To be submitted to the proceedings of the Plume IV: Beyond the Plume HypothesisPenrose conference.

A SHORT HISTORY OF THE PLUMEHYPOTHESIS: THE INSIDE STORY

Don L. Andersondla@gps.caltech.edu

In the Chinese view, all manifestations of the Tao are generated by the dynamic interplayof two polar, opposite forces, yin and yang. These forces, one above and one below, onefirm and one yielding, one full of movement and one fixed, give rise to cyclic patterns,with one replacing the other. This analogy also describes the history of ideas, withparadoxes replacing paradigms replacing paradoxes, in an endless cycle.

AbstractPrior to the development of the plate tectonics idea, the reigning theories of globalgeology were Permanence and Contraction. The oceans and continents were mainlypermanent in position and shape and geology was shaped by contraction of the Earth. Itwas believed that mountains, geosynclines, rifts and other aspects of continental geologywere due to global expansion or contraction, vertical tectonics, or asthenosphericinstabilities (diapirs, domes, plumes) similar to giant salt domes. Mantle diapirs orplumes owed their buoyancy to chemistry and phase changes, as well as temperature. Themodern plume hypothesis started out as a special form of thermal convection, withnarrow upwellings and diffuse downwellings, similar to atmospheric phenomena such asthunderheads [Morgan,1972]. Tozer [1973] showed that what ‘geologists’ had in mindfor mantle upwellings could not be the same as fluid dynamic plumes and could not beexplained by the same physics. The effects of pressure on material properties reinforceTozer’s conclusions. It is still unresolved whether features that have been attributed toplumes are primarily the result of plate tectonics and stress (yin), or fluid dynamics andhigh temperature (yang). Interest in various versions of the diapir and plume hypothesespeaked in 1950, 1970, 1990 and subsequent years but fell into disfavor in some circles inthe intervening years, and prior to 1990, because of various paradoxes, contradictions andinterest in alternative mechanisms. The physical basis was also questioned. Specialists indiverse disciplines have now adopted the hypothesis in spite of the various paradoxes,and the still outstanding lack of a physical basis under conditions appropriate for theEarth’s mantle. The most recent estimate of the number of plumes in the mantle whichgive measurable surface effects is 5200.

IntroductionPlate tectonics and plumes are the yin and yang of global tectonics and the history of onecannot be discussed in isolation from the history of the other. They were developed in

parallel, as competing, even opposite, theories Plate tectonics was developed during the1960s and 1970s by Le Pichon, Oliver, Sykes, Isacks, Wilson, Molnar, Elsasser,McKenzie, Parker, Morgan and a host of others. Plate tectonics was initially a kinematicand descriptive theory and involved such idealizations as rigid (or elastic) and permanentplates, sharp plate boundaries, uniform isothermal mantle, horizontal motions and steady-state. Diffuse plate boundaries, non-plate boundary volcanism, continental geology,linear island chains, swells and vertical motions were taken as failures of the platehypothesis, as were melting and elevation ‘anomalies’ along the global spreading ridgesystem. Although it is generally accepted that the mantle is convecting, convectionsimulations have been unable to account for first order plate tectonics features andprocesses, and the above mentioned departures from rigid plate tectonics.

Prior to the ideas of lateral mobilism - Drift, Seafloor Spreading and Plate Tectonics -geologists tended to be Permanentists, Contractionists. or Expansionists. At the time thatthe idea of plate tectonics was being developed in the west, V.V.Beloussov in Russia wasformulating his theory of vertical tectonics, or mantle diapirism, in order to explaincontinental geology. His text, published in 1956 in Russian, was translated into English in1962. Hans Ramberg (1967,1981), in testing Beloussov’s ideas, showed experimentallythat low-density layers at depth would form mushroom shaped diapers or plumes as theyrose. His results were similar to the injection experiments, some 30 years later, byCampbell and Griffiths (1990,1993) that reinvigorated the mantle plume hypothesis.Beloussov (1962) considered mantle diapirism to be an alternate to plate tectonics, andwas required in order to form mountain belts and uplifted domes. Plumes are currentlybeing used, in a similar way, to rationalize features that are not explained by simple rigidplate tectonics. Plate tectonics rapidly shunted aside Beloussov’s ideas of verticaltectonics, deep diapers and plumes, but phoenix-like, the plume idea has had severalrebirths. The domes and vertical tectonics of Beloussov’s anti-plate tectonic theory havebecome the swells, superswells and continental uplift of current plume scenerios. Butlarge scale lateral transport of material from plumes to spreading ridges and continentalinteriors is now an amendment to the vertical plume hypothesis. The plume hypothesis was developed during the 1970s primarily by Wilson, Morgan,Burke and Vogt. Alternate and shallower mechanisms were being developed by Jackson,Shaw, Tozer, Menard, Richter, Parsons, Elsasser, Jacoby, Turcotte, Oxburgh and others.A partially molten asthenosphere vs. an entirely subsolidus upper mantle in the absenceof perturbations distinguished the shallow vs. deep models.

Some Semantic Preliminaries‘Hotspots’ are defined as regions of anomalous volcanism. Other terms for ‘hotspots’ are‘midplate volcanism’ and ‘melting anomalies’. These terms are all model dependent andsomewhat misleading since hotspots do not appear to be particularly hot(www.mantleplumes.org/Heatflow.html, /MantleTemp.html and/Temperature.html), they are not all midplate, and ‘anomalous’ implies a degree ofhomogeneity or constancy in the mantle that cannot be justified considering whatrecycling and other plate tectonic processes do. Sometimes, large volume, or persistent,

magmatism is taken as a proxy for high temperatures, but midocean ridge and island arcvolcanism also have these characteristics. Other parameters (stress, fertility, focusing,ponding) can control the volumes of melt. What is meant by the term ‘hotspot’ is alocalization of extrusion or volcanism that differs in some respect from plate boundarymagmatism.

The vagueness of the concept of ‘hotspot’ is reflected in the fact that the number ofhotspots has varied from the original 20, defined by Morgan [1971] to 117 [Burke andWilson, 1976]. Most recent ‘official’ hotspot lists include about 40 hotspots. Some ofthese have been labeled as ‘coldspots’, ‘wetspots’, ‘hotlines’ or ‘crackspots’, and to thislist can be added ‘ fertile spots’. Crough [1983] defined a ‘hotspot’ as a region ofmidplate or anomalous ridge crest volcanism that is either persistent or or accompaniedby a broad topographic swell. The assumptions behind this definition are that, in theabsence of hotspots, ridges would rise to the same elevation and be equally productiveeverywhere, and that seafloor topography would otherwise be flat, after age-dependentsubsidence has been subtracted out. In other words, the nominal or reference mantleshould be isothermal and homogeneous in composition and melting point. There is alsosome two-dimensionality in this definition, since linear buoyant upwellings tend to breakup into sprouts or domes (as in salt domes) even along midocean ridges; horizontalRichter rolls and vertical sprouts are possible in three-dimensions. Swells are alsoassumed to be thermal in origin. The uncertainty about what a hotspot really is hashampered attempts to explain them. If the upper mantle is at or near the melting point,then any region of extension is potentially volcanic, even if the underlying mantle is notparticularly hot. If the upper mantle is heterogeneous in composition, fertility or meltingpoint, melting anomalies do not require high temperatures.

Most hotspots occur in extensional regions of the lithosphere, either plate boundaries orintraplate boundaries. Wilson [1963] noted that most hotspots were on midocean ridges.The magmatism and deformation can be localized by mechanical processes in thelithosphere (stress, thermal contraction, extension), by focused processes of fluiddynamics (high temperature plumes), or by fertile or low-melting patches in the mantle.The yin and yang of hotspots is whether they are controlled by stress (plate tectonicprocesses) or by temperature (‘convecting mantle’ fluid dynamic processes). Localizationof deformation is also an issue in fluid dynamic theories of plate tectonics (Bercovici andRicard, 2003). Methods used to make convection simulations aproach plate tectonicbehavior include shear heating, non-linear rheology, activation of pre-exiting faults,lubrication, pore-pressure and so on. These same processes can localize deformation andmagmatism at hotspots and linear island chains. Extensional plate boundaries probablystarted out as linear volcanic chains (incipient plate boundaries). The plume hypothesis,however, assumes that localized high temperature is the cause of volcanic chains (unlessthey are island arcs or moderate depth ridges) rather than localization of stress ordeformation. The word ‘plume’ has replaced the word ‘hotspot’ in the mantlegeochemistry literature (e.g. the Yellowstone plume, the Iceland plume), but ‘hotspot’and ‘plume’ are different concepts. Large igneous provinces, such as continental floodbasalts and oceanic plateaus are often referred to as ‘plume heads’, e.g. the Ontong-Javaplume head. Features that have been labeled ‘hotspots’ do not necessarily require either

plumes or high temperatures. The assumption that they do has spawned the plumehypothesis.

Technically, plumes are buoyant upwellings or downwellings. In the fluid dynamicsliterature they are often called jets or thermals. The passive upwellings at midoceanridges involve melting as the upwelling mantle crosses the solidus. This introduces anextra element of buoyancy and this is sometimes referred to as ‘the plume component’ ofbuoyancy. Low density layers in the crust can also form buoyant upwellings. These havealso been called plumes, but are more commonly referred to as ‘diapirs’ or ‘domes’ (as insalt domes). Instabilities of the cold upper thermal boundary layer are technically‘plumes’. More commonly, however, plumes are considered to be creatures of lowerthermal boundary layers in fluids heated – entirely or mostly - from below. Plumemodeling, however, often involves the injection of hot low viscosity fluid into a tank ofstatic fluid, or the instantaneous creation of a hot sphere [e.g. Cordery et al, 1997] ratherthan the spontaneous development of instabilities in a thermal boundary layer. Initially itwas assumed that all hotspots were underlain by deep mantle plumes. Twenty hotspotsrequired 20 plumes and this seemed to be close to the required number if plate tectonicswas driven by plumes and if plumes were to provide about half of the world’s heatflow[Morgan, 1972]. Malamud and Turcotte [2001], however suggested that there were about5200 plumes (or one every 300 km). This would decouple the concepts of hotspots andplumes, unless most isolated seamounts and short seamount chains represent hotspots.This again raises a semantic issue; when so many plumes and hotspots are invoked, howdoes this differ from shallow small-scale convection? And if the upper mantle is abovethe melting point in so many places, how does one rule out crack and stress mechanismsfor accessing this melt? Dikes from a partially molten asthenosphere will intrude theoverlying plate if the least compressive axis is horizontal. Otherwise the melt is trappedin ponds, or intrudes the plate as sills. Volcanism can be triggered by surface loads aswell as by distal stresses [Hieronymus and Bercovici, 1999]. It has yet to be demonstratedthat concentrated loci of high temperature overlain by even moderately thick plates cantrigger volcanism. In contrast, dike physics and the role of stress are well understood.‘Plumes’ were originally considered to be narrow, ~ 200 km, but broad plume heads,spreading out beneath the lithosphere have been added to the concept, based on thebehavior of injected streams of hot fluids in tanks of cold fluid.

The term ‘plume’ does not have a well defined and agreed upon meaning in the Earthscience community. The term is used differently in different disciplines. For some it issimply a region of anomalous magmatism, anomalous in either volume or chemistry,compared to the average ocean ridge. Some seismologists refer to any slower thanaverage region of the mantle, regardless of depth or depth extent, as a plume. Elevatedregions of ridges or midplate swells are called plumes. Most volcanic islands are nowreferred to as plumes. The defining characteristics of plumes tend to be any characteristicthat is displayed by regions defined as plumes, such as Iceland, Hawaii and Yellowstone.An agreed upon definition and defining attributes are clearly needed, not only for ‘plume’but for ‘anomalous’. In keeping with Morgan’s convention, and to be consistent with themajority of papers from the inception of the hypothesis, I define ‘plume’ as a narrowbuoyant active upwelling that is continuous from a deep thermal boundary layer to a

surface hotspot. Passive upwellings, upwellings associated with plate tectonics or largescale mantle convection, or features not originating as instabilities in a deep thermalboundary layer, are not considered to be plumes. Low-velocity regions of the mantle, ormagmas that differ in some respect from MORB, are not adequate indicators of plumes.

The chemical alternatives to deep mantle reservoirs tapped by plumes are distributedheterogeneities, or blobs, sometimes called marblecake or plum pudding models(Meibom and Anderson, 2003). In these models the component concept replaces thereservoir concept. In some recent papers the word ‘plume’ is attached to anyheterogeneity that is advected around by the mantle flow. The purpose is to ‘explain’ themotions of hotspots but this definition violates the purpose and spirit of the plumehypothesis. The terms ‘superplume’ and ‘megaplume’ have been applied to large lowermantle tomographic features, but plumes. by definition and usage, refer to small scalefeatures, not the normal large scale convection associated with plate tectonics or heatingof the mantle. Otherwise, the word ‘plume’ loses all meaning and is not a useful concept.

Plumes as part of mantle convectionA fluid heated from below and cooled from above will develop hot upwellings and colddownwellings. Although these are referred to as plumes in the fluid dynamics literature,they are just part of the normal behavior of a fluid and can be thought of as normal orbackground convection.Thermal convection at low to moderate Rayleigh number ischaracterized by two scales; one is set by the size of the container (or the depths ofindividual layers), and one is set by the size of the thermal boundary layers and this iscontrolled by the properties of the fluid. In the Earth science literature plumes are usuallythought of as stationary concentrated upwellings that are independent of plate tectonicsand of normal or background convection. But Tozer (1973) pointed out that well-knownfluid dynamic scaling relations, when applied to the mantle, precluded the existence ofnarrow plumes independent of normal large-scale convection. Tozer (1977) suggestedthat ‘ mantle plume’ was simply jargon for a long recognized geological fact, thatigneous/hydrothermal activity is highly localized at any one geological time. In his view,plumes were an ad hoc method of localizing activity. Larsen and Yuen (1997) describethe situation as follows;

“ The enigma of…nearly stationary plumes…in mantle convection arises in the hotspothypothesis. Some sort of separation of time scales between the fast plume and adjacentmantle is necessary and, in fact, was invoked by Morgan in his original concept ofplumes. …plume studies have usually modeled a plume in isolation from the rest of themantle. There has been a tendency to regard plumes as a distinct, secondary mode ofconvection… such a mode of flow has never been observed in any self-consistentnumerical or laboratory experiment. Upwelling plumes always occur as part of the mainconvecting system (rather than independently). In particular, there is a problem ofobtaining hotspot-like plumes, which must satisfy the requirements of being fast ascompared to the ambient mantle circulation and fairly thin…”

Narrow plumes have been observed in fluid dynamic simulations with strong localizedheating from below, or in fluids with strongly stress and temperature dependent rheology

and shear heating, but no phase changes or pressure effects (Larsen and Yuen, 1997) andno internal heating. These simulations, however, do not produce plate tectonics or slab-like behavior for the downwelling plumes. Although temperature anomalies (thermalboundary layers) can be narrow, the physical plumes, or flow velocity anomalies(mechanical boundary layers), can only be narrow for large ratios of the viscosity tothermal diffusivity (Prandtl Number, Pr). or if the container is small. The effect ofpressure on thermal expansion, thermal conductivity, viscosity and Rayleigh numbermust also be taken into account in any theory of deep mantle plumes (Anderson, 1987,1989; Tackley, 1998). This pressure or volume scaling of physical properties cannot beaccounted for in laboratory scale experiments.

The localization issue also arises in fluid dynamic treatments of plate tectonics (Bercoviciand Ricard, 2003). Convection simulations do not explain the first order features of platetectonics, such as flat, coherent plates with sharp boundaries, one-sided subduction, theinitiation of subduction, strike-slip faults, and global plate reorganizations. In this case,the localization is explained by mechanical properties of the lithosphere. The result islinear volcanic chains at ridges and island arcs. These are defined as ‘plate boundaries’.

Asthenospheric DiapirsIn the 1950’s Beloussov described his vertical tectonic undulation theory. Much as in alava lamp, material in the interior heats up and rises, and then cools off and sinks.Chemical and phase change buoyancy was important; the buoyancy was not entirelycreated by thermal expansion. Horizontal motions were minimal and were essentiallygravity sliding of material off of the upwellings. Beloussov considered the mantle to begravitational stratified and vertical tectonics to be the main form of convection. As theEarth formed, the lower mantle expelled the light materials upward to form the crust andupper mantle and expelled the dense materials downward to form the core. In otherwords, the present mantle is chemically stratified, the result of zone refining. Diapirsfrom the upper mantle were responsible for swells, mountain building and rifts. This wasconsidered to be an alternate to plate tectonics and large horizontal motions.

Ramberg (1967,1981) followed up on Beloussov’s model with properly scaled laboratoryand centrifuge experiments and generated diapirs and plumes that were similar toBeloussov’s sketches. He also reproduced many elements of continental geology.Ramberg was one of the pioneers in scaled models. He attempted to scale gravity,material properties, stress and time so that his results could be applied to the Earth.Scaling relations are very important in geodynamic modeling and convection simulationsbut are often ignored. The effect of pressure on material properties is difficult to scale andis usually ignored in mantle convection simulations (the Boussinesq approximation).

Ramberg considered that the term ‘plume’, as used in the geophysics literature, was thesame as the ‘diapir’ of structural geology. He showed that density inversions led tomushroom shaped features, identical to more recent fluid injection experiments that havebeen used to promote the mantle plume hypothesis.

Jason Morgan’s (1972,1973) conception of mantle convection involved narrow hotupwellings and broad distributed downwellings. He combined the concepts of narrowstationary upwellings and moving plates. Morgan made very specific predictions and hishypothesis was elegant, testable and falsifiable. The upwellings were predicted to bringup a large fraction of the Earth’s heat and magma. Plates moving over these narrowplumes would have narrow chains of time progressive volcanism. Plumes would break upand drive the plates. As in Beloussov’s theory, plumes were used to explain a variety ofphenomena not easily explained by plate tectonics, at least the rigid plate version (withno role for incipient or reactivated plate boundaries). The form of convection assumed byMorgan is consistent with a mantle heated from below, but not with one cooled fromabove, or heated from within. In a homogeneous laboratory fluid (e.g. low Prandtlnumber), heated from below, both the top and bottom boundary layers generate narrowplumes and there is symmetry to the problem. In the mantle, the effects of sphericity,pressure and phase changes, among other things, break the symmetry. The mantle is ahigh Prandtl number fluid, which means that mechanical boundary layers cannot benarrow. The high viscosity of the deep mantle also precludes narrow thermal boundarylayers and narrow thermals.

If “ thermal plume” refers to convective flows that are dynamically similar to certainobserved flows that have been named thermal plumes in the atmosphere, ocean and inlaboratory simulations, then they do not exist in the mantle (Tozer, 1973). Theimplausibity of narrow thermal plumes in the mantle prompted Anderson (1975) andothers (Hadley et al, 1976) to propose and test the concepts of chemical plumes andchemically zoned plumes. In these models, as in Beloussov’s and Ramberg’s, one mustexplain the source of the chemical buoyancy. Partial melting and phase changes havebeen proposed. One must also address the return flow problem, unless chemical plumesare considered to be part of the on-going one-way chemical differentiation of the mantle.Laboratory simulations of plumes also tend to be one-shot irreversible isolated injections,rather than a form of small-scale cyclical convection.

Campbell and colleagues in Australia revived the thermal plume hypothesis in 1990.They repeated experiments similar to those pioneered by Ramberg and the results weresimilar to those illustrated in fluid dynamic textbooks. The dramatic plume head-plumetail visualizations, unfamiliar to most geologists and geochemists, who were unaware ofBeloussov, Ramberg, Tozer or even fluid dynamics, gave new impetus to Morgan’sideas. Plumes became a default explanation of observations in a variety of fields,although Tozer’s objections still maintain.

Historical background- the influence of HawaiiThe Hawaiian islands played a special role in the development of hypotheses for ageprogressive volcanic chains. These ideas include propagating cracks, membranetectonics, self-perpetuating volcanic chains and reactivation of weak zones or previousplate boundaries. Concepts such as hotspot fixity, parallelism of island chains,asthenospheric bumps and shear melting were also stimulated by the Hawaiian andEmperor chains. The Hawaiian chain is usually linked with the Emperor Seamount

Chain, although the two may have separate origins; they are separated by the giantMendocino Fracture Zone, and have quite different trends, productivities andmorphology. The northernmost Emperors apparently started on a ridge. In the plumehypothesis the differing trends of the two chains represents a change in plate motion. Inalternative theories, it is stress, cracks, pre-existing seafloor fabric, and variable fertilityof the mantle that causes changes in trend and productivity of volcanic features. It isdifficult to generate abrupt changes in plate direction by thermal and plate tectonicprocesses; it is much easier to change the local and global stress fields.

The distinctive northwest-southeast alignment of the Hawaiian chain was known to theearly Hawaiians. Their legends reveal that they recognized that the islands growprogressively younger from the northwest to the southeast. Charles Darwin noted in 1837that ocean islands often exist in chains that go through changes from volcanically activeislands to older features that we now know as atolls. The first geologic study of theHawaiian Islands (1840-1841) was directed by James Dwight Dana who deduced that theislands young to the southeast from the differences in their degree of erosion. He alsosuggested that some other island chains in the Pacific showed a similar general decreasein age from northwest to southeast. The alignment of the Hawaiian Islands, Danaproposed, reflected localized volcanic activity along segments of a major fissure zone onthe ocean floor. Dana's “great fissure” origin for the islands served as a workinghypothesis for subsequent studies. In 1963, Tuzo Wilson suggested that the time-progressive volcanism along the Hawaiianchain could be explained by the lithosphere moving across a stationary hot spot in themantle [Wilson, 1963]. This suggestion gave rise to a revival of the Beloussov theory ofmantle diapirism in the form of asthenospheric mantle plumes. Wilson thought the lowermantle was rigid and non-convecting so his fixed reference point was actually the top ofthe lower mantle, not the bottom. Menard [1973] suggested that a bump at the base of theasthenosphere may control the location of the Hawaiian swell and the volcanism. Such abump could be caused by thermal expansion in an underlying layer and does not requirematerial transport from deep regions. Because of the large increase of viscosity withpressure the time scale of convection in the lower mantle is longer than in the uppermantle. Therefore bumps at the top of the lower mantle can persist for long periods oftime and this may influence convection in the asthenosphere.

Early Anomalies and AlternativesThe Hawaiian and Emperor systems appear superficially to fit the fixed deep mantleplume hypothesis well, and indeed, the hypothesis was inspired by it. Fixity, however,cannot be demonstrated by a single chain. Crack propagation, self-perpetuating volcanicchains, reactivated plate boundaries, incipient plate boundaries, gravitational anchors, anddike propagation are also consistent with the Emperor and Hawaiian chains (e.g. Jacksonand Shaw, 1975; Jackson et al, 1975; Clague and Dalrymple, 1987; Hieronymus andBercovici, 1999; www.mantleplumes.org/Cracks&Stress.html). The most widely quotedevidence for fixed plumes is geometric (fixity, perceived parallelism with other volcanicchains and the regular time progression of volcanism) along with the high melt

productivity. In the geochemical literature any chemical attribute of a magma that differsform what has been defined as a midocean ridge basalt is often attributed to a plume, andused as evidence for the existence of a plume. Linear time-progression of volcanism andhigh magmatic productivity can be explained by other mechanisms such as propagatingcracks and high mantle fertility. Since plumes are expected to be produced by only asmall fraction of the heat flow that exits the Earth at the top of the mantle, it is expectedthat plumes will be strongly influenced by mantle motion driven by movement of tectonicplates and subduction. This one of the reasons motivating Morgan to require that plumesbe very strong and independent of plate and mantle motions. Ironically, the fixity andtime progressive arguments are no longer considered to be valid [Raymond et al, 2000;Koppers et al, 2000], and high temperatures do not seem to be a characteristic of hotspotsin general [Yaxley, 2000]. Hotspot magma temperatures usually fall within the rangeexpected for the lower part of the upper thermal boundary layer of the mantle (1100-1400 C).Even Hawaiian basalts appear to have temperatures well within the rangeexpected for potential temperatures in the upper mantle(www.mantleplumes.org/MantleTemp.html). Other aspects of hotspot volcanism, such asglobal synchronism, was not, and is not, readily explained by the plume hypothesis[Vogt, 1972]. On the other hand, global synchronism is expected in plate and stress basedtheories. The Hawaiian Swell, at one time attributed to high temperatures and lithosphericrejuvenation, appears instead to be primarily buoyant high-velocity residue.

Plumes; From Conception to First Demise (1971-1978)Morgan [1971; 1972] proposed that a plume from deep primordial mantle continuallysupplied Hawaii, and that there are approximately 20 such plumes. On a global scale,plumes broke up and drove the plates, and were responsible for keeping the midoceanridges open and the asthenosphere replenished. The deep vertical replenishment proposedby Morgan is an alternative to shallow return flow, from subduction zones through themantle wedge and asthenosphere, which was the preferred model at the time [Elsasser, 1967; Jacoby, 1970]. The most testable predictions of Morgan’s version of theplume hypothesis are the diffuse downflow, the required local and global heat fluxes, thetemperatures of the magmas, the heat flow of the surrounding area and the heating andthinning of the lithosphere.

Fixity relative to one-another, time-progressive and parallel volcanic tracks, and a highrate of volcanism were considered to be the primary characteristics of volcanic regionsfueled by deep-mantle plumes. The fluid dynamic basis of the mantle thermal plume ideawas immediately challenged by Tozer [1973, 1977] and Richter and Parsons [1975]. Infact, the years from 1973 to 1975 saw a large number of challenges to the new version ofthe plume hypothesis (see Nature, vol. 240 to 244, and Cowen and Lipps,1975). Both thephysics and the observations were challenged, and alternative explanations were offered(Smith, 1973a,b,c,d, 1975; O’Hara, 1973, McElhinny, 1973; Richter and Parsons, 1975).(The concerns expressed by Tozer and others about Morgan’s gedankenexperimentplumes were even more applicable to the Cambell and Griffith’s laboratory plumes which

caused a rebirth of the idea, without the baggage of recent controversy regarding thetheoretical justification.)The ideas of true polar wander, mantle roll, large radius ‘spots’and lateral transport became part of the plume hypothesis in order to retain the idea of afixed hotspot reference frame [Duncan et al, 1972; McElhinny, 1973; Hargraves andDuncan, 1973]. The global synchronism in hotspot and arc volcanism [Vogt, 1972] wasan early hint of a plate tectonic or lithospheric stress control on hotspot activity. In theyears 1972 to 1974 there were more than 120 papers published which were motivated bythe mantle plume hypothesis.

Seismologists soon reported evidence for core-mantle boundary anomalies, of all kinds,which were attributed to the source for the Hawaiian volcanics. A series of articles[Kanasewich et al 1972, 1973; Kanasewich & Gutowski 1975] detailed a high-velocityanomaly lying in the lowermost mantle, a few degrees northeast of Hawaii (subsequentstudies attributed features to the northwest and southeast of Hawaii to the Hawaiianplume [Nataf, 2000]). Wright [1974] argued that such high velocities were notcompatible with other observations for the same region, and that the analysis was non-unique. They concluded that lithospheric structure beneath the seismic arrays in Canadaexplained the reported anomaly. It was also not clear how a high-velocity anomaly was ‘proof of plume’. This was only the first of many premature claim and refutations ofconnections between deep seismic anomalies and surface hotspots.

In 1975 Best et al [1975] delivered the coup de grace to the plume hypothesis. In anelegant and unique seismic experiment they showed that the seismic velocity beneathHawaii, all the way to the core, was not anomalous. This ruled out a large hot, or partiallymolten region under the world’s largest hotspot. This result was confirmed by subsequentstudies.The shear wave speed in the upper and middle mantle inferred from arrival timesis higher than the average for the southwestern Pacific [Katzman et al., 1998], and thepropagation efficiency is also high [Sipkin & Jordan, 1979]. These parameters aresensitive to temperature and melting and argue strongly against unusually hightemperatures or extensive melting in the upper or lower mantle beneath Hawaii.Elsewhere, Hadley et al [1976] found a high-velocity anomaly in the transition regionunder Yellowstone, inconsistent with a deep thermal plume.

It also did not take geochemists long to adopt the plume hypothesis. Schilling [1973a,b,c] attributed the unusual chemistry at high spots along the mid-Atlantic ridge toenriched plumes or blobs. Most of the chemical attributes originally attributed to plumes,however, can be accounted for by recycling of sediments and crust. The noble gases,most notably helium-3, are the main chemical diagnostics still used for ‘primordial lowermantle’. Craig and Lupton [1976, 1981] used high helium isotopic ratios 3He/4He atYellowstone and Iceland as evidence for a deep mantle source of primordial helium,although they were surprised that the thick continental crust under Yellowstone wastransparent to deep mantle helium. The regions with high 3He/4He ratios also providesamples with low 3He/4He, and high variance of the ratio (relative to midocean ridgebasalts). This is suggestive of a sampling process, and operation of the central limittheorem. Although it is indisputable that most of the Helium-3 in the Universe was madein the Big Bang, and is therefore a ‘primordial ‘ isotope, it is not clear when this material

entered the mantle, and whether there is a Helium-3 rich reservoir (as oppose to lowU/3He componenets.. High ratios can be due to low Helium-4, or low U/He ratios, insteadof high Helium-3 concentrations. Mantle components may have variable ratios, that arewashed out in the ocean ridge sampling and blending process.

In spite of the concerns of David Tozer, Harold Jeffreys, Keith Runcorn, Jack Jacobs andFrank Richter, geophysicists who were most conversant in fluid dynamics [Smith, 1973d]and the new geophysical data, the number of plumes proliferated, reaching a peak ofmore than 100 in 1976 [Burke and Wilson, 1976]. The plume hypothesis was furtherchallenged in the following years [Jacoby, 1977; Tozer, 1977; Sykes, 1978]. Sykes[1978] showed that the Atlantic ‘hotspot tracks’ were actually transform faults andfracture zones. Crough [1978] reduced the number off plumes to about 40 and showedthat thermal plumes would heat and thin the lithosphere (rejuvenate), leading to uplift andthermal swells. Plumes would spread out beneath, and rapidly heat and thin thelithosphere. These predictions were not confirmed [Woods et al, 1991;Woods and Okal,1996;von Herzen et al, 1989; Anderson et al, 1992]. Conduction is too slow to explain theinferred rate of uplift, and alternative mechanisms of thinning such as delamination ordike injection do not require particularly hot mantle. It is not even clear that thelithosphere is hot, thin or rejuvenated [Woods and Okal,]. The suggestion by Burke andWilson [1976] that there were 117 hotspots was the culmination of plume proliferation,but this large number did not last long [Crough, 1978].

By 1977 the number of studies motivated by the plume hypothesis was down to 20 peryear. Interest was steady but low throughout the 1980s.The number of publicationsincreased by an order of magnitude after the injection experiments of Campbell andGriffiths [1990, 1991]. From the geological, mantle dynamics and fluid dynamics pointsof view, these experiments would not seem to be especially relevant. They also did notaddress the apparently fatal issues and contradictory data discussed earlier andconcurrently [Jacoby, 1977; Tozer, 1973, 1977; Sykes, 1978; Woods et al, 1991; vonHerzen et al, 1989; Richter and Parsons, 1975; Best et al, 1975; Hadley et al,1976;Cowen and Lipps, 1975] nor did they address fluid dynamic and solid state physicsscaling issues. The most significant new predictions of the injection experiments were therequired association of a hotspot track (plume tail) with a large igneous province (plumehead) and the large (kilometers) precursory uplift prior to extrusion.

An Aside On TemperatureThe defining characteristic of a hotspot or a thermal plume is high temperature.Surprisingly, measured temperature and heat flow data are seldom discussed in thecontext of tests for the presence of plumes [e.g. Coutillot et al, 2003]. The volumes orrates of magmatism are considered to be proxies for temperature. What absolutetemperature defines a plume? Plate tectonics is driven by cooling of the thermal boundarylayer at the surface. Temperatures in the boundary layer rise from, roughly, 0 to 1400degrees C, with a range in the latter of about 200 degrees (Anderson, 2001). Midoceanridge basalt temperatures are controversial but the range from 1100 to about 1400 degreesC covers most published estimates. These are not necessarily representative of the

sublithospheric adiabat, which can be higher. Mantle from a deeper thermal boundarylayer (the conjectured plume layer) can be expected to arrive at the surface withtemperature excesses of at least 1000 degrees C. Inferred magma temperatures of only1400-1500 C, or temperature excesses of 100 – 200 C, are candidates for derivation fromthe shallow mantle or even the thermal boundary layer. There is little evidence for highmagma temperatures or high heat flow at hotspots. This is a difficulty for the plumehypothesis but is an expected outcome for the alternative mechanisms for excess magmaproduction and production of swells. At the inception of the ‘hotspot’ hypothesis it wassimply assumed that high magma volumes required high absolute temperatures; this doesnot seem to be the case. This, plus the absence of fixity and parallelism of island chains,justify the multiple working hypotheses approach to ‘melting anomalies’. The fluiddynamic and high temperature hypotheses need to be evaluated along side of the athermalmechanisms for localizing magmatism.

Athermal MechanismsThe plume hypothesis focuses on fluid dynamic processes; temperature is the maincontrol parameter. Alternative mechanisms are basically athermal although they requirethat normal mantle is close to the solidus, at least in the upper 200 km or so. Volcanism islocalized by stress and by lithospheric fabric. Variations in melt productivity andchemistry are due to the normal variations in mantle chemistry, melting point andmineralogy that one expects from plate tectonic recycling. Variations in midocean ridgedepths are due to a combination of large scale moderate thermal variations, and localizedchemical variations, both resulting from plate tectonics. Localization of magmatism hasthe same ultimate cause as the localization of plate boundaries.

Many simulations of plumes (experimental, numerical, analytic) in effect, inject narrowstreams of hot fluids into a stationary tank of cold fluid; the plumes are not part of anaturally convecting system. In fact, fluids that are internally heated, and in a pressuregradient, do not spontaneously develop narrow upwelling plumes (Tackley, 1998). Insome fluid dynamic simulations the localization is achieved by using narrow needles toinject the hot fluid, or puncturing a membrane to release a narrow stream of hot fluid.Strong temperature and stress effects favor narrow plume formation only if thecounteractive effect of pressure is ignored. Simple scaling relations [Anderson, 1987,1989] show that instabilities at the base of the mantle should be orders of magnitudelarger and more sluggish than than upper mantle plates and slabs. The pressure effects onthermal properties is ignored in laboratory and Boussinesq simulations.

Alternate ways of localizing magmatism and separating time and spatial scales are tohave eruptions and extrusions controlled by lithospheric physics rather than fluiddynamics (e.g. www.mantleplumes.org/Cracks&Stress.html; Jackson et al, 1975, Favela& Anderson, 1999; Bercovici and Richard, 2003). Volcanic chains may be due toincipient plate boundaries, or reactivated plate boundaries. These, however, are platetectonic concepts, not fluid dynamic concepts. The localization of strain is not readilyaccomplished in a high Prandtl number fluid with uniform Newtonian rheology.Localization naturally occurs in deformed solids, even in fragile materials such as bubble

rafts and granular materials. Conditions in the shallow mantle, however, may controlwhether melting is possible and how much melt is available. This is a function of meltingpoint, volatile content and fertility, and ponding potential, not just absolute temperature.Ponding of magma beneath the plate or in the lithosphere, may be a prerequisite of large-scale surface magmatism; the stress in the lithosphere may control the timing andlocation. This ponding is more likely under midplate, or thick crust, and compressionalenvironments. Ponding and long-distance lateral transport are recent additions to theplume hypothesis but these can also occur without plumes. The asthenosphere canmigrate and pond under thin plate regions.

Instabilities of deep TBL are not the only way to create melting anomalies and volcanicchains. Plate tectonics and large-scale mantle convection are driven by cooling fromabove. Cooling plates and descending slabs are the active elements. They causes stressesin the plates which can move and fracture the plates, and create new plate boundaries.Smaller scales of convection are driven by lateral temperature gradients at the top (Elderconvection), diapers from the asthenosphere (Rayleigh-Taylor instabilities or Rambergconvection), shear-induced instabilities (Richter rolls) and the ascent of buoyant dikes.These are buoyancy driven or secondary flows that are controlled by the top of thesystem. The mantle is close to the melting point, so the upwellings are associated withincreased amounts of melting. Since the plate controls the locations of egress, if any, ofthese upwellings they are called ’opportunistic’, ‘permissive’ or ‘passive’. Theupwellings are rooted in the shallow mantle. Superposed on these, are the plate-scalelateral temperature variations associated with the major plates.

In the plume hypothesis the upper mantle is taken to be roughly isothermal (constantpotential temperature) and homogeneous (“ the convecting mantle”) except where narrowjets of hot mantle impinge on the plates. In the plate hypothesis normal mantle can bemore-or-less isothermal on a local and regional scale, but close to the solidus. In thissituation, melting anomalies can be attributed to fertile patches of variable melting pointsin the shallow mantle, which erupt through weak or thin parts of the lithosphere, usuallyon, or near, past, present or future lithospheric boundaries.

The Plate Model – The Yin Of Mantle DynamicsAll the non-plume explanations for volcanic chains and other features can be consideredas implicit in plate tectonics. Incipient and dying plate boundaries, leaky transform faults,cracks, extentional terranes, reactivated sutures and fracture zones, small-scaleconvection associated with plate motions and architecture, edge effects, focusing andfertility variations, are consequences of plate tectonics and are basically athermal innature. Plate tectonics and mantle convection is driven by cooling of the plates, notheating from the bottom. These mechanisms can be referred to collectively as ‘ the platehypothesis’, or ‘plate mechanisms’ or simply ‘plate’. Whereas, the plume hypothesis wasbased on parallelism of volcanic chains and strict unilateral age progressions, the platehypothesis allows for non-parallel chains, stress-controlled sigmoidal and nested cracks,bilateral and erratic age progression, and variable productivity. The fecundity of a linearfeature depends on tectonic stress; stress can turn on and shut off dikes and modulate

magmatism along a crack or boundary. An essential assumption is that the mantle is nearthe melting point, although it can be variable in fertility, temperature and solidustemperature. A small change in temperature, volatile- content and composition can have alarge effect on melt volumes for a near-solidus mantle.

Whereas criteria for hotspots and plumes should be mainly thermal, criteria for alternatemechanisms are mainly athermal, and include; lithospheric stress and architecture,magma composition, fertility of the source, erratic age progressions and magma output,rapid changes in volumes and orientations of volcanic features, global correlations,evidence for small degrees of melting at hotspots, evidence for recycled near-surfacematerial, tectonic context, and evidence for focusing or ponding. The plume hypothesisrequires rapid and numerous changes in plate directions, to explain the orientation ofvolcanic chains. In the plate model, rapid fluctuations in stress are implied. In the plumehypothesis the concentration of hotspots near current and former plate boundaries, edgesof cratons, and suture zones is purely coincidental. In the plate hypothesis it is expected. In the plate model, the location of volcanism is controlled by stress and fabric of theplate, not by temperature. The volume of magmatism is controlled by fertility(composition, volatile-content, solidus), of the mantle, small-scale convection andfocusing, thickness of the plate, stress state of the plate, and, to a lesser extent, thepotential temperature. Rates of magmatism depend mainly on stress history of the plate,focusing, and ponding (underplating) prior to extension. In contrast to plumes, plateinduced thermal variations are large in extent and moderate in amplitude. Chemical,fertility and solidus variations (primarily due to recycling), on the other hand, can belocal and highly variable on small spatial and temporal scales.

TomographyTomography will play an increasingly important role in mantle dynamics. Because of thelack of resolution and coverage the best seismic experiments will be in the form ofhypothesis tests. For example, do multiple ScS waves between Hawaii and the core-mantle boundary give evidence for low velocities and high attenuation? Are surfacewave,measurements along the Hawaiian chain consistent with thin lithosphere and hotasthenosphere? Is the seismic velocity in the upper mantle in the region surrounding largeigneous provinces particularly slow? Is the transition region beneath hotspots particularlythin? Actually, all of these experiments have been done and negative answers have beenreturned. A tomographic experiment to detect a plume under Iceland has to be able todistinguish a hot plume from the alternatives such as passive upwelling, EDGE inducedconvection, and partially molten slab/suture material. All of these are expected to give awedge or cone-shaped low-velocity anomaly centered between Greenland and Norway,so a definitive experiment must involve more than just an array on Iceland tuned to detectnear-vertical rays.

It is generally agreed that seismic tomography is the best tool for detecting plumes if theyexist. The failure to find consistent repeatable evidence is often attributed to lack ofresolution. If plumes really are 200 km. wide low velocity features that get blown aroundby the ‘mantle wind’ then they will indeed be hard to image. However, certain aspects of

plumes are easy to image. As plumes rise through the mantle they spread out beneathcertain types of phase changes (such as the 650 km. seismic discontinuity) and beneaththe lithosphere. They heat and thin the lithosphere. These type of plume-related effectsare easy to image but are generally lacking where expected, in the plume hypothesis[Anderson et al, 1992; Woods and Okal, 1996].

One of the most important calculations that can be done in order to test the believabilityof deep mantle features, is to compute travel times, finite frequency effects, dispersioncurves and normal modes through a synthetic Earth model with a fully three-dimensionalanisotropic code, and then to invert this data in the same way as is currently done. Thesynthetic model could even have a homogeneous mantle below 650 km. The idea is to seehow much of our current understanding of the lower mantle is based on smearing, sourceanisotropy, slab effects and other projection artifacts, rather than real features of thelower mantle. Whether the low-velocity and high-velocity zones found at various depthsin the mantle are related to plumes and slabs, or are unrelated, or are artifacts, is partly amatter of improved methods of tomographic inference, and partly a matter of statistics.

An Aside On Statistics"Extraordinary claims require extraordinary evidence" Carl Sagan (1934 - 1996)

Suppose that 25 % of the area at a given depth in the lower mantle has seismic velocitiesin the lower quartile of the distribution. There is then a 25 % chance that a randomlyselected point on the Earth’s surface will be above these low velocity regions. If there are48 hotspots then, by chance, about 12 will be above a low velocity feature. The numberof recognized hotspots has varied over time from 20 to 117 to 40 to 10. The actualnumber is of more than passing interest. If the number is over 40 then there is almost a100 % chance that some seismic anomaly in the lower mantle, in some tomographicstudy, will fall within 200-300 km. of a hotspot. Considering the resolution and coverageof seismic data there is a high probability that at least 6 hotspots, on some hotspot list,will be within 300 km. of an extended vertical region of low-velocity in sometomographic study. This is true even if the redspots in various layers of the lower mantleare distributed at random. When correlations are attempted between tomographic modelsand hotspots or subducted slabs it is necessary to compare the results with Monte Carloor similar simulations in order to show that the results could not have been obtained bychance, to a high level of significance. The idea that narrow jets of hot mantle extendfrom the surface to the core, and that seismic anomalies in the lower mantle areconnected to surface volcanoes are extraordinary claims, and require extraordinarydegrees of proof. Visual inspections of tomographic maps or cross-sections, is notadequate. Seismic tomography is a relatively young science and the statistics ofcorrelations and coincidences, and hypothesis testing have not been developed.

Summary

If history is any guide, the plume hypothesis will continue to be the reigning paradigm forsome time to come. It will become a mature science when it makes testable predictionsand is amenable to falsification. At the present time, new data and calculations oftenintroduces paradoxes (in the geochemical literature), enigmas (in the fluid dynamicliterature) and surprises (in the seismological literature), which are either put on the shelfand ignored, or are dealt with by making ad hoc amendments to the hypothesis. Becauseof these amendments, current versions of the plume hypothesis bear little resemblance toMorgan’s plumes.

Internal heating, plate tectonics, ‘normal’ mantle convection, and high ratios of viscosityto thermal conductivity (the mantle situation) do not favor narrow plume formation fromdeep thermal boundary layers. Plates occupy the upper boundary layer and haveproperties of buoyancy, coherency or strength, sharp boundaries, strike-slip motions, andelasticity that are incompatible with fluid behavior. Plumes are fluid dynamicphenomena; plates are solids. The diapir or plume hypothesis was motivated by perceivedlimitations of the plate tectonic hypothesis and by observations of plume like structures inthe atmosphere, in the crust and in fluid dynamic textbooks. Fixity and high-temperaturewere believed necessary to explain parallel island chains and large igneous provinces.These constraints have been dropped [www.mantleplumes.org; Koppers et al, 2001;Raymond et al, 2000; Wessel and Kroenke, 1997]. Other predictions of the plumehypothesis such as thermal swells, large uplift prior to volcanism, global and local heatflow, total required volumes of plume magmas, and large low-velocity asthenospheric‘pillows’ beneath large-igneous provinces have not been confirmed, but the plume ideapersists in different forms (superplumes, plumelets, incubating plumes, starting plumes,silent plumes, lateral plumes, fossil plumes, chemical plumes, new plumes and so on).The crack and stress ideas fell into disfavor because there was no apparent way toaccount for absolute fixity and large and variable volumes of basalt [Clague andDalrymple, 1987]. These are not intrinsic limitations but are a result of approximationsand assumptions in the kinematic theory of plate tectonics, such as an isothermal,homogeneous mantle of fixed melting point, uniformitarianism and plate rigidity. A moregeneral theory of plate tectonics, one that involves the end games (transients associatedwith collision and new plate boundaries), recycling, incipient and reactivated plateboundaries and ephemeral plates, may remove the necessity to have different theories forplate tectonics, large igneous provinces and linear island chains.

Much of the data that has been used to support the plume hypothesis is subject to multipleinterpretations, or is ambiguous or even contradictory. For example, there have beennumerous studies of the core-mantle boundary in the region around Hawaii [Nataf, 2000].Some of these have inferred velocity anomalies 1000 km away from Hawaii to thenorthwest, and others have proposed anomalies to the southeast and northeast. Thesestudies are inconsistent with each other but each claim consistency with a deep origin forHawaii. Other studies have found regions of high seismic gradient, changes in anisotropy,high velocity, low velocity or high scattering in the deep mantle, and all have beenattributed to the base of the Hawaiian plume [Nataf, 2000]. Such features have also beenfound elsewhere, not associated with hotspots, or offset a considerable distances from ahotspot (up to 4000 km in the case of Tristan). These have been termed “surprising”

[Nataf, 2000]. Since there are “anomalies” (in seismic velocity, gradients of velocity,anisotropy, gradients of anisotropy, and scattering) at all depths, methods need to bedeveloped for confirming that these are related to surface features (rather than random, orunrelated), and for determining whether they are continuous rather than isolated deepfeatures. There is a very high probability that the deep mantle within 1000 km of asurface hotspot will be high velocity, or low velocity, or high gradient in velocity, oranisotropic, or not anisotropic, or highly scattering or low scattering. Most of thesefeatures have used, at one time or another, as evidence for plumes [Nataf, 2000]. Thechemical indicators for deep primordial mantle have mostly been reinterpreted in terms ofrecycling and crustal contamination.

The plume hypothesis is still unsupported by a sound or complete theory involvingthermal convection. Laboratory injection experiments [e.g. Campbell and Griffiths,1990]do not take into account pressure effects, background convection or fluid dynamicscalings. Computer simulations usually have appropriate Prandtl numbers but do not takeinto account pressure effects and do not allow the conjectured instabilities to arisenaturally (e.g. Cordery et, 1997). These and similar experiments and calculations providethe theoretical support for plumes, although the initial and boundary conditions, andphysics, used to date are unrealistic, and the simulations are not thermodynamicallyconsistent. The geodynamic equivalent of the injection needle, or the initial singularity inthe computer simulations, is not obvious. This contrasts with alternate theories which useplate tectonic or surface loads to change the stress and trigger dike injection andvolcanism. More important than the incompleteness of the plume hypothesis is the lack ofinvestigation of alternate hypotheses (and critical review of the assumptions andapproximations), because the plume paradigm is so widely accepted.

We are in a period of transition where plate tectonics, mantle convection and conditionsat the core-mantle boundary are becoming an integrated theory. But a thermodynamicallyself-consistent calculation of mantle dynamics does not yet exist. Cooling of the mantlefrom above, and forces from cooling plates and subducting slabs may be adequate todrive the plates, break the plates, close or reactivate plate boundaries, reorganize plates,and drive underlying mantle flow. In such a scenerio the mantle is by and large passivelyresponding to motions of the top; dikes and plate boundaries are the result of variablestress in the lithosphere. This is the yin; the yang is the active mantle fluid dynamicmechanism where temperature is the control parameter.

A general theory of plate tectonics, one that involves recycling, incipient and reactivatedplate boundaries, and ephemeral plates, may remove the necessity to have differenttheories for plate tectonics, large igneous provinces and linear island chains. We are in aperiod of transition where plate tectonics, mantle convection and conditions at the core-mantle boundary are becoming an integrated theory. But, because of computerlimitations, a thermodynamically self-consistent calculation of mantle dynamics,including a realistic surface layer, does not yet exist. It may turn out that lithosphericphysics including dikes and stress, low-pressure petrology, shallow recycling, variablefertility and melting point, ponding/release and volatiles may explain volcanic chains,large igneous provinces and ‘hotspots’, and that the mantle is the passive partner in all

this. But, it is easier to assume, and to teach, that all anomalies are from the core-mantleboundary, deep beneath the mantle rug. This elegant idea may be true, but, if so, it wouldgrow stronger if tested against alternative ideas.

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Web ReferencesThe material discussed in this chapter can be supplemented by referring towww.mantleplumes.org

/Cracks&Stress.html/Energetics.html/FUA.html/MantleTemp.html/Convection.html/Hotspots.html/Seismology.html/TransitionZone.html/Heatflow.html/MantleTemp.html/Temperature.html/HowMany.html/Statistics.html/Philosophy.html /DefinitionOfAPlume/GTofPT.html/Bibliography_Alternatives.html/Bibliography_Plumes,.html