New improved equations for NaK, NaLi and SiO2 geothermometers by outlier detection and rejection

We present new improved equations for three still widely used NaK, NaLi and SiO2 geothermometers (obtained by statistical treatment of the data and application of outlier detection and rejection as well as theory of error propagation) and compare them with those by Fournier and others. New equations are also developed for estimating errors associated with the use of these new geothermometric equations and comparing them with the performance of the original equations. The errors in the use of the new NaK equation for temperatures ranging from 80 to 350 °C vary from about 19 to 34%, which is lower than the corresponding errors (24–43%) for the original Fournier equation. Similarly, for temperatures ranging from about 50 to 320 °C, our new equation for NaLi geothermometer for Cl < 0.3 m shows errors of about 13–34% as compared to 15–39% for the original equation, and for Cl ≥ 0.3 m, from 10 to 44%, much lower than 26–106% estimated for the corresponding original equation. Finally, for temperatures ranging from 20 to 210 °C our results show that the total propagated errors of the new geothermometric equation for SiO2 < 295 ppm are about 1–9%, smaller than 3–12% for the original SiO2 geothermometer. We have proposed a linear equation for the temperature range of 210 to 310 °C (SiO2 ≥ 295 ppm), which shows considerably smaller total propagated errors (2–3%) than for the original equation (5–29%).