Subduction is not the end

Posted on 9 November, 2014 by Metageologist

Subduction is just the beginning. Stuck on the surface of the earth as we are, it’s easy to think that when oceanic lithosphere1 is destroyed when it vanishes into the mantle. But this is wrong. The more we manage to peer into the earth’s depths, the more clearly we see that subducted oceanic lithosphere is still down there. It’s arrival into the deep earth influences many things and sets of changes that in turn affect the surface.

Our growing understanding of what happens to oceanic lithosphere when it reaches the deep earth comes from the integration of a vast repertoire of scientific approaches. Physics, chemistry, mathematical modelling, high-pressure laboratory experiments, tiny grains in diamonds – all these things have something to tell us about the deep earth.

As in the deep oceans, so in the deep earth. We now know that both places are extremely varied environments, warped by extreme pressures, full of the weird and the exotic and some surprising relics from the past. Both are hard (or impossible) to visit, yet they still have influence over surface conditions.

A journey into the deep

This is the first of a series of posts on the deep earth. There’s a great mass of fascinating recent science out there that deserves to be better know. As a taster, let me tell you about lovely little Nature paper from 2005 that picks out the themes I hope to trace through future posts: how much of the deep earth is still mysterious, how we know what we know, the billion-year timescales and how the surface and depths are intimately linked.

In the paper David Dobson and John Brodholt (both, then as now, at University College, London) speculate that some distinctive parts of the deepest mantle are formed from subducted banded-iron formation.

Folded banded iron formation. Photo was not taken at the core-mantle boundary. Image from Wikipedia.

Seismic studies (tracing the shakings caused by earthquakes) have identified parts of the lowest mantle where earthquake waves pass through over 10% slower than expected. This means that these areas, known here as ultralow-velocity zones (ULVZs), must be in some way different – either they are made of different material or they are are at a different temperature to their surroundings.

Nobody knows what the ULVZs are made of, but our authors put the case that they contain large volumes of banded-iron-formation (BIF). Between 2.8 and 1.8 billion years ago photosynthetic organisms (probably bacteria) profoundly changed our planet’s atmosphere by producing vast quantities of Oxygen. One consequence was that ferric iron, dissolved in the ocean, bound with the Oxygen ‘waste’ and was precipitated out as solid minerals of magnetite and haematite. This process created vast volumes of marine sediments rich in iron. These banded iron formation deposits are found in rocks of this age from around the world.

Assuming this material was subducted what would happen and could it account for the properties of the ULVZs at the bottom of the mantle? Tracing through the required steps, our authors show that BIF material would be dense enough to sink to the base of the mantle, able to separate out from the more normal material in the subducted plate and would not dissolve into the underlying iron-rich core. If these steps had occurred, then the material would match the measurable properties of the ULVZs.

Just because something is plausible, doesn’t make it true of course. Proving this link between ULVZs and BIFs definitively may never be possible. But one further clue exists: having an iron rich layer close to the edge of the core might help explain patterns of change in the length of the day we surface-dweller can observe.

The earth’s nutations are daily variations in its rotation. They are caused by the pull of the earth, sun and other bodies, but are also influenced by the degree to which the core and mantle spin independently or are coupled together. The outer core is liquid and the mantle solid, so they would be able to spin independently, but studies of nutations suggest there is some coupling – transfer of momentum – between them. If ULVZs are formed of BIFs and so very rich in iron, they would interact with the earth’s magnetic field causing electromagnetic coupling in a way that matches the observations.

It’s a mind-expanding idea. Sediments formed billions of years ago in a now alien atmosphere sit thousands of kilometres under our feet, subtly modulating the length of the day.

Deep cycles

When listening to a classical orchestra, most often we are paying attention to the high to middling frequency sounds – the violins, flutes and so on. The full experience – a live performance – is vastly enriched by the deepest, lowest frequency instruments. A full desk of double basses, or some bass clarinets make the air itself throb, producing a more physical, visceral and emotional experience2.

Our experience of living on this planet is enriched by our understanding of its cycles of change. The most frequent are most apparent: the year’s seasons; the carbon cycle; Milankovitch cycles that bring ice to sculpt the landscape. Subduction is one of the deepest, the slowest of them all – linking the familiar surface with the mysterious depths, it is the fundamental frequency in the orchestra of the earth.

References

The Nature paper is available here.

Dobson D.P. (2005). Subducted banded iron formations as a source of ultralow-velocity zones at the core–mantle boundary, Nature, 434 (7031) 371-374. DOI: http://dx.doi.org/10.1038/nature03430

Metamorphic petrology: under pressure and getting stressed?

Posted on 2 August, 2014 by Metageologist

High pressure (HP) terranes are areas containing eclogites and other eclogite-facies rocks found within many mountains belts, including the Himalaya and the Alps. HP rocks were metamorphosed at extreme pressures, up to 3 or even 4 billion Pascals (or GPa. Atmospheric pressure is 0.0001 GPa). Based on the assumption that metamorphic pressure relates to depth of burial, these rocks have been to depths below the base of the crust. Explaining how to bury rocks so deeply, and then bring them back again, is a tricky problem.

Two parallel threads of research are challenging the assumption that high metamorphic pressures relate simply to depth of burial. Both seek to show that metamorphic reactions, and the patterns of minerals that they form, are also influenced by the squeezing and squashing rocks receive as they flow deep within the earth.

High pressure rocks looking moody and gorgeous. Photo of the Internal zones of the Alps from John Wheeler.

A little theory (please, don’t get stressed)

Metamorphic petrology is the art and Science of calculating the conditions under which metamorphic minerals form – I’ve written extensively about it already 1. It has its basis in an understanding of the thermodynamics of the reactions that form minerals, which depend (among other things) on the temperature and pressure at the time. The lithostatic pressure that affected the rock is assumed to be caused by the weight of the column of rock overhead, following Pascal’s law2. With some assumptions as to the density of that rock, pressure can be converted into depth.

Earth scientists who study the structure of deeply buried rocks look instead at the patterns that the minerals form: fabrics, lineations, folds and the like. They have a different way of looking at the way rocks are squashed. Theories of rock deformation talk about stress, often visualised as arrows in 3 dimensions. If the stress is isotropic – equal in all three dimensions – then it is conceptually the same as lithostatic pressure. In contrast, differential stress is where the arrows are different sizes. Differential stress drives deformation – the rocks change shape.

Time for an analogy. Lithostatic pressure is like water pressure. Deep hot rocks flow like a fluid (slowly) and so the stress is equal in all directions. Rocks keep the same shape, but are put under tremendous pressure. It’s the same as putting a styrofoam cup into deep water.

Sytrofoam cup crushed at 600m ocean depth. Image from Gina Trapani under Creative Commons.

Differential stress is like putting the cup between the grabbers of the submersible. Squeezing in only one direction will change the shape of the cup.

Now we’re ready to look at the two challenges to the depth-pressure connection.

Challenge 1 – High levels of differential stress exist in the crust

Metamorphic petrologists who argue that high pressures are caused by deep burial believe that the effects of differential stress are unimportant. These rocks are usually extremely deformed, but they were hot and soft – by flowing easily they prevented high differential stresses from building up. In a similar way, as every toddler learns, you can’t squeeze jelly hard with your hands, because it just flows out of your fist.

Some scientists, with an interest in the European Alps, disagree. Neil Mancktelow argues that the effects of differential stress (he uses the ~~basically equivalent~~ similar term ‘tectonic overpressure’3 ) can be dramatic. Mathematical modelling of conditions within a confined channel (like a subduction zone) gives ‘overpressure’ of “perhaps even a few GPa”. Rocks that formed under these conditions would yield high pressure minerals but may not have been buried very deep.

At this years EGU meeting Stefan Markus Schmalholz, Yuri Podladchikov, and Sergei Medvedev used computer modelling of the Alpine orogeny, and other arguments to suggest that Alpine high-pressure eclogites need not have been deeply buried, but instead their distinctive minerals formed under conditions of tectonic overpressure.

Folded layers from eclogite facies rocks in Norway. Photo from John Wheeler

Challenge 2 – John Wheeler’s recent paper in Geology

Computer models are extremely useful, but only as good as the assumptions made in them. Alone they will always have their critics. John Wheeler, a professor at Liverpool University has fingers in many pies: metamorphism; structural geology; field-based studies; laboratory work… He takes a different approach to also puts the assumption that we can apply Pascal’s law under intense pressure 4.

In a recent open source paper in Geology he combines 2 pieces of theory. The first is from thermodynamics as used in metamorphic petrology. The second is an equation relating stress to the phenomena of pressure solution (that can form cleavage in slaty rocks). Both are concerned with the movement of atoms to grow new minerals and neither is controversial. He converts both into terms of chemical potential and combines them to link differential stress to standard metamorphic reactions.

Applying uncontroversial values for differential stress (e.g. 50 MPa, or 1/40th of the levels Mancktelow proposes) to a standard metamorphic reaction he shows that they shift by up to 500MPa – equivalent to 15km of lithostatic pressure.

This is an extremely dramatic result from a provocative paper, as John Wheeler himself acknowledges. Metamorphic rocks are almost always deformed, sometimes dramatically so. If both approaches are correct, then putting differential stresses of Manckletow levels into John Wheeler’s equations suggests any estimates of depth of metamorphism are open to challenge. Maybe eclogites never left the crust after all?

metagabbro deformed and recrystallizing to new minerals at the same time (from Alps).

Metagabbro deformed and recrystallizing to new minerals at the same time (sample from Alps image from John Wheeler).

Where are we now?

John Wheeler expects some “turbulent interactions in the next few years”. I’m sure there are metamorphic petrologists writing their replies to his paper right now. But assuming they can’t find some fundamental flaw he hasn’t spotted (extremely unlikely, I’d say), metamorphic petrology is facing a very big challenge.

This seems like bad news. Much work on metamorphic petrology is put to work refining tectonic models by building P-T-t paths that track metamorphic rocks as they are buried and return to the surface. The error bars on these estimates were big enough already – now a entire literature of estimates that ignore differential stress are thrown into question.

But let’s think positively. Might there be ways to disentangle the effects of lithostatic pressure and differential stress? Might there be ways to get even more information out of deformed metamorphic rocks? John Wheeler certainly thinks so and he aims to get there by integrating detailed studies of rock samples with laboratory experiments.

Big advances in Science often give us new ways to understand evidence that previously didn’t make sense. Studies of metamorphism from the classic locality of the Scottish Highlands (e.g. Viete et al 2011) have noted that the highest grades of metamorphism occur within shear zones. They tried to explain this in terms of the flow of hot fluids, but maybe the answer is simpler: stressing rocks really does cause them to grow different suites of metamorphic minerals.

References:

Mancktelow N.S. (2008). Tectonic pressure: Theoretical concepts and modelled examples, Lithos, 103 (1-2) 149-177. DOI: http://dx.doi.org/10.1016/j.lithos.2007.09.013

Wheeler J. (2014). Dramatic effects of stress on metamorphic reactions, Geology, DOI: http://dx.doi.org/10.1130/g35718.1

Viete D.R., G. S. Lister & I. R. Stenhouse (2011). The nature and origin of the Barrovian metamorphism, Scotland: diffusion length scales in garnet and inferred thermal time scales, Journal of the Geological Society, 168 (1) 115-132. DOI: http://dx.doi.org/10.1144/0016-76492009-087

Six amazing facts about what’s under your feet

Posted on 11 June, 2014 by Metageologist

Just 100s km away from you are right now there is a place where rocks can flow, where once-living matter is turned in jewels, from where deadly plumes once killed nearly all life on earth. We can never visit this place – even though it’s right under you.

1. Human beings will never reach the deep earth

We’ve been to the moon and Mars is almost in our reach but we are never going to the deep earth. The deepest hole ever drilled got just over 12km below the surface – that’s a paltry 0.2% of the 6380km to the earth’s centre. It gets harder to drill the further you go. The rock was already 180°C when they stopped drilling and it gets hotter as you go down, getting as high as maybe 6000°C (as hot as the surface of the sun).

We could *maybe* send a probe down there. In a paper in Nature, David Stevenson came up with the most plausible plan to date. It involves making a crack in the earth (with a nuclear explosion) and filling it with 100,000 tonnes of liquid iron and a small probe. The probe (might) then sink down to the edge of the earth’s core. No-one is planning to try this out at the moment, but it would make for an interesting Kickstarter project.

There is a lot of heat in the earth. Consider that scene in Star Wars when the Millennium Falcon comes out of hyperspace and finds just spinning rocks where Alderaan used to be. If a Death Star destroyed earth you wouldn’t get an asteroid belt immediately afterwards, instead you’d get a extremely hot cloud of liquid, or even vaporised rock. Even Han Solo would have trouble dodging that.

2. A spinning ball of molten metal

The earth’s structure is a bit like that of a peach. There’s a thin skin, a thick juicy layer and a core that’s surprisingly large and totally different from the stuff above it.

We are the thin layer of mould on the surface of our giant peach. The skin is the earth’s crust (that we can’t even drill through). The bulk of the earth is called the mantle and its made up of a dark heavy rock called peridotite. We can never get to the earth’s core, but we know (from indirect observations and by analogy with meteorites) that it’s made of iron and nickel – totally different from the silica-rich rock above. The outer layer of the core is molten, but at the very centre of the earth its solid, made out of giant crystals of iron and nickel.

A giant sphere full of 15 tons of liquid sodium, used to simulate the earth’s core. Source.

The spinning liquid outer core produces the magnetic field that twists your compass and tells dogs which direction to pee in. One way to understand the core better is to simulate it in the lab, by creating a giant sphere containing spinning liquid sodium. It’s also a good way for scientists to look a bit more like Bond villains standing next to their super-weapon.

3. You can’t handle the pressure!

It seems counter-intuitive. The earth gets hotter the deeper you go, yet the outer core is molten and the inner solid. Normally things melt when they get hotter, so why is that?

Pressure.

We’re familiar with the fact that pressure increases in the deep sea, as there is a lot of water above, pushing down. It’s the same in the earth, only rock is heavier and there are thousands of kilometres above, pushing down.

The pressures get so intense that the only way to reproduce them in the lab is to take an tiny unfortunate sample of rock, put it between two diamonds and squeeeeze. To reach the required temperatures, you also fire lasers at it, through the diamonds. Occasionally the diamonds can’t handle the pressure and they explode, sometimes popping loudly or emitting a flash of light.

Diamond damaged by laser fire. Image from Wendy Panero.

Diamond damaged by laser fire in a diamond anvil. Image from Wendy Panero.

Pile of diamond dust after ‘blowout’ of the anvil. Source.

Under high pressure, it’s easier for materials to be solid rather than liquid, as the atoms prefer to be tightly packed together. The metal in the earth’s core is solid at the centre because the pressure is higher there.

4. Solid rock that flows

We know from listening to earthquake waves that pass through it that the earth’s mantle is solid. It’s incredibly hot, but the pressure means that – give or take a few percent in places – there is no liquid rock down there.

Knowing this held back acceptance of the idea that continents move. The geological evidence was known, but it was thought that continents couldn’t move because they were attached to the mantle and ‘solid rock can’t flow’. Only it can.

Hit a piece of the mantle with a hammer and it will break (or break your hammer – it’s tough stuff). But heat it up and push it the same way for millions of years and it will flow. It’s made of crystals, endless ranks of atoms lined up in rigid patterns. Tiny gaps in these patterns allow atoms to slip past each other and slightly change the shape of the crystal. Countless of these tiny steps, in myriad of crystals over millions of years allows the earth’s mantle to flow, convecting in majestic patterns driven by heat leaving the earth.

Patterns of plate tectonics on the surface are driven by this flow. The most dramatic example being subduction, where crust sinks down into the mantle, sometimes sinking deep down to the edge of the core.

Cut-away diagram showing modern convection from computer modelling by Fabio Crameri. Red is rising plumes, blue sinking plates.

Cut-away diagram showing convection in the earth. Red is rising plumes, blue and yellow sinking plates. Image generated from computer modelling by Mario Crameri.

5. Death from below

The link between meteorite impacts and mass extinctions is well known – the image of a dinosaur looking up at an incoming fireball is almost a cliche. However some scientists think they should be looking down, and that the deep earth has caused more extinctions than impacts have.

The event that did for the dinosaurs, at the end of the Cretaceous (66 million years ago) is just the most glamorous of many mass extinction events. The biggest was at the end of the Permian (252 million years) – up to 96% of marine species became extinct. There is no good evidence for a meteorite impact at the end of the Permian, but there is a huge pile of lava, covering much of Siberia. This was caused by a massive mantle plume, a column of hot rock that started at the base of mantle.

To kill nearly anything you need to foul the sky and poison the seas. Volcanoes give off noxious gases which in normal amounts don’t cause problems. But covering 2 million square kilometres of land in lava is not normal. However it was done – by pumping out massive quantities of ash or by producing carbon dioxide by burning nearby coal deposits (or some other way) – the link between mantle plumes, lava and death seems pretty certain.

The end-Cretaceous extinction saw a meteorite impact, but it also saw a massive outpouring of lava from the mantle, this time in India, at exactly the same time. There are those who argue that the death of the dinosaurs is as much due to the deep earth as it is a rock from space.

A huge outpouring of lava. From Wikipedia

A huge outpouring of lava. Image from Wikipedia

6. Visitors from the deep

A lot of what we know about the deep earth comes from indirect measurements, like when a doctor uses a stethoscope or MRI scanner to ‘look’ inside your body. But sometimes to know what’s really going on you need a direct sample from deep inside – a biopsy. To do this for the heavenly body we sit on – in other words to perform a geopsy1 – you need a special kind of volcanic rock. When some molten rock rises from the mantle, it contains crystals that were formed at depth, but carried up in it. The most interesting, most glamorous, most beautiful, and most valuable of these exotic visitors are diamonds.

I could go on about diamonds for a long time (in fact, I already have) but forget that they can be made billions of years old, and may contain traces of an ancient oxygen-free atmosphere, instead let’s focus on the fact that some diamonds contain carbon that was once part of a living thing.

When carbon has passed through a process of photosynthesis, its isotopes have a distinctive pattern . Finding this ‘light carbon’ in diamonds allows us to tell an amazing story. Something was once alive2, died and formed black mud on the ocean floor. This was then forced into the mantle where it sank deeper and deeper. At some point the carbon started flowing up (as part of some sort of fluid) and got pulled into a growing diamond which then got caught up in some fizzy magma that, within hours or days, pushed up to near the earth’s surface, where humans could find it and marvel.

Human beings can never reach the deep earth. Alive. The carbon in our bodies might though. Just arrange to die and get buried in the right bit of the sea bed and part of you might one day end up in the deep earth.

References

What to know more? Don’t believe these amazing facts are true? Either way, read these links for more details.

The idea of how to get a probe into the deep Earth come from a pukka scientific paper.

The Death Star isn’t really real (honest), but scientists model the liquid/gas rock that would happen if the earth was destroyed when they model a collision with another planet. Something that may have happened long ago to create the moon.

If you want to see that huge sphere containing liquid sodium in action, see it here.

My information about exploding diamonds came from Mary Panero, who is on Twitter @mineraltoPlanet

All you ever wanted to know about the Siberian Traps and the end-Permian event can be found on a great Leicester University site.

Scientists who believe mantle plumes rather than the meteorite killed the dinosaurs point to evidence from India. The lava (known as the Deccan Traps) is seen to happen at the same time as the extinctions, but the layer of Iridium enrichment comes after the extinction. More details here.

More more information about diamonds, there’s a useful recent review of the science.

A world without subduction

Posted on 6 May, 2014 by Metageologist

The greatest achievement of the generation of Earth Scientists now retiring is the concept of plate tectonics. The insight that the earth’s surface is made up of rigid plates that move has shed light on all aspects of Earth Science, from palaeontology to geophysics to the study of ancient climates. What’s less well known is that the way the plates interact has changed over time. Key plate tectonic features such as subduction, didn’t happen for large periods of earth history.

Cut-away diagram showing modern convection from computer modelling by Fabio Crameri. White is hot rising plumes, black cold sinking plates.

Cut-away diagram showing modern convection from computer modelling. White is hot rising plumes, black cold sinking plates . Image used with permission of Fabio Crameri.

Earth scientists have a pretty good idea of the details of how modern plate tectonics works. This has required the integration of indirect observation of modern subduction zones (using geophysical techniques) with direct study of rocks that have been inside subduction zones (such as eclogites) plus the creation of subduction zones ‘in silico’ (with computer modelling).

Of these 3 methods of study, only the first (direct observation) cannot be used on the ancient earth. So what do the rocks and computer models tell us?

Old rocks are odd

We’ve known for a while that ancient rocks (Eoarchean–Mesoarchean, older than 2.5 Ga1) are very different from modern ones. Often they consist of greenstone belts – containing an unusual lava called komatiite – surrounded by large areas of granitic gneiss. The pattern of metamorphism in these rocks shows high temperatures, even at shallow depths.

The chemistry of the igneous rocks tells a similar tale. Komatiites only melt at temperatures of around 1600°C – 400 degrees hotter than modern basalt lava. Granitic rocks have tonalite–trondhjemite–granodiorite compositions and are thought to have formed from direct melting of basaltic rock – unlike granites formed above subduction zones today.

Rocks characteristic of modern subduction – blueschists and eclogites – are not found in rocks this age. There is a pretty good consensus, based on field evidence and model modelling, that subduction did not happen in the early earth. The earth’s mantle was much hotter and more heat was flowing up through the crust. Hot rocks are weak rocks – forcing a slab of rock into the deep mantle requires it to be cold and hard. Hotter rocks act not as rigid slabs but as soft blobs.

Computer modelling confirms the importance of temperature, both of the crust and the underlying mantle. Models are our best hope of understanding what a hot planet without subduction looked like. More like a bubbling pan of porridge perhaps, with tectonics dominated by hot upwelling plumes and lithospheric delamination, with blobs dripping-off down again. Some studies of mantle mixing suggest a ‘stagnant-lid’ model where the earth’s surface layer doesn’t move at all.

Subduction starts

At some point in time between 3.2–2.5 Ga, subduction started. The planet had cooled enough that a lithospheric plate stayed rigid enough to sink down into the mantle. Evidence for this is found in ‘paired metamorphic belts’. Rocks within the subduction zone remain cool at depth (as they are pushed down before they can get as hot as the surrounding rocks) and form eclogites or high-pressure granulite rocks. Rocks nearby in the overriding plate are much hotter and enjoyed granulite–ultrahigh temperature metamorphism.

Mathematical modelling of the earth suggests subduction started because the earth cooled below a particular threshold. As an explanation, this is a little dull. Much more excitingly, coverage of a recent paper suggests massive meteorite impacts about 3.2 Ga could have broken up the surface and somehow kickstarted plate tectonics. Scientists who study impacts are always really keen to use them to explain events or features on earth, whereas other scientists are sceptical, preferring to explain them via things that they study. We’ll need to wait to see who is right about this one (but my money is on the dull explanation).

Cut-away diagram showing modern convection from computer modelling. Red is hot rising plumes, blue cold sinking plates. Image used with permission of Fabio Crameri.

Subduction as a cure for boredom

When subduction first started, mantle temperatures were still 175–250 °C hotter than today. Hotter, softer slabs are more likely to break off, perhaps making subduction something that stopped and started.

Blueschists and low-temperature eclogites, high-pressure & low-temperature rocks that are found in modern subduction zones are not found until the the Neoproterozoic at 600–800 Ma. Mantle temperatures by then were less than 100 °C greater than today – this marks the wide spread development of modern-style (cold) subduction on Earth. Cold slabs of oceanic lithosphere break-off deep, allowing large volumes of dense oceanic crust to pull continental lithosphere down, creating the first ultra-high pressure metamorphic complexes.

The Neoproterozoic is the end of what is known as the ‘boring billion’ – a time of tedious environmental and evolutionary stability. A recent open acess paper in Geology suggests a link between the exciting changes that followed (glaciations! Cambrian explosion!) and the onset of subduction. The boring billion was stable in part because most continental crust was part of a supercontinent called Rodinia. The paper argues that the disruptive effects of the onset of cold subduction broke Rodinia apart, setting off a chain of events that transformed the world.

—–

The early earth was a very different planet. Understanding it better informs the general subject of planetology. As we get more and more data about other planets (both within and beyond our solar system) it’s natural to speculate on their tectonic activity. Why does Venus not have subduction? Does subduction here exist because of life and its role in moderating climate and creating the earth’s oceans? Ancient rocks and computer models may help us answer these questions as much as probes and telescopes.

REFERENCES

Brown M. (2014). The contribution of metamorphic petrology to understanding lithosphere evolution and geodynamics, Geoscience Frontiers, DOI: 10.1016/j.gsf.2014.02.005
Available here

Cawood P.A. & Hawkesworth C.J. Earth’s middle age, Geology, DOI: 10.1130/G35402.1
Available here

Gerya T. (2014). Precambrian geodynamics: Concepts and models, Gondwana Research, 25 (2) 442-463. DOI: 10.1016/j.gr.2012.11.008
Available here