Lecture 1: Plate Tectonics and Euler Poles
Lecture 1: Plate Tectonics and Euler Poles
A reminder:
Spherical coordinates:
x =rsinθcosφ, y=rsinθsinφ, z=cosθ
x2+y2+z2=r2
so the question is... what happens to plates on a sphere...
The Basic Framework
Plate tectonic theory assumes a relatively cool rigid outer shell or LITHOSPHERE divided into a network of PLATES. The plates act as stress guides. They move over the underlying, plastic ASTHENOSPHERE.
-divergent/constructive – mid-ocean ridges
-Convergent/destructive – subduction zones or trenches
-
-conservative – transform faults
Euler Poles
Plates move relative to each other. To describe their motion on the surface of a spherical Earth, one needs to use Euler’s ‘fixed point’ theorem, which can be stated as:
“The most general displacement of a rigid body over the surface of a sphere can be regarded as a rotation about a suitable axis which passes through the centre of that sphere. “
Thus all plate motions can be described by a rotation axis, which passes through the centre of the Earth and cuts the surface at two points, called the poles of rotation. The relative motion of two plates then needs a pole of rotation and an angular velocity to be defined.
Relative plate motion can be determined in a number of ways including direct measurements using satellite laser ranging, or very-long baseline interferometry (VLBR) which uses the signal from quasars and terrestrial radio telescopes as receivers.
Much more of Euler poles in 2nd part of lecture
Absolute Plate Motion
In addition to discussing the relative motions of plates, one can also define plate motion relative to the Hot-Spot Reference Frame.
There exist some intraplate volcanic regions, well away from plate boundaries, with distinct chemistry. The location of the active volcano appears relatively fixed with respect to the Earth’s mantle, and at the end of an island chain (in the arc of a small circle), with islands aging with increasing distance from the active volcano. This is a hotspot.
Good example is Emperor-Hawaii chain. Lohi: youngest and presently active, aging through the Hawaii chain NW
until, at ~ 43Ma there is a change in strike thought to arise from a change in the direction of movement of the Pacific plate over the hotspot at that time..
The absolute motion of a plate can be determined from the traces made by island chains such as Hawaii. The absolute motion of all other plates can then be calculated relative to the e.g. Pacific plate. Repeating with a number of hotspot traces from other plates indicates accuracy of method.
The Lithosphere
Exact details of what constitutes a plate are complex, and the meaning of the term lithosphere is not well defined. The plate is formed at spreading ridge and thickens as it moves away and cools.
From seismic studies of the oceanic plates, the boundary between the lithosphere and asthenosphere is often taken as the 4.3 kms-1 S-wave velocity contour. This boundary is often associated with the point at which partial melting starts and the low velocity zone (LVZ) begins. In this context therefore, the base of the lithosphere can be defined by an isotherm (~1300 C).
The figure below shows calculated isotherms (black lines) with Tm - Ts = 1300C. The circles indicate the thickness of oceanic lithosphere in the Pacific determined from seismic studies.
The thickness of the lithosphere can be calculated by defining a thermal boundary layer where the dimensionless temperature has fallen to 0.9:
The thickness of lithosphere in old cold oceanic regions is ~100 km.
The base of the lithosphere under continental areas is more variable and less distinct. Indeed the LVZ is not a globally ubiquitous phenomena and is notably absent underneath Precambrian shield areas. As a result, defining the thickness of continental lithosphere is difficult. Estimates of the thickness of continental lithosphere have come however from the analysis of the elastic rebound from unloading associated with the last deglaciation event hich suggest thickness in excess of 200 km. Such deep roots to old continental areas are also suggest by seismic tomographic studies.
One basic confusion in the use of the term 'lithosphere'. The term 'lithosphere' is normally assumed to be the same as the strong, rigid outer shell of the Earth. Rock physics however shows that silicate minerals have little strength at T>700 C.
Only the shallow, colder part of the plate can be considered rigid. This lithosphere has complex strength structure, which is characterised by having a strong central layer which is the part of the plate that can act as a stress guide.
The “elastic thickness” of a plate is a term also used – it relates to this stronger part of the plate, but there is no agreement on how to define it exactly. Values range from 5 to 130 km!
The Asthenosphere
This is the non-rigid part of the Earth, which readily undergoes viscous flow. As will be inferred from the above discussion, the detailed definition of the extent of the asthenosphere is very poor.
Some associate it with the Low Velocity Zone, others with the upper mantle not within plate, and some the whole mantle not in plate. Seismic tomographic studies suggest that the entire mantle beneath the lithosphere is dynamic, and so perhaps this latter definition is to be preferred.
The problems with the definition of the terms lithosphere and asthenosphere reflect the problems in defining boundaries between parts of a rheological spectrum. Whether a material behaves as a rigid or plastic body depends on its viscosity.
Viscosity is a measure of how easily flow occurs when a material is subjected to stress, and is defined by:
η = σ / (dε/dt)
where, η = Viscosity (Pa.s); σ = Stress (Pa = Nm-2); Strain rate = dε / dt (s-1).
Typical viscosities for liquids are - ηH2O = 10-3 Pas, ηPORRIDGE = 102 Pas, but ηMANTLE ~ 1021 Pas as estimated from glacial rebound studies.
More detailed results indicate that the LVZ has η approx. 4 x 1019 Pas, while the rest of the whole mantle has approx. constant η with range 1021 - 1022 Pas.
The viscosity depends on the mechanism of flow. H2O is a liquid with no long range atomic order, but the mantle is crystalline. Once past the elastic limit crystal creep occurs, either by dislocation glide + climb or by diffusional flow involving atomic vacancy movement.
Both processes need atomic motion so they are thermally activated, and so the viscosity of a rock or crystals is highly temperature dependent. The cold lithosphere with η -> ∞ is elastic and brittle, but hot mantle has large but finite η and so can be plastic at geological strain rates.
Part 2: Euler poles (below and bbk Geophysics)