It is nice to live on the crust. It gives a degree of stability which the rest of the Earth lacks. It is not perfect: the quiet can be punctuated by earthquakes or volcanoes, and lacking those there is still the off-chance of a landslip or flood. The atmosphere may also interfere with our lives. Take Kansas (to UK readers: that is like Milton Keynes without the roundabouts (traffic circles), the people, or the city): it is amazing how much destructive weather a place without an alleged atmosphere can still have. Actually, living on the crust can be pretty precarious. But don’t complain too much. Dig down into the solid rock and below those you’ll find ever-moving currents. We are living on a thin shell above a seething ocean of rock. Do you remember those people of the previous post walking on thin ice? That is us.
The picture above shows the location of the Kola superdeep hole. Over a period of 20 years, the Russians dug down to more than 12 kilometer below the surface. It was an amazing feat. It is near the Norwegian border and there may have some concern that parts of Norway could fall in. After almost 25 years, the project ended in 1994. Since 2008 all maintenance has ended and the buildings are now in ruins. If you have seen the ruins of Chernobyl already, you may want to try this next, although I am not sure that it is possible to get permission to visit it. The Kola project penetrated only about a third of the crust before the increasing heat made any further progress impossible. The scientists complained about the rocks down there being more like plastic than like rocks. It is hard being a scientist.
The previous instalment discussed the pliability (or otherwise) of the material of the Earth’s crust. Cold rock is stiff and immovable. Hot rock, as found in the Kola drill, is more deformable and can creep. Glass stays put while honey runs. We saw how mountains grow and volcanoes sink, on the shaky foundation of the warm rock below. But now it is time to look deeper. A lot deeper.
The crust consists of two very different regions: oceanic plates and continents. They have in common is that they form the top layer of the Earth, immediately below the oceans and atmosphere; also they are the only parts of the Earth broken into pieces (called plates). But if you had found a bit of continent and a bit of oceanic plate, you would not have put them together in the same category. Oceanic crust is dense, thin (almost always around 6-7km), and mafic. Continental crust is thick, light, and felsic (rocky). Continents rise far above oceanic crust: this is because their rocks have much lower density: they float on the denser material below. The thickness of continental crust varies tremendously from place to place, ranging from 20 to 70 km. Oceanic crust, on the other hand, is dense – almost the same density as the mantle below. The density depends a bit on temperature: when it is hot it is a bit less, when cold a bit more. This is the reason that oceans are shallow above mid-oceanic ridges (where the crust is young and warm – if 2 kilometer depth can be considered shallow), but 5-6 kilometer deep where the oceanic crust is old, has cooled, become denser, and therefore lies much deeper. Don’t age oceanic crust too much, as it will begin to sink. That gets ahead of the post, though.
The crust almost everywhere, whether oceanic or continental, is cold and stiff. It acts as a tough solid. Think biscuits. If you flex a biscuit, it will break into two or more pieces. Dunk it into tea first (I have no idea why the British do this), and it now bends with the pressure. The crust is like an un-dunked biscuit, and it too has broken into pieces under stress. Each plates moves as a single , solid entity. Only where the crust is hot (say Iceland) does it become flexible enough to bend. Here, the plate boundaries become fuzzy, and bits can change allegiance and glue themselves to a different plate.
Just below the crust sits the top-most layer of the mantle. The composition here changes: the mantle is ultra-mafic, and so also differs a bit from oceanic crust. The line between the crust and mantle is called the Moho. The top-most mantle is rather cold, at least when compared to the rest of the mantle. The deeper one goes, the warmer it becomes. The bottom of the top-most mantle is defined as where the temperature is around 1600 K. The depth varies between locations: underneath the oceans it is typically at 100 km depth, while underneath continents it can be as much as 200 km. To put this into context: it would have taken the Kola project 400 years to get to this depth, at the rate which they were going!
The temperature is important because higher rocks are below this temperature and are rigid, while below this level they become deformable. The rigid top-most mantle is frozen to the crust and they move together as a single block: plates consist of crust and top-most mantle, combining regions with very different compositions. The crust and the top-most layer together are called the lithosphere.
The bottom of the lithosphere is warm enough that the rocks begin to show measurable creep. This raises the question how to measure their viscosity! The best way is to add a mountain and see how quickly it sinks. Hekla did this, but it is rare to have mountains that grow fast enough for this. The next best thing is ice. During the ice ages, ice caps grew on the continents, eventually measuring 2-3 kilometers tall and thousand of kilometers across. That is a sizable mountain, even allowing for the fact that ice weighs less than rock! The tremendous weight pushed down on the land, and it began to sink. The nice thing for geologists came afterwards. At the end of the ice age the glaciers melted very fast, much faster than even the warm lithosphere could respond. The land started to rebound at a rate set by the viscosity of the lower lithosphere. Even now, ten thousand years later, the recovery is still not complete. The Hudson Bay is an example of a large depression left by the weight of the ice, which is still recovering.
If you don’t like equations, feel free to skip the next bit. Let’s take a look immediately after the ice is gone. There is now a depression where the ice used to be. Let’s assume that this depression is completely filled with water (not unreasonable), as it is in the remnant of such a depression, the Hudson Bay. At the depth of the lower lithosphere, the pressure is equal to the weight of rocks (and water) above it. Outside the depression, the weight is that of the rocks, but inside the depression, the upper rocks are replaced by water. Water weighs less than rocks, and so there is a pressure deficit. The deficit is equal to ( ϱ – ϱw) g d where d is the depth of the water, ϱ is the density of rock, ϱw is the density of water, and g is the gravitational acceleration. The depth of the lithosphere does not come into it.
This pressure deficit gives rise to the buoyancy force: it is what makes the depression rise up. As it does so, material of the lithosphere must be flowing in to fill the gap, sucked in by the same force. It comes from beyond the depression, and so flows in over a considerable distance. But this flow suffers from the viscosity, which slows it down – rather severely because the viscosity is very high. Friction acts as a force which is pulling back. The total friction force is equal but opposite to the total buoyancy force. We know the velocity (from the speed of the rise), and the force (from the equation above), and therefore can calculate the viscosity constant which relates the velocity to the friction force. For the Hudson Bay area, it gives a value of around 1021 Pa s. Even the lower half of the lithosphere is about as stiff as glass. The flow velocity is therefore very slow, about 1 cm per year.
The value of 1021 Pa s is typical for the lower lithosphere, but values can vary a lot depending on local conditions. Values can be as high as 1025 Pa s, but much lower values are also possible if there is a local heat source. This happens for instance underneath Hekla: a normal lithosphere would have had no problem carrying its weight, but a magma chamber does not behave like a normal lithosphere. Mountains and volcanoes both tend to have lower viscosity underneath them.
Mauna Loa is a good example. This enormous mountain has depressed the local lithosphere. If you look at a map of the sea around Hawaii, you will see a trough running along the east and south side of the Big Island (which in spite of its name is a lot smaller than Australia). It is called (no prizes for guessing) the Hawaiian trough, and it is more than a kilometer below the surrounding ocean. Blame Hawaii. Sediment has filled in the trough on the other side of Hawai’i.
So if you feel the ground sink underneath your feet, and you can rule out quick sand, think lithosphere and perhaps consider the need for some weight loss to gain rebound.
Go further down and you reach the asthenosphere, the boundary layer between the lithosphere and the upper mantle. Here something else comes into play. As you continue to go further down, the temperature increases. The pressure also increases, and the higher pressure makes the melt temperature increase as well. But the temperature increases faster than the melt temperature and at the bottom of the lithosphere, the temperature becomes marginally higher than the melting temperature of the pure solid. This layer is partly melted (it is the yellow area in the figure). Go even deeper, and the temperature increase becomes much slower while the melt temperature increases further. Below 200 to 300 km everything again is solid. The whole region has a lower viscosity than the lithosphere, but the partly melted area is particularly low.
The solid lithospheric plates sit on this layer of low viscosity layer, and it acts as a lubricant. This layer allows the plates to slide. And whereas the glass-like lithosphere would only move at 1 cm/yr in response to ice ages, the asthenosphere is happy to allow faster motion. The plates manage to move at speeds as fast as 20 cm/yr. It sounds impressive – but can we put some numbers on this?
So the plates slide at their leisurely 5-20 centimeters per year over the lubricant of the asthenosphere. The asthenosphere does not take this lying down, and tries to stop the plates with friction. The friction force depends on the friction coefficient (similar to the viscosity), the weight of the overlying plate (ouch) and the velocity (miniscule). From this you can expect that plates can go faster if they are less massive (small or thin), sit on top of some serious heat (higher temperatures reduce the viscosity), or experience a stronger pull.
The hottest areas are in the southwest Pacific, and indeed Australia is moving towards there at breakneck speed. India is a better example, though. After it left Madagascar behind, it moved across the newly named Indian Ocean, initially slow, than accelerating to 20 cm/year, and later slowing down again to 5 cm/yr (still far too fast). Why the acceleration? A suggested cause is the Deccan hot spot. India encountered it in the middle of the ocean, and it provided the heat necessary to reduce the viscosity. It also melted part of the underplating, thus reducing the weight of the subcontinental plate. The friction reduced, so India sped up. After it left the hot spot behind, friction increased and India slowed down again. People move faster with a bit of heat under their feet.
How much energy is involved in moving a plate? This may surprise you. Consider a continental or oceanic plate as a square of 2000 km on the side, with a thickness of 100 km. Let’s give it a velocity of 5 cm yr-1 and a density of 3000 kg m-3. The kinetic energy of the plate is a measly 1.5 kJ. This is similar to a car driven at 10 km h-1! Archimedes said that with a long enough lever, he could move the Earth. It turns out, he could have done it with his Landrover. India hitting Asia really was like a car crash. Of course there is one basic difference: the Earth kept pulling on India during the collision, and so the energy lost in collision was constantly being replaced. It was like a car crash where the car just wouldn’t stop.
So the plates are constantly being powered. The question is now, where is the engine?
Below the asthenosphere lies more mantle. The asthenosphere ends at around 250 km deep. Below this the mantle is exclusively solid. There are two layers, the upper layer down to 670 km, and the lower mantle below that down to 2900 km where the core begins. Both consists of forms of silicates: the form changes at the 670 km boundary. Don’t underestimate these depths. The Kola project could have reached the bottom of the crust in 60 years, the mantle transition zone in 1300 years, and the bottom of the mantle in 6000 years. We are really living on a very thin shell.
The mantle consists of a variety of silicates. They are not stone: it is more like compressed sand. (Actually it is nothing like sand but ignore that.) The viscosity increases with depth, reaching around 1022 Pa s in the lower mantle.
The temperature keeps rising as you go deeper. The temperature gradient makes the mantle convective. This is the same effect you see in a pan of heating water, where you can see hexagonal cells of rising water. You can also see it in a growing thunderstorm in the atmosphere. Take a pocket of air. Heat it, and it expands. The expansion lowers the density and suddenly it is lighter than the surrounding air. It becomes buoyant and rises. As it rises, the pocket cools but so does the air around it. What happens next depends on how quickly the temperature in the atmosphere drops with height. If there is a steep temperature change, the rising pocket will continue to rise. If the gradient is shallow, it won’t.
Here is an example in the atmosphere, over the Sandia mountains in New Mexico during the summer monsoon. The convection is driven by the heating of ground by the Sun. The hot ground heats the air above it, and the temperature gradient is now large enough that it will rise – and fast. Later in the day, the ground will cool again, the temperature gradient becomes smaller and the convection stops.
There are two ways to start convection: heat the bottom or cool the top. Both happen in the mantle: heat from the core enters from below, and heat escapes at the top. The escape is mainly through the oceanic crust; the continental plates are much thicker and insulate well. This makes the top mantle warmer underneath the continents and should suppress convection there.
But it is never as simple as this. First, the continents move, and it takes a long while for the mantle to warm up. Heat transfer (‘thermal diffusion’) in the mantle is very slow and can take more than 100 million years. So the temperatures of the upper mantle relate to where the continents were some tens of millions of years ago. Second, if there are different temperatures in the upper mantle, you get sideways flow as well. The hot material at the centre of the continents will flow towards the cooler edges. That will suck up material from lower down, and so you still get an updraft started underneath the centre of large continents. But as there is no buoyancy involved, it will not go deep but instead give shallow convection.
This introduces the first big problem with mantle convection. The 670 km layer acts as an inversion layer, and it is hard for convective cells to punch through. There are two main models for mantle convection, one where the whole mantle acts in unison, and one where the upper and lower mantle convect separately. The two models are shown in the figure (reproduced from http://www.see.leeds.ac.uk/structure/dynamicearth/convection/).
There are more problems. The nice picture with a few cells and well-defined plumes and downdrafts appears optimistic. The problem lies in the Rayleigh number of the mantle. This number gives the ratio of the heat transfered by convective bubbles over the heat transfered by conduction. This number is around 107 for the mantle and that is very large. It means that the ‘plumes’ can form anywhere and be of any size, and it makes the convection highly turbulent. Because the convection is so efficient in transporting heat, the temperature gradient in the mantle is much less than that in the lithosphere. The convection warms the top and cools the bottom.
The whole mantel is vigorously convective, and left on its own the convection can become chaotic. Here is a simulation that begins to show the effect. Initially, the mantle convection is well behaved. But over time, it begins to resemble spaghetti.
This raises questions. Plates are quite large and their motion seems related to the convection below. If the convection is chaotic, the plates should be pulled in all directions simultaneously and therefore not move at all. Also, there are some clear mantle plumes such as the one below Hawai’i and under Reunion. These show that there are large scale convective cells which are well behaved and not chaotic. Such clear cases are actually quite rare. For Iceland we don’t know whether there is a deep source and for Yellowstone there is also still some doubt although its case is stronger. If the convection is caused by heat from below, why are there only few such strong plumes? If it is cooling of the oceanic plates, shouldn’t the updrafts be close to subduction zones where the surface is coolest?
The answer seems to be that the mantle convection is not caused by either. It is caused by those plates. As the oceanic plate cools over time, it becomes denser than the mantle below. Now the plate starts to sink: there is subduction. The subducting plate sinks, often at an angle of around 45 degrees. As it sinks it compresses and warms up but it remains colder than the mantle around it and therefore keeps sinking. The sinking pulls the rest of the plate with it. The drift of the plate is not driven by convective currents in the mantle: it is driven by the pull of the descending plate. This plate descends to a mantle with high viscosity, and therefore also pulls that along with it. The mantle begins to move.
The mantle is very unstable to convection. It would be filled with rising and descending bubbles of all sizes. But the descending plates bring order to the chaos. They induce a large scale pattern. Whether this pattern is shallow or deep depends on whether the plates penetrate the inversion layer at 670 km. There is strong evidence that some do, but plates can spend considerable time near the boundary. This suggests that much of the regular convection pattern of the mantle may be shallow. However, the two regions are not fully separated and some convection does penetrate the layer and combines the whole mantle.
So what is the engine for the plate drift? It is in the plates themselves: the driving force comes from the subducting part of the plate. (This topic is discussed in more detail in the old post The Dancing Earth.)
There are 43 recognized hotspot swells, where sufficient heat arrives at the surface to create a notable bulge. That includes Hawai’i where the bulge is visible on the sea floor, surrounding the depression caused by Mauna Loa. Such bulges may be associated with mantle plumes, but not all of these may be deep. A bulge indicates heat, but does not say where the heat comes from.
If we rank these spots according to mass flux, we get the following list. Here the mass flux is the amount of mantle material flowing up through the rising plume in km3 per year. I calculated it from the buoyancy flux. This is not the same as the magma production rate, as only a small fraction (of order 1%) of the material will melt. For instance, the mass flux for Hawaii is 12 km3 per year, but the magma production is only 0.25 km3 per year. The magma may also derive from material arriving near the surface over millions or tens of millions of years: flood basalts obtained their volume by tapping into a pre-loaded reservoir.
1. Hawaii 12 km3 per year
2. Tahiti 7.5
3. Marquesas Islands, 6.5
4. McDonald Seamount 5.9
5. Easter Island 5.4
6. Pitcairn Island 4.0
7. Louisville 3.2
7. San Felix 3.2
9. Samoa 2.6
9. Caroline Island 2.6
9. Juan Fernandez 2.6
12. Yellowstone 2.4
13. Iceland 2.3
13. Reunion 2.3
The numbers are not highly accurate as I have assumed that all plumes have the same temperature. For cooler plumes (with smaller temperature difference between the plume and the surrounding mantle) the numbers may be a bit underestimated. The amount of magma may also differ from this order, as it depends on what fraction of the rising plume melts, and magma may have build up over a longer time.
The plumes themselves are not large: even for Hawaii, the rising column is less than 100 km across. The bulbous heads of the plume are much larger: for Hawaii, the swell that is caused by the head is a 1000 km across.
Knowing the mass flux, we can calculate how much heat they deposit at the surface. It turns out, if we add up all 43 hot spots, the total is only about 6% of the full heat flux from the Earth. The remaining 94% comes out mainly through the oceanic plates, and comes to the surface through normal mantle convection. The plumes therefore account for a very small part of the mantle activity. The plumes are fast though. They may rise as much as 0.5 meters per year, compared to the typical speed of mantle flow of 5-10 cm/yr.
What is causing those plumes? They appear anchored to the core (because those hot spots keep more or less the same position, apart from some deflection, while the plates move over them). They must therefore be heated from below. But the core is liquid and therefore pretty good at distributing heat. There is also some heating inside the mantle by radioactivity, but this cannot be very much because if you heat a material throughout, it reduces or suppresses convection which is not what we see. So why do some areas at the bottom of the mantle have excess heat?
It has been suggested that the answer lies not in the core but in the plate tectonics. As oceanic plates subduct, they dive down and if they can get through the 670 km barrier, they’ll sink to the bottom and may form pyramid-shaped piles on the CMB. It is possible that such pyramids anchor the hot spots. They can be slightly warmer because they are denser, and gain some heat from compression. This model explains the fact that the hot spots appear fixed with respect to the core, and it links their life time to the Wilson cycle of around 200 million years. But it is far from proven. And many ‘hot spots’ are not linked to deep plumes, but to much shallower heat reservoirs, which may have been left by a past continental plate or an extinct plume. The spaghetti structure of the mantle is not conducive to develop many such plumes.
This comes back to the previous problem. If the convective pattern of the mantle is rather irregular, how does mantle convection drive plate tectonics? In the traditional model, the mantle current which is flowing underneath a plate pulls the plate along. That has difficulty to work, not only because the currents don’t easily develop but also because the friction along the asthenosphere is rather low – and this friction is needed to pull the plate. It turns out that these objections are correct. As discussed above, mantle convection does not cause plate tectonics. That should already be clear from the fact that the motion of plates near the well-known hot spots seems utterly unaffected by those plumes.
Instead, plate tectonics is largely driven by the oceanic plates themselves. As they cool, they subduct, as they subduct they change to a denser mineral and sink faster. The sinking plate pulls the rest of the plate with it. It acts on the lithosphere which is much stiffer than the asthenosphere – so the plate moves as a complete block. Don’t blame the mantle – blame the crust.
Putting in some numbers for a typical oceanic piece of crust, based on its over density and size, and assuming it descends to the 670 km layer, you’ll find that is exerts a force of a few times 1013 N/m. Now using the equation for the velocity, v = F/η, with a typical speed of 7 cm/yr, we find a viscosity of 1022 Pa s. This is quite a high viscosity. The asthenosphere has a much lower viscosity. The friction that slows down the plate comes from the most viscous layers that the plate encounters. This may also include mantle acting on the plate that is already descending.
How long does a subducting plate survive? It can be surprisingly long. An oceanic plate is around 7 km thick, and so the question is how long it takes mantle material to enter this, until it fully mixes into the plate. If the plate is stationary, that takes forever. Even helium, normally very mobile, would only have migrated around 50 cm since the Earth formed. But the plate is moving, and the shear at the edge speeds up the mixing. Now it takes 1-2 billion years before the plate is no longer there. The heat of the mantle enters a bit faster, but it can still take several hundred million years before it has the same temperature as the surrounding mantle. That doesn’t stop it sinking, because the oceanic crust is about 5% denser than the mantle (poor in Mg, rich in Al and Si).
What happens when a convective cell reaches the surface? It meets the lithosphere, and this is a rather tough nut to crack. The temperature drops a lot over the lithosphere so in principle it too could convect. In practice, it is far too hard for that. The mantle material below which is convecting is not a soft touch, with a viscosity of up to 1022 Pa s. It does its very best to make the mantle great again. The asthenosphere gives way to the onslaught but still acts as a buffer. The lithosphere has an even higher viscosity, though.
If the viscosity of the overlying layer is no more than 100 times higher than that of the incoming convective bubble, the convection just moves on, upward. If it is more than 3000 times higher, the surface repels any attempt of the bubble to move up, and it acts as a stagnant, immovable lid. In between, there is some flow but no convection at the surface, and the surface may bulge and move sideways. On Earth, this in-between situation applies, and the crust is mostly mobile. In many places, an incoming bubble will create a bulge, and this is indeed how we detected the presence of a rising plume. But continental crust, with its thick lithosphere, may respond reluctantly. The sluggish response makes the plume move outward, and the head become much wider than the narrow tail below.
Here are video examples of the two cases
First a mobile lid
and second a stagnant lid
In a stagnant lid, convection completely stops below the lithosphere, and the two regimes remain separated. In a mobile lid, there is some turn-over where lithosphere material descends into the mantle. That makes heat transfer to the surface much more efficient. In a mobile lid situation, the mantle is relatively cool. A stagnant lid insulates, and keeps the mantle warmer. As far as we know, Earth is the only planet in the solar system with a mobile lid. The mantle of Venus may be quite a bit warmer than ours.
It s not entirely clear why the Earth has plate tectonics. The plates are the driving force of convection, heat transfer, mountain building, etc. But the Earth could quite happily have had a stagnant lid. A major question in Earth sciences is when plate tectonics first began. I would put it quite early, because of the change in diamond composition which happened 3 billion years ago, which seems to require oceanic plates to go down and mix into the upper mantle. But others have put it more recently, or argued that plate tectonics has been intermittent.
The tip of the iceberg of mantle convection are the volcanoes. They get their energy from the mantle but the melt from the lithosphere. Without plate tectonics, there would still be volcanoes – Venus and Mars both have them. But they might be quite different from ours.
The Earth still has many mysteries, and hides many secrets. Kola has barely scratched the surface of the Earth’s exoskeleton. Underneath is darkness. Our thin shell depends on the boiling rocks below. Kola has long been abandoned and its buildings are ruins. But the wish to understand more of the world below us remains. Perhaps one day we will drill into the mantle.
Albert, June 2019