OCEAN/ESS 410
6. Cooling of the Ocean
Plates (Lithosphere)
William Wilcock
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≈√ t or equivalently t=h2/
• 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
Oceanic Plates form by Cooling
island arc
trench
fracture
zone
trench
MOR
earthquakes
Heat Loss
ocean crust
melt
magma
1300°C
sediments, cold adiabatically rising
crust & mantle
mantle material
continental crust
earthquakes
Mantle
Mantle
melt
Chemical &
Crust/Mantle versus
Lithosphere/Asthenosphere
Geophysical
Thermal and mechanical
structure
Composition
1300°
C
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 ~100 - 200 km depth) is weak (has a low
viscosity). This is because it lies near its melting point.
TemperatureDepth Plot for
Mantle Beneath
Old Oceanic
Plates
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.
1300°C
Lithosphere
Asthenosphere
Geotherm
for Old
Ocean Plate
The Lithosphere Forms by
Conductive Cooling
Heat Conduction
Fourier’s Law
Heat Flux,
W m-2
dT
q = -k
dy
Negative because heat flows
down the temperature gradient
Temperature, T
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
Heat Flow
Depth, y
Temperature
gradient, K m-1
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
Cooling of a Half-space
Temperature
T0
T0
Tm
Tm
T0
Tm
T
t = 0+
t>0
Depth
t = 0-
y, km
y, km
y, km
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.
How Quickly Do Objects Cool By
Heat Conduction?
A simple thought Experiment
T1
T
Temperature
2
Depth
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.
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
h ~ kt
2
h ~ kt
where  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 86400 s)
-6
h ~ 10 ´ 60 ´10 ´ 365 ´ 86400 ~ 45km
6
Temperature
Profiles
(Geotherms)
at 2 different
ages
15 Myr
60 Myr
70 km
35 km
Consequences of Plate Cooling
1. Heat Flow
Heat Conduction
Fourier’s Law
Heat Flux,
W m-2
dT
q = -k
dx
Negative because heat flows
down the temperature gradient
Temperature, T
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
Heat Flow
Depth, z
Temperature
gradient, K m-1
Heat Flow Probe
Heat Flow Measurements
Requires Sediments - Difficult near the ridge
Average value for the oceans is ~100 mW m-2
Seafloor
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.
1 hfu (heat flow unit) = 42 mW m-2
Heat Flow Versus Age
Mean Value
Range of Values
Prediction of the
half space model
Model Exceeds
Observations.
Hydrothermal cooling
Observations exceed
model. Plate reaches
maximum thickness
Plate Cooling Model
The lithosphere has a maximum thickness of ~100 km.
Convective instabilities in the asthenosphere prevent it
growing any thicker
Consequences of Plate Cooling
2. Seafloor Depth
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  ) than cold ones, the seafloor is
shallower above young ocean lithosphere.
Cool ,  = 3400 kg
m-3
Hot,  = 3300 kg m-3
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
Age of the Seafloor - Inferred from Magnetic Lineations
Revisiting Lab 2
Relative amount of surface area
Age of Terrestrial Planet Surfaces
2/3 of Earth’s surface formed
within the last 200 million years
Planets
form
4
3
2
1
Age of Surface (billions of years)
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
1. Linear rifts and arcuate compression zones
2. Transform faults and fracture zones (adjacent
transform faults are parallel).
3. Continuous plate boundaries
4. Volcanic Island chains - plates moving over fixed
mantle plume (melt source)
5. Topography variations consistent with aging plates.
Global Bathymetry
Sandwell and Smith
Mars
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
Mantle Convection in Mars
model by Walter Kiefer
Venus
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.
TemperatureDepth Plot for
Mantle Beneath
Old Oceanic
Plates
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.
1300°C
Lithosphere
Asthenosphere
Geotherm
for Old
Ocean Plate