SUPPLEMENTARY INFORMATION

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Aleesha Willis
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1 Supplementary Information, Page of doi:.8/nature to 5% SiO KO (Weight %) ge (Ma) to 5% SiO KO (Weight %) ge (Ma) to 5% SiO C KO ge (Ma) Supplementary Figure : Schematic illustration of Monte Carlo analysis for the example case of KO. (a) raw data; (b) results of 7 out of, weighted bootstrap-resampling Monte Carlo simulations, illustrating peak smearing due to uncertainties in reported sample ages; (c) sample means with -sigma standard errors of the mean. Note that figures are cropped at wt. % KO but the averages shown in C are calculated from the full dataset. Supplementary Figure Schematic illustration of Monte Carlo analysis for the example case of KO. (a) raw data; (b) results of 7 out of, weighted bootstrap-resampling Monte Carlo simulations, illustrating peak smearing due to uncertainties in reported sample ages; (c) sample means with -sigma standard errors of the mean. Note that figures are cropped at wt. % KO but the averages shown in (c) are calculated from the full dataset.

2 RESERCH Prior age distribution Posterior age distribution ge (Ma) Prior latitude distribution ge (Ma) Posterior latitude distribution 5 5 Latitude 5 5 Latitude Prior longitude distribution Posterior longitude distribution Longitude Longitude Supplementary Figure Prior (original data; left) and posterior (after Monte-Carlo analysis; right) sampling distributions (histograms) compared to ideal distributions (solid lines), where the ideal spatial distributions are based on the current exposed area of the continents. Scale of the ideal curve is normalized to the height of the highest peak in the distribution for both the prior (raw data) and posterior (resampled data) cases. Since the true value of age distribution is unknown, no curve is shown for comparison. Instead, one sees that undersampled age ranges increase in importance during Monte Carlo simulation.

3 RESERCH Supplementary Information, Page of Distribution of estimated mean content in -5% SiO samples. Ga.. Ga.. Ga.. Ga..5 Ga.5. Ga..7 Ga.7.8 Ga.8.9 Ga.9 Ga. Ga.. Ga.. Ga.. Ga..5 Ga.5. Ga..7 Ga.7.8 Ga.8.9 Ga.9 Ga Number of Samples. Ga.5. Ga.. Ga..7 Ga.. Ga.7.8 Ga.. Ga.8.9 Ga..5 Ga.9 Ga. Ga.. Ga.. Ga.. Ga..5 Ga.5. Ga..7 Ga.7.8 Ga.8.9 Ga.9 Ga Supplementary Figure Histograms of the estimated mean content of -5% SiO Supplementary Figure : Histograms of the estimated mean content of -5% SiO samples samples in each in of each, of, Monte Monte Carlo Carlo simulations simulations for for each each Ma bin between and and Ga, Ga, illustration illustration the approximately the Gaussian gaussian distribution of the means.

4 RESERCH Supplementary Information, Page of Response of Monte Carlo simulation to choice of uncertainty distribution data, n=7 E data, n= Number of Samples 8 Monte Carlo simulation using Gaussian distribution 8 Monte Carlo simulation using log normal distribution C 5 Monte Carlo simulation using Gaussian distribution F 5 Monte Carlo simulation using log normal distribution G 8 Monte Carlo simulation using chi squared distribution D 5 Monte Carlo simulation using chi squared distribution H 8 (wt. %) 5 rbitrary units Supplementary Figure 5: the result of Monte Carlo simulation of () content of mafic igneous samples between and Ma (left, a-d), and () synthetic lognormal distribution with location parameter and variance parameter.5 (right, e-h), where % (two sigma) analytical uncertainty is simulated using three different distributions for the analytical error. (a,e): distribution of the raw data; (b,f): distribution of Monte Carlo results when a Gaussian error distribution is used; (c,g): distribution of results when a log-normal distribution is used; (d,h): distribution of results when a chi-squared distribution is used. Red vertical lines show the position of the mean; inset shows distribution of the mean. Supplementary Figure the result of Monte Carlo simulation of () content of mafic igneous samples between and Ma (left, a-d), and () synthetic lognormal distribution with location parameter and variance parameter.5 (right, e-h), where % (two sigma) analytical uncertainty is simulated using three different distributions for the analytical error. (a,e): distribution of the raw data; (b,f): distribution of Monte Carlo results when a Gaussian error distribution is used; (c,g): distribution of results when a log-normal distribution is used; (d,h): distribution of results when a chi-squared distribution is used. Red vertical lines show the position of the mean for each set of results; inset illustrates the distribution of individual means about that line (not to scale).

5 RESERCH Sensitivity of geochemical trends produced by Monte Carlo analysis to choice of uncertainty distribution 5 Gaussian age uncertainty and geochemical uncertainty 9 5 Gaussian age uncertainty and log normal geochemical uncertainty (wt. %) 9 5 C Log normal age uncertainty and geochemical uncertainty ge (Ma) Supplementary Figure 5 Monte Carlo simulation of content through time in mafic (-5% SiO) samples using (a) a Gaussian distribution for both geochemical error and geochronological error (as in Figures -); (b) a Gaussian distribution for geochronological error and a log-normal distribution for geochemical error; and (c) a log-normal distribution for both geochemical error and geochronological error. 5

6 RESERCH Supplementary Information, Page of Response of Monte Carlo simulation to incomplete data with stepwise starting distribution % 5% % 5% rbitrary units C D % % E F ge (Ma) Supplementary Figure Monte Carlo analysis of simulated dataset with an abrupt change in mean Supplementary and variance Figure at 5 : Monte Ma under Carlo analysis the influence of simulated of varying dataset degrees with an of abrupt data loss change between in mean and and variance Ma (dashed at 5 blue Ma lines) under ranging the influence from of % varying of degrees data preserved of data loss (a) to between all data and Ma (dashed blue lines) ranging from % of data preserved (a) to all data deleted deleted (f). ackground (f). ackground of of plot plot (a) (a) shows shows the the initial initial synthetic synthetic dataset dataset (note (note that that data data is cropped is cropped by the by range the range of the of plot). the plot). Note that in the case of a complete lack of input data between and Ma (%), output data is only defined due to the age uncertainty of the adjacent input data.

7 RESERCH Response of Monte Carlo simulation to incomplete data with continuous starting distribution % 5% % 5% rbitrary units C D % % E F ge (Ma) Supplementary Figure 7 Monte Carlo analysis of simulated dataset under the influence of varying degrees of data loss between and Ma (dashed blue lines) ranging from % of data preserved (a) to all data deleted (f) as in Supplementary Figure, but with linear instead of stepwise trend in the initial simulated dataset. Note that in the case of a complete lack of input data between and Ma (%), output data is only defined due to the age uncertainty of the adjacent input data. 7

8 RESERCH 5 5% SiO Nb / U 5 5 ge (Ma).5 5% SiO Pb / Ce.5 ge (Ma) Supplementary Figure 8 Mean Pb/Ce and Nb/U through time for mafic lithologies, illustrating the lack of a clear trend that would be required to explain observed trends in compatible and incompatible element concentration through changes in degree of crustal contamination through time. Error bars represent -sigma standard errors of the mean from Monte-Carlo bootstrap resampling. 8

9 RESERCH Supplementary Information, Page 9 of Evolution of basalt fractionation trends through time 5% SiO 5 5 NaO NaO 5 Ga 8.5 CaO / lo CaO / lo Supplementary Figure 9 Secular evolution of basalt fractionation trends through time, following an approach modified from Klein and Langmuir for (a) NaO vs and (b) CaO/ lo vs. Each color illustrates a bootstrap-resampling Monte Carlo estimate of global mean NaO and CaO/lO at a given range during a different a Ma time interval between the present (blue) and Ga (red). Inset shows the full range of the plot.trends within a particular time interval are interpreted to approximate a globally averaged liquid line of descent for that time period; the parallel fractionation trends showing an increase in NaO and decrease in CaO/lO with time for given demonstrate decreasing mantle melt fraction for a given time period. It may be noteworthy that the evolution of NaO values through time at ~8% (i.e. Na8.) corresponds closely to the evolution of mean NaO through time in Figure. 9

10 RESERCH pparent Percent Melt at. GPa 5 ge (Ma) pparent Percent Melt at GPa 5 ge (Ma) Supplementary Figure Estimated percent mantle melt from -5% SiO samples at (a). GPa and (b) GPa. Error bars are -sigma standard errors of the mean.

11 RESERCH Mean V/Sc of mafic (-5% SiO) samples 9 8 V / Sc 7 5 ge (Ma) Supplementary Figure Mean V/Sc ratio through time for mafic (-5% SiO) samples, illustrating the lack of a visible trend that would indicate changes in mantle oxygen fugacity.

Lecture 36. Igneous geochemistry

Lecture 36. Igneous geochemistry Lecture 36 Igneous geochemistry Reading - White Chapter 7 Today 1. Overview 2. solid-melt distribution coefficients Igneous geochemistry The chemistry of igneous systems provides clues to a number of important