula for heat flow at the surface, z=0, for this temperautre distribution.

I think the answer is the following, but I don't know how to derive it:



3) Derive the formula for the thickness of lithosphere as a function of age  t, where t is expressed in units of million years. Use Ts=300Kelvin, Tm =1300Kelvin, T=1100Kelvin and K = 10-6 m2/s. You may have to consult a table of the error function.

I think the answer is the following, but I don't know how to derive it.
0.84

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