CPT Q. 003: Is not the resistance to subduction far too great to allow a plate to subduct?

Q. 3. Why does not a subducting plate experience so much resistance in diving down through just the top of the mantle that it could never penetrate any significant distance? Would not the blunt front end alone prevent any movement? Would not the force needed to overcome such large resistance (if a pushing force) crush the plate or (if a pulling force) pull the plate apart?

Response: A crucially important issue here is the strength contrast between the lithosphere at the earth’s surface and the rock layer lying immediately beneath it. This zone, discovered to be very weak relative to the lithosphere above it, is known as the asthenosphere (from Greek asthenēs ‘weak’ + sphere). The British geologist Joseph Barrell in 1914, in connection with his studies of post-glacial rebound, first introduced the idea of a strong outer layer (which he named the lithosphere) overlying a much weaker layer (which he named the asthenosphere).¹ He realized such a weak zone in which lateral flow of rock could occur was required for isostatic compensation to take place. Seismologists, beginning notably from their analyses of the large 1960 Chilean earthquake, have identified that low seismic wave speeds characterize this region. They now refer this portion of the upper mantle as the ‘low velocity zone’. Since seismic wave speeds depend on the shear strength, or rigidity, of the rock, the strikingly lower seismic wave speeds at asthenospheric depths imply significantly lower rock strength in that region. Just how weak is the asthenosphere relative to the lithosphere? Various lines of observational evidence indicate that thicker oceanic lithosphere has an inelastic or viscous strength on the order of [[10^{22}]]-[[10^{23}]] Pa-s, while the asthenosphere has a viscosity on the order of [[10^{18}]]-[[10^{19}]] Pa-s. In other words, the lithosphere typically is at least a thousand times, and more typically ten thousand times, stronger than the asthenosphere.

Why is the asthenosphere so weak relative to the overlying lithosphere? The primary reason is its high temperature. Rock strength depends very strongly (exponentially) on temperature, and the difference in the strength due to temperature alone is huge. Indeed, since the temperature of the asthenosphere is not that far below the melting (solidus) temperature of its lowest melting point minerals, it is not that surprising that its strength is so far below that of the overlying lithosphere. Laboratory experiments show that the viscous strength η of silicate minerals² obeys an Arrhenius law of the form:

$$ \eta = \eta_0^{(E^* + pV^*)(\frac{1}{T} - \frac{1}{T_0})/R} $$

where E* is the mineral’s activation energy, V* is its activation volume, p is the pressure, T is the absolute temperature, [[R = 8.3145]] J/mol-K is the ideal gas constant, and η0 is the reference viscosity at reference temperature T0. For the upper mantle mineral olivine, E* is about 500 kJ/mol and V* is about [[4 \times 10^{-6}]] m3/mol.

However, yet another factor contributing to asthenospheric weakness is the likely presence of water and carbon dioxide, at 100 ppm or so levels, within the lattices of the minerals of the asthenosphere rocks.^3,4 Laboratory experiments show that the presence of these volatiles leads to a further dramatic reduction in rock strength. To summarize thus far, the layer of rock that underlies the lithospheric plates is dramatically weaker than the plates themselves. Hence, lithospheric plates should be readily able to penetrate into the layer of rock beneath them. Moreover, given the extreme contrast in rock strength between the asthenosphere and lithosphere, the drag forces on the base of the plates also should be small compared to the plate strength.

A useful tool that can be brought to bear on the mechanics of subduction is numerical simulation. Many numerical simulations of these mechanics over the last 30 years, including my own, clearly demonstrate that subduction is a robust and viable physical process. To understand the basic mechanics, several points are important to grasp. First, rocks not only can and do display reversible elastic deformation when subjected to stresses (as do most solids) but also can and do undergo inelastic non-reversible changes in shape. (Inelastic deformation is a standard and important topic included in most every graduate level mechanical engineering curriculum.) In subduction not only does the slab itself bend inelastically, it can also stretch or compress inelastically in its downward journey. But not only does the slab deform inelastically, but the mantle rock into which it sinks also deforms inelastically to accommodate the downgoing slab. The numerical methods that simulate these mechanics typically guarantee perfect conservation of mass and energy while enforcing perfect consistency of forces acting on each parcel of material throughout the computational domain. These methods also usually allow the material strength to vary from cell to cell as a function of temperature and also, in many cases, the local stress conditions. These methods are highly developed and are routinely applied in a broad spectrum of engineering applications, from the mechanical designs of turbine blades to anti-tank projectiles to nuclear weapons. The methods work. Applied to the earth and to the deformation that occurs as rock rises and sinks in the mantle as a result of differences in its buoyancy, the methods show clearly that subduction can and does take place when physically realistic values for densities, temperatures, and various material parameters are applied. Simulations confirm that the large contrast in strength between the asthenosphere and the lithosphere leads to traction forces on the base of the lithosphere which are relatively small. This in turn implies that not much pushing or pulling is required to move a plate over the underlying mantle. It also means that the stresses within the horizontal portion of a plate are generally small and well below the stress levels needed to fracture the plate.

These basic conclusions apply both to the case of uniformitarian plate tectonics (UPT) and to the regime of catastrophic plate tectonics (CPT). In the case of UPT, stress weakening in the rock deformation law is either omitted or switched off, and therefore the rocks remain strong and the deformation rates remain at the levels we observe in the present. However, when stress weakening is included (as it ought to be), the potential for runaway exists and CPT can occur. In the CPT regime, the strength contrast between lithosphere and asthenosphere remains; lithosphere subducts and behaves in largely the same way as in the non-CPT case, except that velocities are dramatically higher and the time scale is dramatically shorter.