Methodology to derive well-calibrated thermometers: a new glass-composition geothermometer for olivine-bearing glassy samples at one atmosphere

This work describes the methodology used to develop a new glass-composition geothermometer by multiple linear least-squares regression analysis of experimental data available in literature. The geothermometer is applicable to natural olivine-bearing glassy samples quenched at one atmosphere. The calibration data set includes a total of 543 anhydrous experiments performed at one atmosphere which produced olivine coexisting with glass (± other phases). The accuracy of the geothermometer has been verified using an independent set of randomly selected one atmosphere anhydrous experimental samples external to the calibration data set. The new proposed equation reads: T(°C) = 1054.1±6.5 + (1458.0±23.5)(XMgO)liq – (267.1±45.8)(XCaO)liq + (116.3±30.9)(XNa2O + XK2O)liq, where the terms such as (XMgO)liq represent the cation fraction of MgO in the liquid. The new geothermometer is able to reproduce the calibration temperatures within a standard error of estimate (SEE) of ±23° C and to predict the temperatures for the test data set with a SEE of ±25° C. The proposed equation, when compared to previous models, gives the lowest systematic error. Moreover, we mathematically demonstrate that the comparison of the slope and the intercept parameters of the regression line against the 1:1 line leads to correct evaluation of the model only when a regression of observed or measured (in the y-axis as dependent variable) vs. predicted or calculated (in the x-axis as independent variable) is used.