Kinematics: Plate movement

Introduction and history of ideas

It's common in sedimentary courses to use the 'present as the key to the past'. This idea, that features in the rock record are to be explained by looking at the present-day world, was called 'uniformitarianism' by the pioneers of geology. We now recognize that there are some features of the Earth that cannot be explained by a strict application of uniformitarianism. The term actualism is sometimes applied to a 'less strict' version of the principle.

In courses on structural and metamorphic processes, it has historically been difficult to apply an actualistic approach, because at present the processes are occurring deep beneath the surface. This is beginning to change, however. GPS systems enable us to measure plate movement and the distortion of the lithosphere; geophysical investigations allow us to infer the physical state of deep crustal and mantle rocks.

This segment of the course takes an actualistic approach to deformation. We look first at plate kinematics to determine the rates and types of deformation that might be occurring at the present day. We will use this as a framework for interpreting the past.

Continental drift was proposed by Wegener in the early 20th century to explain certain features of the continents. In Wegener's concept, continents drifted somewhat like large icebergs through surrounding material that formed the mantle and the ocean floors.

Wegener's continental drift was not supported by most European and North American geologists, because geophysical information indicated that the ocean floors were too rigid to flow. The major divisions of crust, mantle and core were defined based on the speed of propagation of seismic P and S-waves which seemed to indicate that the crust and mantle were solid and elastic, while only the outer core was liquid. However, from about 1950 onwards, new ideas in geophysics began to appear that generated some support for ideas of moving continents.

Major subdivisions of the Earth

By Composition

When an earthquake occurs, seismic waves are picked up around the Earth. The timing of arrival of the waves can be used to deduce where within the Earth those waves are refracted and reflected, giving basic information on the location of major boundaries within the Earth. These major boundaries were established in the 1950s, before the nature of rheological constrasts was fully understood.

These major boundaries are shown in VDPM Fig. 14.03 and 14.04

Core

Core: The core starts 2900 km below the Earth's surface. The outer surface of the core is marked by a strong change drop in the velocity of p-waves, and a material that is a barrier to S waves. In addition, gravity data show that there is an increase in density at this boundary, while the Earth's magnetic field indicates that the core is likely to be an electric conductor. Taken together, these data indicate that the core consists mainly of liquid metal.

A boundary within the core occurs about 5200 below the Earth's surface. This marks the inner core which is probably solid metal.

The composition of the core is thought to be mainly Iron, with a proportion (probably around 10%) of Nickel and lesser amounts of other elements.

The inner core is probably growing slowly over geologic time as the liquid outer core material solidifies on to the inner core. The heat of fusion released by this process contributes to the Earth's overal thermal budget.

Mantle

The mantle makes up the bulk of the Earth by volume, extending from the outer surface of the core up to the base of the crust only 5-70 km below the surface.

This vast mass of material is probably rather uniform in composition, corresponding to a rock that would be described as peridotite at the Earth's surface, consisting dominantly of Mg-rich Olivine, together with Cpx, Opx, and typically an aluminous phase such as feldspar (near the surface), spinel, or garnet.

However, it would not be quite correct to say that the mantle consists of peridotite, because the above minerals all become unstable with increasing pressure, and the familiar SiO4 tetrahedra of crustal mineralogy are converted to other structures.

Such boundaries probably occur ~400 and ~670 km down, where there are distinct jumps in P-wave velocity.

Crust

The base of the crust is marked by one of the first major seismic velocity discontinuities to be identified by geophysics - the Mohorovicic discontinuity or Moho, which varies in depth from about 5 km to about 70 km. T

The crust is the most varied part of the Earth compositionally, as a result of 4.6 Ga of the operation of the rock cycle.

We recognize two overall types of crust.

Oceanic crust

Oceanic crust is predominantly mafic in composition. The crust is 5-10 km thick and is constantly being recycled by plate tectonic processes. The oldest oceanic crust is probably about 200 Ma.

Within the generally oceanic crust there are some variations, however.

Mid-ocean ridges, with exposed igneous rock, stand 2-3 km above the abyssal plains covered with fine-grained sediment. Oceanic islands and seamounts are scattered on the abyssal plains. Oceanic plateaux are larger areas of thicker oceanic crust that stand above the surrounding ocean floor and may have character intermediate between continental and oceanic crust. Guyots are flat-topped seamounts.

Trenches mark the deepest parts of the ocean floor (up to 11 km deep) and are flanked on one side by island arcs. Island arc crust is also thicker than normal oceanic crust.

Continental crust

Continental crust is enormously variable in composition and structure. Some broad groupings exist:

Cratons represent large areas of continental crust that have not seen major deformation, igneous activity, metamorphism, typically since the beginning of the Cambrian. The oldest cratons are of Archean age (>2.5 Ga) and represent the Earth's earliest continents. Exposed cratons are known as shields, whereas those with a cover of undeformed sedimentary rock are platforms.

Linear belts of deformed rock are known as orogens. Proterozoic orogens occur within the cratons, wheras Phanerozoic orogens represent more recently deformed continental crust. There is some controversy as to whether the orogen concept is useful in Archean cratons, which generally have less obviously linear distribution of deformed belts.

Passive continental margins are marked by thick accumulations of sedimentary rock without major igneous activity. They probably evolve from continental rifts - deep fault-bounded valleys.

Active continental margins are adjacent to oceanic trenches or other plate boundaries, and are marked by deformation and by continental volcanic arcs.

By Rheology

As plate tectonics developed in the late 20th century, it was realized that seismic data contained more information than the simple layer-structure described above. In particular, the attenuation of S-waves by liquid showed that portions of the upper mantle were close to their melting point, or were partially molten, and could therefore flow easily.

Asthenosphere

The portion of the upper mantle that was able to flow was named the Asthenosphere. Estimates of the amount of melt in the asthenosphere range from <5% to 30% beneath the mid-ocean ridges.

Lithosphere

The lithosphere is the more rigid outer shell of the Earth, composed of the lithospheric mantle plus the overlying crust. (It is unfortunate that the term 'crust' - which in popular usage means a strong and brittle outer layer - was applied to a compositional layer before plate tectonics was discovered. In the popular imagination it is the crust that is divided into plates, not the lithosphere. Structural geologists are expected to avoid falling into this trap!)

The lithosphere is of rather variable thickness, though 100 km is often stated as typical. Below Archean cratons the lithosphere may be as much as 400 km thick, whereas oceanic lithosphere is often thinner - only about 60 km, thinning to nothing at the mid-ocean ridges.

Isostasy

Overall, the topography of the Earth's surface reflects the density of the lithosphere. Less dense continental lithosphere has a surface that sits (mostly) above sea level whereas denser oceanic crust has a surface that is at a level flooded (mostly) by the oceans. High mountains are underlain by rocks less dense than average.

This idea was actually discovered in the 19th century, when surveyors mapping the Indian subcontinent realized that the mass of the Himmalayan mountains should be causing deflection of plumb lines used to measure vertical. However, when they calculated the deflection it was found to be substantially less than predicted, indicating that the mass of the mountains above sea level was isostatically compensated by lighther than average rocks below.

In practical terms, isostatic compensation of two areas means that if you add up the mass of a column in each area (make it 1 m2 in area for ease of calculation), extending from the surface to the asthenosphere, the two masses will be the same.

Much of the lithosphere is approximately isostatically compensated. The largest exceptions are the deep ocean trenches, which appear to be being held down by something.

Plate boundaries

Plate tectonics in its original form is an idealized version of lithosphere kinematics that uses translation and rotation of plates to explain many observations of tectonic activity. Distortion and dilation are assumed to be restricted to very narrow plate boundaries. Plate boundaries are of three types [VDPM Fig. 14.14a):

Structural observations on the continents, and more recently GPS measurements of deformation, show that some plate boundaries, expecially on the continents, are actually zones of distortion that are hundreds of km wide. A lot of structural geology deals with the features of such broad deformation zones in ancient rocks, so it is worth knowing more about what goes on at the present day: we are finally able to use 'the present as a key to the past' (actualism) in structural geology.

Zones of distortion at plate boundaries

Measuring plate movement

This section looks at the sources of information which can tell us about the rate of plate motion. The relative movement between two plates at a given point (e.g. the movement on the San Andreas Fault Zone at San Francisco) is a vector quantity. It has a magnitude (typically some tens of mm/yr) and a direction (an azimuth relative to north). This vector is known as a slip vector.

Several lines of information are available for determining slip vectors. All are limited in one way or another, but together they can be combined to give a reasonable picture of plate movment as it occurs at the present day.

Magnetic information

Magnetic surveys over many areas of the ocean floor show patterns of linear magnetic anomalies. Positive anomalies are strips where the magnetic field measured by a ship-born magnetometer is slightly stronger than the average value for that part of the Earth's surface. Negative anomalies have a weaker field.

anomaly map

Magnetic reversal time-scale

v= w/t.

Map showing age of oceanic lithosphere

Seismic information

The study of the kinematics of active faults is called neotectonics. Typically, neotectonics can provide good information on the direction of the slip vector at all three types of plate boundary but provides little information on the magnitude of slip. To understand how this is done, we need to know something about deformation and seismicity at faults.

Elastic deformation prior to fault slip

The diagram shows an idealized east-west transform fault with dextral motion.

Of course, for a sinstral fault, or one with dip-slip motion, the directions will be different. Note also that the actual strains occurring in rocks are exceedingly small.

Failure

Fault after slip

Focal mechanisms

At the instant of earthquake, the rocks abruptly return to their 'normal' state.

General focal mechanism

Early focal mechanism diagrams were constructed laboriously by hand. Now, when a major earthquake occurs, computer programs in major seismic centres automatically produce focal mechanism diagrams, typically within a few hours of the event. Focal mechanisms for recent events can be consulted at the US National Earthquake Information Centre.

Example - Northern Sumatra Earthquake of December 26 2004

Examples - focal mechanisms recorded over a 1 month period

Plate motion from focal mechanisms

Pole to auxiliary plane

Slip vector

Direct measurement by GPS etc.

The global positioning system (GPS) depends on a set of satellites orbiting earth, which transmit signals to receivers on Earth. The receivers can locate themselves very precisely in space, with an accuracy of centimetres or millimetres if the devices are run over a long period of time, or sites like the one in the slide are reoccupied at intervals of months or years.

Plate kinematics

Kinematics of plate motion on a sphere

[VDPM Fig. 14.14a] Plate boundaries on a flat Earth

Euler (pronounced Oiler) showed that the motion of any rigid body on the surface of a sphere can be represented by a rotation about an axis - the point where the axis intersects the Earth's surface is the Euler pole (actually there are two on opposite sides of the Earth)

[Relative motion of two plates VDPM Fig 14.20a]

For every pair of plates, their relative motion is defined by

So it's a vector quantity.

Velocity at a point on a boundary depends on

v= ωrsinθ [VDPM 14.20d]

or in vector terms

AVB = AΩB x r

In this equation

AvB means "velocity of A relative to B at the Earth's surface" (also known as the slip vector)

AΩB means "rotation vector of A relative to B"

and r is the radius vector of the Earth through the point on the plate boundary, and x signifies the vector cross product.

Because it's a vector quantity, if we know the motion of plate B relative to A, and C relative to B, we can calculate C relative to A using the following relationship

AΩB + BΩC + CΩA = 0

By matching this result to observations of plate velocity vectors it has proven possible to come up with an internally consistent set of plate rotation vectors that fits the observations well; actually there are several different versions, but they are generally similar.

Plate velocity model

Kinematics of plate boundaries and triple junctions

It's also possible to use vectors to analyse motion around triple junctions. Triple junctions are places where three plates (and three boundaries) meet. For example, at a ridge-ridge-ridge junction all the plates are separating, and all three are moving relative to the junction itself. How do we calculate the velocity of the junction itself?

Map of Plates and RRR Triple Junction

To do this we plot motions in velocity space. (For this purpose we typically assume the Earth is flat! This is actually reasonable for the small area (<500 km) around a triple junction.) For three plates A, B, C that meet at a triple junction we can say that

AVB + BVC + CVA = 0

Hence we can plot the 3 vectors nose to tail as a velocity triangle.

Diagram of RRR triple junction in velocity space.

What about the velocity of the junction itself. For the RRR triple junction we can plot a bisector (dashed line) of each side of the triangle. The bisector represents the possible locus of the triple junction based on that pair of plates, assuming that spreading is orthogonal and symmetrical. The three bisectors meet at a point that represents the motion of the triple junction itself.

Now let's look at another example, the triple junction located just off the north tip of Vancouver Island. This is the junction between the Queen Charlotte Islands fault (a dextral transform fault), the Juan da Fuca Ridge, and the Cascadia Subduction zone.

TFR junction

The relative motions are as follows

  Motion on QCI fault motion of JF ridge motion on Cascadia trench
rate 44.35 55.10 46.60
direction -16.23 109.18 58.31

TFR Junction in velocity space

Note, in plotting the triple junction,

Summary of velocity space vector diagrams

These principles can be extended to all possible triple junctions

Note that if the three constraint lines do not meet in a point, then the triple junction is unstable and must evolve immediately into a new configuration.

Diagram of all possible triple junctions

Engebretson et al (1985) were able to use poles of rotation and analysis of triple junctions to set up a framework of plate motion along western North America since the early Cretaceous

Animated versions of the evolution of the North American margin

One interesting consequence of this type of modelling is the concept of slab windows: as a ridge is subducted, the two subducted plates on either side of it presumably continue to diverge. This potentially creates a gap in the overlying volcanic arc, and possibly a place where upwelling asthenosphere comes affects the overriding plate.

Causes of plate motion

Plate tectonics as originally defined was a purely kinematic theory, without attention to determining the forces that drive plates.

What can we say about the processes that drive the plates.

First, it is clear that the only set of forces capable of driving plate tectonics are those associated with convection - the circulation of material due density variations under the influence of heat. That said, it is not immediately clear whether the density contrasts that drive plates are within the plates themselves or whether they are in the underlying mantle and are transmitted to the plates through their surfaces.

List of plate-driving forces. VDPM 14.23

Of these forces it is clear that the first two have the primary role in driving the plates. Trench suction adds a smaller but significant extra component. Most of the other forces listed above probably act mainly so as to resist plate motion.