## Abstract

We have investigated the effects of the latent-heat release on the kinetics of the olivine-spinel phase transition to clarify the role of the thermo-kinetic coupling process for the structure of the metastable olivine-wedge in subducting slabs. We have laid out the mathematical formulation of a two-dimensional time-dependent model consisting of the kinetic equations, which are cast as a system of four nonlinear ordinary differential equations (ODE) at each spatial grid point and the time-dependent partial differential equation (PDE) for the temperature, which is coupled to the kinetics by virtue of latent-heat release. This set of ODE-PDE system has been solved by the differential-algebraic method. The structure of the kinetic phase boundary is strongly determined by thermo-kinetic coupling effects during the phase transition. For slow, warm slabs a very narrow phase boundary is obtained near the typical depth for equilibrium phase transformations. From laboratory data we obtain a small latent-heat release (< 10 kJ mol^{-1}), which results in a small heating up of the slab (around 50°). Hence thermo-kinetic coupling effects will not significantly influence the structure 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 release drastically reduces the depth and the width of the region where olivine and spinel coexist in the cold slab interior. Below the metastable wedge the latent-heat results in a significant and localized heating of the cold slab interior (around 150°), because in this regime 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 propose that deep or intermediate earthquakes occur due to a thermal runaway-effect caused by shear instabilities while these effects are enhanced by the latent-heat release associated with the olivine-spinel transformation. The correlation between fast subducting velocity and the concentration of deep-focus earthquakes at around 600 km depth, as shown for the Tonga-Kermadec trench, can be predicted by this 2-D thermo-kinetic model.

Original language | English (US) |
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Pages (from-to) | 217-239 |

Number of pages | 23 |

Journal | Physics of the Earth and Planetary Interiors |

Volume | 94 |

Issue number | 3-4 |

DOIs | |

State | Published - Apr 1996 |

### Bibliographical note

Funding Information:We thank Slava Solomatov for his helpful discussions and Linda Petzold, Werner Rath and Jamie Smedsmo for help in implementing DASPK. We thank Prof. U. Bayer for his support in computation. This research was supported by the Deutscher Akademischer Austauschdienst Deutschland (DAAD), the Geosciences program of DOE and the National Science Foundation (Geophysics and Geochemistry programs).