Unique Thermal Histories from Whole-Rock 40Ar/39Ar Step-heating Data

Abstract:

Step-heating ⁴⁰Ar/³⁹Ar analysis can reveal spatial distributions of ⁴⁰Ar^* at the micron scale imparted by post- crystallization heating events through complex, multi-diffusion domain models. These efforts have largely focused on single-phase, terrestrial samples with only scant attention paid to multi-phase or extra-terrestrial materials. Generalizing these models to incorporate the multiple activation energies (E) expected from bulk rock samples introduces significant interpretational ambiguity. This is because the thermal crossovers explicit in multi-E cases make the age spectrum a function of the lab heating schedule in thermally disturbed samples. A further difficulty is that unique interpretation of the associated Arrhenius plot is no longer possible and a range of E’s can be fitted with equal goodness of fit. In order to address these challenges, we developed a new computational approach that simultaneously inverts the Arrhenius spectra and release pattern using a variant of the Adaptive Particle Swarm Optimization (APSO) algorithm for a square-pulse heating event. Our version uses a Levy Flight to break the swarm out of a local minima rather than randomly modifying a single dimension as in the original APSO. Further we explored issues of Pareto efficiency arising from fitting two fitness functions (i.e., the fit to the age spectra and to the Arrhenius plot) and found an adequate resolution to the classic inability to have a single best fit. By utilizing multiple-E samples, we are able to obtain unique thermal history solutions. Application of these methods to high resolution age spectra of the Jilin chondrite and Apollo 16 samples (North Ray Crater) and found fits of sufficiently high fidelity to constrain the absolute temperature of the thermal episode to better than ±10%.