Inversion of cosmogenic-nuclide data from iron meteorites

Abstract

The interpretation of the observed abundances of cosmogenic nuclides in meteorites involves two considerations, namely, the cosmic-ray-exposure ages and the past behaviour of the particle flux. Traditional methods of analysis do not have the mathematical structure to simultaneously deal with both questions in a convenient and rigorous fashion. Reformulating this problem within the framework of inverse theory allows for a new and powerful perspective: it enables us to make simultaneous, self-consistent estimates of the flux prehistory and the exposure ages, and of their uncertainties. In this paper we have focussed on inversions that would, if possible, give constant-flux prehistories, and, in any case, would give the flattest model in a least-squares sense. This allows us to show by rigorous examination that the available data are inconsistent with the assumption that the flux was constant over a period of 109 years. While this is not an original conclusion, it is reached here by a much more direct analysis, and we are able to make a defensible estimate for the change in the 109 years. The analysis also yields new estimates of the exposure ages that are consistent with the time-varying flux. That is, one does not need to presuppose any particular functional form for the flux. The application of inverse theory to such problems also makes available additional benefits that have been widely recognized in geophysical analysis. For example, it forces one to explicitly acknowledge the inherent assumptions, it provides quantitative estimates of the uncertainty of the results, and it provides a means of anticipating the value of new experimental data. We have based our demonstration on published data from four individual iron meteorites, since these data apparently provide a self-consistent set. Smoothed estimates are derived of the long-term prehistory of the particle flux at similar depths within these bodies (1000 kg m−2 as inferred from the cosmogenic nuclides 21Ne and 40K). With our preferred choice for the present value of the particle flux, the results independently support a model in which the magnitude of the particle flux 109 years ago was about 40% less than the present value; the individual estimates for the four meteorites of the ratio of the present flux to the flux 109 years ago are 1.75 (Mount Ayliff), 1.66 (Yardymly), 1.64 (Williamstown), and 1.72 (Carbo). The exposure ages consistent with this history are smaller, by some 10–20%, than previous estimates. One can choose a smaller value for the present particle flux to bring the ages into agreement with previously estimates values, but then a substantially larger change in flux with time is required. Thus our analysis provides a sophisticated test of the possibility of a constant-flux model.