Assessing metasomatic mass and volume changes using the bootstrap, with application to deep crustal hydrothermal alteration of marble

A statistically rigorous approach for determining likely errors on estimates of mass and volume change in metasomatic systems is presented and then used to assess mass transfer resulting from hydrothermal alteration of marble during regional metamorphism. Analysis of metasomatic effects using standard statistical methods designed for unconstrained, univariant data often fails to provide useful results for several important reasons: 1. The concentration of any constituent in a composition is constrained to be between 0 and 100 wt percent. 2. The sum of the concentrations of all constituents must be 100 wt percent (the closure constraint). Compositions are multivariate and provide information only about the relative proportions of constituents. 3. The maximum possible mass or volume loss is -100 percent (-100% corresponds to complete mass or volume loss). 4. Rock bulk density must be greater than 0 g cm ^-3. 5. The underlying probability distributions for mass and volume changes are commonly non-normal. To address these issues, we use statistical procedures recently developed to treat the special properties of compositional data, including closure, and the bootstrap method to compute accurate confidence intervals for assessing how far in error best estimates of mass and volume change are likely to be. The bootstrap deals effectively with non-normality and constraints (1), (3), and (4). We apply our approach to gain a better understanding of synmetamorphic (Acadian orogeny) hydrothermal alteration of upper greenschist facies and amphibolite facies marble beds of the Wepawaug Schist, Connecticut. The marbles lost significant amounts of volatiles (dominantly CO ₂ and H ₂O), Si, Ti, K, Rb, Sr, and Ba. Best estimates of total mass and volume change are -27 and -32 percent, respectively. The bulk of the lost mass was volatiles (∼140 g kg ^-1), SiO ₂ (∼60 g kg ^-1), and K ₂O (∼15 g kg ^-1) (numbers are g lost per kg of parent rock). Volatile loss was probably regional in scope. Loss of Si, Ti, K, Rb, Sr, and Ba occurred over minimum length scales on the order of typical hand sample dimensions; maximum length scales remain to be determined. The FORTRAN 77 computer code that performs the calculations described herein is available from the senior author.