Formation of a metastable olivine wedge in a descending slab

We present a thermal model of a descending slab in which the transformation of olivine to spinel is controlled by pressure-and temperature-dependent reaction kinetics. Two different formulations of the kinetics are considered with the main discriminant being the temperature range over which olivine converts to spinel at pressures of about 15 GPa (about 500 degrees-515 degrees C and 560 degrees-650 degrees C). We use a finite element method to solve the coupled heat conduction (perpendicular and parallel to the dip of the slab) and kinetics equations, and we include the latent heat of the phase transformation. Latent heat release together with beat conduction parallel to the dip of the slab reduces significantly the length of the metastable olivine wedge and results in a very thin (less than or similar to 5 km) two-phase region. We employ the thermal parameter v tau sin delta (v is the velocity of the descending slab, tau is the age of the slab, and delta is the dip of the slab to the horizontal) to interpret the results for the length of the metastable wedge. For values of the thermal parameter smaller than about 4000 and 7000 km, depending on the model of the kinetics, no metastable olivine wedge exists (the critical value of 7000 km for the thermal parameter corresponds to the kinetics model with the lowest transition temperature range). The length of the metastable olivine wedge is also found to be very sensitive to the model of the kinetics and to the effects of adiabatic heating. If the occurrence of deep earthquakes is related to the transformation of metastable olivine to spinel, then data on earthquake depth versus thermal parameter require that the onset of the reaction takes place at temperatures of about 550 degrees-575 degrees C. In this case the slab thermal parameter must be larger than 10,000 km for the metastable olivine wedge to extend down to 660 km depth. But deep earthquakes occur near 660 km depth in slabs with thermal parameter as small as about 5000 km (South America, for example). Either some deep earthquakes are unrelated to olivine metastability or our knowledge of olivine-spinel reaction kinetics is incomplete.