Stochastic Dominance and the Lorenz Curve

Abstract

\tMost analyses of natural iron-titanium oxides contain small but significant amounts of minor components. In order to determine the "mole" fractions of endmember ilmenite and ulv{ö}spinel in coexisting oxides for geothermometry, a new recalculation scheme is proposed based on models of ionic substitution. This new schme is consistent with a new thermodynamic model for the pure Fe-Ti system (Spencer and Lindsley, 1981). It should also provide better basis for consideration of the actual effects of minor components on the geothermometer as the necessary data become available.The temperature and oxygen fugacities were calculated using several recalculation schemes for a large number of published analysis of coexisting Fe-Ti oxides from igneous rocks. Significantly different temperatures and oxygen fugacities were obtained with the Spencer and Lindsley geothermometer as opposed to the ealier Buddington and Lindsley version. Generally the differences between values using various recalculation schmes were less than 30ºC and less than 0.5 units of log f02. The new scheme proposed here tends to give temperature and log fO2 values falling in the middle of the range of variation. Simply ignoring, or not analyzing for, minor components can lead to errors in excess of 150ºC and 4 units of log fO2.Fe-Ti 酸化物中に含まれる無視できない微量成分について考慮。イオン交換モデルに基づいて、共存するilmenite とulv{ö}spinelのモル費を決定。Spencer and Lindsleyによる純粋な鉄チタン系での熱力学モデルに対応。今後、実際に微量成分が地質温度計に及ぼす影響を考慮する際にも本研究は土台に。温度と酸素分圧は火成岩に関する多数の文献値からいくつかの方法で再計算を行った。温度と酸素分圧の値は、B&Dのと異なりS&Lのものは大きく違う値を得た。その違いは30℃、酸素分圧で0.5ユニット。本論文の新しい方法ではこれまでの方法の中間あたりに落ちる。微量成分を分析をしなかったり、存在を無視した場合誤差は150℃、4ユニット程度になる。