Heat - The Solid Earth - page 284

variation ( ω = 2 × 10 − 7 s − 1 ), L is 3.3 m; and for an ice age (with period of the order
of 100 000 yr), L is greater than 1 km. Therefore, provided that temperature
measurements are made at depths greater than 10-20 m, the effects of the daily and
annual surface temperature variation are negligible. The effects of ice ages cannot
be so easily ignored and must be considered when borehole measurements are
made. Measurement of temperatures in ocean sediments is not usually subject to
these constraints, the ocean-bottom temperature being comparatively constant.
Equation (7.45) shows that there is a phase difference φ between the surface
temperature variation and that at depth z ,

ωρ

c P
2 k

φ = z (7.47)

At the skin depth, this phase difference is one radian. When the phase difference is
π , the temperature at depth z is exactly half a cycle out of phase with the surface
temperature.

7.4 Worldwide heat flow: total heat loss from the Earth
The total present-day worldwide rate of heat loss by the Earth is estimated to be
(4.2-4.4) 10 13 W. Ta b l e 7.3 shows how this heat loss is distributed by area:

71% of this heat loss occurs through the oceans (which cover 60% of the Earth's
surface). Thus, most of the heat loss results from the creation and cooling of
oceanic lithosphere as it moves away from the mid-ocean ridges. Plate tectonics
is a primary consequence of a cooling Earth. Conversely, it seems clear that the
mean rate of plate generation is determined by some balance between the total
rate at which heat is generated within the Earth and the rate of heat loss at the
surface. Some models of the thermal behaviour of the Earth during the Archaean
(before 2500 Ma) suggest that the plates were moving around the surface of the
Earth an order of magnitude faster then than they are today. Other models suggest
less marked differences from the present. The heat generated within the Archaean
Earth by long-lived radioactive isotopes was probably three-to-four times greater
than that generated now (see Table 7.2). A large amount of heat also has been
left over from the gravitational energy that was dissipated during accretion of the
Earth (see Problem 23) and from short-lived but energetic isotopes such as 26 Al,
which decayed during the first few million years of the Earth's history.
Evidence from Archaean lavas that were derived from the mantle suggests that
the Earth has probably cooled by several hundred degrees since the Archaean
as the original inventory of heat has dissipated. The Earth is gradually cooling,
and the plates and rates of plate generation may be slowing to match. Presumably,
after many billion years all plate motion will cease.
Measured values of heat flow depend on the age of the underlying crust, be it
oceanic or continental (Figs. 7.6 and 7.11). Over the oceanic crust the heat flow
generally decreases with age: the highest and very variable measurements occur

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