*This applet shows the contribution of crustal
heat sources to the geotherm for the exponential
and homogeneous models respectively (i.e.,
the mantle heat flow contribution has been removed. Note that for identical
length scales the exponential model produces twice the effect of the homogeneous
model. For explanation, see discussion below.*

The temperature field for the exponential model is given by :

(1)

In Eqn 1 *q _{r}* is the reduced heat
flow that applies at deep levels within the lithosphere, beneath all significant
heat production. One physical interpretation of

In the *homogeneous model*
the temperature field in the heat-producing layer is

(2)

Note that in both Eqn 1 and Eqn 2, the first term
on the right represents the component of the temperature field due to the
heat flow from beneath the heat producing parts of the lithosphere. The
second term on the right represents the contribution due to heat sources
in the crust. This term can be used to define the quantity D*T.*
the temperature contribution due to crustal heat production in the crust.
D*T* reaches
its maximum value (D*T** _{max}*)
at the depth at which heat production becomes negligible (i.e. at the base
of the heat-producing layer). The appropriate expressions for D

(3)

(4)

In Eqn 3 *z _{c}* is the depth at which
the exponential heat production distribution is terminated, which we approximate
as the Moho depth.

One attribute of the length scales for these two
models is that, for such distributions it can be evaluated from the regression
of surface heat production and heat flow data. Typically, such regressions
yield a value of ~10 km. An alternative, more general, formulation of the
length-scale, which makes no explicit assumption about the form of the
heat production distribution, can be made directly in terms of D*T _{max}*.
Defined in this way the length-scale,

(5)

where *q _{c}* is the depth integrated
heat production :

(6)

This parameterization also highlights the fact that
the temperature deviation, D*T _{max}*,
is very sensitive to the depth at which the heat production is located.
For both the homogeneous and exponential heat production models outlined
above

which reduces to

.

These scaling relations imply that for identical values of