EXPLORATORY DATA-ANALYSIS IN THERMOBAROMETRY - AN EXAMPLE FROM THE KISSEYNEW SEDIMENTARY GNEISS BELT, MANITOBA, CANADA

Generalized thermobarometry uses measured partial molar free-energy fu nctions computed from standard state properties, activity models, and measured compositions, along with the linear dependence of the solutio ns to these functions at equilibrium to estimate pressure, temperature , and partial molar free energies of individual mineral end-members. S uch problems are often inconsistent, i.e., there are no values of pres sure and temperature that simultaneously satisfy all the equations. Th ese inconsistencies result from errors in the measured partial molar f ree-energy functions and may be classified into random errors (those t hat can be modeled as arising from a statistical population) and syste matic errors (those that cannot). Because the systematic error may dom inate, exploratory data analysis is an essential step in the interpret ation of thermobarometry results. Several complementary techniques may be used to provide insight into the sensitivity of estimated pressure s and temperatures to systematic errors in the measured partial molar free-energy functions for individual end-members. The number of equati ons is small, and there are usually only one to three fewer unknowns t han equations; hence, statistical methods designed to investigate inco nsistencies in large data sets cannot be readily applied. However, sev eral procedures can be used to guide interpretation of the results of thermobarometric calculations. (1) Examination of residuals provides a direct indication of relative misfit of the measured partial molar fr ee-energy functions to the theoretical values of chemical potential at equilibrium. The intrinsic correlation of residuals in small data set s limits the utility of this approach. (2) Contours of the sum of squa res of residuals illustrate the covariance and overall reliability of the least-squares solution to the problem. Assigning actual confidence levels to contours requires that the errors have statistical properti es that may not exist in practice. (3) Case deletion studies require t hat the equations be solved repeatedly, eliminating the equation for e ach individual end-member in turn. Diagrams illustrating these results serve to confirm or refute the existence of end-members that are high ly influential in determining best-fit pressures and temperatures. (4) Perturbation analysis also requires the repeated solution of the prob lem, but, instead of deleting individual end-members, their measured f ree-energy estimates are perturbed by fixed amounts, and a new pressur e and temperature are determined. Displays of this kind provide quanti tative estimates of the change in estimated pressures and temperatures resulting from arbitrary perturbations in thermodynamic constants and measured compositions.