Plate Tectonics and Euler Poles

Historical overview:

Plate tectonics is a uniting concept in Earth Sciences, first put forward in the mid 1960's building on the idea of Continental Drift.

Francis Bacon (1561-1620) - Suggested Western Hemisphere once joined with Eurasia.

�In 1858 Snider-Pellegrini presented this map:

But idea developed most fully by Wegener in the years after WW1.

The evidence for drifting continents was largely based on:

� continental geometry

� palaeoclimatelogy

� palaeontological provinces

� structural correlation

The mechanism for the drift was poorly defined, however it is important to note that Holmes suggested in the late 20's that mantle convection may be involved, then�..

� 1944

Arthur Holmes authored the classic textbook, Principles of Physical Geology.

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Following an idea dating back to the 1830s, revitalised in the 1930s by himself, F.A. Vening Meinesz and David Griggs, Holmes reintroduced thermal convection in the mantle as a possible mechanism for continental drift.

� 1946

Harry H. Hess published his discovery of guyots, flat-topped submarine volcanoes in the Pacific, which provided early evidence for seafloor spreading.

� 1952

H.W. Menard and Robert S. Dietz discovered fracture zones in the Pacific Basin that were recognised as being associated with lateral faulting. These zones later became significant as a means of determining the direction of plate movement.

� 1954

Benioff and Wadati defined down going slabs from earthquake foci:

� 1956

Maurice Ewing and Bruce Heezen, Lamont Geological Observatory, reported that narrow troughs or rift valleys run along the crests for most of the length of the extensive submarine mountain chains in the Antarctic, Indian and Atlantic oceans.

J. Hospers, S.K. Runcorn, K. Creer and E. Irving, graduate students at Cambridge University in the early 1950s, began applying an intensively statistical method of paleomagnetism to the problems of polar wandering associated with continental drift. By 1956 Runcorn and Irving had refuted the belief that the Earth was too rigid for polar wandering or continental drift by using paleomagnetic data to demonstrate that both had occurred.

� 1959

Allan Cox began paleomagnetic research that confirmed the earlier work (1920s) of Motonari Matuyama, which concluded that the earth's magnetic field had reversed during the early Pleistocene.

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� 1962

Hess's historic article, "History of the Ocean Basins," was published, suggesting that the continents do not plow through oceanic crust, but are carried on mantle that is overturning due to thermal convection.

� 1963

Fred Vine and Drummond Matthews

�Vine

of Cambridge explained the linear magnetic anomalies parallel to active ridges by correlating earlier theory on seafloor spreading with research then being done on the time scale for geomagnetic reversals.

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� 1964

J. Tuzo Wilson, University of Toronto, postulated that oceanic islands such as the Hawaiian Islands were formed by the movement of a plate over a hot spot deep in the mantle. In 1965 he recognised a new class of faults and wrote the definitive paper on transform faults and their bearing on continental drift.

� 1965

Bullard, Everett and Smith of Cambridge introduced axis of rotation to describe displacement on a sphere, a geometric technique that became an important tool for later plate tectonic studies.

� 1967

Dan McKenzie,

�McKenzie

Scripps Institute of Oceanography (now at Cambridge), created a geometric model that employed rigid-body rotations to explain the mechanics of plate tectonics on a sphere.

Robert Parker, Scripps, completed a computer program called Supermap for plotting worldwide geophysical data using any projection. He hit upon the idea of using a Mercator projection to plot plate tectonics, which proved highly useful in later studies.

Today

Plate models are now generally accepted as providing good descriptions for surface evolution of the oceanic regions.

The exact nature of plates, etc is less well defined in some continental regions or in collision zones, where boundaries may become diffuse (e.g. E Med, N Arabia,� N Siberia). Indeed Molnar (Nature, 335, p 131-137, 1988), observed:

�"But the basic tenet of plate tectonics, rigid-body movements of large plates of lithosphere, fails to apply to continental interiors, where buoyant continental crust can detach from the underlying mantle to form mountain ranges and broad zones of diffuse tectonic activity."

Nevertheless, plate tectonic models now allow the palaeo-reconstruction of the gross relative distribution of large continents blocks back to ~600 Ma. These reconstructions become more ambiguous as one goes back beyond 200 Ma.

The reconstructions work at a regional scale as well as a continental one. One of the first plate tectonic analyses of a regional scale problem was presented by Atwater (Bull of Geol Soc America, 81, p 3513-3536, 1970) where she presented a reconstruction of the tectonic evolution of western North America.

Similar analyses are still underway for more complex regions. More examples are discussed in for example Kearey & Vine in Chapters 6,7,8 and 9.

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The Basic Framework

Click here for more detailed notes.

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.

There are three types of margin between plates:

�������������������� -����� constructive � mid-ocean ridges

- destructive � subduction zones or trenches

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- conservative � transform faults

The different types of margin can be defined and located by seismic studies.� Constructive + conservative -> shallow EQ, destructive have shallow, intermediate and deep foci in a dipping Benioff zone.

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.

These 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.

The basic geometry of plate motions has been thoroughly analysed, and discussed in a number of classic papers, eg� McKenzie & Morgan, Nature, 224, p 125-133, 1969 but see Cox and Hart for a detailed discussion of the geometry of plate tectonics.

In addition to discussing the relative motions of plates, one can also define plate motion relative to the Hot-Spot Reference Frame.

This gives a so-called Absolute Plate Motion (see Fowler sec. 2.7), and is a guide to the motion of the lithosphere relative to the underlying mantle. This will be of interest when discussing the forces which drive plates.

Modern research shows that the hot spot reference frame is not exact, as hot spots drift at a velocity of ~5 mm per year.

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 T_m - T_s = 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 (see Peltier JGR, 89, p 11303-11316, 1984), which suggest thickness in excess of 200 km. Such deep roots to old continental areas are also suggest by seismic tomographic studies (e.g. Dzeiewonski and Woodhouse, Science,� 236, p 37-48, 1987).

Anderson (Nature, 367, p 226, 1994) however points out 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.

He stresses that 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!

See this review from the Geoscientist (vol 16, 2006) on Continental Crustal Rheology.

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 - η_H2O� =� 10^-3 Pas, η_PORRIDGE� =� 10² Pas, but η_MANTLE� ~� 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.

See Coursework Exercise

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