Mass balance equations for open magmatic systems: Trace element behavior and its application to open system melting in the upper mantle

A general mass conservation equation for either stable or radioactive chemi cal components in an open magmatic system is formulated. The equation is ap plied to trace elements by assuming melt-mineral equilibrium defined by a p artition coefficient. A derived analytic expression has very wide applicabi lity, and most of the mass conservation equations in the literature for sta ble trace elements are obtained by choosing appropriate values for the cont rolling model parameters, such as material influx or separation rate and me lt fraction in the system. The general equation is also modified to facilit ate an application to multistage problems. It is demonstrated that the gene ral open system mass conservation equation for melting processes expressed without melt fraction is mathematically identical to that for one-dimension al steady state two-phase flow with sink and source terms. This one-dimensi onal steady state model is applied to depleted abyssal peridotites to const rain their melting processes in an ascending mantle beneath ridges. The rar e earth element (REE) patterns of clinopyroxene are fitted by optimizing me lting parameters, and the results indicate a continuous influx of light REE (LREE)-enriched melt up to 3 - 11% in degree of melting, which amounts in total to less than 1% of the initial peridotite mass. The open system melti ng equation for trace elements is also applied to peridotites from the Haya chine-Miyamori ophiolite, northeastern Japan. The REE contents in clinopyro xene and the modal abundances in four peridotite groups are fitted all toge ther to estimate melting reaction stoichiometry and REE contents in the inf luxing material. The estimated REE pattern is characterized by a strong LRE E enrichment, which is comparable to that of melt in equilibrium with hornb lende in the most refractory harzburgite from the ophiolite.