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 est imates of mass and volume change in metasomatic systems is presented a nd then used to assess mass transfer resulting from hydrothermal alter ation 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 imp ortant reasons: 1. The concentration of any constituent in a compositi on is constrained to be between 0 and 100 wt percent. 2. The sum of th e concentrations of all constituents must be 100 wt percent (the closu re constraint). Compositions are multivariate and provide information only about the relative proportions of constituents. 3. The maximum po ssible mass or volume loss is -100 percent (-100% corresponds to compl ete mass or volume loss). 4. Rock bulk density must be greater than 0 g cm(-3) 5. The underlying probability distributions for mass and volu me changes are commonly non-normal. To address these issues, we use st atistical procedures recently developed to treat the special propertie s of compositional data, including closure, and the bootstrap method t o compute accurate confidence intervals for assessing how far in error best estimates of mass and volume change are likely to be. The bootst rap deals effectively with non-normality and constraints (1), (3), and (4). We apply our approach to gain a better understanding of synmetam orphic (Acadian orogeny) hydrothermal alteration of upper greenschist facies and amphibolite facies marble beds of the Wepawaug Schist, Conn ecticut. The marbles lost significant amounts of volatiles (dominantly CO2 and H2O), 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 (similar to 140 g kg(-1)), SiO2 (similar t o 60 g kg(-1)), and K2O (similar to 15 g kg(-1)) (numbers are g lost p er kg of parent 1 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 t he calculations described herein is available from the senior author.