Practical #2
Practical 2: Forward Modeling and Sensitivity Tests for EC-AFC
Objective: Now that you have experience running the EC code, it is important to develop an
appreciation of the importance of the range of input parameters. For example, what is the
impact of varying the initial temperature of wallrock on the Sr isotope signatures of the
derivative magmas?
Supporting Documentation: Spera and Bohrson, 2001; Bohrson and Spera, 2001
1a. Using parameters from Table 1, perform three simulations that assess the consequences of
changing the magma liquidus temperature. Tlm = 1400°C, 1280° C, 1100°C. (Note that the
1280° C case is the one listed in Table 1). Keep all other parameters the same.
1b. Plot the results of the three simulations on one [Sr]-87Sr/86Sr diagram. Why are the curves
different for the three cases?
2a. In this set of simulations, we are going to vary the initial T of the wallrock. Before doing the
simulations, predict what the relative changes will be in 87Sr/86Sr of magma at Teq for different
Tao. In other words, will increasing Tao to 600°C yield a magma at Teq = 980 with more
radiogenic or less radiogenic 87Sr/86Sr, compared to the standard case? Explain your reasoning.
2b. Perform simulations of the case in Table 1 as well as cases Tao = 450°C, 600°C. Keep all
other parameters the same.
2c. Plot the results of the three simulations on one [Sr]-87Sr/86Sr diagram. Are your predictions
from question 2a confirmed? If no, speculate why your reasoning was incorrect.
2d. For each of the three cases from question 2b, list the Mao and Ma*. Which case has the
highest Ma*? Is this the case that exhibits the most “crust-like” signature (because the wallrock
is more radiogenic, the most “crust-like” signature is the curve that is most radiogenic at Teq)?
Why or why not? (Examine the Sr-87Sr/86Sr diagram again, and think about what controls the
ability of the assimilant to change the Sr-87Sr/86Sr characteristics of the magma body).
3a. Perform simulations of the case in Table 1 as well as cases with Dao (bulk D of Sr in
assimilant) = 0.75, 0.05 Keep all other parameters the same.
3b. Plot the results of these three simulations on one [Sr]-87Sr/86Sr diagram. Explain why the
[Sr]-87Sr/86Sr trends have the shape they do. Paper II (Bohrson and Spera, 2001 may provide
some help; see figure 4b. We will review this concept tomorrow).
4. Examine Fig. 3 of Bohrson and Spera (2001). Describe the differences between the EC and
“classical” trends, and relates these differences to aspects of the EC formulation. For example,
why does the EC-AFC lower crustal case differ so significantly from the ‘classical’ lower crustal
case?
1
Practical #2
Table 1: EC-AFC Parameters
Thermal Parameters
Pristine magma liquidus temperature, Tl,m
Pristine magma initial temperature, Tm
o
1280°C
crystallization enthalpy, hm (J/kg)
1280°C
isobaric specific heat of magma, Cp,m
(J/kgK)
o
assimilant liquidus temperature, Tl,a
assimilant initial temperature, Ta
o
isobaric specific heat of magma, Cp,m
(J/kgK)
1000°C
fusion enthalpy, ha (J/kg)
300°C
isobaric specific heat of assimilant,
Cp,a (J/kgK))
total (normalized) mass of recharge magma
solidus temperature, Ts
900C
equilibration temperature, Teq
980C
Paramters for Non-Linear Paramterization
Magma a, recharge a
450
Magma b, recharge b
-12
Assimilant a
450
Assimilant b
-12
Compositional Parameters
Sr
pristine magma initial conc. (ppm), Cmo
pristine magma isotope ratio, m
pristine magma trace element distribution
coefficient, Dm
700
0.7035
1.5
recharge magma initial conc. (ppm), Cmo
recharge magma isotope ratio, m
recharge magma trace element distribution
coefficient, Dm
assimilant initial conc. (ppm), Cao
assimilant isotope ratio, a
assimilant trace element distribution
coefficient, Da
1484
crystallization enthalpy, hr (J/kg)
Recharge magma liquidus temperature, Tl,m
Recharge magma initial temperature, Tm
396000
350
0.7220
1.5
2
274000
1370