IMPROVING THE STATISTICAL VIABILITY OF U-TH MODEL AGE HISTOGRAMS AND PROBABILITY DENSITY CURVES WITH MONTE CARLO SIMULATION

Histograms of U-Th model age distributions (typically for zircon or other accessory minerals) with overlying probability density curves (PDCs) are a widely utilized tool in geochronological studies of young (<~350 ka) volcanic systems. However, interpretation of these diagrams is not always straightforward. Examples of subjective decisions that must be made in some instances include: (1) Do two or more closely-spaced peaks represent multiple crystallization ages or one single age?; (2) Do shoulders in the PDC mark statistically meaningful ages?; and (3) Do PDCs constructed from a small number of U-Th disequilibria analyses (fewer than ~20–25) accurately reflect the true distribution of mineral growth ages? Furthermore, traditional histograms and PDCs do not reflect potential variation in the initial melt values of (²³⁸U/²³²Th) and (²³⁰Th/²³²Th).

We have written an Excel (i.e., Visual Basic) program that runs Monte Carlo simulations of U-Th age spectra in an attempt to make interpretation of U-Th PDCs more objective. The program randomly samples the probability distributions for the (²³⁸U/²³²Th) and (²³⁰Th/²³²Th) values of each individual U-Th analysis. The initial melt activity values may also be included in the random sampling in order to account for variation in the original melt. A new histogram and PDC is generated from the new randomly sampled values and results are added together over numerous iterations. The end result is a cumulative histogram and PDC that reflects more statistically viable crystallization ages than conventional diagrams.

Conventional U-Th age spectra for zircons extracted from rocks of Mount St. Helens commonly exhibit peaks and shoulders that suggest three or four discrete populations of crystallization ages. In contrast, PDCs produced from Monte Carlo simulations indicate that most Mount St. Helens lithologic units contain zircons that grew during two distinct phases: prior to 100 ka and after 60 ka.