Practical Aspects of Mineral Thermobarometry
Error Estimation in P-T Calculations
There are several sources of uncertainty associated with a pressure-temperature determination. The most important are probably the following:
Uncertainty on the thermobarometer calibration,
e.g. uncertainty in the position of an end member equilibrium determined by bracketed phase equilibrium experiments. If the calibration has been derived from an optimised, self-consistent thermodynamic data set, it should be possible to provide a reasonable estimate of this uncertainty. A calculation using THERMOCALC will quote for you an uncertainty based on the correlated uncertainties of the enthalpies of end members in the Holland and Powell data set.
Analytical uncertainty on the mineral analyses.
This is derived from counting statistics, standardisation and correction procedures in the electron microprobe. It will be made up of a mixture of random errors (e.g. those deriving from counting statistics) and systematic errors. The contribution from random errors can be estimated quite readily (see part 1).
Uncertainty in activity-composition relationships.
This source of error is much less quantifiable. We may not know the most appropriate formulation for the thermodynamic mole fraction (see part 3). We may be assuming ideal behaviour for a phase which is non-ideal. If we have a non-ideal model, it may not extrapolate correctly to the P, T or composition range of interest.
Under this heading are the systematic, non-statistical errors introduced by us, the petrologists, in selecting phase compositions which may not be those in chemical equilibrium at the stage of interest in the rock's history. (Alternatively we may blame it all on the rock for not equilibrating properly)
In addition, we should distinguish between overall uncertainty, which is the sum of all the above errors, and comparison uncertainty, which affects our ability to resolve two pressures or temperatures determined using the same calibration of a particular thermobarometer. The comparison uncertainty depends largely on the analytical imprecision (No 2 above), and may be a great deal smaller than the overall uncertainty.
The subject is dealt with by Spear, chapter 15, pp. 537-540.
How to minimise analytical uncertainty
A simple but effective way to minimise analytical uncertainty, and thus to improve comparisons between rocks using the same calibrations, is to pool mineral analyses for statistically homogeneous populations of the mineral of interest in your rock. To determine what is statistically homogeneous you need to have a good feeling for the expected analytical uncertainty on a single microprobe analysis, and to get the right populations you need to know your rock well (microstructure, zoning, spatial distributions) so as not to introduce "geological error". This being done, every analysis you add to the pool helps to smooth out the random error involved, by increasing the effective counting time on the pooled analysis. Crudely, an average of four analyses is twice as good as a single one.
An example: Phengite geobarometer for eclogites
As an example of the possible source and magnitude of errors, take the barometer proposed for phengite-bearing eclogites by Waters and Martin (1993):
6 diopside + 3 Al2Mg-1Si-1 (in phengite) = pyrope + 2 grossular
- The barometer was calibrated directly from the Holland and Powell (1990) data set. The calibration uncertainty is estimated at 0.8 to 0.9 kbar from the least-squares fitting of the dataset enthalpies (Holland and Powell, 1990).
The mineral analyses have to be propagated through rather complex formula recalculations, which for Cpx at least, must include ferric iron estimation. One way of estimating the uncertainty on the pressure from these sources is by the Monte Carlo technique, in which the measured wt% of each oxide in each mineral is presumed to be distributed normally, with a given standard deviation, about the "true" (i.e. measured) value. Values are randomly selected from the normal distribution, and a value calculated for the pressure. The pressure calculation is then repeated a large number of times, so that the statistical distribution of calculated pressures can be examined. With typical mineral compositions, it turns out that analytical uncertainty contributes ± 0.9 to 1.3 kbar to the overall uncertainty.
The Monte-Carlo treatment can be extended to solid solution mixing parameters if the uncertainties on these are also assumed to be known and independent of each other. Parameters in garnet and pyroxene contribute about ± 0.6 to 1.5 kbar, using the uncertainties on mixing parameters given in Holland (1990) and Newton et al. (1979). Given the doubt as to the choice of appropriate mixing models, this figure is an underestimate.
- Geological error may arise from inappropriate use of zoned or re-equilibrated mineral compositions, or from a false assumption that white mica is part of the peak eclogite assemblage.
The overall uncertainty of the barometer can be obtained by combining these contributing errors, and it will generally be in excess of 2 kbar (1 sigma). Not very good, perhaps, but better than no barometer at all. The overall uncertainty correlates with the Na content of clinopyroxene, since at low mole fractions of diopside the diopside activity term dominates the uncertainty on lnK. For jadeite% < 50 the contributions from end members are more evenly balanced. Garnet terms dominate only if XCa or XMg is significantly less than 0.1.
Comparison uncertainties, involving just random errors, are approximated by the propagation of analytical uncertainty, and are therefore typically in the range 0.9 to 1.3 kbar.
This page last modified 12 October 2004