Bina, C. R., and S. H. Kirby, The petrological buoyancy cost of slabs with metastable olivine descending into the transition zone and lower mantle: Model results for the Tonga subduction zone, Terra Nostra, Abstracts of the Alfred Wegener Conference on Processes and Consequences of Deep Subduction, Verbania, Italy, 99/7, 56-57, 1999.
Published tomographic images [e.g., van der Hilst, 1995] and the presence of numerous deep earthquakes outboard and west of the bottom of the inclined Tonga Wadati-Benioff zone argue for some form of increase in resistance to slab descent into the transition zone and lower mantle. This deflection produces a seismically-active recumbent slab structure extending as much as 750 km west of the bottom of the inclined seismic zone. Recent work by Okal and Kirby  concluded that the petrological buoyancy of metastable olivine may be an important source of such resistance for the very rapidly descending and hence very cold Tonga slab. The presence of such hypothetical metastable olivine may facilitate deep earthquake occurrence by, for example, transformational faulting, dehydration embrittlement, or a thermal instability [e.g., Kirby et al., 1991; 1996; Silver et al., 1995; Kanamori et al., 1998]. We model the deep Tonga slab by computing the thermal structure for 120-Ma-old lithosphere subducting at 45° at 24 cm/yr [Bevis et al., 1995]. Employing a bulk composition of Fo90 olivine and published thermodynamic parameters for the olivine polymorphs [See Bina, 1997], we calculate the resulting mineralogy in such a slab for both the equilibrium case and the case in which the alpha phase olivine persists metastably at temperatures less than 1000 K. We then calculate the net thermal and petrological buoyancy of the slab as a function of depth, thereby estimating the resistance to slab descent into the transition zone and lower mantle just due to buoyancy forces. We find that the petrological buoyancy of low-density metastable olivine increases stepwise near 410 and 550 km and again at 660 km, where it is more than twice that expected for thermal depression of the equilibrium spinel -> pv + mw transformation. A finite-element model of the stress effects of such buoyancy forces using a purely elastic rheology indicates that attempts to subduct a metastable olivine wedge would produce extremely large slab compressive stresses in the transition zone and large bending moments and stresses associated with upward slab deflection at depths exceeding 660 km. Seismological evidence indicates intense deformation of the Tonga slab occurs near 660 km, producing westward deflection and fault offsets of the seismic zone [Giardini and 1984]. This deformation may be linked with the marked positive (floating) petrological buoyancy and increased resistance below 660 km to the descent of slab material with metastable olivine indicated by our models. The metastability model also gives insight into some of the characteristics of the numerous outboard earthquakes west of the Tonga Wadati-Benioff zone [Okal and Kirby, 1998].
This large buoyancy cost of the deep descent of metastable olivine also offers a simple explanation of why no deep earthquakes have been detected in the lower mantle: The buoyancy cost of such untransformed olivine would be too high for seismically-active slab material to descend into the lower-mantle. Slab fragments can be produced by faulting of slab material in the transition zone. A deep, cold slab fragment will be positively buoyant at depths of 450, 550 and 720 km if the volume percent of metastable olivine exceeds about 20, 12 and 5%, respectively. Such fragments would float if the positive buoyancy of the fragment was sufficient to overcome viscous resistance to ascent. This may help explain why outboard deep earthquakes tend to occur at depths shallower than 660 km. Lastly, stagnation of slab material containing metastable olivine would cease after heating sufficiently for rates of transformation to spinel to consume metastable olivine and resume descent into the lower mantle [Okal and Kirby, 1998].
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Bina, C (1997): Patterns of deep seismicity reflect buoyancy stresses due to phase transitions. Geophys. Res. Lett. 24, 3301-3304.
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