MODELS OF ISOTOPIC EXCHANGE IN REACTIVE FLUID-ROCK SYSTEMS: IMPLICATIONS FOR GEOCHRONOLOGY IN METAMORPHIC ROCKS

Abstract

A model is presented that describes diffusive isotopic redistribution in layered fluid-rock systems where the solid and fluid interact by solution-precipitation. The models lead to guidelines for sampling in metamorphic and diagenetically modified rocks that could substantially increase the probability of recovering desired geochronological and geochemical information. The defining parameters of a fluid-rock system are the reaction rate, R, and the effective diffusivity (D^eff) of the chemical element in question, the latter a function of ionic diffusivity in the fluid, porosity, and the solid/fluid distribution coefficient. Reactive fluid-rock systems can be uniquely characterized in terms of a wavelength L = 2π(D^effR)^12, below which the local equilibrium approximation breaks down. The estimated values of L vary over several orders of magnitude depending on the element of interest and the conditions. For Sr in amphibolite facies metamorphic rocks, for example, L^Sr is about 1-10 cm, whereas for lower greenschist or zeolite facies rocks L^Sr may be 50 m. For oxygen in sedimentary rocks undergoing diagenesis, L^O is greater than 1000 m. The premetamorphic isotopic structure of layered rocks can be conceptualized in terms of a Fourier series representation of isotope ratio vs. distance normal to layering. The effect of metamorphism is to alter the amplitude-wavelength spectrum of the isotopic ratio variations in the solid. Although, in the model transport in the fluid is solely by diffusion, the attenuation of the isotopic variations does not behave like diffusion at all wavelengths. In particular, at wavelengths smaller than L, the rate of isotopic homogenization is limited by the reaction rate rather than the wavelength. The large variability of L in rock systems produces corresponding variability in the effects of isotopic redistribution. The implications of the models are discussed for whole rock and mineral isochrons, porphyroblast-matrix geochronology, and the retrieval of initial isotopic ratios from metamorphic rocks.