Melt transport

Spiegelman M, Elliott T. (1993) Conseqnences of melt transport for uraninm series diseqnihbrinm. Earth Planet Sci Lett 118 1-20... 

Spiegelman M, (1996) Geochemical conseqnences of melt transport in 2-D the sensitivity of trace elements to mantle dynamics. Earth Planet Sci Lett 139 115-132 Spiegelman M, Kelemen PB, Aharonov E (2001) Canses and consequences of flow organization dnring melt transport The reaction infiltration instability in compactible media. J Geophys Res 106 2061-2077... 

Equation (A9) accounts for the change in the amount of daughter within the solid while Equation (A 10) accounts for that in the fluid. The transfer of the nuclide from the solid to the fluid phase is governed by the first term on the right side of both equations. Note that in this formulation, as given in Spiegelman and Elliott (1993), the time of melt transport is accounted for and depends on the physically based transport velocity. Like Equation (A8), both equations can be solved simultaneously by numerical integration or more sophisticated numerical method. 

Spiegelman, M. Elliott, T. (1993). Consequences of melt transport for uranium series disequilibrium in young lavas. Earth Planet. Sci. Letters, 118, 1-20. 

According to Spiegelman and Elliott (1993), the consequences of melt transport through a steady-state dCj/dt = 0), one-dimensional melting column on the concentration of radioacitive isotopes can be... 

In a one-dimensional steady-state melting column, the variation of the enrichment factor or, with depth due to melt transport is given by Spiegelman and Elliott (1993) (after correction of another typographical error in their Eq. 15)... 

Equations (5.95), (5.96) and (5.97) are suitable for constant critical melting porosity. In a one dimensional steady state melting column as a result of decompression melting, the porosity may increase from the bottom to the top of the column. If melting porosities change as a function of the spatial position, the related differential equations need to be solved numerically. More details of various melt transport models by porous flow have been given by Spiegelman and Elliott (1993), Iwamori, (1994), and Lundstrom (2000). 

Melt transport with initial secular equilibrium... 

For melt as porous flow, the enrichment factors due to melt transport over batch melting at variable depths in a one dimensional melting column are given by (5.95), (5.96) and (5.97). 

Figure 26 Schematic drawing for recently proposed crustal models, (a) Ductile flow model in its simplest form (e.g., Phipps Morgan and Chen, 1993 Quick and Denlinger, 1993 Nicolas et al., 1988). Ductile flow down and outward from a mid-crustal magma chamber constructs the lower crust, (b) Ductile flow model incorporating a basalt sill (Schouten and Denham, 1995). (c) Hybrid ductile flow model with on- and off-axis sill intrusions (Boudier et al., 1996). (d) Sheeted sill model with melt transport by hydrofracture and in situ emplacement of the lower crust by on-axis sill intrusions (Kelemen et al., 1997 Bedard et al., 1988) (reproduced by permission of Elsevier from...

The aim of this chapter is to review the observations of uranium series nuclide studies on mid-ocean ridge basalts (MORBs) and discuss their implications for melt transport processes. We note that a recent review by Lundstrom (2003) has a similar remit and makes a useful companion contribution. We initially recap the fundamental behavior of the naturally occurring actinide decay chains, and outline the analytical challenges of... 

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