In the previous introduction and article on cycles I explained that we need some kind of time delay or timing element to explain the ice age cycles. This is because one of the key problems with explaining the ice-ages is explaining why they tend to occur every 110,000 years (or less ).
This article looks at one potential delay mechanism that could set the time between Ice-ages. In doing so, this article introduces a little discussed phenomenon which is the effect of long-term change of temperature on the earth’s crust. It then introduces a mechanism I called the “Caterpillar effect” which must play a significant part in tectonic plate movement.
As the surface air of the earth changes in temperature, that change causes a heat flux into or out of the ground causing the earth to tend to cool or warm. The result is as shown to the right which is the daily change in temperature near the surface for a +/- 15C swing. The earth’s surface warms and cools with the changing air temperature. Layers nearest the air change with the change in air temperature, but the affect become reduces with depth as the rock is more insulated from changes at the surface.
Thermal Profile of Soil
Assuming that conduction is the heat transfer mechanism within the bedrock, the relevant thermal problem can be approximated as a 1-d conduction problem with a sinusoidal variation of temperature at the top boundary of a half space (Carslaw and Jaeger, 1959; see also Gold and Lachenbruch, 1973 for applications to permafrost problems). The thermal dependence on time (t) and depth (z) is expected to be
T(z, t) = Tave(z) + [Taexp(-z/z*) cos(ωt – z/z*)]
where T is the mean temperature profile (geotherm), and Ta is the (half) amplitude of the temperature variation at the surface, z = 0. The length scale, z*, for the decay of the amplitude of the signal is dictated by the thermal diffusivity of the material, κ, and the period of the oscillation of the temperature at the boundary, P (= 2π/ω, where ω is the angular frequency):
z* = (κP/π )½
For typical diffusivities of about 1-2 mm2 s-1, this length scale is about 20 cm for a daily cycle, 3 to 4 m for the annual cycle.
Temperature variation with Ice-ages
Based on the figure of diffusivity given by Whittington et al., (2009) of around 2mm2 s-1 a variation of +/-4C above around the average temperature, the variation of temperature with depth for a 112,000 sinusoidal change in surface temperature would be as follows:
As can be seen above in Fig 3.2, the change in crustal temperature is significant up to 4km.
The Creaking earth
As everyone knows, warming causes expansion, so how much will the earth’s crust warm for a 1C change in crustal temperature? Expansion coefficient of most rocks are around 5-10 x10-6 per degree change. Taking the crust as being granite with an temperature expansion coefficient of (8×10-6) the expansion of the crust at the equator of approximately 40,000km due to a 1C change in temperature is approximately:
1.0 x 40,000 x 1000 x 8×10-6 = 320m
For a 100,000 year heating cycle that amounts to:
320/100,000 = 3.2mm/year
However closer to the surface the expansion is much greater as shown by the following graph:
How does this compare with the rate of movement of tectonic plates?
Data on the movement of plates is relatively hard to find. Typical figures are:
- It is said the Eurasian Plate is moving away from the North American Plate at a rate about 30 mm per year.(source)
- Relative speed of plates adjoining Pacific plate are:
|Plate||Relative Velocity with Pacific plate (mm/yr)|
Table 3.1 Figures based on the The Physics Factbook
Which suggests plates are moving around 2-30mm/year compared to a maximum thermal expansion of around:
|Depth||Total movement (km)||Relative Velocity (mm/yr)|
Table 3.2 Movement of earth’s crust around circumference
over 100,000 ice-age cycle
So, whilst the change in size of the crust is very small amounting to only 58PPM at the surface, given the size of the earth, the actual effect at the plate boundaries is huge.
Differential Thermal Expansion
There is clearly a massive difference over an ice-age cycle between expansion due to temperature change at the surface and even a few kilometres down. This will lead to differential expansion and contraction, both between different layers at different depths and therefore exposed to different temperature changes, but also between rocks with different coefficients of thermal expansion.
Taking warming first, the increase in temperature at the surface will tend to make rocks there expand and so press outward of adjacent rock resulting in an outward force. This force will reduce the further down we go, until it changes into a tensional force tending to hold the rocks together. As rocks are about ten times stronger under compression than tension, it is possible for a thin layer of surface rock to cause deep cracking beneath the surface. And because the crust effectively floats on the molten magma beneath it, it is possible an intrusion of magma may take the place of the contracting crust (Alternatively, such cracks may be filled by mineralisation) A diagram of rock filling with magma is shown above-right (note: vastly expanded horizontal axis)
At the surface, the rock is compressed via thermal expansion. The diagram shows the crust as having split allowing magma to intrude into the cracks. This magma will then cool reforming a solid crust.
But when the surface then cools, because the intruded magma has had time to solidify as the surface shrinks. This now tends to pull apart the surface opening up cracks as shows to right (note vastly expanded horizontal scale).
However, this time because the compression at depth seals the crust, it stops magma coming to the surface. Deep surface cracks cannot be filled by magma, so instead the crack is unstable and tends to collapse or be filled by water and surface debris. However, whilst the material is different, the effect over several thousand years is to refill the crack with solid material so that when the surface heats again, the cycle repeats.
The other effect is that different rocks will expand and contract at different rates and by different amounts.
|Rock Type||linear-expansion coefficient (in 10−6 per degree Celsius)|
|granite and rhyolite||8 ± 3|
|andesite and diorite||7 ± 2|
|basalt, gabbro, and diabase||5.4 ± 1|
|sandstone||10 ± 2|
|limestone||8 ± 4|
|marble||7 ± 2|
|slate||9 ± 1|
Table 3.3 (Encyclopedia Britannica)
Thus, layers such as sandstone will be expanding and contradicting twice as much as basalt. This will lead to bend, twisting and other stresses which eventually may lead to catastrophic re-alignments and earthquakes. Again, the effect of this differential expansion and higher compressive strength of rock will be to tend to cause the highest expanding rocks to push out when heating causing cracking in the rocks with lower thermal expansion. These cracks will then tend to fill – and the cycle repeat.