文档介绍：Chapter 1
Batch Melting
. Overview of Melting Models
Partial melting of Earth and ary materials is a fundamental process
that contributes to the differentiation and evolution of the Earth.
Modeling of partial melting using trace element concentrations is often
required to understand the melt generation and segregation process and
to interpret the position of primary melts. The behaviors of
trace elements during partial melting present a good problem for the
application of mathematics.
There are three general models based on the extent of chemical
equilibrium between the solid and melt: batch, fractional (Schilling and
Winchester, 1967; Gast, 1968; Shaw, 1970) and dynamic melting
(Langmuir et al., 1977; McKenzie, 1985; Zou, 1998; Zou, 2000; Zou and
Reid, 2001). Another model is called continuous melting (Williams and
Gill, 1989; Albarede, 1995) or critical melting (******@e, 1982; Sobolev
and Shimizu, 1992). Although continuous melting monly
distinguished from dynamic melting in that in the former an excess melt
is removed from a static column whereas in the latter the entire melting
region migrates and new fertile material is added to the column, the real
difference between them is only the aggregation time required to produce
the magmas. The difference in aggregation time certainly affects the
activity of a short-lived radioactive nuclide in magmas, however, it will
not affect the concentration of stable trace elements (Williams and Gill,
1989). Therefore, although continuous melting and dynamic melting
1
2 Quantitative Geochemistry
appear different conceptually, for the purpose of mathematical treatment
of stable trace element fractionation, they are mathematically identical.
Among the three general models, the batch melting model assumes
that melt remains in equilibrium with the solid throughout the melting
event whereas the fractional melting model assumes that (1) the melt is
removed from