The smoking gun

Don L. Anderson of CalTech joins the assault on Saunders et al's defence of Plume Theory - 16 September 2003

The recent exchange supports the view of critics of Popper's falsification scheme. Scientists are unable to abandon a paradigm simply because its empiric base has crumbled. Denial ("None of the observations listed?were ?modified? to fit the plume model? the anti-plume groups have not convinced us that their models are valid.") then anger ("We hear plenty of aggressive nihilistic attacking of the plume model") is evident, just as in other bereavements [acceptance usually comes with the next generation, after a period of bargaining (ad hoc adjustments, rationalisations ("The uplift associated with the Siberian plume was probably mostly in the adjacent West Siberian Basin? This may be part of the reason why no anomaly is seen on the Hawaiian Swell"),changes in the protective shield of auxiliary hypotheses?(" 'we don't know the age of the Hawaiian plume, as the oldest surface products are likely to have been subducted at the Kurile Trenc', perhaps not all plumes begin life with large heads.").

According to philosophers of science a research program is progressing if it displays the power to anticipate and accommodate additional data . Otherwise the program is called degenerating. A sign of an impending crisis in a paradigm is the number of times the words anomaly, paradox, unexpected, dilemma, counterintuitive, not understood, and problem appear in papers defending a hypothesis, or the number of rationalizations and additional assumptions made for failed predictions.

The smoking gun against the plume hypothesis is pressure. Fluid dynamic boundary layer theory, using parameters appropriate for upper mantle conditions, shows that surface plates should be of the order of 100km in thickness and have lifetimes of order 100 million years, in good agreement with observations. At core-mantle boundary conditions the thermal conductivity and viscosity are much higher and the thermal expansivity is much lower. Much of the buoyancy and negative buoyancy in the mantle is at the top. Furthermore, only a fraction of the Earth's heat flows through the core-mantle boundary, while all of the heat in the mantle and core eventually flows through the Earth's surface thermal boundary layer.

The net result is that the lower thermal boundary layer, by simple volume scaling arguments [1,2] is of the order of thousands of km in dimensions with a time constant comparable to the age of the Earth. The deep mantle equivalent of the surface boundary layer is not a narrow plume, as seen in laboratory injection experiments and calculations using the Boussinesq approximation [4-6], but a broad sluggish, almost static, upwelling. Furthermore, temperature has little effect on seismic velocities and density at lower mantle conditions. Pressure also serves to irreversibly stratify the mantle [2,3]; deep reservoirs are not accessible. On the other hand, the upper mantle is heterogeneous, accessible and has all the materials, components, volume and properties (including temperature) needed to explain the various types of volcanism [1], by normal plate tectonic processes.

Saunders et al. admit that they don't fully understand plate tectonics. This is a key issue, and the crux of the matter. Plate tectonics actually is consistent with the formation of volcanic chains and the existence of melting anomalies, including transient LIPs. In a convecting system, primarily cooled from above (which the mantle assuredly is) it is the surface boundary layer that is the active element and it drives (and breaks and reorganizes) itself and the underlying mantle [7,8]. By investigating the implications of plate tectonics, including recycling, refertilisation of the shallow mantle, introduction of volatiles, sublithospheric ponding, ridge migration, and continental insulation, we can understand variable volcanism along ridges and volcanism through thick plates, which is precluded in purely thermal theories [4-6], unless ad hoc singularities are introduced .

This alternate theory can, in fact, be called the plate paradigm. In contrast to assumptions in the plume paradigm the mantle is not dry, homogeneous, isothermal, refractory peridotite but is variable in fertility, volatile content, melting point and temperature. The upper mantle is close to or above the solidus almost everywhere between 50-100 and 200-300 km., except in cratonic lithosphere. Melts drain and collect (pond, underplate) beneath the plate until lithospheric stress conditions (horizontal least compressive axis) allow dikes and extrusions, and hence, volcanoes to form [9]. All of this is aided by decompression melting.

Fabric and stress of the plates control where plate boundaries and volcanic chains form. "Melting anomalies" form when migrating ridges or incipient plate boundaries intersect fertile regions of the shallow mantle. They also occur as a transient response at new plate boundaries and ridge jumps. It is the fertility and the temperature relative to the local solidus, not the absolute temperature, that is important. Thus, in the plate paradigm it is plate stress and fabric and mantle composition that are the important parameters, and relative, not absolute temperature. In addition, breaking of thick cratonic lithosphere induces vigorous upwelling that can entrain and melt previously subducted material [8], Korenaga, personal communication].

Another assumption in most discussions is that the shallowest mantle is homogenized by convection and can only provide MORB; Hawaii and other OIB, being different, must therefore come from deep. Sampling theory (small volume vs. large volume sampling) is an alternative to the reservoir and plume concepts [11-14]. Large degree melting does not occur under thick plates (because of pressure) but large volumes of melt can collect prior to eruption. These pooled melts will be different from the more homogeneous large degree melts (MORB) that form under thin lithosphere or thin crust regions. This is a simple consequence of the central limit theorem, and the location of the melting column.

The alternatives to high absolute temperature (plumes) are low melting temperature, focusing, and ponding/release . High temperatures alone cannot produce extensive melting beneath thick plates [4-6] . Petrology, heat flow, seismic and uplift studies have ruled out high temperature thermal models so we are left with athermal mechanisms to provide the volumes and rates of observed magmatism. Clearly, high absolute temperature is not the only, or even a likely option. The maximum temperature excess permitted by the petrological and geophysical data is five times lower than the excess expected from a deep thermal boundary layer but is well within the range expected from normal plate tectonic processes [15].In fact, variations in upper mantle and magma temperatures, inferred from petrology, are available in the surface conduction layer itself, particularly if the geophysically derived potential temperature of 1400°C is appropriate [1,15].

Plume theory not only predicts narrow vertical anomalies, which are hard to image, but also broad shallow anomalies beneath the plates and below the 650 km endothermic phase change, which are easy to detect. These features are not seen and only a few hotspots are associated with slow narrow seismic velocity anomalies below 400km [16,17, see also www.mantleplumes.org]. Upper mantle LVZ are most prominent below back-arc basins, western North America, eastern Pacific, and near New Zealand, not under hotspots . LVZ in the lower mantle show no connection to the surface. Some are within 1000 km of surface hotspots but the correlations are no better than random. A map of 48 random points is expected to provide about 6 coincidences with LVZ of a typical tomographic map with current resolution and coverage (velocities in the lowest 12 % are defined as anomalies).

Hawaiian and Emperor lavas are not MORB-like, since they represent different degrees of melting from a heterogeneous source, and interact with quite different lithospheres and crusts. The oldest Emperor magmas are in fact MORB-like, presumably because they erupted on thin lithosphere . The mantle is not a homogeneous single component system that is sampled exactly the same by all volcanoes, as assumed in the Saunders et al arguments. In the plume paradigm it is a paradox that ridge basalts represent large degrees of melting while hotspot basalts represent small degrees of melt. Small degree melts will exhibit higher variance than large degree melts. This is the defining geochemical characteristic of hotspot magmas [13,14]. MORB should be, and is, more homogeneous. This is not a result of vigorous convection in "the homogeneous" convecting upper mantle but is a consequence of sampling theory.

Substantial volumes of picritic basalts were produced during the initial (transient) phases of the North Atlantic Igneous Province, and these testify to source temperatures in the range predicted by plate tectonics and long periods of continental insulation. Dense picritic magmas, even eclogite slabs, can be entrained by the currents induced by the initial stages of rifting [Korenaga, personal communication]. The 1000-degree temperature excesses of deep TBL are not seen.

The Siberian Traps, which are adjacent to thick cratonic lithosphere, are a well studied example of a LIP emplaced at sea level, not the 1-2km elevation predicted by plume models [18]. The Ontong-Java plateau, the largest LIP, was emplaced entirely below sea level, in clear contradiction of any thermal model. These are candidates for the ponding-stress release and other transient mechanisms .If the largest of the so-called large igneous provinces (LIPs) cannot be due to thermal plumes then the paradigm itself is called into question. This dilemma, for the plume hypothesis, can be traced to the steady-state assumption that basalts must be produced as fast as they are erupted. An analogy is an oil well, which takes advantage of the long accumulation time in a reservoir.

The plume model also does not account for the short burst of magmatism found in some LIPs [4-6] . Ponding, followed by a change in stress, however, can explain this kind of transient. Edge (and rift) convection is also intrinsically episodic. The valving action of the lithosphere provides an elegant explanation for the formation of LIPs . Ponding and underplating, evolution in magma chambers, magma mixing, and formation of dikes, are well-recognised processes in petrology. Melts are trapped beneath the plate as long as the plate is in lateral compression, which most plates are. Magma mixing and melt homogenization is less likely under thick lithosphere.

The Top-Down hypothesis [3] asserts that cooling of the surface of the Earth (upper thermal boundary layer), plate tectonics, lithospheric plates, and their influence on mantle convection, composition and temperature, can explain most of the features we see at the Earth's surface. Cooling plates drive and organise mantle flow. The energy for melting is drawn from the mantle reservoir of heat, a much larger source of energy (and more accessible) than the core. Heat from the core drives a much broader scale and sluggish convective system that is interesting and important but which appears to be isolated from the surface [1,2,7,8]. The 670km discontinuity is a phase change, not a chemical thermal boundary layer as assumed in Saunders et al.

In addition to heat sources, there must be low thermal conductivity and high expansivity in order for thermal instabilities to form on the appropriate time scale at a chemical boundary. On the other hand magma fracture by dykes, passive upwelling at ridges and new rifts, and diapiric upwellings of the asthenosphere have nothing to do with deep thermal boundary layer instabilities.

The fact that ridges and trenches annihilate, that ocean basins close up and that continents collide, means that there is a variety of material in the outer layers of the mantle, including ophiolites, that never subducts very deeply. Some older colder slabs sink deep, but not before contributing their sediments and incompatible elements to the mantle wedge and then to the asthenosphere.

This heterogeneous material is sampled by migrating ridges and is available wherever the lithosphere allows penetration. Because of ponding, large amounts of magma can be released in short periods of time, thus overcoming a basic limitation of the plume model [4-6]. The extent of melting is controlled by the temperature relative to the liquidus, and the fertility, not the absolute temperature. The rate of magmatism is controlled by lithospheric stress and architecture, as well as mantle conditions and history. It is the assumptions of mantle homogeneity (chemical, thermal, melting point, pressure) and insensitivity to pressure that are most critical to the plume hypothesis. In summary, a partially molten and heterogeneous asthenosphere and the realities of plate tectonics remove the necessity for deep mantle plumes.

References

Author's Note : much background material and references for this discussion can be found on www.mantleplumes.org and in:

The Hotspot Handbook, Proceedings of Penrose Conference Plume IV: Beyond the Plume Hypothesis, Hveragerdi, Iceland, August 2003) www.mantleplumes.org/Penrose/PenroseAbstracts.html).

1. Don L.Anderson, Theory of the Earth, Blackwell Scientific Publications, Boston, 366 pp.1989

2. Don L. Anderson, International Geology Review, 44, 97-116. 2002

3. Don L. Anderson, Science 293, 2016-2018,2001.

4. M. Albers & U. Christensen, GRL, 23, 3567-3570, 1996

5. M. J. Cordery, G. F. Davies, I. H. Campbell, J. geophys. Res. 102,

20,179-20,197,1997.

6. C.G. Farnetani, C.G., GRL, 24, 1583-1586, 1996.

7. Don L. Anderson . Geology, 30, 411-414. , 2002

8. Don L.Anderson, Plate tectonics as a far- from- equilibrium self-organized system, AGU Monograph: Plate Boundary Zones, Geodynamics Series 30, 411-425, 2002.

9. J. Favela, and Don L. Anderson, in Problems in Geophysics for the New Millennium, E. Boschi, G. Ekström, and A. Morelli, eds., Editrice Compositori, Bologna, p. 463-498,2000

10. Don L. Anderson, Physics Today, March, p. 38-46, 1989

11. A.Meibom et al, Earth Planet. Sci. Lett., 208, 197-204, 2003

12. Don L. Anderson, Proceedings of the American Philosophical Society, 146, 56-76, 2002

13. Don L. Anderson, GRL,42, 289-311. 2000

14. A. Meibom, A., and Don L. Anderson, submitted to Earth and Planetary Science Letters, 2003

15. Don L. Anderson, GRL, v. 27, no. 22, p. 3623-3626,2000

16. Don L. Anderson, T.Tanimoto, and Y.-S. Zhang, Science, 256, 1645-1650. 1992.; H. Bijwaard, W. Spakman, Earth planet. Sci. Lett. 166, 121-126,1999.

17. J. Ritsema & R.M. Allen. Earth Planet. Sci. Lett., 207, 1-12, 2003.

18. G. Czamanske et at, The Demise of the Siberian Plume www.mantleplumes.org

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