Don L. Anderson

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

The core-mantle boundary is often considered to be a hot-plate that drives convection. But that boundary is also part of the core-mantle 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 an essentially infinite outer space. Thermal convection in the laboratory is also such a system since the isothermal boundaries are externally maintained, using municipal power sources. Mantle convection differs from laboratory scale thermal convection in that:

The temperature of the core-mantle boundary decreases with time, as it must in order to drive the geodynamo. 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 boundary layer than one held at constant temperature and the implications for mantle convection are quite different (Arkani-Hamed, 1994). One cannot arbitrarily impose a thickness and temperature to the boundary layer; it is a result of the entire Earth-cooling history. There is a subtle, but important difference, between the views that the core is heating the mantle and that the mantle is controlling the cooling rate of the core.

It is not the current cooling rate that is important, but the integrated history. A boundary held at constant temperature develops a different kind of boundary layer structure than one that is the result of core temperature lagging behind the mantle temperature. If one imposes a certain thermal gradient then it does not matter if the core is cooling or not. However, the thermal gradient cannot be imposed–it is dependent on the history of core cooling.

The effect of pressure on thermal conductivity, coefficient of thermal expansion, specific heat and viscosity is such that it is difficult to heat and expand this region and to create any instabilities, much less narrow ones. The huge “Large Low-Shear-Velocity Provinces”, unfortunately nicknamed “superplumes”, identified beneath the south Atlantic and the Pacific are, at least in part, chemical anomalies and may be neutrally buoyant.

• Della Mora, S., Boschi, L., Tackley, P.J., Nakagawa, T. and Giardini, D., 2011, Low seismic resolution cannot explain S/P decorrelation in the lower mantle, Geophys. Res. Lett., 38, L12303, 10.1029/2011GL047559.
• Dziewonski, A.M., V. Lekic, and B.A. Romanowicz, 2010, Mantle Anchor Structure: An argument for bottom up tectonics, Earth Planet. Sci. Lett., 299, 69-79.

The D” layer above the core has only a quarter the volume of the upper boundary layer of the mantle. Because of the effects of radioactive heating and secular cooling on the geotherm it cannot be assumed that this lower boundary layer of the mantle has a higher potential temperature than the upper boundary layer.

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 (McKenzie & Bickle, 1988), meaning that it is ~200 K hotter (Anderson, 2011; Hofmeister, 1999). The main evidence for a thick thermal boundary layer (TBL) at the surface is the decrease of shear seismic velocity with depth, in particular the SH velocity (Anderson, 2011). For a given heat-flow the decrease of conductivity with depth (Hofmeister, 1999) implies a more insulating and higher temperature boundary layer. The core-mantle boundary cools with time, meaning that is does not act like a constant temperature hot-plate, and an infinite source of energy. Arkani-Hamed (1994) shows that this effect is significant. It is not the instantaneous cooling rate that is significant; it is the fact that the cooling mantle controls core temperatures and the nature of the boundary layer.

The mantle is not like a pot on a stove, or on a burner in a microwave. In practice, plumes are never modelled that way anyway. They are modelled by injecting buoyant dyes into tanks of still fluids or by varying one parameter and ignoring the temperature and pressure effects on other parameters. Thermodynamically-constrained high-resolution mantle convection simulations, do not produce:

There are long-wavelength correlations between some surface features and mid-lower mantle tomography. The lower mantle is so sluggish that the boundary condition at the base of the upper mantle is one of a long wavelength lateral temperature gradient that eventually imposes itself at the base of the upper mantle by conduction. Likewise, flat, cold, long-lived plates, which accumulate at 650 km, will cool the top of the lower mantle by conduction. Thus, it may appear, in low-resolution seismic images, that there is continuity across the boundary. However, the locations of volcanically active regions correlate much better with seismic velocities in the transition region, with past slab positions, and with plate extension, and shallow mantle shear than with features at the core-mantle boundary. Flat slabs and long-lived sluggish, lower-mantle features can explain the long-wavelength tomographic correlations by thermal coupling.

There is isotopic evidence from Hawaii that young material is sampled by the volcanoes, ruling out a surface-core-surface round trip. The ages inferred from isotopic data are isolation ages, not whole-mantle convective time scales, as originally assumed by W. Jason Morgan.

It bears repeating that the effect of temperature and pressure on thermal properties is such that the upper-mantle boundary layer is hotter and the core-mantle boundary is cooler, than generally supposed.

Fixity of magma sources can be achieved at 200 km depth, in and below the upper-mantle decoupling layer. All the geochemical characteristics (including isotopic ratios) of supposed mantle-plume-related basalts (e.g., OIBs) necessitate the presence of shallow lithologies (essentially in the form of recycled crustal material), not deep (and geochemically totally unknown) mantle sources. These considerations further eliminate the rationale for the deep mantle plume hypothesis and force attention onto the surface boundary layer.

The most important take-home message is that the mantle plume hypothesis violates thermodynamics and has no physical basis. It violates the Second Law of Thermodynamics, and fluid dynamic scaling relations.

Although Francis Birch was not involved in the plume debate, his classic 1952 paper rules them out in a very fundamental way.