Natural age dispersion arising from the analysis of broken crystals, part II. Practical application to apatite (U-Th)/He thermochronometry

We describe a new numerical inversion approach to deriving thermal history information from a range of naturally dispersed single grain apatite (U-Th)/He ages. The approach explicitly exploits the information about the shape of the 4He diffusion profile within individual grains that is inherent in the pattern of dispersion that arises from the common and routine practice of analysing broken crystals. Additional dispersion arising from differences in grain size and in U and Th concentration of grains, and the resultant changes to helium diffusivity caused by differential accumulation and annealing of radiation damage, is explicitly included. In this approach we calculate the ingrowth and loss, due to both thermal diffusion and the effects of α-ejection, of helium over time using a finite cylinder geometry. Broken grains are treated explicitly as fragments of an initially larger crystal. The initial grain lengths, L0, can be treated as unknown parameters to be estimated, although this is computationally demanding. A practical solution to the problem of solving for the unknown initial grain lengths is to simply apply a constant and sufficiently long L0 value to each fragment. We found that a good value for L0 was given by the maximum fragment length plus two times the maximum radius of a given set of fragments. Currently whole crystals and fragments with one termination are taken into account. A set of numerical experiments using synthetic fragment ages generated for increasingly complex thermal histories, and including realistic amounts of random noise (5-15%), are presented and show that useful thermal history information can be extracted from datasets showing very large dispersion. These include experiments where dispersion arises only from fragmentation of a single grain (length 400μm and radius 75μm, c. 6-50% dispersion), including the effects of grain size variation (for spherical equivalent grain radii between 74-122 μm, c. 10-70% dispersion) and the combined effects of fragmentation, grain size and radiation damage (for eU between 5-150 ppm, c.10-107% dispersion). Additionally we show that if the spherical equivalent radius of a broken grain is used as a measure of the effective diffusion domain for thermal history inversions then this will likely lead to erroneous thermal histories being obtained in many cases. The viability of the new technique is demonstrated for a real data set of 25 single grain (U-Th)/He apatite ages obtained for a gabbro sample from the BK-1 (Bierkraal) borehole drilled through the Bushveld Complex in South Africa. The inversion produces a well constrained thermal history consistent with both the (U-Th)/He data and available fission track analysis data. The advantage of the new approach is that it can explicitly accommodate all the details of conventional schemes, such as the effects of temporally variable diffusivity, zonation of U and Th and arbitrary grain size variations, and it works equally effectively for whole or broken crystals, and for the most common situation where a mixture of both are analysed. For the routine application of the apatite (U-Th)/He thermochronometry technique with samples where whole apatite grains are rare our experiments indicate that 15-20 single grain analyses are typically required to characterise the age dispersion pattern of a sample. The experiments also suggest that picking very short crystal fragments as well as long fragments, or even deliberately breaking long crystals to maximise the age dispersion in some cases, would ensure the best constraints on the thermal history models. The inversion strategy described in this paper is likely also directly applicable to other thermochronometers, such as the apatite, rutile and titanite U-Pb systems, where the diffusion domain is approximated by the physical grain size