4 Summary and Conclusions
2.4 Statistical analysis
2.4.2 Multivariate statistics on compositional data
3.2.1.1 Kriging models and Principal Component analysis (PCA) for
3.2.1.1.2 Kriging
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Fig. 2: Comparison of lead isotope data by sample type. A: Boxplots of 206Pb/204Pb variations shown around the mean value for the respective groups (ignimbrites, intrusions, lava and metamorphic). B: same as A but variations are shown around the median. C: 206Pb/204Pb values plotted along latitude.
3.2.1.1.2 Kriging
Predictive surfaces and prediction standard error maps for 208Pb/204Pb, 207Pb/204Pb,
206Pb/204Pb, 144Nd/143Nd and an IDW interpolation for 87Sr/86Sr are included in the supplementary database. Simple Kriging proved to return best models for our data and detailed model summaries are given in Appendix A. Fig.4A-B exemplifies results for
206Pb/204Pb. Validation results with our data-subset are also included in the database and give mean errors of around zero. The predictions are quite robust but there are areas with very little data that cannot be predicted or validated very well as can be seen in the standard error map. Models were kept as simple as possible as we found that including anisotropy or using nested models could not improve prediction but made results more inaccurate. The mm
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Fig. 3: Exploratory data analysis for 208Pb/204Pb. A: Histogram: Normal distribution can be accepted for this dataset; B: Normal Q-Q plot; C: Semivariogram: Model type, major range, sill, partial sill and nugget parameters are estimated here (These parameters are given in Appendix B for each model). Changes in direction (anisotropy parameter) in the semivariogram can also be checked. D: Trend analysis: A global, polynominal trend is clearly visible. This trend corresponds to the change in basement domains.
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most important factor to improve modeling would be to have spatially more evenly distributed data.
Comparing our model to the previously published map by (Mamani et al., 2008) with the same classification thresholds, differences are greatest in areas with a low sample density.
However, as lead data is rather continuous and shows no real classes, a better way to visualize results is to give a continuous prediction surface with a prediction error. One striking difference are high 206Pb/204Pb (and 208Pb/206Pb) values for part of the Mejillones Terrain and low 206Pb/204Pb (and 208Pb/206Pb) values within the northern Paracas domain that cannot be due to a modeling error as there are enough samples in this location. This indicates either substructures within the Mejillone and Paracas Terrains or some other process capable of modifying lead isotopes. The samples related to the high values in the Mejillone domain are undated lava samples that are probably quite old (Mesozoic Chocolate arc? Lucassen et al.
(2002)) and are therefore different in isotopic values.
206Pb/204Pb indicates the same tendency as the other maps with the exception of some more radiogenic values within the Arequipa domain. Estimating lead isotope values for samples based on their location is now possible. Predictions for magmatic rocks are within a narrow error range as could be shown with our data-subset. Prediction errors for areas with a low sample density are still quite high and could be improved by adding more data to the database and re-running the model with or without changes in model parameters.
87Sr/86Sr IDW map does not show a very homogeneous surface reflecting mantle and crustal mixtures with more radiogenic values for higher crustal components. As shown by Mamani et al. (2009), lead and strontium isotope ratios are defined by mixing of basement with mantle magma (Fig.5). For 87Sr/86Sr, crustal assimilation does not modify values as easily as for lead isotopes due to the less pronounced bend of the 87Sr/86Sr mixing hyperbola, and therefore 87Sr/86Sr in the model reflects the amount of contamination within a crustal domain rather than the basement signature.
The combined information of all models with a reduction of noise was derived from Principal Component Analysis (PCA) (Fig.6). From five models, 3 PCs were calculated with the first two PCs explaining 99.9 % of the overall variability. The first PC clearly delineates the crustal domains as expected. The second PC still reflects the basement structure but is strongly influenced by the degree of assimilation. The high values within the Arequipa Domain correspond to the samples with a higher degree of assimilation (Direction of the Mollendo basement in Fig. 4). The more pronounced low values of the Mejillones Terrain correspond to the low degree of assimilation and more mafic nature of this area. The third PC reflects residual variations in 87Sr/86Sr and 143Nd/144Nd and therefore again the degree of
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crustal assimilation within the domains (compare vertical axis of Fig. 4). High values correspond to higher 144Nd/143Nd while the second PC reflects high 87Sr/86Sr.
Fig. 4: 206Pb/204Pb Kriging model (A) and error surface (B). Lead domains named after Mamani et al. (2010)
Thus, PC analysis can be used to decipher different processes acting simultaneously.
The overriding effect of basement isotope signature is captured by PC 1 while the process of assimilation can be shown in PCs two and three. The advantage is noise reduction achieved by reducing dimensions from five original datasets to only three PCs. However, errors involved in the original interpolation models and due to sampling bias are propagated into the analysis and results have to be handled with care.
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Fig. 5: 87Sr/86Sr and 206Pb/204Pb ratios for samples used for kriging. Data points are scaled from green to red according to Pb isotope values. As discussed in detail by Mamani et al. (2009), isotope signatures can be explained by mantle magma and crustal assimilation. Values for the basements and mantle used by Mamani et al.
2010 are: Mantle: Jurassic lava close to a mantle source: Sr and Pb contents [ppm] and isotopic ratios are 111/0.7033, 4/18.221, respectively; Paleozoic Cotahuasi basement: Sr and Pb content/ratios are 96/0.735, 11/20 respectively; Proterozoic Mollendo basement: Sr and Pb content/ratios are 150/0.73, 7/17, respectively.
Fig. 6: Results of PC analysis. A: First PC; B: Second PC; C: Third PC.
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3.2.1.2 Areal extent and volume estimates for ignimbrites through time as a measure