1. LEAST SQUARES CALCULATIONS – IGPET 2009

The Parent magma(P) is 2012B

The Daughter magma(D) is 2012B-3

Phases Removed:

Coef Solid Min/Magma

0.005 00.7 AP2 (see mineral table)

0.705 91.9 FSP1

0.021 02.7 CPX2

0.036 04.7 TIMT

0.232 Fraction of Liquid Remaining

SiO2 TiO2 Al2O3 FeO MnO MgO CaO Na2O K2O P2O5

Daughter 75.08 0.33 10.58 4.43 0.18 0.00 0.10 3.91 5.34 0.04

Parent 2012B

Obs 65.10 0.77 15.58 4.67 0.89 0.53 1.03 5.57 5.68 0.17

Calc 65.66 0.62 15.71 4.83 0.09 0.03 1.05 5.70 6.04 0.18

Diff*Wt -0.22 0.15 -0.06 -0.16 0.80 0.51 -0.04 -0.13 -0.35 -0.04

Sum of squares of residuals= 1.138

Weighting:

SiO2 / TiO2 / Al2O3 / FeO / MnO / MgO / CaO / Na2O / K2O / P2O5
0.4 / 1 / 0.5 / 1 / 1 / 1 / 2 / 1 / 1 / 3
  1. TRACE ELEMENT MODELING – IGPET 2009

Trace element modeling based on values above:

D Obs(P) Calc(P) Diff 2012B-3(D) F=0.232

LA 2.58 50.8 1466.3 -1415.50 146.7

CE 3.16 80.5 6789.5 -6708.95 290.8

PR 3.68 12.6 1771.7 -1759.10 35.7

ND 5.18 54.1 59632.0 -59577.88 133.8

SM 5.48 12.1 18562.4 -18550.35 27.0

GD 4.69 11.5 6601.9 -6590.39 30.1

TB 3.98 1.95 403.5 -401.58 5.24

DY 2.93 11.5 543.7 -532.29 32.4

ER 2.35 7.33 149.6 -142.31 20.9

YB 1.17 7.47 26.8 -19.38 20.8

Y 2.36 60.0 1449.3 -1389.31 200.0

Mineral / SiO[2] / TiO[2] / Al[2]O[3] / Fe[2]O[3] / FeO / MnO / MgO / CaO / Na[2]O / K[2]O / P[2]O[5]
AP1 / 8.78 / 0 / 0 / 0 / 0.6 / 0.14 / 0 / 38.18 / 0.08 / 0 / 25.95
AP2 / 11.7 / 0 / 0 / 0 / 0.72 / 0.17 / 0 / 32.46 / 0.13 / 0 / 21.06
Il / 0.09 / 49.74 / 0.04 / 0 / 47.24 / 1.23 / 0.08 / 0 / 0 / 0 / 0
FSP1 / 66.89 / 0 / 18.78 / 0 / 0.25 / 0 / 0 / 0.56 / 6.76 / 6.81 / 0
FSP2 / 66.85 / 0 / 18.39 / 0 / 0.87 / 0 / 0 / 0 / 6.29 / 8.05 / 0
OL1 / 29.41 / 0.05 / 0 / 0 / 67.15 / 2.24 / 0.74 / 0.19 / 0 / 0 / 0
CPX1 / 48.63 / 0.18 / 0.3 / 0 / 27.8 / 0.93 / 2.48 / 19.47 / 0.52 / 0 / 0
CPX2 / 47.73 / 0.31 / 0.19 / 0 / 30.3 / 0.81 / 0.44 / 17.86 / 1.26 / 0.03 / 0
AE / 40.99 / 8.76 / 0.38 / 0 / 38.01 / 0.12 / 0 / 0.29 / 7.08 / 0.01 / 0
TIMT / 0.21 / 14.11 / 0.51 / 0 / 78.33 / 0.75 / 0.46 / 0 / 0 / 0 / 0

D Values

name / AP1* / AP2* / FSP1 / FSP2 / Il / Ol1 / CPX1 / CPX2 / AE / TIMT
La / 360 / 360 / 0.03 / 0.03 / 0.01 / 0.01 / 0.74 / 0.74 / 0.01 / 0.01
Ce / 441 / 441 / 0.03 / 0.03 / 0.01 / 0.01 / 1.2 / 1.2 / 0.01 / 0.01
Pr / 512 / 512 / 0.03 / 0.03 / 0.01 / 0.01 / 1.9 / 1.9 / 0.01 / 0.01
Nd / 722 / 722 / 0.04 / 0.04 / 0.01 / 0.01 / 2.6 / 2.6 / 0.01 / 0.01
Sm / 762 / 762 / 0.03 / 0.03 / 0.01 / 0.01 / 3.5 / 3.5 / 0.01 / 0.01
Gd / 650 / 650 / 0.03 / 0.03 / 0.01 / 0.03 / 3.7 / 3.7 / 0.01 / 0.01
Tb / 550 / 550 / 0.02 / 0.02 / 0.01 / 0.07 / 3.5 / 3.5 / 0.01 / 0.01
Dy / 402 / 402 / 0.02 / 0.02 / 0.01 / 0.12 / 3.3 / 3.3 / 0.01 / 0.01
Er / 321 / 321 / 0.02 / 0.02 / 0.01 / 0.33 / 2.8 / 2.8 / 0.01 / 0.01
Yb / 151 / 151 / 0.02 / 0.02 / 0.01 / 0.69 / 3.5 / 3.5 / 0.01 / 0.01
Y / 324 / 324 / 0.02 / 0.02 / 0.01 / 0.17 / 2.3 / 2.3 / 0.01 / 0.01

*These are the only elements reported for the only study on the enrichment of apatite in peraklaine rock by MacDonald and are not strictly D values but ratios of solid/liquid

Sources of minerals and D values - this study plus:

MacDonald, R., Baginski, B., Belkin, H.E., Dzierzanowski, P., and Jezak, L., 2008, REE partitioning between apatite and melt in a peralkaline volcanic suite, Kenya Rift Valley: Mineralogical Magazine, v. 72, p. 1147-1161.

Peccerillo, A., Barberio, M.R., Yirgu, G., Ayalew, D., Barbieri, M., and Wu, T.W., 2003, Relationships between mafic and peralkaline silicic magmatism in continental rift settings: A petrological, geochemical and isotopic study of the Gedemsa volcano, central Ethiopian rift: Journal of Petrology, v. 44, p. 2003-2032.

Marshall, A.S., MacDonald, R., Rogers, N.W., Fitton, J.G., Tindle, A.G., Nejbert, K., and Hinton, R.W., 2009, Fractionation of Peralkaline Silicic Magmas: the Greater Olkaria Volcanic Complex, Kenya Rift Valley: Journal of Petrology, v. 50, p. 323-359.

The modeling using these data produce substantially different results to those observed so we have performed a rough calculation to deduce the contribution of apatite to the system.

  1. APPARENT APATITE CONTRIBUTION TO D

Assuming values from the least squares modeling (F= 0.232) then the required D values to explain the progression from 2012B to 2012B-3 are:

Parent Conc / Daughter Conc / Apparent D value (Rayleigh)
La / 50.8 / 146.7 / 0.27
Ce / 80.5 / 290.8 / 0.12
Pr / 12.6 / 35.7 / 0.29
Nd / 54.1 / 133.8 / 0.38
Sm / 12.1 / 27 / 0.45
Gd / 11.5 / 30.1 / 0.34
Tb / 1.95 / 5.24 / 0.32
Dy / 11.5 / 32.4 / 0.29
Er / 7.33 / 20.9 / 0.28
Yb / 7.47 / 20.8 / 0.30
Y / 60 / 200 / 0.18

Using the D values and modes from the least squares calculation we can calculate the bulk D value ignoring the contribution of apatite and examine how different this is from the apparent D value:

BULK D / Difference to apparent D value
La / 0.05 / 0.23
Ce / 0.06 / 0.06
Pr / 0.08 / 0.21
Nd / 0.11 / 0.27
Sm / 0.12 / 0.33
Gd / 0.13 / 0.21
Tb / 0.11 / 0.21
Dy / 0.11 / 0.18
Er / 0.09 / 0.19
Yb / 0.11 / 0.19
Y / 0.08 / 0.09

Using the modeled mode of Apatite of 0.7%, then we have an apparent D of Apatite of:

Apparent D
La / 32.30
Ce / 8.64
Pr / 29.69
Nd / 38.97
Sm / 46.87
Gd / 30.50
Tb / 30.01
Dy / 26.15
Er / 26.91
Yb / 26.53
Y / 13.57

These values are consistent with other magmatic apatites – in particular the D values peaking at Sm. Notably the Ce values are low.

Performing a least squares model with the alternate apatite composition yielded similar results:

Apparent D of AP
La / 37.57
Ce / 10.08
Pr / 34.64
Nd / 45.46
Sm / 54.68
Gd / 35.58
Tb / 35.01
Dy / 30.51
Er / 31.40
Yb / 30.95
Y / 15.83