6. Cooling of the Ocean Plates (Lithosphere)

William Wilcock

OCEAN/ESS 410

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

Oceanic Plates form by Cooling

Mantle melt

adiabatically rising mantle material

magma

MOR

Mantle

sediments, cold crust & mantle

island arctrench

earthquakes

ocean crust earthquakescontinental crust

melt

fracture zone

trench

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Heat Loss

Chemical &

Composition

Geophysical

Crust/Mantle versus Lithosphere/Asthenosphere

1000°C

1300°C

Thermal and mechanical structure

TerminologyOceanic 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 MirIt 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.

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Wet S

olidus

Dry S

olidus

Geothermfor Old Ocean Plate

Asthenosphere

Lithosphere

Temperature-Depth 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.

The Lithosphere Forms by Conductive Cooling

Heat Conduction

Fourier’s Law

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 gradient, K m-1

Temperature, T

Depth, y

Heat Flow

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 column of the lithosphere

Cooling of a Half-space

T

Dep

th

y, km

TmT0

y, km

TmT0

y, km

TmT0

t = 0- t = 0+ t > 0

Temperature

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?

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.

A simple thought Experiment

Depth

TemperatureT1 T

2

Approximate Thickness of the Cooled LayerThe exact shape of the curves is difficult to derive but we can write an approximate thickness for the cooled region as

where κis 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)

60 Myr

35 km

70 km

15 MyrTemperature Profiles

(Geotherms) at 2 different

ages

Consequences of Plate Cooling1. Heat Flow

Heat Conduction

Fourier’s Law

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 gradient, K m-1

Temperature, T

Depth, z

Heat Flow

Heat Flow Probe

Heat Flow Measurements

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

Requires Sediments - Difficult near the ridge

Average value for the oceans is ~100 mW m-2

Heat Flow Versus Age1

hfu

(h

eat

flo

w u

nit)

= 4

2 m

W m

-2

Model Exceeds Observations. Hydrothermal cooling

Mean Value

Range of Values

Prediction of the half space model

Observations exceed model. Plate reaches maximum thickness

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

Consequences of Plate Cooling2. Seafloor Depth

Seafloor Depth

Hot, ρ = 3300 kg m-3

Cool , ρ = 3400 kg m-

3

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.

Seafloor Depth Versus AgeThe 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)

Misfit suggests Plate model

Half-Space model

Age of the Seafloor - Inferred from Magnetic Lineations

Revisiting Lab 2

Age of Surface (billions of years)

4 3 2 1

Rel

ativ

e am

ount

of

surf

ace

are

a

Planetsform

2/3 of Earth’s surface formedwithin the last 200 million years

Age of Terrestrial Planet Surfaces

EarthPlate 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.

1300°C

Wet S

olidus

Dry S

olidus

Geothermfor Old Ocean Plate

Asthenosphere

Lithosphere

Temperature-Depth 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.