Source: https://wileyearthpages.wordpress.com/tag/plate-tectonics/
Timestamp: 2019-04-22 10:59:38+00:00

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As DNA is to tracing human evolution and migration, so various isotope systems are to the evolution of the Earth. One of the most fruitful is the samarium-neodymium (Sm-Nd) system. The decay of 147Sm to 143Nd is used in dating rocks across the full range of Earth history, given coeval rocks with a suitable range of Sm/Nd ratios, because the decay has a long half life (1.06 x 1011 years). However, samarium has another radioactive isotope 147Sm with a half life that is a thousand times shorter (1.06 x 108 years). So it remains only as a minute proportion of the total Sm in rocks, most having decayed since it was formed in a pre-Solar System supernova. But its daughter isotope 142Nd is present in easily measurable quantities, having accumulated from 147Sm decay over the first few hundred million years of Earth’s history; i.e. during the Hadean and earliest Archaean Eons. It is this fact that allows geochemists to get an indirect ‘handle’ on events that took place in the Earth’s earliest, largely vanished history. The principle behind this approach is that when an ancient rock undergoes partial melting to produce a younger magma the rock that crystallizes from it inherits the relative proportions of Nd isotopes of its source and thereby carries a record of the earlier history.
The eastern shore of Hudson Bay in Canada hosts the oldest tangible geology known, in form of some metamorphosed basaltic rocks dated at 4200 Ma old known as the Nuvvuagittuq Greenstone Belt – the only known Hadean rocks. They occur in a tiny (20 km2) patch associated with gneisses of tonalite-trondjhemits-granodiorite composition that are dated between 3760 and 3350 Ma. Engulfing both are younger (2800 to 2500 Ma) Archaean plutonic igneous rocks of felsic composition. Jonathan O’Neil and Richard Carlson of the University of Ottawa, Canada and the Carnegie Institution for Science, Washington DC, USA respectively, measured proportions of Nd isotopes in both sets of felsic igneous rocks (O’Neil, J. & Carlson, R.W. 2017. Building Archean cratons from Hadean mafic crust. Science, v. 355, p. 1199-1202; doi:10.1126/science.aah3823).
The oldest gneisses contained relative proportions of 142Nd commensurate with them having been formed by partial melting of the Hadean mafic rocks about a few hundred million years after they had been erupted to form the oldest known crust; no surprise there. However, the dominant components of the local continental crust that are about a billion years younger also contain about the same relative proportions of 142Nd. A reasonable conclusion is that the Archaean continental crust of NE Canada formed by repeated melting of mafic crust of Hadean age over a period of 1.5 billion years. The modern Earth continually replenishes its oceanic crust over about 200 Ma due to plate tectonics. During the Archaean mantle dynamics would have been driven faster by much higher internal heat production. Had this involved simply faster plate tectonics the outermost skin of mafic crust would have been resorbed into the mantle even faster. By the end of the Archaean (2500 Ma) barely any Hadean crust should have been available to produce felsic magmas. But clearly at least some did linger, adding more weight to the idea that plate tectonics did not operate during the Hadean and Archaean Eons. See Formation of continents without subduction below.
As computing power and speed have grown ever more sophisticated models of dynamic phenomena have emerged, particularly those that focus on meteorology and climatology. Weather and climate models apply to the thin spherical shell that constitutes Earth’s atmosphere. They consider incoming solar radiation and longer wavelength thermal radiation emitted by the surface sources and sinks of available power, linked to the convective circulation of energy and matter, most importantly water as gas, aerosols, liquid and ice in atmosphere and oceans. Such general circulation models depend on immensely complex equations that relate to the motions of viscous media on a rotating sphere, modulated by other aspects of the outermost Earth: the absorptive and reflective properties of the materials from which it is composed – air, rocks, soils, vegetation, water in liquid, solid and gaseous forms; different means whereby energy is shifted – speeds of currents and wind, adiabatic heating and cooling, latent heat, specific heat capacity of materials and more still. The models also have to take into account the complex forms taken by circulation on account of Coriolis’ Effect, density variations in air and oceans, and the topography of land and ocean floor. The phrase ‘and much more besides’ isn’t really adequate for such an enormous turmoil, for the whole caboodle has chaotic tendencies in time as well as 3-D space. The fact that such modelling does enable weather forecasting that we can believe together with meaningful forward and backward ‘snapshots’ of overall climate depends on increasing amounts of empirical data about what is happening, where and when. Models of this kind are also increasingly able to address issues of why such and such outcomes occur, an important example being the teleconnections between major weather events around the globe and phenomena such as the El Nino-Southern Oscillation – the periodic fluctuation of ocean movements, winds and sea-surface temperatures over the tropical eastern Pacific Ocean.
The Earth’s lithosphere and deeper mantle in essence present much the same challenge to modellers. Silicate materials circulate convectively in a thick spherical shell so that radiogenic heat and some from core formation can escape to keep the planet in thermal balance. There are differences, the obvious ones being sheer scale and a vastly more sluggish pace, but most important are the interactions between materials with very different viscosities; the ability of the deep mantle to move by plastic deformation while the lithosphere moves as rigid, brittle plates. For geophysicists interested in modelling there are other differences; information that bears on the system is orders of magnitude less, its precision is much poorer and all of it is based on measurement of proxies. For instance, information on temperature comes from variations in seismic wave speed given by analysis of arrival times at surface observatories of different kinds of wave emitted by individual earthquakes. That is, from seismic tomography, itself a product of immensely complex computation. Temptation by computing power and the basic equations of fluid dynamics, however, has proved hard to resist and the first results of a general circulation model for the solid Earth have emerged (Mallard, C. et al. 2016. Subduction controls the distribution and fragmentation of Earth’s tectonic plates. Nature, v. 535, p. 140-143).
As the title suggests, the authors’ main objective was understanding what controls the variety of lithospheric tectonic plates, particularly how strain becomes localised at plate boundaries. They used a circulation model for an idealised planet and examined several levels of a plastic limit at which the rigidity of the lithosphere drops to localise strain. At low levels the lithosphere develops many plate boundaries, and as the plastic limit increases so the lithosphere ends up with increasingly fewer plates and eventually a rigid ‘lid’. The modelling also identified divergent and convergent margins, i.e. mid-ocean ridges and subduction zones. The splitting in two of a single plate must form two triple junctions, whose type is defined by the kinds of plate boundary that meet: ridges; subduction zones; transform faults. Both the Earth and the models show significantly more triple junctions associated with subduction than with extension, despite the fact that ridges extend further than do subduction zones. And these trench-associated triple junctions are mainly those dividing smaller plates. This suggests that it is subduction that focuses fragmentation of the lithosphere, and the degree of fragmentation is controlled by the lithosphere’s strength. There is probably a feedback between mantle convection and lithosphere strength, suggesting that an earlier, hotter Earth had more plates but operated with fewer, larger plates as it cooled to the present. But that idea is not new at all, although the modelling gives support to what was once mere conjecture.
So, when did plate tectonics start up?
Tiny, 4.4 billion year old zircon grains extracted from much younger sandstones in Western Australia are the oldest known relics of the Earth system. But they don’t say much about early tectonic processes. For that, substantial exposures of rock are needed, of which the undisputedly oldest are the Acasta gneisses 300 km north of Yellowknife in Canada’s North West Territories, which have an age of slightly more than 4 Ga. The ‘world’s oldest rock’ has been something of a grail for geologists and isotope geochemists who have combed the ancient Archaean cratons for 5 decades. But since the discovery of metasediments with an age of 3.8 Ga in West Greenland during the 1970s they haven’t made much headway into the huge time gap between Earth’s accretion at 4.54 Ga and the oldest known rocks (the Hadean Eon).
There have been more vibrant research themes about the Archaean Earth system, specifically the issue of when our planet settled into its modern plate tectonic phase A sprinkling of work on reconstructing the deep structural framework of Archaean relics has convinced some that opposed motion of rigid, brittle plates was responsible for their geological architecture, whereas others have claimed signs of a more plastic and chaotic kind of deformation of the outer Earth. More effort has been devoted to using the geochemistry of all the dominant rocks found in the ancient cratons, seeking similarities with and differences from those of more recent vintage. There can be little doubt that the earliest processes did form crust whose density prevented or delayed it from being absorbed into the mantle. Even the 4.4 Ga zircons probably crystallized from magma that was felsic in composition. Once trapped by buoyancy at the surface and subsequently wrapped around by similarly low density materials continental crust formed as a more or less permanent rider on the Earth’s deeper dynamics. But did it all form by the same kinds of process that we know to be operating today?
Plate tectonics involves the perpetual creation of rigid slabs of basalt-capped oceanic lithosphere at oceanic rift systems and their motions and interactions, including those with continental crust. Ocean floor cools as it ages and becomes hydrated by seawater that enters it. The bulk of it is destined eventually to oppose, head-to-head, the motions of other such plates and to deform in some way. The main driving force for global tectonics begins when an old, cold plate does deform, breaks, bends and drives downwards. Increasing pressure on its cold, wet basaltic top transforms it into a denser form: from a wet basaltic mineralogy (feldspar+pyroxene+amphibole) to one consisting of anhydrous pyroxene and garnet (eclogite) from which watery fluid is expelled upwards. Eclogite’s density exceeds that of mantle peridotite and compels the whole slab of oceanic lithosphere to sink or subduct into the mantle, dragging the younger parts with it. This gravity-induced ‘slab pull’ sustains the sum total of all tectonic motion. The water rising from it induces the wedge of upper mantle above to melt partially, the resulting magma evolves to produce new felsic crust in island arcs whose destiny is to be plastered on to and enlarge older continental masses.
Relics of eclogites and other high-pressure, low-temperature versions of hydrated basalts incorporated into continents bear direct and unchallengeable witness to plate tectonics having operated back to about 800 Ma ago. Before that, evidence for plate tectonics is circumstantial and in need of special pleading. Adversarial to-ing and fro-ing seems to be perpetual, between geoscientists who see no reason to doubt that Earth has always behaved in this general fashion and others who see room for very different scenarios in the distant past. The non-Huttonian tendency suggests an early, more ductile phase when greater radioactive heat production in the mantle produced oceanic crust so fast that when it interacted with other slabs it was hot enough to resist metamorphic densification wherever it was forced down. Faster production of magma by the mantle without slab-pull could have produced a variety of ‘recycling’ turnover mechanisms that were not plate-tectonic.
One thing that geochemists have discovered is that the composition of Archaean continental crust is very different from that produced in later times. In 1985 Ross Taylor and Scott McLennan, then of the Australian National University, hit on the idea of using shales of different ages as proxies for the preceding continental crust from which they had been derived by long erosion. Archaean and younger shales differed in such a way that suggests that after 2.5 Ga (the end of the Archaean) vast amounts of feldspar were extracted from the continent-forming magmas. This left the later Precambrian and Phanerozoic upper crust depleted in the rare-earth element europium, which ended up in a mafic, feldspar-rich lower crust. On the other hand, no such mass fractionation had left such a signature before 2.5 Ga. Another ANU geochemist, now at the University of Maryland, Roberta Rudnick has subsequently carried this approach further, culminating in a recent paper (Tang, M., Chen, K and Rudnick, R.L. 2016. Archean upper crust transition from mafic to felsic marks the onset of plate tectonics. Science, v. 351, p. 372-375). This uses nickel, chromium and zinc concentrations in ancient igneous and sedimentary rocks to track the contribution of magnesium (the ‘ma’ in ‘mafic’) to the early continents. The authors found that between 3.0 to 2.5 Ga continental additions shifted from a dominant more mafic composition to one similar to that of later times by the end of the Archaean. Moreover, this accompanied a fivefold increase in the pace of continental growth. Such a spurt has long been suspected and widely suggested to mark to start of true plate tectonics: but an hypothesis bereft of evidence.
A better clue, in my opinion, came 30 years ago from a study of the geochemistry of actual crustal rocks that formed before and after 2.5 Ga (Martin, H. 1986. Effect of steeper Archean geothermal gradient on geochemistry of subduction-zone magmas. Geology, v. 14, p. 753-756). Martin showed that plutonic Archaean and post-Archaean felsic rocks of the continental crust lie in distinctly different fields on plots of their rare-earth element (REE) abundances. Archaean felsic plutonic rocks show a distinct trend of enrichment in light REE relative to heavy REE as measures of the degree of partial melting decreases, whereas the younger crustal rocks show almost constant, low values of heavy REE/light REE whatever the degree of melting. The conclusion he reached was that while in the post Archaean the source was consistent with modern subduction processes – i.e. partial melting of hydrated peridotite in the mantle wedge above subduction zones – but during the Archaean the source was hydrated, garnet-bearing amphibolite of basaltic composition, in the descending slab of subducted oceanic crust. Together with Taylor and McLennan’s lack of evidence for any fractional crystallization in Archaean continental growth, in contrast to that implicated in Post-Archaean times.
The geochemistry forces geologists to accept that a fundamental change took place in the generation and speed of continental growth at the end of the Archaean, marking a shift from a dominance of melting of oceanic, mafic crust to one where the upper mantle was the main source of felsic, low-density magmas. Yet, no matter how much we might speculate on indirect evidence, whether or not subduction, slab-pull and therefore plate tectonics dominated the Archaean remains an open question.
Global Tectonics Centenary: Any Inspiring Papers?
Although Alfred Wegener first began to present his ideas on Continental Drift in 1912 his publication in 1915 of The Origin of Continents and Oceans (Die Entstehung der Kontinente und Ozeane) is generally taken as the global launch of his hypothesis. Apart from support from Alexander du Toit and Arthur Holmes, geoluminaries of the day panned it unmercifully because, in the absence of evidence for a driving mechanism, he speculated that his proposed ‘urkontinent’ (primal continent) Pangaea had been split apart by a centrifugal mechanism connected to the precession of Earth’s rotational axis. This ‘polflucht’ (flight from the poles) is in fact far too weak to have any such influence. Wegener’s masterly assembly of geological evidence for former links between the major continents was ignored by the critics, suggesting that their motive for excoriation of his suggested mechanism was as much spite against an ‘outsider’ as a full consideration of his hypothesis. It must have been hurtful in the extreme, yet Wegener defended himself with a series of revised editions that amassed yet more concrete evidence. What is often overlooked, even now that his ideas have become part of the geoscientific canon, is that in his initial Geologische Rundschau paper in 1912 he mused that the floor of the Atlantic is continuously spreading by tearing apart at the mid-Atlantic Ridge where ‘relatively fluid and hot sima’ rises. Strangely, he dropped that idea in later works. Anyhow, neither 2012 nor 2015 was celebrated in the manner of the centenary-and-a-half of Darwin’s On the Origin of Species: 2009 was marked by palaeobiologists and geneticists metaphorically dancing in the streets, if not foaming at the mouth. There have been a few paragraphs, and some minor symposia about Wegener’s dragging geology out of the 18th century and into the 20th, but that’s about it. The best centenary item I have seen is by Marco Romano and Richard Cifelli (Romano, M. & Cifelli, R.L. 2015. 100 years of continental drift. Science, v. 350, p. 916-916).
In the shape of plate tectonics the Earth sciences hosted what was truly a revolution in science, albeit 50 years on from its discoverer’s announcement. It was through the persistent agitation by his tiny band of supporters, that the upheaval was unleashed when the revelations from palaeomagnetism, seismology and many other lines of evidence were resolved as plate tectonics by the discovery of ocean-floor magnetic stripes by Vine, Matthews and Morley in 1963. Despite an explosion of papers that followed, elaborating onthe new theory and showing examples of its influence on ‘big’ geology , counter-revolutionary resistance lasted almost to the first years of the new century. By then so much evidence had emerged from every geological Eon that opponents looked truly stupid. Even so, the skepticism among those sub-disciplines that were ‘left out’ of geodynamic thought continued to blurt out with the emergence of other exciting aspects of the Earth’s history. I remember that, when three of us in the Open University’s Department of Earth Sciences proposed in 1994 that the influence of impacts by extraterrestrial objects ought to figure in a new course on the evolution of Earth and Life we were sneered at as ‘whizz-bang kids’ by those more earth-bound. Trying belatedly in 1996 to introduce students to another revolutionary development – the use of sedimentary and glacial oxygen isotopes in unraveling past climate change – became a huge struggle in the OU’s Faculty of Science. It went to the press eventually and for 2 years our students had the benefit. But the murmuration of dissent ended with a force-majeur re-edit of the course, by someone who had played no role in its development, expunged the lot and changed the ‘offending’ section back to the way it had been a decade before. As they say: ho hum!
Oddly, in the last 15 years or so of trying to follow in Earth-Pages what I considered to be the most exciting developments in the geosciences, it has become increasing difficult to find papers in the top journals that are truly ground-breaking. Of course that may just be ageing and a certain cynicism that often companies it. From being spoiled for choice week after week it has become increasingly difficult from month to month to maintain the standards that I have set for new work. Has Earth science entered the fifth phase of a ‘paradigm shift’ predicted by philosopher Thomas Kuhn in his 1962 book The Structure of Scientific Revolutions? According to him once a science has entered a period when there is little consensus on the theories that might lie at the root of natural processes there is a drift in opinion to a few conceptual frameworks that seem to work, albeit leaving a lot to be desired. Weaknesses at the frontier between theory and empirical knowledge become increasingly burdensome as a result of the steady plod of ‘normal science’ until the science in question reaches a crisis. If existing paradigms fail repeatedly, science is ripe for the metaphorical equivalent of a ‘Big Bang’: maybe an entirely new discovery or hypothesis, or an idea that has been suppressed which new data fits better than any others that have been common currency. Plate Tectonics is the second kind. After the revolution much is reexamined and new lines of work emerge, until in Kuhn’s 5th phase scientists return to ‘normal science’. That looks like a pretty good story, on paper, but other forces are at work in science; external to scientific objectives. Most of these are a blend of economics, political ideologies and managerial ‘practicalities’. If the Earth sciences have entered the doldrums of novelty, I suspect it is these forces that are bearing some kind of glum fruit.
The old concept of academic freedom has gone by the board. Institutions demand that research is externally funded – the more the better as the institution, at least in the UK, demands a kind of tax (40% of that proposed) supposedly to cover corporate overheads including salaries of support staff. If an academic doesn’t pull in the dosh, she is not much favoured. If the individual doesn’t publish regularly either, there is a weasel sanction: Josephine Soap is declared ‘research inactive’. Consortia of researchers are more and more in vogue: managers and funders like ‘team players’, so individuals who are bright and confident enough to ‘stick their necks out’ cannot do that in a consortium publication and as often as not are ‘left on the bench’. Risk taking is more dangerous now and to stay ‘research active’, and in many cases of non-tenured posts getting a salary, an individual, even a few like-minded colleagues have to publish 2 or 3 papers a year.
It’s worth mentioning that open access publishing is not just all the rage, it has become more or less compulsory. Of course, it has some benefits for scientists in less well-heeled countries, but there is a downside. You have to raise the cash demanded by journals for the privilege or potentially universal access – at least US$1000 a pop, depending on a journals Impact Factor, and that of course is an odiously essential corporate consideration – and having done that woe betide those who do not publish and spend it. Academic publishing is the most profitable sector of the trade, the more so as print is supplanted by electronic delivery – the 50 free reprints is a thing of the past. So there are more and more journals and each of them strives to get out more issues per year, and of course those have to be filled. To me, this all adds up to more and more ‘pot-boiler’ articles and a tendency to maximise the flesh rendered from the body of research work and into the pot. Taken together with the stresses of commodification in higher education and the now vertical corporate structures from which it is constituted, it shouldn’t be a surprise that excitement and inspiration are at a premium in the weekly and monthly output of such a marginal science as that concerned with how the world works.
The core’s influence on geology: how does it do it?
Although no one can be sure about the details of processes in the Earth’s core what is accepted by all is that changes in core dynamics cause the geomagnetic field to change in strength and polarity, probably through some kind of physical interaction between core and deep mantle at the core-mantle boundary (CMB). Throughout the last 73 Ma and especially during the Cenozoic Era geomagnetism has been more fickle than at any time since a more or less continuous record began to be preserved in the Jurassic to Recent magnetic ‘stripes’ of the world ocean floor. Moreover, they came in bursts: 5 in a million years at around 72 Ma; 10 in 4 Ma centred on 54 Ma; 17 over 3 Ma around 42 Ma; 13 in 3 Ma at ~24 Ma; 51 over a period of 12 Ma centring on 15 Ma. During the Late Jurassic and Early Cretaceous the core was similarly ‘busy’, the two time spans of frequent reversals being preceded by quiet ‘superchrons’ dominated by the same normal polarity as we have today i.e. magnetic north being roughly around the north geographic pole.
Until recently geomagnetic ‘flips’ between the two superchrons were regarded as random , perhaps suggesting chaotic behaviour at the CMB. But such a view depends on the statistical method used. A novel approach to calculating reversal frequency through time, however, shows peak-trough pairs recurring 5 times through the Cenozoic Era, approximately 13 Ma apart: maybe the chaos is illusory (Chane, J. et al. 2015. The 13 million year Cenozoic pulse of the Earth. Earth and Planetary Science Letters, v. 431, p. 256-263). So, here is a kind of yardstick to see if there may be any connection between core processes and those at the surface, which Chen of the Fujian Normal University, Fushou China and Canadian and Chinese colleagues compared with the very detailed Cenozoic oxygen-isotope (δ18O) record preserved by foraminifera in ocean-floor sediments, which is a well established proxy for changes in climate. Removing the broad trend of cooling through the Cenozoic resulted in a plot of more intricate climatic shifts that matches the geomagnetism record in both shape and timing of peak-trough pairs. It also turns out, or so the authors claim, that both measures correlate with changes in the rate of Cenozoic subduction of oceanic lithosphere (a measure of plate tectonic activity), albeit negative – peaks in magnetism and climate connecting with slowing in the pace of tectonics.
The analyses involved some complicated maths, but taken at face value the correlations beg the questions why and how? Long-term climate change contains an astronomical signal, encapsulated in the Milankovich hypothesis which has been tested again and again with little room for refutation. So is this all to do with gravitational influences in the Solar System. More exotic still is the possibility of 13 Ma cyclicity linking the Milankovich mechanism with the vaster scale of the Sun’s orbit oscillating through the disc of the Milky Way galaxy and theoretical hints of a mysterious role for dark matter in or near the galaxy. Or, is it a relationship in which climate and the magnetic field are modulated by plate tectonics through varying volcanic emissions of greenhouse gases and the deep effect of subduction on processes at the CMB respectively? To me that seems more plausible, but it is still as exceedingly complex as the maths used to reveal the correlations.
One of the pioneers of plate tectonics, W. Jason Morgan, recognised in the 1970s that chains of volcanic islands and seamounts that rise from the ocean floor may have formed as the movement of lithospheric plates passed over sources of magma that lay in the mantle beneath the plates. He suggested that such hotspots were fixed relative to plate movements at the surface and likened the formation of chains such as that to the west of the volcanically active of the Hawaiian ‘Big Island’ to linear scorching of a sheet of paper moved over a candle flame. If true, it should be possible to use hotspots as a framework for the absolute motion of lithospheric plates rather than the velocities of individual plates relative to the others. But Morgan’s hypothesis has been debated ever since he formulated it. A test would be to see whether or not plumes of rising hot material in the deep part of the mantle can be detected. This became one of the first objectives of seismic tomography when it was devised in the last decade of the 20th century: a method that uses global earthquakes records to detect parts of the mantle where seismic waves traveled faster or slower than the norm: effectively patches of hot (probably rising) and cold rock. The first such evidence was equally hotly debated, one view being that the magma sources beneath oceanic islands such as Hawaii and Iceland were actually related to plate tectonics and that the hotspot hypothesis had become a kind of belief system.
The problem was that mantle plumes supposedly linked to magmatic hotspots in the upper mantle would be so thin that they would be difficult to detect even with seismic tomography. Geophysicists have been trying to sharpen up seismic resolution partly by using supercomputers to analyse more and more seismic records and also by improving the theory about how seismic waves interact with 3-D mantle structure. This has culminated in more believable visualisation of mantle structure (French, S.W. & Romanowicz, B. 2015. Broad plumes rooted at the base of the Earth’s mantle beneath major hotspots). The two researchers from the University of California at Berkeley in fact showed something different, but still robust support for Morgan’s 40-year old ideas. Instead of thin plumes, they have been able to show much broader conduits beneath at least 5 and maybe more active ends of hotspot chains. The zones extend upwards from the core-mantle boundary to about 1000 km below the Earth’s surface, where some bend sideways towards hotspots, perhaps as a result of another kind of upper mantle circulation.
The sources of these hot columns at the core-mantle boundary appear to be zones of very low shear-wave velocities; i.e. almost, but not quite molten blobs. French and Romanowicz suggest that the columns are extremely long-lived and may even have a chemical dimension – as in the hypothesis of mantle heterogeneity. Another interesting feature of their results is that the striking vertical linearity of the columns could indicate that the overall motion of the lower mantle is extremely sluggish and punctured by discrete convection.

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