Mathematics
Scientific paper
Jan 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004e%26psl.217....1s&link_type=abstract
Earth and Planetary Science Letters, Volume 217, Issue 1-2, p. 1-17.
Mathematics
16
Helium, Diffusion, Thermochronometry, Isotope, Proton Beam, (U-Th)/He
Scientific paper
Using classical diffusion theory, we present a mathematical technique for the determination of 4He concentration profiles in minerals. This approach should prove useful for constraining the low-temperature cooling histories of individual samples and for correcting (U-Th)/He ages for partial diffusive loss. The calculation assumes that the mineral of interest contains an artificially produced and uniform distribution of 3He obtained by proton irradiation [Shuster et al., Earth Planet. Sci. Lett. 217 (2004) 19-32]. In minerals devoid of natural helium, this isotope allows measurement of He diffusion coefficients; in minerals with measurable radiogenic He, it permits determination of 4He profiles arising during ingrowth and diffusion in nature. The 4He profile can be extracted from stepwise degassing experiments in which the 4He/3He ratio is measured. The evolution of the 4He/3He ratio as a function of cumulative 3He released can be compared with forward models to constrain the shape of the profile. Alternatively, we present a linear inversion that can be used to directly solve for the unknown 4He distribution. The inversion incorporates a standard regularization technique to filter the influence of random measurement errors on the solution. Using either approach we show that stepwise degassing data can yield robust and high-resolution information on the 4He profile. Profiles of radiogenic He are a sensitive function of the time-Temperate (t-T) path that a cooling sample experienced. Thus, by step heating a proton-irradiated sample it is possible to restrict the sample's acceptable t-T paths. The sensitivity of this approach was explored by forward-modeling 4He profiles resulting from a range of realistic t-T paths, using apatite as an example. Results indicate that 4He profiles provide rich information on t-T paths, especially when the profiles are coupled with (U-Th)/He cooling ages on the same sample. Samples that experienced only moderate diffusive loss have 4He concentration profiles that are rounded at the edge but uniform in the core of the diffusion domain. Such profiles can be identified by nearly invariant 4He/3He ratios after the first few to few tens of percent of 3He have been extracted by step heating. We show how such data can be used to correct (U-Th)/He ages for partial diffusive loss.
Farley Kenneth A.
Shuster David L.
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