2-DIMENSIONAL THERMO-KINETIC MODEL FOR THE OLIVINE-SPINEL PHASE-TRANSITION IN SUBDUCTING SLABS

We have investigated the effects of the latent-heat release on the kin etics of the olivine-spinel phase transition to clarify the role of th e thermo-kinetic coupling process for the structure of the metastable olivine-wedge in subducting slabs. We have laid out the mathematical f ormulation of a two-dimensional time-dependent model consisting of the kinetic equations, which are cast as a system of four nonlinear ordin ary differential equations (ODE) at each spatial grid point and the ti me-dependent partial differential equation (PDE) for the temperature, which is coupled to the kinetics by virtue of latent-heat release. Thi s set of ODE-PDE system has been solved by the differential-algebraic method. The structure of the kinetic phase boundary is strongly determ ined by thermo-kinetic coupling effects during the phase transition. F or slow, warm slabs a very narrow phase boundary is obtained near the typical depth for equilibrium phase transformations. From laboratory d ata we obtain a small latent-heat release (<10 kJ mol(-1)), which resu lts in a small heating up of the slab (around 50 degrees). Hence therm o-kinetic coupling effects will not significantly influence the struct ure of the phase boundary in this regime. For fast, cold slabs narrow regions with metastable olivine may be pushed down to a depth of about 600 km while the thermo-kinetic coupling due to the latent-heat relea se drastically reduces the depth and the width of the region where oli vine and spinel coexist in the cold slab interior. Below the metastabl e wedge the latent-heat results in a significant and localized heating of the cold slab interior (around 150 degrees), because in this regim e the heat release is three times higher. The depth of the metastable wedge in the subducting slab is found to be very sensitive to certain thermodynamic parameters such as the activation energy for growth and the internal slab heating caused by the phase transformation. We propo se that deep or intermediate earthquakes occur due to a thermal runawa y-effect caused by shear instabilities while these effects are enhance d by the latent-heat release associated with the olivine-spinel transf ormation. The correlation between fast subducting velocity and the con centration of deep-focus earthquakes at around 600 km depth, as shown for the Tonga-Kermadec trench, can be predicted by this 2-D thermo-kin etic model.