In a recent paper, Forsyth (1993) concludes that fractional melting leads to unexpected relationships between the degree of melting (F), crustal thickness, and the depth of melting beneath mid-ocean ridges. Specifically, he suggests that a commonly cited rule of thumb, that 10% mean melting of a 60-km column of mantle leads to 6 km of crustal thickness (Klein et al., 1991; Langmuir et al., 1992), is incorrect for fractional melting of the mantle. Here we show that the rule of thumb remains valid for Langmuir et al.'s definition of mean F and that confusion has arisen because there has been disagreement on the definition of mean F. Plank and Langmuir (1992) have defined mean F as the ratio of the mass flux of melt added to the oceanic crust to the mass flux of mantle entering the melting region; Forsyth (1993) has defined mean F as the average degree of melting of all pooled melt increments, with degree calculated at the last point of chemical equilibration. We show here that both definitions of mean F are valid conceptually and mathematically, clarify the differences between them, show how they relate differently to observables such as crustal thickness and crustal composition, and propose nomenclature to clarify usage in the future (FB for Plank and Langmuir's bulk melt fraction and Fv for Forsyth's mean value).
We present a macro program which greatly simplifies the process of making X–Y (scatter) and triangular plots using the spreadsheet program Microsoft Excel®. The program draws on user-defined “type-plots” to establish plot format, allowing a great amount of flexibility in style and presentation. Predefined templates can be used to define fields or lines for specific purposes and these can be retained easily from plot to plot facilitating rapid comparison of different data sets. The program requires only the addition of some simple control characters to be able to draw data from existing spreadsheets with little or no reformatting.
Boron behaves as a highly incompatible trace element in oceanic settings, while in arcs it shows unique systematics indicative of fluid-rock interactions. Boron analyses conducted on well-characterized mid-ocean ridge basalt (MORB) suites show that B approximates K most closely in its solid/ melt distribution behavior, with inferred bulk distribution coefficients of 0.004-0.009 during melting in the mantle and up to 0.07 during low-pressure crystallization. During differentiation processes in volcanic arc lavas B and K also vary similarly, but the B enrichments in basalts from different arc volcanoes are highly heterogeneous relative to those of K, Be, or other incompatibles. Boron shows strong affinities for fluids such as are liberated during the devolatilization of subducting slabs. Boron enrichments correlate directly with extents of melting in arc basalts, and inversely with the enrichments of most other lithophile trace elements. Boron enrichments at arcs are lower in those volcanoes that sample deeper portions of the slab, becoming indistinguishable from MORBs in the rearmost volcanic centers. That such B depletions are evident in lavas entails that magmatic processes and other transport mechanisms efficiently flush B through the mantle wedge and return it to surface reservoirs. The great mobility of boron apparent from the arc data precludes any long-term B enrichment in the sub-arc mantle and requires the existence of strong return fluxes for B in addition to arc volcanism.
Okmok and Recheshnoi are adjacent volcanoes on the island of Umnak in the Aleutian Arc. Ninety-five new chemical analyses of lavas from the two volcanoes show that Okmok exhibits a classical tholeiitic and Recheshnoi a calc-alkaline differentiation trend. Both volcanoes have erupted lavas that range in composition from basalt to rhyolite. This allows investigation of differences in both the differentiation systematics and the parental magma compositions. In contrast to the predictions of many recent models for calc-alkaline and tholeiitic volcanism, the major and trace element data show that the parental magmas for the two volcanoes have different compositions. These different parental compositions might themselves be produced by in situ differentiation or other complex fractionation processes from a very magnesian parental magma (16% MgO) with Okmok being derived by low-pressure fractionation and Recheshnoi by in situ fractionation at higher pressures. An alternative and simpler explanation is that the inferred high-MgO Okmok parent and the Recheshnoi parent are derived by different extents of melting in the mantle wedge. Modelling based on the rare earth elements suggests approximately 7% melting for the calc-alkaline parent and 20% for the tholeiitic parent. For these two volcanoes therefore, there may be a correlation between extent of melting and the tendency to follow a calc-alkaline or tholeiitic differentiation trend. Larger enrichments of highly fluid-mobile elements such as boron and cesium in the tholeiitic Okmok source suggest that variability in the volume of fluid flux from the slab may be responsible for the different extents of melting. If the partial melting model is applied generally to the Aleutian Arc, it provides an alternative explanation for the volcanic regularities of the arc described by Kay et al. (1982). Smaller extents of melting lead to less melt, fractionation at higher pressures, often including hydrous phases, a preponderance of plutonic rather than volcanic rocks, and smaller calc-alkaline volcanoes. Large tholeiitic volcanoes are often associated with fracture zones on the subducting Pacific plate (Kay et al., 1982; Marsh, 1982). Since fracture zones are more extensively altered than average oceanic crust and might also serve as sediment traps, they could serve as sources of a larger volatile flux from the slab, leading to greater extents of melting and large, tholeiitic volcanoes. If this explanation is correct, then the origin of the volcanic segmentation of the arc may be found within the subducted slab. This contrasts with the alternative model of control by the stress regime of the overlying plate (Kay et al., 1982; Singer and Myers, 1990; Kay and Kay, 1991). Inferences from Okmok and Recheshnoi may also apply to global variations in convergent margin chemistry. In general, arcs built On thick crust tend to be more calc-alkaline in character. On the Basis of the negative correlation between convergent margin crustal thickness and inferred extent of melting (Plank and Langmuir, 1988), lower extents of melting may contribute to a tendency towards calc-alkaline differentiation on a global basis.
The physical form of the melting regime and the mechanisms of melt extraction influence the composition of magmas erupted at ocean ridges. We investigate aspects of this relationship, beginning with the assumption that melts can be extracted from the melting regime without significant reequilibration during their passage to the surface. The ocean crust thus represents a mixture of the individual melts. Many melting regimes lead to the same “residual mantle column” (RMC), defined as a vertical section through the mantle external to the melting regime. The RMC is the integrated result of melt extraction and is useful in evaluating the geochemical effects of many different types of melting regimes. Consideration of the RMC shows that the “shape” of the melting regime is not necessarily an important parameter in affecting the composition of the ocean crust. The important parameters are the way mantle flows through the melting regime and the relationship between melt fraction and pressure during adiabatic melting. Calculating the volume and composition of the ocean crust can be reduced to a simple mixing problem. Virtually all ridge models predict continuous mixing of melts from the solidus to the maximum extent of melting. Given these boundary conditions, even complex melting regimes lead to geochemical results that are similar to those produced by batch melting. Thus batch melting may approximate the net effects of the melting process remarkably well. An important exception to these generalizations is binary mixing between melts of very different composition. This is possible beneath ocean ridges if very low degree melts, formed at the volatile-present solidus, mix with higher-degree melts formed directly beneath the ridge. There are limitations to the effectiveness of such a mixing process because the source volume for the low-degree melts is constrained by the finite pressure interval between the dry and volatile-present solidi of the mantle. These constraints place an upper limit of a factor of 5 on the incompatible element enrichment that can be explained by such mixing. This is a small factor relative to the global variability of mid-ocean ridge basalts. A few local regions, however, show major and trace element covariations that may be consistent with this type of mixing. Adequate data sets to fully test the possibility are lacking. If such mixing occurs, there must be a physical mechanism to focus the lowest degree melts from the furthest reaches of the melting regime into the mantle directly beneath the ridge axis. The physical difficulties associated with horizontal transport of low-degree melts over tens to hundreds of kilometers are imposing and suggest that alternative models should be seriously considered.
The ocean basin south of Australia contains the Australian-Antarctic Discordance, an anomalously deep portion of the Southeast Indian Ridge that marks a boundary between isotopic provinces characteristic of the Indian and Pacific oceans. Samples recovered from the ridge within the discordance display unusual chemical compositions compared to normal mid-ocean ridge basalt (N-MORB) of the same MgO contents, including low iron, high silica, and high sodium abundances and elevated abundances of highly incompatible trace elements. In contrast, samples from the ridge east of the discordance, where the ridge is of average axial depth, display major and trace element systematics more typical of N-MORB. Major and moderately incompatible trace elements show no evidence of a discontinuity in source composition corresponding to the location of the known isotopic discontinuity within the discordance. Ratios of highly incompatible trace elements, however, reveal a gradational change in the range of values across the location of the isotopic discontinuity. Modelling of along-strike variations in major element chemistry suggest they may result from systematic variations in the extent and pressure of melting. The lowest solidus pressures and least extents of melting occur in the mantle beneath the discordance, supporting geophysical inferences based on bathymetric, gravity, and seismic evidence that the discordance overlies a region of cooler mantle temperatures.
This paper presents a general method for the calculation of mineral-melt phase equilibria based on mass balance, stoichiometry, and single component distribution coefficients. An algorithm for the practical application of this method is developed, and a computer program using this algorithm for calculation of phase stability, phase proportions, and phase composition has been included. The program includes both equilibrium and fractional models for melting and crystallization. This particular implementation incorporates a specific distribution coefficient model for olivine, plagioclase, and clinopyroxene crystallization in basaltic systems. Calculated results from the program agree with those from experiments on terrestrial basaltic compositions. The program has been designed to be modified easily to incorporate other distribution coefficient models for detailed application to specific data sets. In this way, the program should be able to be applied to diverse compositions, phase assemblages, and physical processes of crystal/liquid interaction. In general, the algorithm and its implementation provide a practical method for calculating equilibria in multicomponent, mineral-melt systems.