Olivine-spinel geospeedometry: Analysis of diffusion-controlled Mg-Fe2+ exchange

Subsolidus Mg-Fe²⁺ exchange between olivine and spinel is governed by Mg-Fe²⁺ interdiffusion. Incomplete exchange results in Mg-Fe²⁺ heterogeneity in both olivine and spinel, which provides information on the thermal histories of the host rocks. A composite sphere model has been developed to obtain quantitative cooling rates or heating duration from the Mg-Fe²⁺ heterogeneity. The model assumes that a spherical core of spinel and a surrounding semi-infinite spherical shell of olivine interact by diffusion-controlled exchange of Mg and Fe²⁺. The differential equations describing the model are solved numerically by finite difference approximations. The numerical solution reveals that cooling rates or heating duration can be estimated from the relationship between the grain size of spinel and temperature calculated from the chemical compositions of the core of a spinel grain and of olivine far away from it. The calculated temperature is employed in place of $\text{Mg}\text{(Mg + Fe}{}^{\mathrm{2+}}\text{)}$ at the center of spinel to obtain the absolute temperature of thermal events.This olivine-spinel geospeedometer has been applied to peridotites. gabbro, and picrites from some ophiolite complexes in Japan to estimate their cooling rates. The estimated cooling rates for the peridotites range from 10^?4 to 10^?1 °C/yr, and those for the picrites from 10³ to 10⁴ °C/yr. The geospeedometer has been extended to estimate the heating duration of lherzolite xenoliths in basalt from the Ichinomegata crater, northeast Japan. The estimated heating duration of the xenoliths is less than one day.