Multidimensional Scaling (MDS): A quantitative approximation of zircon ages to sedimentary provenance with some examples from Mexico

During the last decades, provenance studies have proven to be an invaluable tool to evaluate modern and ancient sedimentary environments and to reconstruct the paleogeography and evolution of different tectonic settings. Whereas in the past provenance studies were mainly based on qualitative comparisons of whole-rock sandstone detrital modes, the advance and implementation of microanalytical techniques driven by the community during the last ~15 years permit the quantification of detrital-mineral ages and the isotopic characterization by in situ analysis. The combination of ages, isotopes, and mineral chemistry of individual detrital components provides a better understanding and reconstruction of source-to-sink systems. However, the introduction of these largely accessible microanalytical techniques has produced a large amount of data that requires proper management to be objectively interpreted. While a quantitative comparison between the age distributions of detrital sample pairs can be easily performed by Kolmogorov-Smirnov (K–S) statistics, comparing multi-samples data sets requires a more complex statistical approach. One of those is Multidimensional Scaling analysis (MDS), which allows, by using K–S statistics, to compare the dissimilarity between two or more samples. To compare among samples, a dissimilarities matrix, based on the stress from the ideal fit, is constructed. Dissimilarities are graphically represented in a “map” that tends to group more similar samples, pulling apart those that are more dissimilar. We contribute with three examples from the Mexican geology, showing how MDS can be used to evaluate in a more objective way the provenance of clastic rocks. We show that the MDS is more suitable than the visual comparison of probability density plots and kernel density estimations in marking the similarities and differences between the available samples; thus, it is a more suitable approach to reconstruct more rigorously the evolution of source-to-sink systems. Particularly, we examine fluvial to deep-marine Triassic strata, Paleozoic–lower Mesozoic metasedimentary rocks of the Ayú and Acatlán complexes, and Upper Jurassic–Cretaceous successions of the Pacific continental margin. The MDS challenges the scenario in which all Triassic submarine fan deposits of Mexico were part of a giant single fan developed along the Mexican Pacific margin, and supports the idea that the western margin of Pangea was drained by different fluvial systems that supplied distinct submarine fans. Applied to the Paleozoic–lower Mesozoic metasedimentary rocks of southern Mexico, this approach shows major dissimilarities between the Ayú and the Acatlán complexes, supporting the idea that these are likely two different tectonic complexes. Finally, the MDS suggests that two distinct and independent provenance domains were established in Mexico during the development of the Upper Jurassic–Early Cretaceous Arperos back-arc basin, and that such a detrital signature compartmentalization was lost by the end of Early Cretaceous time with the advent of compressive tectonics and the development of orogenic belts.