The meaning of “mean F”: Clarifying the mean extent of melting at ocean ridges

Abstract:

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).

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