Earth System Science II – EES 717

The Earth Interior – Mantle Convection & Plate Tectonics

Anatomy of Earth

Layering based on different criteria

1. Density (crust, mantle, core)

2. Chemical composition (consistent with density)

3. Mechanical behavior of materials (lithosphere, asthenosphere, mantle, core)

Physiology of ‘solid ‘ Earth – driving mechanism for plate tectonics

Plate Tectonics is the surface expression of the mechanism by which heat escapes the Earth’s interior

Origin of heat in the Earth’s interior

1. radioactive decay

2. residual heat from Earth’s formation

and to a lesser extent, heat contribution from the growth of the inner core which drives the convection in the outer core

Two possible patterns of mantle convection: 1. smaller cells may be generated separately within the upper mantle and within the lower mantle or, 2. the whole mantle below lithosphere may be involved in a single, larger pattern of convection cells, depending on the nature of the lower/upper mantle transition zone.

If the transition zone marks a change in chemical composition 1.

If the transition zone results from mineralogical changes that take place quickly relative to the rate of convection 2

Mantle Convection

Onset of Thermal Boundary Layer Instability

The fluid is initially of the same temperature 1. Starting at time 0, the fluid is cooled from the above with boundary temperature of 0 at the surface. The top thermal boundary layer thickens with time. After a certain period of time, the thermal boundary layer becomes unstable as Rayleigh number characterizing the top boundary layer reaches a critical level. Cold downwellings develop from the thermal boundary layer, which limits the thickening of the boundary layer. The downwellings also cool the mantle.

Forces acting on the plates

F1: mantle drag – friction between the convecting asthenosphere and the overlying rigid lithosphere

F2: gravitational ‘push’ – generated by high topography of MOR on the rest of oceanic plate

F3: ‘pull’ on the opposite end of the plate into a subduction zone due to the increasing density of the oceanic lithosphere as it cools

F4: the elastic resistance of the oceanic plate to being bent into a subduction zone

F5: the tendency of the overriding plate to be drawn toward a subduction zone as the subducting slab bends (otherwise it would move away from the overriding plate)

F6: friction between the subducting slab and the overlying lithosphere

F7: tendency of the oceanic plate to sink as it cools and becomes denser (we can call that negative buoyancy)

And the forces are:

Go to handout for 3 primary forces now.

How Well Convection Explains Plate Tectonics:

Section 3 of BYR

What Convection Can not explain thus far:

Section 4 of BYR

A Primer on Convection

• A system cooled from above or heated from within will develop an upper thermal boundary layer which drives the system.

• The thermal boundary layer (plate, slab) is the only active element.

• All upwellings are passive, and diffuse.• For large Prandtl number (the mantle) the

mechanical boundary layers are the size of the mantle.

• The scale of thermal boundary layers (plate thickness) is controlled by the Rayleigh number (Ra), which for the top is of the order of hundreds of km.

• Ra is controlled both by physical properties (conductivity, expansivity etc.) and environment (heat flow, temperature gradients etc.).

A Primer on Convection

• Both of these, physical factors and environment, cause Ra to be orders of magnitude lower at the base of mantle than at top. Therefore convective vigor is orders of magnitude less at the base of mantle.

• The mechanical and thermal boundary layers at the base of mantle are therefore of the order of thousands of kilometers in lateral dimensions.

The Wilson Cycle – how continents might come together and drift apart in a regular rather than random pattern

EES 7172.5. Influence of

Temperature-Dependent Viscosity 

Spring 2010

Hanii Takahashi

• Mantle material have temperature dependent viscosity (VT) for subsolidus flow. In this section, we will learn how VT plays a significant role in plate-mantle system.

• Subsolidus flow occurs bydiffusion creep dislocation power-law creep

The mobility of the molecules depends on thermal activation!

Viscosity law of silicates contain the factor of eHa/RT (Arrhenius factor)

where Ha: activation enthalpy, R: gas const, and T: temperature

• A little change in T lead huge change in viscosity

• Viscosity become very sensitive at lower temperature

Viscosity may changes as much as 7 orders in the top 200 hundred km on the mantle. (King, 1995; Beaumont, 1976; Watts et al., 1982)

• VT on mantle convection make top colder thermal boundary much stronger than the rest of the mantle.

Plate-like thermal convection Less plate-like thermal convection

• VT lead asymmetry between upwelling and downwelling.

Colder, stronger, less mobile

Hotter, weaker, more mobile

Induces heat plug that forces fluid

interior to warm up

Induces heat plug that forces fluid

interior to warm up

T difference bw fluid interior & surfacefluid interior & underlying medium

Hence, there are larger T jump across the top boundary layer and smaller jump across the bottom

• VT causes a significant change in the lateral extent of convection sell.

The top thermal boundary is cool enough to become negatively buoyant and sink

Travel horizontally a long distanceCauses the upper thermal boundary layer and its

convection cell to have extremely large lateral extents relative to the layer depth

This effect has been verified in lab (Weinstein and Christensen, 1991; Giannandrea and Christensen, 1993; Trackley, 1996a; Ratcliff et al., 1997)

• VT can explain the large aspect convection cells of mantle convection (we will discuss more later…)

• Top thermal boundary layer with VT(strongly

dependent) can become completely immobile because too strong to move.

The large aspect ratio effect vanishesTop boundary layer successfully impose a rigid

lid on the rest of the underlying viscous convection with a no-slip to boundary condition

Convection has cells which are as wide as they are deep

The planform can assume various simple geometries (Fig.3), although hexagons or squares might be not well assumed because of asymmetry between upwelling and downwelling

• However, the immobilization of the top layer leads to convection that is unlike the Earth.

• There are three different regime of convection with VT (Christensen,1984a; Solomatov,1995) which depends on Rayleigh number.

VT weakly : convection is nearly isoviscous . Nearly-isoviscous or low-viscousity-contrast regime

VT moderately : convection develops a sluggish cold top boundary layer with mobile and large horizontal dimension. Sluggish convection regime

VT strongly : convection assumes much of the appearance of isoviscous convection below a rigid lid. Stagnant –lid regime : it is the most likely regime for Earth’s plates

However, mobile plates shows that the lithosphere-mantle system has effects which mitigate the demobilization of the top thermal boundary layer caused by VT

It is not clear that extreme Arrhenius-type mantle or lithosphere viscosity occurs from a practical standard point…..discuss later….

• To consider the effect of VT is very important regard to the concept of “self-regulation” in solid-sate convection.

• If mantle viscosity is too high or convection to be strong enough to remove the heat generated internally, then mantle will simply heat up until the viscosity is reduced sufficiently.

• There is a more profound role for VT and consideration of long-term evolution of the plate-mantle system must account for the extreme sensitivity of heat flow to inthernal temperature through viscosity variability[Davies, 1980; schubert et al., 1980]

Conclusions:

Is the movement of the plates continuous? Not so clear.

Intermittent Plate Tectonic?