1. 6. Cooling of the Ocean Plates (Lithosphere) William Wilcock
OCEAN/ESS 410
6. Cooling of the Ocean Plates (Lithosphere) William Wilcock

2. Lecture/Lab Learning Goals
Understand the terms crust, mantle, lithosphere and asthenosphere and be able to explain the difference between oceanic crust and lithosphere
Understand the concepts that govern the relationships that describe the cooling of a halfspace.
Be able to use h≈√κt or equivalently t=h2/κ
Know how heat flow is measured and how it varies with the age of the ocean lithosphere.
Understand the relationship between ocean depth and plate age
Be able to obtain and fit a profile of seafloor bathymetry to a square root of age model - LAB

3. Oceanic Plates form by Cooling
fracture zone
island arc
trench
trench
MOR
earthquakes
Heat Loss
continental crust
ocean crust
earthquakes
magma
melt
Mantle
melt
Mantle
1300°C
sediments, cold crust & mantle
adiabatically rising mantle material

4. Crust/Mantle versus Lithosphere/Asthenosphere
Chemical &
Geophysical
Thermal and mechanical structure
Composition
1000°C
1300°C

5. Terminology
Oceanic Crust - Obtained by partial melting of the mantle (~6 km thick)
It is a chemical boundary layer
Lithosphere - The upper rigid layer that has cooled below ~1000ºC. It is the rigid layer that defines the plate. It thickens with age and approaches 100 km at 100 Mir
It is a mechanical boundary layer and a thermal boundary layer.
Asthenosphere - The region immediately underlying the lithosphere (from ~ km depth) is weak (has a low viscosity). This is because it lies near its melting point.

6. Temperature-Depth Plot for Mantle Beneath Old Oceanic Plates
Wet Solidus
Dry Solidus
Geotherm
for Old
Ocean Plate
Asthenosphere
Lithosphere
The solidus is the temperature at which a rock first starts to melt. The mantle contains a small amount of water (<1%) which lowers the solidus temperature.

7. The Lithosphere Forms by Conductive Cooling

8. Heat Conduction Fourier’s Law Heat Flow Temperature gradient, K m-1
Heat Flux, W m-2
Negative because heat flows down the temperature gradient
Thermal Conductivity, W K-1m-1
Typical values
Aluminum, 237 W K-1m-1
Expanded Polystyrene, 0.05 W K-1m-1
Rocks 1 to 5 W K-1m-1
Temperature, T
Depth, y
Heat Flow

9. Cooling of a column of the lithosphere
Because the heat flow is vertical, the cooling of any column of the oceanic lithosphere is the equivalent to the cooling of a half space. The relationship between age, t and horizontal position x is
t = x / u
where u is the half spreading velocity

10. Cooling of a Half-space
Temperature
y, km Tm T0
y, km Tm T0
y, km Tm T0 T
t = 0-
t = 0+
t > 0
Depth
The math is quite complex but we can gain some insight into the form of the solution from the simple thought experiment that we considered during the last lecture.

11. How Quickly Do Objects Cool By Heat Conduction?
A simple thought Experiment
Depth
Temperature T1 T2
The green object contains twice as much heat energy (because it is twice as thick), but looses heat at only half the rate (because the temperature gradient is halved). It takes four times as long to cool the green object.
It takes four times as long to cool to twice the depth.

12. Approximate Thickness of the Cooled Layer
The exact shape of the curves is difficult to derive but we can write an approximate thickness for the cooled region as
where κ is the thermal diffusivity and has an a value of 10-6 m2 s-1
For example at t = 60 Myr (= 60 x 106 x 365 x s)

13. Temperature Profiles (Geotherms) at 2 different ages
15 Myr
35 km
60 Myr
70 km

14. Consequences of Plate Cooling 1. Heat Flow

15. Heat Conduction Fourier’s Law Heat Flow Temperature gradient, K m-1
Heat Flux, W m-2
Negative because heat flows down the temperature gradient
Thermal Conductivity, W K-1m-1
Typical values
Aluminum, 237 W K-1m-1
Expanded Polystyrene, 0.05 W K-1m-1
Rocks 1 to 5 W K-1m-1
Temperature, T
Depth, z
Heat Flow

16. Heat Flow Probe

17. Heat Flow Measurements
Requires Sediments - Difficult near the ridge
Average value for the oceans is ~100 mW m-2
Thermistors. Measure temperature gradient
Heater. After measuring the thermal gradient a pulse of heat is introduced and the rate at which it decays is can be used to estimate the thermal conductivity.
Seafloor

18. Heat Flow Versus Age Mean Value Range of Values
Prediction of the half space model
1 hfu (heat flow unit) = 42 mW m-2
Model Exceeds Observations. Hydrothermal cooling
Observations exceed model. Plate reaches maximum thickness

19. Plate Cooling Model
The lithosphere has a maximum thickness of ~100 km. Convective instabilities in the asthenosphere prevent it growing any thicker

20. Consequences of Plate Cooling 2. Seafloor Depth

21. Seafloor Depth
The depth of the seafloor can be calculated using the principal of isostacy - different columns contain the same mass (i.e., the lithosphere floats). Because warm rocks have a lower density (denoted by the symbol ρ) than cold ones, the seafloor is shallower above young ocean lithosphere.
Hot, ρ = 3300 kg m-3
Cool , ρ = 3400 kg m-3

22. Seafloor Depth Versus Age
The half-space model predicts that the depth increases as the square root of age. This model works out to about 100 Myr at which point depths remain fairly constant (more evidence for the plate model)
Half-Space model
Misfit suggests Plate model

23. Age of the Seafloor - Inferred from Magnetic Lineations

24. Revisiting Lab 2

25. Age of Terrestrial Planet Surfaces
Relative amount of surface area
2/3 of Earth’s surface formed
within the last 200 million years
Planets 4 3 2 1
form
Age of Surface (billions of years)

26. Earth
Plate tectonics replace 2/3 of the surface every ~100 Myr and modifies the remaining 1/3 on geologically short timescales.
Evidence at a scale we might see on other planets
Linear rifts and arcuate compression zones
Transform faults and fracture zones (adjacent transform faults are parallel).
Continuous plate boundaries
Volcanic Island chains - plates moving over fixed mantle plume (melt source)
Topography variations consistent with aging plates.

27. Global Bathymetry
Sandwell and Smith

28. Mars

29. Mars Last eruption on Olympus Mons 2 to ~100 Myr ago
Surface appears to be one plate
Evidence for plate tectonics in the past is controversial
Smaller radius means it cooled down quicker than earth and the lithosphere (the rigid cold layer) is thicker - too strong for plate tectonics
Large volcanoes show surface has not moved relative to mantle plumes

30. Mantle Convection in Mars
model by Walter Kiefer

31. Venus

32. VENUS Burst of volcanism 600-700 MYrs ago
Either steady state ‘plate tectonics’ stopped then or Venus undergoes episodic bursts of volcanism
Venus has lost its water.
Water in the mantle may be critical for plate tectonics because it weakens the mantle and lubricates the motion of the plates.
In the absence of lubrication the heat from radioactivity may build up inside Venus until it is released in catastrophic mantle overturning events.

33. Temperature-Depth Plot for Mantle Beneath Old Oceanic Plates
Wet Solidus
Dry Solidus
Geotherm
for Old
Ocean Plate
Asthenosphere
Lithosphere
The solidus is the temperature at which a rock first starts to melt. The mantle contains a small amount of water (<1%) which lowers the solidus temperature.