Jj. Ague et Jlm. Vanharen, ASSESSING METASOMATIC MASS AND VOLUME CHANGES USING THE BOOTSTRAP, WITH APPLICATION TO DEEP-CRUSTAL HYDROTHERMAL ALTERATION OF MARBLE, Economic geology and the bulletin of the Society of Economic Geologists, 91(7), 1996, pp. 1169-1182
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.