Numerical investigations of apatite 4He/3He thermochronometry

Apatite He-4/He-3 thermochronometry has the potential to constrain cooling histories for individual samples provided that several presently untested assumptions are valid. Here we simulate the sensitivity of He-4/He-3 spectra to assumptions regarding geometric model, crystallographic anisotropy, broken grain terminations, parent nuclide zonation, and the accuracy of results obtained from analyses of aggregates of multiple crystals. We find that He-4/He-3 spectra obtained from a cylinder with isotropic diffusion are almost indistinguishable from those obtained from an equivalent sphere with an equivalent initial He-4 distribution. Under similar conditions anisotropic diffusion from the cylinder can greatly bias He-4/He-3 spectra, but only if diffusion is >10 times faster in the axial than the radial direction. Existing data argue against anisotropy of this magnitude. We find that analysis of apatites with broken terminations will also bias He-4/He-3 spectra, but not greatly so. In contrast, we find that zonation of a factor of 3 in parent nuclide concentration produces He-4/He-3 spectra that deviate substantially from the homogeneous model. When parent nuclides are highly concentrated near the grain rim and/or cooling is fast, the resulting He-4/He-3 spectra will be readily identified as aberrant. However, more subtle zonation, higher concentrations in the grain interior, or samples that have cooled slowly regardless of zonation style can yield He-4/He-3 spectra that look acceptable but will lead to inaccurate thermochronometric interpretation if parent homogeneity is assumed. Finally, we find that analysis of an aggregate of crystals with identical He-4 distributions can yield He-4/He-3 spectra (and diffusion Arrhenius arrays) that are very different from those that would be obtained on the individual crystals if even small variations in He diffusion exist among the grains. Overall, our observations suggest that modeling tools that assume spherical geometry and isotropic diffusion are appropriate for interpreting apatite He-4/He-3 spectra. However, it is essential to analyze only individual crystals and to assess the degree of parent nuclide zonation in those crystals.