Don L. Anderson

Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125, dla@gps.caltech.edu

Recent observations and calculations have turned the rational for the plume hypothesis on its head. In the last two years it has become clear that even the largest igneous provinces on Earth do not require plume heads for their formation–there is plenty of magma in the surface boundary layer. The hottest magmas, and the most enriched, can also be derived from the boundary layer. The upper mantle boundary layer is thick enough, hot enough and has the appropriate chemistry to explain all mid-plate volcanic phenomena. The melt is stored in melt-rich lamellae and crustal underplate and released by tectonic and magma fracturing processes.

Classical seismology and surface waves show that the surface boundary layer is >200 km thick, not the 100 km assumed in the plume hypothesis. This, plus the high thermal gradient implied by new estimates of thermal conductivity, imply that temperatures can be as high as 1600°C in the boundary layer, eliminating the need for plumes. Because of radioactive heating and secular cooling it cannot be assumed that the lower boundary layer of the mantle has a higher potential temperature than the upper boundary layer. The D” layer above the core has only a quarter the volume of the upper boundary layer of the mantle. Relative fixity of magma sources can be achieved at 200 km depth and below, in and below the decoupling layer. These considerations further eliminate the rationale for the deep mantle plume hypothesis and force attention on the surface boundary layer. The seismological arguments for mantle plumes have not stood up.

This information is scattered about the literature and generally does not appear in Science and Nature, the two main plume-advocacy publications. This readers guide may therefore be helpful in disseminating specialized seismological and petrological information to workers in other disciplines–geochemists, geophysical fluid dynamicists, and editors.

Bottom line: The source of midplate volcanoes is more like a sheared, squeezed sponge than a hot layer of fluid above a hotplate.

• Anderson, Don L., Hawaii, Boundary Layers and Ambient Mantle–Geophysical Constraints, J. Petrology, 52, 1547-1577; doi:10.1093/petrology/egq068, 2011.
• Bryan, S.E. I. Ukstins Peate, D.W. Peate, S. Self, D.A. Jerram, M.R. Mawby, J.S. Marsh, J.A. Miller, The largest volcanic eruptions on Earth, Review Article, Earth-Science Reviews, 102, 207-229, 2010.
• Cañón-Tapia, E., 2010, Origin of Large Igneous Provinces: The importance of a definition, in Cañón-Tapia, E., and Szakács, A., eds., What Is a Volcano?: Geological Society of America Special Paper 470, 77–101, doi: 10.1130/2010.2470(06).
• Doglioni C., Green D. and Mongelli F., On the shallow origin of hotspots and the westward drift of the lithosphere: in Plates, Plumes and Paradigms, G.R. Foulger, J.H. Natland, D.C. Presnall, and D.L. Anderson (Eds), GSA Sp. Paper 388, 735-749, 2005.
• Doglioni C., Ismail-Zadeh A., Panza G., Riguzzi F., Lithosphere-asthenosphere viscosity contrast and decoupling. Physics of the Earth and Planetary Interiors, 189, 1-8, 2011.
• Leahy, G.M., J.A. Collins, C.J. Wolfe, G. Laske and S.C. Solomon, Underplating of the Hawaiian Swell: evidence from teleseismic receiver functions, Geophys. J. Int., 183, 313–329, 2010, doi: 10.1111/j.1365-246X.2010.04720.x
• Presnall, D.C. and G.H. Gudfinnsson, Oceanic Volcanism from the Low-velocity Zone–without Mantle Plumes, J. Petrology, 52, 1533-1546; doi:10.1093/petrology/egq093, 2011.
• Niu, Y. and M. Wilson, J. Petrology, 52, 1239-1242; doi:10.1093/petrology/egr028.
• Niu, Y., M. Wilson, E.R. Humphreys, and M.J. O'Hara, The Origin of Intra-plate Ocean Island Basalts (OIB): the Lid Effect and its Geodynamic Implications, J. Petrology, 52, 1443-1468; doi:10.1093/petrology/egr030, 2011.
• Pilet, S., M.B. Baker, O. Muntener, and E.M. Stolper, Monte Carlo Simulations of Metasomatic Enrichment in the Lithosphere and Implications for the Source of Alkaline Basalts, J. Petrology, 52, 1415-1442; doi:10.1093/petrology/egr007, 2011.
• Heron, P.J. & Lowman, J.P., Thermal response of the mantle following the formation of a "super-plate", Geophys. Res. Lett., 37, No. 22, L22302, 2010.

The net rotation or westward drift of the lithosphere implies a decoupling and a shearing in the boundary layer

Decoupling between the lithosphere and sub-asthenospheric mantle involves a shear gradient in the mantle below the magmatic source.  Estimates of the net rotation of the Earth’s surface can be obtained if melting anomalies are sourced in the middle of the low-velocity layer, i.e., within the decoupling layer of the plates relative to the underlying mantle (Doglioni et al., 2005, 2011, and personal communication, Carlo Doglioni, 2011).

• Doglioni C., Green D. and Mongelli F., On the shallow origin of hotspots and the westward drift of the lithosphere: in Plates, Plumes and Paradigms, G.R. Foulger, J.H. Natland, D.C. Presnall, and D.L. Anderson (Eds), GSA Sp. Paper 388, 735-749, 2005.
• Doglioni C., Ismail-Zadeh A., Panza G., Riguzzi F., Lithosphere-asthenosphere viscosity contrast and decoupling. Physics of the Earth and Planetary Interiors, 189, 1-8, 2011.

Modeling shows that hotspot swells and midplate volcanoes can be explained even if there is no heat or mass transport from below 240 km. If a plume is introduced artificially then the seismic data are not satisfied. High resolution seismic imaging under Hawaii that includes surface waves, absolute velocities and anisotropy find high, not low, seismic velocities. This does not contradict the evidence that half of the teleseismic arrivals to Hawaii are slower than the other half.

• Adam, C., Yoshida, M., Isse, T., Suetsugu, D., Fukao, Y., Barruol, G., South Pacific hotspot swells dynamically supported by mantle flows, Geophys. Res. Lett., 37, L08302, 2010.
• Ballmer, M.D., G. Ito, J. van Hunen & P. J. Tackley, Spatial and temporal variability in Hawaiian hotspot volcanism induced by small-scale convection, Nature Geoscience, 4, 457–460, 2011, doi:10.1038/ngeo1187, 2011.
• Cao, Q., R. D. van der Hilst, M. V. de Hoop, and S.-H. Shim, Seismic imaging of transition zone discontinuities suggests hot mantle west of Hawaii, Science, 332, 1068-1071, 2011.

Thermodynamically constrained mantle convection simulations, do not produce:

1. narrow hot upwellings,
2. adiabatic gradients, or
3. potential temperatures

in D” that exceed upper mantle temperatures.

• Schuberth, B. S. A., Bunge, H. P., Steinle-Neumann, G., Moder, C. & Oeser, J. (2009). Thermal versus elastic heterogeneity in high-resolution mantle circulation models with pyrolite composition, Geochemistry, Geophysics, Geosystems, 10, Q01W01, doi:10.1029/2008GC002235.

Partial melt in the low-velocity zone eliminates the need for hot plumes from the core-mantle boundary, and long-distance lateral transport. The melt can be removed by shearing and flow through lithospheric conduits in addition to buoyancy removal. The term “partial melt” is misleading since the melt can be introduced by dynamic processes, such as shearing. The melt content may exceed equilibrium considerations.

• Hirschmann, M.M., Partial melt in the oceanic low velocity zone, PEPI, 179, 60-71, 2010.
• Duggen, S., K.A. Hoernle, F. Hauff, A. Kluegel, M. Bouabdellah and M.F. Thirlwall, Flow of Canary mantle plume material through a subcontinental lithospheric corridor beneath Africa to the Mediterranean: Reply, Geology, 38, p. e202, doi:10.1130/G30516C.1, 2010.
• Conrad, C.P., Benjun Wu, E.I. Smith, T.A. Bianco, A. Tibbetts, Shear-driven upwelling induced by lateral viscosity variations and asthenospheric shear: A mechanism for intraplate volcanism, PEPI, 178, 162-175, 2010.
• Kawakatsu, H., Kumar, P., Takei, Y., Shinohara, M., Kanazawa, T, Araki, E. & Suyehiro, K., Seismic evidence for sharp lithosphere-asthenosphere boundaries of oceanic plates. Science, 324, 499-502, doi:10.1126/science.1169499, 2009.
• Kohlstedt, D.L. & Holtzman, B.K., Shearing melt out of the Earth: An experimentalist’s perspective on the influence of deformation on melt extraction, Annual Review of Earth and Planetary Sciences, 37, 16.1-16.33, doi:10.1146/annurev.earth.031208.100104, 2009.
• Holtzman, B.K., and J.-M. Kendall), Organized melt, seismic anisotropy, and plate boundary lubrication, Geochem. Geophys. Geosyst., 11, Q0AB06, doi:10.1029/2010GC003296, 2010.

Hawaii and other Pacific hotspots have high upper-mantle seismic velocities, even though half of the relative arrival times are later than the other half.

• Katzman, R., Zhao, L. & Jordan, T. H., High-resolution, two-dimensional vertical tomography of the central Pacific mantle using ScS reverberations and frequency-dependent travel times. Journal of Geophysical Research, 103, 17933-17971, 1998.
• Maggi, A., Debayle, E., Priestley, K. & Barroul, G., Multimode surface waveform tomography of the Pacific Ocean: a closer look at the lithospheric cooling signature. Geophysical Journal International, 166, 1384-1397, 2006.

The plume and whole-mantle convection hypotheses are dependent on each other. The idea that the mantle can convect as a whole, in spite of the large changes in physical properties, is based on perceived correlations of some very long wavelength features in the upper and lower mantles. However, there are very sharp decorrelations at 220 and 650 km. Flat slabs at 650 km and sluggish convection in the lower mantle means that thermal coupling is possible, giving the appearance of continuity across the boundary. The correlations of hotspots with shearing in the upper mantle, and with the absence of flat slabs at 600-800 km depth is much stronger than claimed correlations with deep mantle structure. In addition, the so-called superplumes in the lower mantle are compositional, not thermal, and it has been shown that the spawning of plumlets from these lower mantle features is not plausible. The best correlations with basalt chemistry and temperature are with lid thicknesses and age of the plate. There are no significant correlations of hotspots and transition zone or lower mantle properties, but there are also no correlations between different tomographic models at the plume and slab scale, or even plate and continent scales.

• Della Mora, S., Boschi, L., Tackley, P.J., Nakagawa, T., Giardini, D., Low seismic resolution cannot explain S/P decorrelation in the lower mantle, Geophys. Res. Lett., 38, No. 12, L12303, 10.1029/2011GL047559, 2011.
• Dziewonski, A.M., V. Lekic, B.A. Romanowicz, Mantle Anchor Structure: An argument for bottom up tectonics, Earth Planet. Sci. Lett., 299, 69-79, 2010.
• Fukao, Yoshio, Masayuki Obayashi, Tomoeki Nakakuki and the Deep Slab Project Group, Stagnant Slab: A Review, Annu. Rev. Earth Planet. Sci., 37, 19-46, 2009.
• Torsvik, T.H., K. Burke, B. Steinberger, S.J. Webb & L.D. Ashwal, Diamonds sampled by plumes from the core-mantle boundary, Nature, 466, 352–355, doi:10.1038/nature09216, 2010.
• Ritsema, J., A. Deuss, H. J. van Heijst and J. H. Woodhouse, S40RTS: a degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements, Geophys. J. Int., 184, 1223–1236, 2011.
• Sun, Daoyuan, D. Helmberger, Upper-mantle structures beneath USArray derived from waveform complexity, Geophys. J. Int., published online: 30 Nov. 2010, doi: 10.1111/j.1365-246X.2010.04847.x
• Ballmer, M. D., J. van Hunen, G. Ito et al. (2009) Intraplate volcanism with complex age-distance patterns: A case for small-scale sublithospheric convection, Geochem. Geophys. Geosys., 10, doi:10.1029/2009GC002386.
• Humphreys, E.R. & Y. Niu, On the composition of ocean island basalts (OIB): The effects of lithospheric thickness variation and mantle metasomatism, Lithos, 112, 118–136, 2009.

Harry Green and his group have used a novel approach to rule out the transport of water into the transition zone. This means that slab dehydration fluxes the shallow mantle and lowers the melting temperature of the boundary layer. This in turn suggests that the source of MORB may be in the transition region, below the contaminating effects of recycling. Slabs displace this material upwards.

• Green, H.W. II, Wang-Ping Chen & M.R. Brudzinski, Seismic evidence of negligible water carried below 400-km depth in subducting lithosphere, Nature, 467, 828–831, doi:10.1038/nature09401
• Faccennaa, C., T.W. Beckerb, S. Lallemandc, Y. Lagabriellec, F. Funiciellod and C. Piromallo, Subduction-triggered magmatic pulses: A new class of plumes?, Earth Planet. Sci. Lett., 299, 54-68, 2010.

Primordial noble gas signatures can be stored in the shallow mantle, and are evident in crustal fluids, olivines and diamond crystals. The shallow part of the boundary layer is composed of cold refractory harzburgite. This cold, low-U environment is ideal for storing ancient fragments.

• Castro, M.C., L. Ma & C.M. Hall, A primordial, solar He-Ne signature in crustal fluids of a stable continental region, Earth Planet. Sci. Lett., 279, 174-184, 2009.
• Sumino, H., L.F. Dobrzhinetskaya, R. Burgess, H. Kagi, Deep-mantle-derived noble gases in metamorphic diamonds from the Kokchetav massif, Kazakhstan, Earth Planet. Sci. Lett., 307,439-449, 2011.
• Sobolev, A.V., A.W. Hofmann, K.P. Jochum, D.V. Kuzmin & B. Stoll, A young source for the Hawaiian plume, Nature, Published online 10 August 2011, doi:10.1038/nature10321

No well constrained seismic model has ever imaged a mantle plume. All plume sightings are based on the vertical tomography travel-time method, or ACH. This is not only subject to streaking, but it also makes gross mathematical approximations that render the results unreliable. The method also ignores anisotropy and absolute velocities. Monte Carlo simulations, and comparisons of all reliable tomographic models, show that claims of images of plumes and slabs in the lower mantle cannot be substantiated. Surface waves and body waves that cross the upper mantle horizontally instead of vertically show that regions attributed to plumes actually have high seismic velocities.

• Bastow, I.D., Pilidou, S., Kendall, J.-M., Stuart, G.W., 2010. Melt-induced seismic anisotropy and magma assisted rifting in Ethiopia: evidence from surface waves, Geochem. Geophys. Geosyst., 11, Q0AB05. doi:10.1029/2010GC003036.
• Christoffersson, A. & E.S. Husebye, Seismic tomographic mapping of the Earth's interior–Back to basics revisiting the ACH inversion, Earth-Science Reviews, 106, 293-306, 2011.
• Fouch, M.J. et al., Three-dimensional geophysical structure of the Yellowstone/Snake River Plain hotspot system: is a deep mantle plume required?, 2011 GSA Annual Meeting, Minneapolis, 9–12 October, Abstract # 143-5, 2011.
• Hadley, D.M., Stewart, G.S., Ebel, J.E., 1976, Yellowstone - seismic evidence for a chemical mantle plume, Science, 193, 1237-1239.
• Masson, F. & Trampert, J., On ACH, or how reliable is regional teleseismic delay time tomography? Physics of the Earth and Planetary Interiors, 102, 21-32, 1997.
• O'Donnell, J.P., E. Daly, C. Tiberi, I.D. Bastow, B.M. O'Reilly, P.W. Readman & F. Hauser. Lithosphere-asthenosphere interaction beneath Ireland from joint inversion of teleseismic P-wave delay times and GRACE gravity, Geophys. J. Int., doi:10.1111/j.1365-246X.2011.04921.x, 2011.
• Ritsema, J., A. Deuss, H. J. van Heijst and J. H. Woodhouse, S40RTS: a degree-40 shear-velocity model for the mantle from new Rayleigh wave dispersion, teleseismic traveltime and normal-mode splitting function measurements, Published online 14 Dec 2010 | doi: 10.1111/j.1365-246X.2010.04884.x
• Shapiro, N.M. & Ritzwoller, M.H., Monte-Carlo inversion fora global shear velocity model of the crust and upper mantle, Geophysical Journal International, 151, 88-105, 2002.
• van der Lee, S. and G. Nolet, Upper mantle S velocity structure of North America, J. Geophys.
  Res., 102, 22,815–22,838, 1997.

There are two kinds of boundary layers; shear-driven and buoyancy-driven. In either case, uplift and magmatism are due to boundary layer, top-down, processes. Delamination is often considered a Rayleigh-Taylor instability but it can also be due to shearing.

• Conrad, C.P., T.A. Bianco, E.I. Smith & P. Wessel, Patterns of intraplate volcanism controlled by asthenospheric shear, Nature Geoscience, 4, 317–321, 2011, doi:10.1038/ngeo1111.
• Levander, A., B. Schmandt, M.S. Miller, K. Liu, K.E. Karlstrom, R.S. Crow, C.-T. A. Lee & E.D. Humphreys, Continuing Colorado plateau uplift by delamination-style convective lithospheric downwelling, Nature, 472, 461-465, 2011, doi:10.1038/nature10001
• Jackson, M.G. & R.W. Carlson, An ancient recipe for flood-basalt genesis, Nature, 476, 316–319, doi:10.1038/nature10326, 2011.
• Sun, Daoyuan, D. Helmberger, Upper-mantle structures beneath USArray derived from waveform complexity, Geophys. J. Int., published online: 30 Nov 2010 | doi: 10.1111/j.1365-246X.2010.04847.x

There are various tectonic and enrichment mechanisms that are side effects to global plate tectonics and involved in mid-plate magmatism. Essentially all mid-plate magmas can be explained by shallow recycling of crustal components. Even sea water has contaminated the Mauna Loa source rock. The presence of 200-650 Ma oceanic crust in the source of Hawaiian lavas implies a shallow boundary source, rather than rapid transit to the core-mantle boundary and back. The boundary layer of the mantle differs in composition and temperature from the mantle sampled at ridges.

• Heron, P.J. & Lowman, J.P., Thermal response of the mantle following the formation of a "super-plate", Geophys. Res. Lett., 37, L22302, 2010.
• Schellart, W.P., Mount Etna-Iblean volcanism caused by rollback-induced upper mantle upwelling around the Ionian slab edge: An alternative to the plume model, Geology, 38, 691-694, doi: 10.1130/G31037.1, 2010.
• Sobolev, A.V., A.W. Hofmann, K.P. Jochum, D.V. Kuzmin & B. Stoll, A young source for the Hawaiian plume, Nature, Published online 10 August 2011, doi:10.1038/nature10321
• Valentine, G.A. & N. Hirano, Mechanisms of low-flux intraplate volcanic fields—Basin and Range (North America) and northwest Pacific Ocean, Geology, 38, 55-58, doi: 10.1130/G30427.1, 2010.

Non-MORB isotopic compositions are usually assumed to be from the lower mantle but they can also represent ancient materials stored in the crust and mantle boundary layer. MORB then represents regions where the boundary layer has been carried away or dissipated. Geochemistry provides very few constraints on locations of sources. The “geochemical constraints” are actually assumptions, and most “plume components” are actually crustal components.

• Jackson, M.G., R.W. Carlson, M.D. Kurz, P.D. Kempton, D. Francis & J. Blusztajn, Evidence for the survival of the oldest terrestrial mantle reservoir, Nature, 466, 853–856, 2010.

A key seismological test of the thermal plume hypothesis involves the sharpness of hypothetical plume conduits. If low-velocity regions in the mantle have sharp edges they cannot be due to long-lived thermal plumes. It also helps to have information about absolute seismic velocity, attenuation and anisotropy. All tomographic images that have been interpreted as plumes lack these kinds of supporting data.

• Sun, Daoyuan, D. Helmberger, Upper-mantle structures beneath USArray derived from waveform complexity, Geophys. J. Int., published online: 30 Nov 2010 | doi: 10.1111/j.1365-246X.2010.04847.x
• Schmandt, B., E. Humphreys, Complex subduction and small-scale convection revealed by body-wave tomography of the western United States upper mantle, Earth Planet. Sci. Lett., 297, 435-445, 2010.
• O'Reilly, Suzanne Y., W.L. Griffin, The continental lithosphere-asthenosphere boundary: Can we sample it?, Lithos, 120, 1-13, 2010.
• Faccennaa, C., T.W. Beckerb, S. Lallemandc, Y. Lagabriellec, F. Funiciellod and C. Piromallo, Subduction-triggered magmatic pulses: A new class of plumes?, Earth Planet. Sci. Lett., 299, 54-68, 2010.
• Willbold, M., A. Stracke, Formation of enriched mantle components by recycling of upper and lower continental crust, Earth Planet. Sci. Lett., 297, 188-197, 2010.
• Jackson, M.G., R.W. Carlson, M.D. Kurz, P.D. Kempton, D. Francis & J. Blusztajn, Evidence for the survival of the oldest terrestrial mantle reservoir, Nature, 466, 853–856, 2010.

In addition to the strong anisotropy of the central Pacific, high-resolution surface wave models show that negative SH gradients extend to >200 km depth, implying a conduction gradient to at least that depth and high absolute temperatures. The minimum in SV velocity at 150 km depth implies a maximum melt content at that depth.

• Ekstrom, G. & Dziewonski, A.M. The unique anisotropy of the Pacific upper mantle, Nature, 394, 168-172, 1998.

All the active volcanoes in China and Europe that were previously thought to be the result of deep mantle plumes have now been recognized as being related to underlying slabs. Yellowstone may have a similar explanation.

• Wortel, M.J.R. et al. Subduction and Slab Detachment in the Mediterranean-Carpathian Region, Science, 290, 1910, 2000.
• Zhao, D. et al., Origin of the Changbai intraplate volcanism in Northeast China: Evidence from seismic tomography, Chinese Science Bulletin, 49, 1401-1408, 2004.

The core mantle boundary is often considered to be a hotplate that drives convection, as does a stove top. But that boundary is also part of the system and it cools with time. It is not an infinite source of energy. Things that happen at the surface of the Earth, including life and atmospheric convection, are examples of far-from-equilibrium, self-organized systems since they have an essentially infinite supply of external energy and can radiate to outer space. Thermal convection is also such a system since the isothermal boundaries are externally maintained.

Mantle convection differs from laboratory scale thermal convection in that only the upper boundary is maintained at constant temperature but energy can still be disposed of through the surface. The core-mantle boundary is often treated as a constant temperature renewable source of heat, like a stove, but in fact its temperature decreases with time, as it must in order to drive the dynamo. Both the mantle and the core are top-down phenomena, driven by heat extraction through their surfaces. One might view the universe as being heated by a cooling Earth and the  mantle as being heated and driven by a cooling core but it is more useful to think of both as cooling at a rate dictated by the overlying media. A cooling core-mantle boundary has a weaker core-mantle boundary layer than one held at constant temperature and the implications for mantle convection are quite different.

The mantle does not work like a pot on a stove, or a pot on a burner in a microwave. Plumes are never modelled that way anyway.

• Jafar Arkani-Hamed. Effects of the core cooling on the internal dynamics and thermal evolution of terrestrial planets, J. Geophys. Res., 99, 12,109-12,119, 1994.

Assorted older papers on the upper and lower boundary layers of the mantle

Tomographic features similar to those attributed to plumes are found under the Canadian and Brazilian Shields, Britain, and in regions influenced by long-sustained subduction. This alone indicates the non-uniqueness of color images that do not contain any information about the underlying seismic structure. Color images cannot be used to discuss absolute, homologous or potential  temperatures. Even absolute seismic velocity is not a proxy for temperature.

• Sol, S., C.J. Thomson, J.-M. Kendall, D. White, J.C. VanDecar, I. Asudeh, Seismic  tomographic images of the cratonic upper mantle beneath the Western Superior  Province of the Canadian Shield—a remnant Archean slab?, PEPI, 134, 53–69, 2002.
• Wortel, M.J.R., W. Spakman,  Subduction and slab detachment in the Mediterranean-Carpathian region, Science, 291, 437, 2001.

The coup de grace to classical plume theory is the recognition that radioactivity and secular cooling make D” colder, in the potential temperature sense, than the upper mantle. The upper conduction layer, however,  is thicker, and lower conductivity than in the canonical Cambridge model, meaning that it is ~200°C hotter. The core-mantle boundary cools with time, meaning that is does not act like a constant temperature hot plate. Also, the mantle under Hawaii has higher than average seismic velocities.

• Jeanloz, R., S. Morris, Is the mantle geotherm subadiabatic, Geophys. Res. Lett., 14, 335–338, 1987.
• Schuberth, B.S.A. et al., Thermal versus elastic heterogeneity in high-resolution mantle circulation models with pyrolite composition: High plume excess temperatures in the lowermost mantle, Geochemistry Geophysics Geosystems, 10, Q01W01, doi:10.1029/2008gc002235, 2009.
• Shapiro, N.M. & Ritzwoller, M.H., Monte-Carlo inversion for a global  shear velocity model of the crust and upper mantle. Geophys. J.  Int., 151, 88-105, 2002.
• Hofmeister, A.M., Mantle values of thermal conductivity and the geotherm from phonon lifetimes, Science, 283,1699-1706, 1999.
• Arkani-Hamed, Jafar, Effects of the core cooling on the internal dynamics and thermal evolution of terrestrial planets, J. Geophys. Res., 99, 12,109-12,119, 1994.
• Maggi, A., Debayle, E., Priestley, K. & Barroul, G., Multimode surface waveform tomography of the Pacific Ocean: a closer look at the lithospheric cooling signature, Geophys. J.  Int., 166, 1384-1397, 2006.