Plate Tectonics

Two coastlines that used to be one#

Open an atlas to the Atlantic and look at the bulge of Brazil against the notch of the Gulf of Guinea. They fit. Not vaguely — the way two halves of a torn page fit, with the tear line still legible after you have separated them. Francis Bacon noticed it in 1620. Everyone who has ever looked at a decent world map has noticed it since.

In 1912 Alfred Wegener, a German meteorologist, argued that this was not a coincidence. He assembled the case: identical Mesosaurus fossils in Brazil and southern Africa, in a freshwater reptile that could not have crossed an ocean; the Glossopteris flora scattered across South America, Africa, India, Australia, and Antarctica; scratched and polished bedrock recording Permian glaciers in places now tropical, with the ice-flow directions pointing outward from a single centre that only exists if the continents are reassembled; and mountain belts that run off the edge of one continent and resume on another. He called the assembled supercontinent Pangaea.

The geological community rejected it, in many quarters scornfully, for about fifty years. The reason was not the evidence. It was the mechanism. Wegener proposed that continents ploughed through the ocean floor, driven by tidal forces and a poleward drift force. Harold Jeffreys, the leading geophysicist of his generation, calculated the magnitudes and showed they were smaller than required by many orders of magnitude, and that a granite raft cannot bulldoze its way through solid basalt without disintegrating. Jeffreys was right about the mechanism. He simply drew the conclusion that the continents therefore had not moved.

The resolution, when it arrived in the 1960s, came from a direction nobody in 1912 could have looked: the floor of the ocean, mapped for the first time by wartime and post-war sonar and magnetometer surveys. The continents were not ploughing through the seafloor. The seafloor was moving too — being manufactured along a global mountain range down the middle of the Atlantic, and swallowed again at the deep trenches of the Pacific rim. Everything rides. That is plate tectonics, and it is the organising theory of the entire Earth sciences.

A rigid shell on a ductile interior#

The first thing to fix is what a "plate" is, because the everyday word "crust" gets in the way.

The Earth's outermost layer is defined chemically: crust, either thin dense basaltic ocean crust (typically 6–7 km) or thick buoyant granitic continental crust (30–50 km, and up to about 70 km under the Himalaya). Below the crust, across a sharp seismic discontinuity called the Moho, sits the mantle — peridotite, silicate rock, solid.

But plates are not defined chemically. They are defined mechanically. The lithosphere is everything cold and strong enough to behave as a brittle, elastic solid on geological timescales: the crust plus the uppermost mantle welded to it. It is about 100 km thick under old ocean basins and up to 200–250 km under ancient continental cratons. Directly beneath lies the asthenosphere, chemically almost identical mantle rock that happens to be hot enough — within a couple of hundred degrees of its solidus, with perhaps a trace of partial melt — to creep. Seismically it shows up as a low-velocity zone; mechanically it is the layer the plates slide on.

That distinction is the whole idea. The asthenosphere is not liquid. You could not swim in it. Its viscosity is around $10^{21}\ \mathrm{Pa\,s}$ — roughly $10^{24}$ times that of water. But over millions of years, rock at that viscosity flows like a glacier, and a rigid lid floating on it can be pushed sideways without needing to plough through anything.

There are seven or eight major plates and a couple of dozen minor ones. Crucially, a plate is not a continent. The African Plate carries Africa and a large slice of the Atlantic seafloor. The Pacific Plate is almost entirely ocean. The North American Plate stretches from California to the middle of the Atlantic. Plate boundaries do not follow shorelines, which is exactly why Wegener's continents-as-rafts picture could never work.

Because a plate is rigid and the Earth is a sphere, plate motion is not a translation. Euler's rotation theorem says any motion of a rigid cap on a sphere is a rotation about some axis through the centre, so each plate pair has an instantaneous pole of rotation, and the surface velocity at any point on the boundary is

$$v = \omega R \sin\Delta$$

where $\omega$ is the angular rate, $R$ is the Earth's radius, and $\Delta$ is the angular distance from the pole. Velocity therefore vanishes at the pole and is greatest 90° away — which is why a single boundary, like the San Andreas system or the Mid-Atlantic Ridge, does not slip at one uniform speed along its whole length.

Three ways plates can meet#

There are only three things two plates can do at their shared boundary, and every tectonic landform on Earth follows from which one it is.

Divergent. The plates move apart, the asthenosphere beneath decompresses, melts, and fills the gap with fresh basalt. In the ocean this builds a mid-ocean ridge — the Mid-Atlantic Ridge is part of a 65,000 km seam running through every ocean basin, the longest mountain range on the planet, and almost all of it is underwater. On land the same process produces a rift valley: the East African Rift is a continent in the act of splitting, and the Red Sea is what it looks like once the ocean gets in.

Convergent. Something has to give, and which plate gives depends on buoyancy. Where ocean lithosphere meets continent, the dense ocean plate subducts — dives beneath — producing a trench, and, a hundred-odd kilometres inboard, a chain of volcanoes. The Peru–Chile trench and the Andes are the type example; the Cascades and Japan are the same machine. Where two continents meet, neither will go down: continental crust is too buoyant to subduct. Instead the crust crumples and doubles in thickness, and you get the Himalaya and the Tibetan Plateau, still rising as India drives north into Asia.

Transform. The plates slide past each other, with crust neither created nor destroyed. J. Tuzo Wilson worked out in 1965 that the fracture zones offsetting mid-ocean ridges are a distinct boundary class with a distinctive sense of slip — a result that only makes sense if the ridges really are spreading. The San Andreas fault is the famous continental example, taking up the Pacific–North American motion at roughly 3–5 cm/yr.

The widget is a cross-section you drive. What to try:

• Start on Divergent. Watch the ticks in the crust drift away from the axis in both directions and notice the seafloor getting deeper with distance. That is not decoration: ocean floor subsides as it cools, following a square-root-of-age law, $d \approx 2500 + 350\sqrt{t}$ metres with $t$ in millions of years (Parsons & Sclater, 1977). The Atlantic is deep at its margins and shallow at its middle for the same reason a poker cools from the tip.
• Watch the earthquake colours. On a ridge they are all gold — shallower than about 20 km, because that is the full thickness of rock cold enough to break rather than flow.
• Switch to Convergent O–C. Now the foci run down a plane from the trench to nearly 700 km depth: gold, then blue, then violet. That is a Wadati–Benioff zone, and it is the sinking slab itself, imaged by its own earthquakes. There is nowhere else on Earth that quakes happen 600 km down, because nowhere else is there rock that cold that deep.
• Switch to Convergent C–C. The slab disappears, the quakes go shallow and spread over a wide belt, and the crust grows a root. Mountains are held up isostatically by that root, like an iceberg: the Himalaya are as much a downward bulge as an upward one.
• Switch to Transform and read the map-view strip at the top: a stream crossing the fault is progressively offset, which is precisely how geologists measured slip rates before GPS.
• Then slide the rate. The plate speeds are real — 2 to 10 cm/yr covers essentially every plate on Earth. The readout accumulates model time and total displacement, and the numbers get large frighteningly fast.

What the numbers do over geological time#

Plate motion is slow in the way that matters least and fast in the way that matters most. The arithmetic is trivial:

$$d = v\,t$$

The trick is the unit conversion. One centimetre per year is exactly ten kilometres per million years. So a modest 5 cm/yr — about the rate at which the Nazca Plate approaches South America — is 50 km/Myr, 500 km per 10 Myr, and 5,000 km in 100 Myr. Fingernail growth, integrated over deep time, moves an ocean.

Check it against the Atlantic. GPS and geological rates give a full spreading rate averaging something like 2.5 cm/yr, and the ocean began opening around 180 Ma. That predicts $25 \times 180 = 4{,}500$ km, which is the right answer to within the precision of the inputs. Rates vary widely: the Mid-Atlantic Ridge is a slow ridge at 2–5 cm/yr full rate, while the East Pacific Rise runs at 15 cm/yr and locally more. Modern plate motion models (NUVEL-1A, and its successor MORVEL) are built by combining spreading rates from magnetic anomalies, transform-fault azimuths, and earthquake slip vectors, and they now agree closely with space-geodetic measurements — which means the average over millions of years and the rate measured this decade are the same rate.

Why the mantle convects at all is a question with a dimensionless answer, and it is the same Rayleigh number that governs a pan of soup:

$$Ra = \frac{\rho g \alpha \Delta T D^3}{\kappa \eta}$$

with $\alpha$ the thermal expansivity, $\Delta T$ the temperature contrast across a layer of depth $D$, $\kappa$ the thermal diffusivity, and $\eta$ the viscosity. Convection begins when $Ra$ exceeds a critical value of order $10^3$. Plug in mantle values — $D \sim 3\times10^6\ \mathrm{m}$, $\Delta T \sim 2000\ \mathrm{K}$, $\eta \sim 10^{21}\ \mathrm{Pa\,s}$ — and you get $Ra$ somewhere in the range $10^7$–$10^9$. Enormously supercritical. Given that the mantle is heated from within by radioactive decay and from below by the core, and cooled at the top, it must overturn. The only question was ever what form the overturn takes.

And why the shaking is concentrated at boundaries follows from how earthquakes store and release energy. The seismic moment of a rupture is

$$M_0 = \mu A \bar{D}$$

the shear modulus of the rock times the fault area that slipped times the average slip. Moment magnitude is then defined as

$$M_w = \tfrac{2}{3}\log_{10} M_0 - 6.06$$

with $M_0$ in newton-metres. Because it is logarithmic with a $2/3$ coefficient, one unit of magnitude is a factor of about 32 in energy, and two units a factor of 1000. It also explains why the largest earthquakes are only found at subduction zones: to get $M_w > 9$ you need $A$ of order $10^5\ \mathrm{km^2}$, and the only faults on Earth big enough are the gently dipping megathrusts where one plate slides under another. The 2011 Tohoku earthquake ruptured roughly 500 km by 200 km with up to 50 m of slip, for $M_0 \approx 5\times10^{22}\ \mathrm{N\,m}$ and $M_w$ 9.0–9.1. A vertical strike-slip fault like the San Andreas is limited by the ~15 km depth of the brittle crust, and tops out near $M_w$ 8.

The stripes that converted the field#

Here is the observation that ended the argument.

In 1962 Harry Hess circulated a paper he cheerfully labelled "geopoetry", proposing that ocean floor is created at mid-ocean ridges and destroyed at trenches, so the ocean basins are young and continually recycled while continents merely ride along. It explained why no ocean floor older than about 200 Ma has ever been found, on a planet 4.5 billion years old, and why ocean sediment is thin near ridges and thickens outward. But it was still a story.

Two things then collided. First, palaeomagnetists working on land had established that the Earth's magnetic field reverses — north and south magnetic poles swap — at irregular intervals of roughly $10^5$ to $10^6$ years, and had dated the recent reversals from lava flows. Second, naval magnetometer surveys had found that the ocean floor carries a bizarre pattern of magnetic anomalies: long parallel bands of slightly stronger and slightly weaker field, running parallel to the ridges, that nobody could explain.

In 1963 Fred Vine and Drummond Matthews at Cambridge — and independently Lawrence Morley in Canada, whose paper was rejected by two journals — put the two together. Basalt erupting at the ridge cools through its Curie temperature and locks in the direction of the ambient field. If the seafloor is spreading, then the ridge is a tape head and the ocean floor is the tape: each strip of new crust records the polarity of the moment it froze, and is then split down the middle and carried away in both directions. The prediction is exact and severe. The anomaly pattern must be symmetric about the axis, the stripe widths must be proportional to spreading rate times the known durations of the reversals, and the same sequence must appear in every ocean at widths scaled by that ocean's rate.

It is. The Eltanin-19 profile across the Pacific–Antarctic Ridge, published in 1966, is so cleanly symmetric that people who had spent careers opposing drift changed their minds on seeing it. Fold the profile at the axis and the two halves lie on top of each other.

The barcode here uses the real geomagnetic polarity timescale for the last 6 Myr — Brunhes, Matuyama with the Jaramillo and Olduvai subchrons inside it, Gauss, Gilbert — so the irregularity of the pattern is genuine. That irregularity is the point: a regular stripe pattern could be produced by all sorts of things, but a specific, ragged, unrepeating sequence appearing in mirror image on both flanks of every ridge in the world can only be a recording. What to try:

• Press Play. The model clock runs from 6 Myr before present to today. Crust piles outward from the axis, and the blue magnetometer trace above is what a ship towing an instrument would actually measure.
• Set the half-rate to 1 cm/yr, reset, and play again. Same sequence, same order, but squeezed into a narrow band. Now push it to 10 cm/yr: identical barcode, stretched out. Stripe width is nothing but rate times duration, which is why a magnetic profile measures the spreading rate of a ridge you have never visited.
• Drag the probe. Distance from the axis divided by rate gives an age directly — a clock you can read with a ship and a magnetometer. This is how the age map of the entire ocean floor was built, and it is why we know the Pacific Plate is old in the west and young in the east.

Once you can date the seafloor, everything becomes measurable: when each ocean opened, how fast, and where the continents were at any moment in the past 200 Myr.

What actually moves the plates#

The textbook cartoon — neat convection cells in the mantle with plates riding passively on top like packages on a conveyor belt — is worth setting aside. It is a useful first image and it is not what the evidence supports.

The problem is geometric. Plates come in wildly different sizes and shapes, boundaries migrate, and ridges themselves wander across the surface; no fixed set of convection cells has the right plan view. The modern picture inverts the relationship: the plates are not passengers on the convection, the plates are the convection. A subducting slab is the cold descending limb of a convecting system, and the surface plate is its cold upper boundary layer. The flow organises around the plates, not the other way round.

Within that picture the forces are:

• Slab pull. Oceanic lithosphere cools, thickens, and grows denser with age; past roughly 20–30 Myr it is denser than the asthenosphere it sits on, and it is sinking under its own weight. The gravitational pull of the descending slab, transmitted up the plate as tension, is generally considered the dominant driver. The classic evidence is Forsyth and Uyeda (1975): plate speed correlates strongly with the fraction of a plate's perimeter that is a subducting margin, and weakly with the length of ridge it carries. Plates with big slabs — Pacific, Nazca, Cocos — are the fast ones, at 6–10 cm/yr. Plates without — Eurasia, Africa, Antarctica — creep along at 1–2 cm/yr. Continental area, which should matter if basal drag dominated, mostly acts as a brake.
• Ridge push. More accurately, gravitational sliding: the ridge is elevated, the lithosphere thickens away from it, and the resulting horizontal pressure gradient pushes the plate away from the axis. Real, but generally estimated at a few times smaller than slab pull.
• Basal drag from mantle flow beneath, which can help or hinder depending on whether the flow runs with or against the plate, and which remains the least well constrained term.

There is a satisfying self-consistency here. Slab pull needs old, cold, dense lithosphere; lithosphere gets old, cold, and dense by spreading away from a ridge; ridges spread because plates are being pulled away from them. The system drives itself, powered ultimately by the Earth's internal heat — radiogenic decay of uranium, thorium, and potassium, plus primordial and core heat — which has to escape somehow, and mostly escapes by making new ocean floor.

Earthquakes, volcanoes, and the cycle of oceans#

Plot every earthquake epicentre recorded in the twentieth century and you do not get a scatter. You get lines: a thin bright seam down the middle of the Atlantic, a broad and violent band around the rim of the Pacific, a diffuse smear from the Mediterranean through Iran to the Himalaya. Those lines are the plate boundaries. The map was one of the strongest arguments for the theory in the 1960s, and it is now simply how boundaries are located.

The same is nearly true of volcanoes. The Ring of Fire is the subduction zones of the Pacific rim; the melt there is not from friction but from water. Hydrated minerals carried down in the slab release their water at 100–150 km depth, and water dramatically lowers the melting point of the overlying mantle wedge, so it melts and rises. That is why volcanic arcs sit a fairly consistent distance inboard of their trenches, and why their eruptions are so explosive — the magma is wet and silica-rich.

The instructive exceptions are the hotspots. Hawaii is thousands of kilometres from any boundary, and it forms a chain: an active volcano at one end, progressively older and more eroded islands and then drowned seamounts stretching away, with the Emperor bend recording a change in plate motion. The standard interpretation is a stationary or slowly moving plume in the mantle with the plate travelling over it — the details of plumes remain actively debated, but the chain's age progression is a direct measurement of plate motion that is entirely independent of the magnetic stripes, and the two agree.

Finally, run the whole thing forward and backward and you get the Wilson cycle. A continent rifts (East Africa today). The rift floods and becomes a narrow sea (the Red Sea). It widens into an ocean with a spreading ridge (the Atlantic). Eventually a margin fails, subduction begins, and the ocean starts closing (the Pacific). The ocean is consumed, the continents on either side collide, and a mountain belt is sutured together (the Himalaya, and before them the Appalachians and the Urals). Then the assembled supercontinent rifts again. Pangaea was the most recent assembly, not a unique event; Rodinia preceded it, and roughly every 400–600 Myr the pieces come back together in a new arrangement.

It also puts a limit on what the seafloor can tell us. No ocean floor older than about 200 Myr survives — it has all been subducted — so the entire magnetic-stripe archive covers only the last 4% of Earth's history. Everything before that has to be reconstructed from the continents, which is why Precambrian tectonics remains genuinely hard, including the basic question of when plate tectonics started at all.

Wegener died on the Greenland ice in 1930, thirty-odd years before the ships with magnetometers went out. He had the phenomenon and not the mechanism, which in physics is usually a losing hand. But the coastlines were never a coincidence, and they were never the argument either — they were the thing that made a few people keep looking until the seafloor gave up the answer.