OLIVINE CONTROL LINES IN HAWAIIAN ROCKS

Hawaiian lavas display a range of MgO contents reflecting mixing between Mg-rich olivine (ol) and liquid (with ~6–7% MgO [1]). However, for the same suite of lavas, different oxide-MgO pairs often project to different ol compositions [2, 3]. These apparently inconsistent mixing trends have been attributed to multiple distinct parental magmas [2] or mixing between ol-rich and ol-poor liquids [3]. Monte Carlo techniques can address whether differences in projected ol Mg# are significant and how they might change with sample size. Mixing an average low MgO Mauna Loa (ML) composition (with uncertainties) with variable amounts of ol and spinel (with compositional uncertainties; ol Mg# of 87.4±0.2; 100Mg/(Mg+Fe), atomic) we generated 40,000 “lavas” with MgO contents (6.7-35%) distributed similarly to those observed in 502 ML lavas [4]; uncertainties > 0.2 on ol Mg# produce distributions in FeO*-MgO space unlike that seen in the ML data. From this parent population, we randomly pulled 25 samples and calculated an ol Mg# for each oxide-MgO pair (based on the intersection of the regression line with the Fo-Fa join). Repeating the exercise 5000 times generates a mean ol Mg# and an uncertainty for each oxide-MgO pair. We then doubled the sample size, repeated the sampling exercise, and continued till we reached a sample size of 400. Here we focus on FeO*-MgO and CaO-MgO: the mean ol Mg# calculated for each sample size matches the ol Mg# calculated for the parent population (using the same regression approach) to < 0.1%, but 2σ uncertainties and maximum and minimum values vary substantially. For FeO*-MgO, the 2σ bounds on ol Mg# shrink from 88.3–86.5 (at 25; max and min values are 91.2 & 83.8) to 87.6–87.2 (at 400; 87.7 & 87.1); in contrast, the bounds for CaO-MgO are 91.1–83.6 (at 25; 100 & 72.6) and 88.0–86.6 (at 400; 88.6 & 86.2). For lavas that define an ol control line, FeO*-MgO is the best pair for calculating the mean composition of the added ol. For the ML data, ol Mg# from CaO-MgO is sufficiently larger than that calculated using FeO*-MgO that the difference is unlikely due to sampling, but requires processes like those referenced above or the addition of small amounts of augite along with ol and spinel.

[1] Rhodes (1995) Geophys Monograph 92, 241; [2] Maaløe (1979) Lithos 12, 59; [3] Rhodes and Vollinger (2004) G³, 5, Q03G13; [4] GEOROC database