R. Dassler et al., 2-DIMENSIONAL THERMO-KINETIC MODEL FOR THE OLIVINE-SPINEL PHASE-TRANSITION IN SUBDUCTING SLABS, Physics of the earth and planetary interiors, 94(3-4), 1996, pp. 217-239
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.