Material on this page is copyright © 2016 John W.F. Waldron

Kinematics: Plate movement

Introduction

Actualism is the idea that features in the rock record are to be explained by looking at the present-day world. It's common in sedimentary courses to use the 'present as the key to the past'.

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 has changed in recent years. 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 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.

• See: short history of ideas on continental drift and plate tectonics

Major subdivisions of the Earth

By composition

Based on seismic velocity: 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.

Core

Outer core

Starts 2900 km below the Earth's surface. The outer surface of the core marked by

• drop in the velocity of p-waves
• barrier to s-waves
• increase in density
• magnetic field indicates electric conductor.

Seismic and magnetic properties, taken together, indicate that the core consists mainly of liquid metal.

• mainly Iron,
• a proportion (probably around 10%) of Nickel
• lesser amounts of other elements.

Inner core

• top is about 5150 km below the Earth's surface.
• probably solid

Mantle

• Bulk of the Earth by volume
• From the 2900 km to base of the crust 5-70 km below the surface
• Rather uniform composition: Mg-rich silicates
• Outer part is mainly olivine and other silicates with SiO₄ tetrahedra .
• These minerals become unstable with increasing pressure; SiO₄ tetrahedra converted to SiO₆octahedra. Such changes probably occur in the transition zone where there are distinct jumps in seismic velocity.
• ~400 km
• ~670 km

Crust

Moho

The base of the crust is marked by a major seismic velocity discontinuity - the Mohorovicic discontinuity or Moho.

• varies in depth ~5 km to about 70 km
• p-wave velocity jumps from ~7 km/s to >8 km/s.

Composition

The crust is the most varied part of the Earth compositionally, as a result of 4.5 Ga of the rock cycle.

Two overall types...

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;
• Guyots are flat-topped seamounts.
• 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.
• 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.
• Back arc basins. Smaller ocean basins that lie adjacent to an arc on the side opposite to the trench

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 tectonic activity since the Precambrian. The oldest cratons are Archean (>2.5 Ga) and represent the Earth's earliest continents.
  • Shields: Exposed cratons
  • Platforms: Cratons with a cover of undeformed sedimentary rock
  • Foreland basins: thicker belts of sedimentary rock adjacent to....
• Orogens: linear belts of deformed rock. Proterozoic orogens occur within the cratons, wheras Phanerozoic orogens represent more recently deformed continental crust. There is controversy as to whether the orogen concept is useful in Archean cratons, which have less obviously linear 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 plate boundaries - either subduction zones or transform faults; they may be marked by deformation and by continental volcanic arcs.

By Rheology

As plate tectonics developed in the late 20th century, it was realized that the S-wave attenuation showed that portions of the upper mantle were close to their melting point, and could therefore flow easily.

Asthenosphere

• The portion of the upper mantle that is able to flow.
• Amount of melt ranges from ~5% (typical) to 30% beneath the mid-ocean ridges.

Lithosphere

Thickness

More rigid outer shell of the Earth, composed of

• lithospheric mantle plus
• 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 must avoid this trap!)

• The lithosphere is of rather variable thickness,
• 100 km is typical.
• Below Archean cratons the lithosphere may be up to 400 km thick
• oceanic lithosphere is typically thinner - ~60 km, thinning to nothing at the mid-ocean ridges.

Lithospheric plates

Plate tectonics in its basic 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 of three types:

• Spreading centres or ridges, where the relative motion of plates diverges from the boundary; new lithosphere is formed.
• Subduction zones or trenches, where the relative motion is convergent; lithosphere is consumed.
• Transform faults, where the relative motion is parallel to the boundary; lithosphere is conserved.

Structural observations and GPS data show that some plate boundaries, expecially on the continents, are actually zones of distortion, hundreds of kilometres wide.

Isostasy

Vertical movements of the lithosphere are largely controlled by density, which can be estimated from gravity data.

• Less dense continental lithosphere has a surface that sits (mostly) above sea level
• Denser oceanic lithosphere is at a level flooded (mostly) by the oceans.
• High mountains are underlain by rocks less dense than average.

These observations lead to the idea of isostasy. Isostatic compensation of two areas means that if you calculate the mass of two typical columns of rock, extending from the surface to the asthenosphere (with unit cross-sectional area) the two masses will be the same.

Some generalizations about isostasy and the lithosphere:

• Much of the lithosphere is approximately isostatically compensated.
• Deep ocean trenches are exceptions. They appear to be being held down by the slab of subducted lithosphere.
• Contintental crust is probably prevented by isostasy from being subducted, but metamorphic rocks in orogens indicate that continental crust can sometimes get down to ~150 km before it detaches from the subducted lithosphere and returns to the surface.

Measuring plate movement

Slip vectors

Slip vector describes the relative movement between two plates at a given point (e.g. the movement on the San Andreas Fault Zone at San Francisco).

• magnitude (typically some tens of mm/yr)
• direction (an azimuth relative to north).

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 movement as it occurs at the present day.

Magnetic information

Paleomagnetism

Remanent magnetism is magnetism preserved by rocks from early in their history. In ideal cases remanent magnetism preserves the orientation of the Earth's magnetic field at the time of formation of the rock.

• Inclination of remanent magnetism indicates distance to Earth's magnetic pole. The mathematical relationship is tan(I) = 2tan(λ) where I = inclination, λ=latitude
• Azimuth (or declination) of remanent magnetism indicates direction to magnetic pole.

Apparent pole position is a good way of plotting this information

Apparent polar wander path is obtained if multiple paleomagnetic results of different ages are available for a single continent. Of course, in most cases it's the continent that actually wandered, not the pole. However, true polar wander (controversial!) may have occurred at some times in Earth history and may complicate the picture.

This method is almost the only way to get information on plate movements before 200 Ma. Its major limitation is that it gives only paleolatitude and not paleolongitude, so E-W movements are not measureable. Typically the rates of movement deduced from paleomagnetic studies are averaged over tens to hundreds of Myr.

Linear magnetic anomalies

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

Pattern of oceanic magnetic anomalies

• The pattern of linear magnetic anomalies is thought to be due to remanent magnetism, acquired by basaltic oceanic crustal rocks as they cooled during formation of ocean floor.
• The dipole field of the Earth has reversed its polarity repeatedly but haphazardly during Earth history, typically at intervals of a few hundred thousand years.
• Ocean floor formed during normal polarity adds remanent magnetism to the ambient field, producing a positive anomaly.
• Ocean floor with reversed polarity subtracts remanent magnetism from the ambient field producing a negative anomaly.
• The history of magnetic reversals is now well known. The pattern can be matched with the pattern of ocean floor anomalies.

Calculating slip rates

• The rate of spreading for a sequence of anomalies of width w and duration t, can be calculated as:

v= w/t

• Typical rates in SI units are of the order of 10^-9 m/s. It is usually more convenient to quote the rate in cm/yr or mm/yr. 1 mm/yr = 1 km/Myr.
• Note that is actually a 'half rate' - that is, the rate at which ocean floor is generated on one side of the ridge.
• At most ridges, spreading is symmetric: lithosphere is formed at approximately the same rate on each side. The true slip rate between the two plates is double the 'half rate'.
• For a ridge where spreading is orthogonal (ie the slip vector is perpendicular to the ridge crest) this calculation gives rather good constraint on the average rate of spreading.
• However, not all ridges show orthogonal spreading.
• Transform faults at many mid-ocean ridges produce fracture zones, which give better control on spreading direction.
• Linear magnetic anomalies are only useful at spreading centres (ridges).
• The rates provided are averaged rates, over periods typically of a few million years.
• The oldest ocean floor is from about 200 Ma, so the method is useless before the Jurassic.

Seismic information

Neotectonics is the study of the kinematics & dynamics of active faults. Typically, neotectonics can provide good information on the direction of slip at all three types of plate boundary but provides little information on the rate of slip.

Elastic deformation prior to fault slip

• Slip on faults is typically fast, sporadic and unpredictable. We know this because earthquakes make the news.
• Nonetheless we have geologic evidence that plate motion is continuous and slow.
• Between earthquakes, plates experience high stresses at their edges and undergo local distortion through the mechanism of elasticity.
• Elasticity is recoverable strain: strain that disappears when the stress that caused it is removed.
• Energy stored in the strained rocks is released during an earthquake.

The following relates to an idealized E-W transform fault with dextral motion (diagram to be drawn in class).

• During plate movement shear strain builds up in the wall rocks.
• For a dextral transform fault the shear strain is clockwise: positive by convention.
• Lines oriented NE-SW undergo extension (s>1); the direction of maximum extension is sometimes referred to as the T-axis for exTension.
• Lines oriented NW-SE undergo shortening (S<1). The direction of maximum shortening is called the P axis for comPression.
• 

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

Failure

• Hooke's Law states that In elastic deformation, stress and strain are proportional.
• Hence as strain increases, the stress on the fault surface increases.
• Eventually brittle failure or fracture occurs over a region of the fault plane when stress exceeds the strength of material at the fault.
• The stress on the fault plane falls rapidly, and in a few seconds, the strained rocks in the walls of the fault lose some or all of their strain.
• The stored energy is converted into seismic waves that propagate through the surrounding rocks from the focus of the earthquake.
• The seismic waves contain information about the focal mechanism, including the sense of slip.

Focal mechanisms

At the instant of earthquake, the rocks abruptly return to their 'normal' state. The first motion of particles determines the nature of the first seismic wave that propagates from the focus.

Example focal mechanism

• In the example, particles just north of the fault plane move abruptly east; those to the south move abruptly west.
• 
• Towards the NE and SW the first wave involves motion of particles away from the fault. In other words it is a wave of compression.
• Towards the NW and SE the first wave, though it travels away from the focus, actually involves motion of particles towards the focus, producing momentary dilation (expansion) of the rocks. (Though this sounds paradoxical, it's quite easy to replicate this type of wave with a slinky. Try it!)
• Notice that the first wave that travels towards the T (extension) axis is one of compression, and vice versa. This is because the seismic wave is generated by the loss of the strain that was accumulated prior to the earthquake.
• Seismic energy is radiated in all directions from an earthquake focus, as an expanding, approximately spherical wavefront.
• If this energy is picked up by enough seismographs, we can divide the sphere into four quadrants, characterized by compressional and dilational first waves.
• The T and P axes lie in the centre of these quadrants.
• A stereographic projection can show this sphere (shown in class for the dextral strike-slip fault we considered above).

General focal mechanism

• More generally, the T and P axes may be plunging lines
• The quadrants are separated by two nodal planes.
• One of these is the fault plane, and the other is called the auxiliary plane, which is perpendicular to the fault plane.
• The slip vector is the pole to the auxiliary plane.
• Unfortunately, it's not possible to determine which nodal plane is the fault plane using seismic data alone. We need to look at local geology to determine this.

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 minutes of the event. Focal mechanisms for recent events can be consulted at the US National Earthquake Information Centre.

Plate motion from focal mechanisms

• For measuring plate motion over the surface of the Earth, we are interested in the horizontal component of the slip vector (i.e. its trend).
• This will always be at 90° to the strike of the auxiliary plane, as can be verified easily with a stereographic projection.
• Transform fault focal mechanisms provided an early test of plate tectonics

Limitations

• This method gives direction but not speed of relative motion
• The movement measured is built up over the length of the earthquake cycle, perhaps hundreds to thousands of years, so these measurements are averaged over a very short timescale compared to the magnetic methods.

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 are reoccupied at intervals of months or years.

• The results when compared between different plates can show plate motion velocities.
• When results are compared over regions of 100s or 1000s of km near plate boundaries, they show that many boundaries are not in fact sharp, but are characterized by a displacement gradient.
• A displacement gradient is equivalent to a strain.
• The major limitations of this method are:
  • GPS receivers only work on land
  • Movements are averaged over very short timescales (5 - 20 yr), much shorter than the earthquake cycle, so may not be representative of long-term slip rates.

Overall conclusions of slip-vector determinations

• Summary of slip vector determination methods:

  Method	Good for...	Not so good for...	Back to..	Rates averaged over..
  Paleomagnetism (APW)	N-S movement	E-W movement	4 Ga	10 - 100 Myr
  Linear magnetic anomalies	Spreading centres (ridges)	Subduction zones	200 Ma	1 - 10 Myr
  Earthquake focal mechanisms	Directions	Speeds	1950	100 - 1000 yr
  GPS	Continents	Oceans	2000	5 - 10 yr

• Results of all these methods confirm that:
  • Lithosphere is divided into plates
  • Strain rates are low within plates
  • Strain rates are high at plate boundaries
  • Plate boundaries within oceanic lithosphere are typically narrow
  • Plate boundary zones within continental lithosphere can be broad zones of deformation
• Plate boundaries: 3 types
  • Ridges: plates moving apart
    • Spreading is typically symmetric
    • Spreading is typically orthogonal
  • Trenches: plates converging
    • Subduction is highly asymmetric
    • Subduction is not usually orthogonal
  • Transform faults: motion parallel to boundary

Plate kinematics

Kinematics of 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?

Example: RRR Junction in Indian ocean

To do this we plot motions in 2D 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

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

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.

Example TFR Junction off Vancouver Is.

Now let's look at a trench-transform-ridge 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.

The relative motions are as follows

Note, in plotting the triple junction, the constraint lines work as follows

• For the ridge, as before, a perpendicular bisector of the velocity vector
• For the subduction zone a line
  • parallel to the geographic orientation of the trench, and
  • attached to the point representing the upper plate, in this case the North American plate. This signifies that a triple junction on a subduction zone can move up and down the subduction zone parallel to the edge of this plate.
• For the transform fault, a line through the points representing both plates NA and PA. A triple junction on a transform fault is constrained to move parallel to the transform fault, itself parallel to the velocity vector.

Summary of velocity space vector diagrams

• Each plate is represented by a point
• The relative motion of two plates is represented by a vector between the two points
• The relative motion of the triple junction itself can be added to the vector diagram as a point.
• Triple junctions can only migrate along plate boundaries
• The motion of triple junction (its position in velocity space) is constrained by lines (constraint lines), each parallel to the map orientation of a plate boundary:
  • The constraint line for a ridge bisects the vector joining the two plates;
  • The constraint line for a trench passes through the point representing the conserved (upper) plate;
  • The constraint line for a transform fault passes through both points representing the two plates.

All possible triple junctions

These principles can be extended to all possible triple junctions

The triple junction is unstable if the three constraint lines do not meet in a point; then the triple junction must evolve immediately into a new configuration.

Kinematics of plate motion on a sphere

Plate rotation vectors

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)

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

• a direction (axis)
• a magnitude (rate of rotation)

So it's a vector quantity:

_AΩ_Bmeans "rotation vector of B relative to A"

[Note: some texts use the opposite convention, notably the text by Van der Pluijm and Marshak, formerly used in this course]

Calculating slip vectors

Velocity at a point on a boundary depends on

• the rate of rotation
• the angular distance from the Euler pole

or in vector terms

In this equation

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

_AΩ_B means "rotation vector of B relative to A"

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

Global plate velocities

Euler poles and rotation vectors are related in 3D by the following equation

_AΩ_B + _BΩ_C + _CΩ_A = 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.

Evolution of Western Margin of N. America

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

• Pacific Plate
• Animation of plate motion at the west edge of the North American Plate

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 affects the overriding plate.

Dynamics of plate motion

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

Absolute motion of the plates

Reference frame? In describing the motion of any plate we always have to say what is our reference frame. Is any one reference frame better than any other?

Hotspots are magma sources that appear to be connected to phenomena deep within the mantle and therefore provide an opportunity torelate plate motion to something deeper down. However, attempts to relate plate movements to a hotspot frame of reference have only been partially successful. It seems that the hotspots are moving relative to each other.

Alternatively, a no net rotation frame of reference is often used. This is a frame of reference in which the sum of the rotations of all the plates (when weighted for varying plate areas) is zero.

Forces on the plates

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

Convection in a broad sense is the only set of forces capable of driving plate tectonics.

Convection is the circulation of material due to thermal density variations under the influence of gravity. The density contrasts could be within the plates themselves or in the underlying mantle. Some of these forces can be estimated.

List of plate-driving forces.

• Ridge "push": Forces due to the topographic slope on the flanks of the mid-ocean ridges.
• Slab "pull": Forces due to the dense slab of oceanic lithosphere (including very dense eclogite) below subduction zones.
• Trench suction: Forces due to the topographic slope at the inner trench wall.
• Mantle drag
  • Base of plate: shearing resistance or acceleration as a plate moves relative to the asthenosphere.
  • Top and bottom of slab: shearing resistance to the descending slab.
  • Tip of slab: resistance to the tip of the slab as it pentrates into the mantle.
• Bending resistance: Force required to bend plate at a subduction zone.
• Transform resistance: Shear force at transform faults
• Subduction zone resistance: Shear force at subduction zone.
• Membrane stresses: Forces required to bend plates as they move over a non-spherical Earth.

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 but they are more difficult to quantify.

Overall style of convection

There has been controversy over the style of convection. Some geophysicists have suggested that the convection cells that drive the plates extend no deeper than the 700 km base of the mantle transition zone. This is the deepest point at which the subduction slabs can be detected from earthquakes. Below this, in 2-layer models, it is possible that another set of convection cells operate.

Other geophycisists and modellers prefer to explain plate convection in a whole mantle circulation model.