Practical #6
Practical 6: Forward Modeling and Sensitivity Tests for ECRAFC
Objective: To conduct sensitivity tests on EC-RAFC.
Supporting Documentation: Spera and Bohrson, 2004
1. To assess the consequences of variable  on the geochemistry of a magma body, run
simulations on the following four cases. Where relevant, use parameters from Table 2. Note that
recharge will be treated as continuous functions.
Table 1: Cases for Question 1
Case

1
1.0
2
0.5
3
1.0
4
0.5
Mro
0
0
0.3
0.3
2a. Plot the results of these four simulations on [Sr] vs. 87Sr/86Sr and [Nd] vs.
diagrams. Plot all four simulations on one graph in order to see the variations.
143
Nd/144Nd
2b. Describe the element-isotope trajectories and explain why the =1 cases are distinct from the
 = 0.5 cases. Provide an example of geologic evidence that might indicate <1.
For the cases with Mro=0, the trajectory begins with decreasing concentration of Sr and
increasing concentration of Nd. Once the assimilant is brought up to near solidus
temperatures the 87Sr/86Sr ratio begins to increase relatively rapidly while the 143Nd/144Nd
ratio decreases. During this period the trajectory is dominated by the assimilant. The Nd
concentration continues to increase, while the Sr concentration remains relatively
constant during the assimlant dominated period. Once the anatectic melt is done mixing
with the magma body fractionation continues. The Sr concentration continues to decrease
while the Nd concentration decreases as well. In the cases where  = 0.5, the isotope
ratios are not affected by the assimlant as much because only half as much anatectic melt
was incorporated into the magma body. When Mro=0.3, there are small variations in the
begining of the event because of the recharge magma being incorporated into the magma
body. An example of geologic evidence indicating <1 would be an isotope ratio closer
to the pristine magma. If there is a 1:1 ratio of magma and assimilant, the isotope ratio
would most likely be pretty close to the middle of the ratios (if magma is .702 and
assimlant .704, the middle would be .703).
3. For the two cases where =1, why is the RAFC case distinct from the AFC case?
The RAFC case is distinct from the AFC case in that there is less radiogenic 87Sr/86Sr and
a slightly higher concentration of Sr in the RAFC case. There is also less radiogenic
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Practical #6
143
Nd/144Nd, and a slightly higher concentration of Nd. In the begining of the event there
is a "spike" in which there is a decrease in radiogenic 87Sr/86Sr and an increase
143
Nd/144Nd.
4. Using relevant data from Table 2 and =1, construct a sensitivity test to examine the
consequences of varying Mro. Note that for this question, recharge will be treated as a
continuous function. Run simulations that include recharge and no recharge. Start with Mro=0.0,
then procede up from there in increments of 0.2 until Mro=1.0. Produce binary diagrams that aid
your understanding of the importance of recharge in the thermal, chemical and mass evolution of
the magma body.
Based on your results, answer the following questions.
5a. What are the relationships between Mao, Ma* (at Teq) and the variations of recharge?
Explain these relationships in the context of energy balance.
5b What are the relationships between on Mm (at Teq) and the variations of recharge? Explain
these relationships in the context of mass balance.
5c. Which case has the most “crustal” signature at Teq? Why?
The case with no recharge is the most crustal. The recharge magma in this case would
cause the magma body to have less crustal signatures because the recharge is most likely
mantle derived. When there is no recharge there is simply magma assimlating wallrock,
which would lead to the most "crustal" signatures.
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Practical #6
Table 2: EC-ERAFC Parameters
Thermal Parameters
Pristine magma liquidus temperature, Tl,m
1320°C
crystallization enthalpy, hm (J/kg)
396000
Pristine magma initial temperature, Tmo
1320°C
isobaric specific heat of magma, Cp,m (J/kg K)
1484
Recharge magma liquidus temperature, Tl,m
1320°C
crystallization enthalpy, hr (J/kg)
396000
Recharge magma initial temperature, Tmo
1320°C
isobaric specific heat of magma, Cp,m (J/kg K)
1484
assimilant liquidus temperature, Tl,a
1150°C
fusion enthalpy, ha (J/kg)
354000
assimilant initial temperature, Tao
600°C
isobaric specific heat of assimilant, Cp,a (J/kg K))
1388
solidus temperature, Ts
950C
equilibration temperature, Teq
1090C
Paramters for Non-Linear Paramterization
Magma a, recharge a
450
Magma b, recharge b
-11.
Assimilant a
400
Assimilant b
-11.
Compositional Parameters
Sr
Nd
Pristine magma initial conc. (ppm), Cmo
700
30
Pristine magma isotope ratio, m
0.7050
0.5129
1.5
0.25
1000
20
0.703
0.5132
1.5
0.25
Pristine magma trace element distribution coefficient, Dm
Recharge magma initial conc. (ppm), Cr
o
Recharge magma isotope ratio, r
Recharge magma trace element distribution coefficient, Dr
Assimilant initial conc. (ppm), Ca
o
230
12.7
Assimilant isotope ratio, a
0.7200
0.5120
Assimilant trace element distribution coefficient, Da
0.05
0.25
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