TRACE-ELEMENT FRACTIONATION DURING MODAL AND NONMODAL DYNAMIC MELTINGAND OPEN-SYSTEM MELTING - A MATHEMATICAL TREATMENT

Dynamic partial melting model has recently drawn considerable attentio n because this model may explain the fractionation of some strongly in compatible nuclides in the uranium decay series (McKenzie, 1985; Beatt ie, 1993) and may account for ultra-depleted melt inclusions in olivin e grains from mid-ocean ridge basalts (Sobolev and Shimizu, 1993) and Icelandic picrites (Eggins, 1992). There are three subsystems for dyna mic melting model: the residual melt, the extracted melt, and the resi dual solid. This paper systematically derives consistent equations for the residual melt, the extracted melt, and the residual solid in the context of both modal and nonmodal dynamic melting models. Previous av ailable equations are also evaluated. The keys for the derivation or e valuation of equations for dynamic melting models are (1) the exact re lationship between the melting rate and the melt extraction rate, (2) the exact relationship between the total melting degree and the fracti on of extracted melt relative to the initial amount of source before m elting, and (3) clear concepts of physical parameters. In addition, th e equation for the residual melt during open-system (nonmodal dynamic) melting (Ozawa and Shimizu, 1995) with material influx in the melting region is corrected and an equation for the extracted melt in the con text of open-system melting is proposed here. Since melting and melt e xtraction processes Ire often coupled with slab-derived material influ x in the melting region in the are environments, these two new equatio ns for the residual melt and the extracted melt during open-system mel ting are very useful in modeling are magmatism. Copyright (C) 1998 Els evier Science Ltd.