Quantitative Geochemistry(定量地球化学教材)7.Inverse Geochemical Modeling.pdf

Chapter 7
Inverse Geochemical Modeling
Chapters 1-6 present forward modeling of the behaviors of trace
elements and isotopes during geological processes. In this chapter, we
focus on inverse geochemical modeling. For forward modeling, we may
plex models by adding more parameters into simples ones. We
may evaluate the effects of these additional parameters paring the
complex models with simple ones. For inverse modeling, we try to use
relatively simple models to reduce the number of parameters for
inversion. Inverse modeling is useful in geochemistry because
geochemical investigation often involves deciphering information from
the measured elemental abundances and positions (Allegre
and Minster, 1978; Frey et al., 1978; Minster and Allegre, 1978;
Hofmann and Feigenson, 1983; McKenzie and O’Nions, 199 1 ; Maaloe,
1994; Zou and Zindler, 1996; Class and Goldstein, 1997).
. Batch Melting Inversion of positions
Problem. Demonstrate low-degree ( 6 )/high-degree ( F, ) concentration
ratio (Q) of the same element decreases with increasing partition
coefficients ( Do ) during modal batch melting.
During batch melting, the concentration in the melt (C,) is given by
CO - CO
c, = ()
Do+F(I-Do) F+Do(l-F)’
where Co is the position, F is the degree of partial melting,
Do is the initial bulk partition coefficient.
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Inverse Geochemical Modeling 125
For batch melting, the lowdegreehigh degree concentration ratio is
given by
Q=‘= C F2 +Do(l-F2)
(7 .a
c, &+D,(l-F,) ’
where 4 < F2.
By differentiating Q with respect to Do, we find the first derivative
-=aQ (6
42) ()
800 [F, +(1-F,)D0]2*
Since 4 < F2, we have aQ/aD <O . Therefore, Q decreases with
increasing D .
. Concentration ratio method
Assuming eutectic batch melting, the variation in concentration of a trace
element of the melt, C,, is given by (Shaw, 1970):
CO
c, = ()
Do + F(l- P) ’
where Co is the conc