Marton, F. C., C. R. Bina, S. Stein, and D. C. Rubie, Olivine phase transitions and subduction rates, Terra Nostra, Abstracts of the Alfred Wegener Conference on Processes and Consequences of Deep Subduction, Verbania, Italy, 99/7, 65-66, 1999.
The role of mineralogy and phase transitions in the subduction process has been investigated with respect to slabs' interactions with mantle seismic discontinuities. Their role in the state of stress and the generation of deep earthquakes has also been of interest. Attention has been recently been paid to the influence of mineralogy on the buoyancy of subducting slabs and the possible influence it may have on subduction rates [Rubie 1993; Kirby et al., 1996]. The negative thermal buoyancy of cold lithosphere is thought to be a major control of these velocities. Therefore, changes in the density of the slab relative to the surrounding mantle via phase transitions of olivine [(Mg,Fe)2SiO4] should have a significant effect on the subduction rates. In addition to deflecting equilibrium phase boundaries, cold temperatures in the interior of the slab may kinetically inhibit these transformations [Rubie and Ross, 1994]. The resulting metastable wedge of olivine might then act as a "parachute" and slow the descent of the slab [Kirby et al., 1996].
We have developed a thermo-kinetic model to investigate the effects of olivine phase transitions on slab velocities. Temperature structure is computed via a finite difference algorithm [Minear and Toksöz, 1970] with initial lithospheric temperatures from a plate model with GDH1 parameters [Stein and Stein, 1992]. Equilibrium phase assemblages are determined thermodynamically [Fei et al., 1991] and a kinetic model [Rubie and Ross, 1994] with latent heat feedback determines the extent of metastability. A simple two-dimensional model slab is moved through a mantle with constant viscosity. A calculated terminal velocity (CTV) is found via the balance of the driving negative buoyancy and opposing viscous drag forces. As we are concerned with the thermal state of the slab, we use the thermal parameter, j, to describe it to first order [Molnar et al., 1979]. j was developed for a conductive heating model where isotherms are advected to maximum depths that are proportional to the vertical descent rate vz. If the plate thickness is proportional to the square root of the age of the slab, as it is in a cooling halfspace model, these depths are proportional to j = vz x age. We have previously found that the presence of metastable olivine can cause slabs to decelerate by as much as 20-30% relative to slabs that only undergo equilibrium phase changes [Marton et al., 1999]. This "parachute effect" is greatest for the coldest slabs.
The parachute effect should act as a negative feedback on subduction rates. The colder the slab, the larger the metastable wedge, and the greater the parachute effect. As the slab slows, however, it will heat by conduction and the metastable wedge will thermally erode. This in turn should cause the slab's negative buoyancy to increase and the slab should speed up. In order to test this, we modified our model to feed the CTV for a slab extending to a depth of 750 km back into the model, adjusting the time-step increments between iterations. The results, shown for a slab with an age of the lithosphere at the trench of 140 My, a dip angle of 60°, and an initial velocity of 8 cm/yr (j = 9700 km), show the CTV and the cross-sectional area of the metastable wedge quickly approach a steady state after it fully penetrates the transition zone (Fig. 1). Moreover, over short time scales, area and CTV can be seen to be negatively correlated (Fig. 2). This suggests that the parachute effect does cause a negative feedback on subduction rates, thus narrowing the range of the rates and helping to control plate speeds.
References
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Kirby, S.H., S. Stein, E. A. Okal, and D. C. Rubie, Metastable phase transformations and deep earthquakes in subducting oceanic lithosphere, Rev. Geophys., 34, 261-306, 1996.
Marton, F. C., C. R. Bina, S. Stein, and D. C. Rubie, Effects of slab mineralogy on subduction rates, Geophys. Res. Lett., 26, 119-122, 1999.
Minear, J., and M. N. Toksöz, Thermal regime of a downgoing slab and new global tectonics, J. Geophys. Res., 75, 1379-1419, 1970.
Molnar, P., D. Freedman, and J. S. F. Shih, Lengths of intermediate and deep seismic zones and temperatures in downgoing slabs of lithosphere, Geophys. J. Int., 56, 41-54, 1979.
Rubie, D. C., Mechanisms and kinetics of solid-state reconstructive phase transformations in the Earth's mantle, in Short Course handbook on Experiments at High Pressure and Applications to the Earth's Mantle, edited by R. W. Luth, pp. 247-303, vol. 21, Mineralogical Association of Canada, Edmonton, 1993.
Rubie, D. C., and C. R. Ross II, Kinetics of the olivine-spinel transformation in subducting lithosphere: Experimental constraints and implications for deep slab processes, Phys. Earth Planet. Inter., 86, 223-241, 1994.
Stein, C. A., and S. Stein, A model for the global variation in oceanic depth and heat flow with lithopsheric age, Nature, 359, 123-129, 1992.
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