Liquid line of descent

Figure 1.10 The liquid line of descent upon olivine removal from basalt in the AFM diagram using equations (1.4.3) and (1.4.4). Olivine has a fixed composition (data from Tablel.lla). Each open circle indicates removal of 5 percent olivine.

Cumulate control lines vs liquid lines of descent. In a study of the 1931-1986 basaltic eruptions from the Reunion Island (Indian Ocean), Albarede and Tamagnan (1988) found the Ni and Cr concentrations (in ppm) listed in Table 3.1 and shown in Figure 3.2. Samples with Ni>100ppm were found to contain large amounts of cumulus olivine. The last five samples of Table 3.1 are picrites. The smooth trend observed for all the rocks is suggestive of a complementary fractionation-accumulation relationship out of a single magma batch. Therefore, it is asked whether the trend observed for Ni and Cr in basalts with less than 100 ppm Ni may be ascribed to the removal of the olivine found in the cumulates. 

Figure 3.3 Schematic residual magma-cumulate relationships for instantaneous and average magmatic products in a linear plot of Ni and Cr concentrations. For mass balance to be obeyed, the instantaneous cumulate must lie on the tangent to the liquid line of descent at the point representing the instantaneous liquid.

In the present case, the question is whether Reunion olivine-rich rocks belong to a cumulate control line of the basaltic rocks. Through a simple log-log regression, we find that the basalt trend (= the liquid line of descent) can be approximated by a power law, a form justified in Sections 1.5 and 9.3. 

Table 1 Five basaltic glasses from the East Pacific Rise near the Clipperton Transform that, to first order, form a coherent liquid line of descent for fractional crystallization from the highest MgO magma ( 1) to lowest ( 5).

Figure 6 MgO variation diagrams for microprobe data for basalt glasses from near the Clipperton Fracture Zone (from RidgePetDB Lehnert et aL, 2000). Also shown is a calculated liquid line of descent for fractional crystallization at <50 MPa using the program of Weaver and Langmuir (1990) (labeled W + L) for a primitive composition at 9 wt.% MgO. Oxides in wt.% (Langmuir et aL, 1992) (reproduced by permission of American Geophysical Union from /. Geophys. Res., 1992, 71, 183-280).

One method projects the composition of each magma along a presumed slope of the liquid line of descent to a constant value of MgO, in this case 8 wt.% (Klein and Langmuir, 1987 see also updated algorithms in Castillo et al., 2000). The calculated Na20 value at 8 wt.% MgO is therefore referred to as Nag o- In theory, if the liquid line of descent is known for any major or trace element. 

Figure 5 MgO vs. NaaO in MORE from five different Ridge segments (Mid Cayman Rise in the Caribbean near Kane Fracture Zone on the Mid-Atlantic Ridge, 23°N AMAR on the Mid-Atlantic Ridge around 37°N East Pacific Rise near the Clipperton Fracture Zone around 10°N Kolbeinsey Ridge north of Iceland. Lines are calculated Liquid Lines of Descent (LLDs) from high MgO parents. Bar shows where clinopyroxene joins plagioclase and olivine as a fractionating phase. Nag is determined by the values of NaaO when the LLD is at MgO of 8 wt%. (Adapted with permission from Langmuir ef a/., 1992.)...

Extract calculations may also be limited in their use if (1) the liquid line of descent is actually a mix of several lines (2) solid solution changes the composition of the crystallizing phases during fractionation (3) the phenocrysts present in magma are not representative of the fractionating phases. 

Neilsen RJL., 1988, A model for the simulation of combined major and trace element liquid lines of descent GeocAim, Cosmochim. Acta, 52, 27-38. 

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