Math 2.0

Geophysics Definition

Geothermal gradient

Builds on Gradient

Definition

Let T(z)T(z) be the temperature in the Earth at depth z≥0z \geq 0 below a point of the surface, a differentiable function of zz. The geothermal gradient at depth zz is the derivative dTdz(z).\frac{dT}{dz}(z). More generally, it is the vertical component of the gradient ∇T\nabla T of the temperature field, taken positive downward.

Remarks

It is measured in kelvin per kilometre, or equivalently degrees Celsius per kilometre. If heat moves only by vertical conduction with thermal conductivity kk, the upward surface heat flow is q=k dTdz(0)q = k \, \frac{dT}{dz}(0) by Fourier's law. Example: in a borehole where T(z)=10+0.028zT(z) = 10 + 0.028 z in degrees Celsius, with zz in metres, the gradient is 2828 K/km, and with k=2.5k = 2.5 W/(m K) the heat flow is 0.070.07 W/m². Non-example: the temperature contrast between the surface and the centre of the Earth, divided by the radius, is not a geothermal gradient. It is an average, and the temperature does not increase linearly with depth.

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Further reading

  1. Web https://en.wikipedia.org/wiki/Geothermal_gradient
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