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

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Highlights

  • International Geology Review, v. 61, pp. 915-935.

  • The Guerrero terrane, a para-autochthonous block. GSA Special Paper 546.

  • International Geology Review, v. 56. No. 2, pp. 237–261.

Abstract

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.

Introduction

Clastic successions in sedimentary basins are the most complete record of the geologic history of our planet, being the sites where sediment, eroded from mountain belts formed during orogenic, rift and transcurrent tectonic events, were accumulated after aeolian, fluvial, marine, and gravity-induced transport processes (e.g., Allen and Allen, 2013). The study of clastic rocks and sediments is key to understanding the evolution of paleogeography and tectonic processes that acted during sediment generation and deposition (Dickinson, 1985; Garzanti, 2016). Clastic succession studies have focused on the stratigraphic assessment, reconstruction of sedimentary processes and depositional environments, as well as on provenance and geotectonic setting mostly interpreted based on traditional petrographic analysis represented in canonical QFL diagrams (Gazzi, 1966; Dickinson and Suczek, 1979), whole-rock geochemistry, Sm–Nd or Rb–Sr-isotope, and chemical composition of major components (McCulloch and Wasserburg, 1978; McLennan and Hemming, 1992; Fralick and Kronberg, 1997; Ocampo-Díaz et al., 2016, 2019). However, the interest in detrital heavy minerals has rapidly increased during the last two decades (Mange and Wright, 2007; Ortega-Flores et al., 2019; Martini et al., 2020). Among heavy minerals, zircon is ubiquitous in many felsic igneous and metamorphic rocks and, because of its strong mechanical and chemical resistance to weathering, transport, and diagenetic processes, it is always present in clastic deposits. Moreover, zircon is a high-temperature geochronometer because of the U incorporation into its crystalline network at the moment of its igneous and metamorphic crystallization; consequently, zircon can be dated by the U–Pb method (e.g., Kösler and Sylvester, 2003; Gehrels et al., 2011). The introduction, during the last twenty years, of microanalytical techniques such as laser ablation inductively-coupled plasma mass spectrometry (LA-ICPMS) has produced a wealth of in situ U–Pb zircon data, significantly improving the analytical precision and through put (Park et al., 2010; Gehrels et al., 2011; Pullen et al., 2014; Solari et al., 2010, 2015). These characteristics make zircon U–Pb geochronology a prime technique for source-to-sink analysis when combined with other methods such as mineral chemistry, isotopic analysis (Hf, for instance, Ortega-Flores et al., 2020; Solari et al., 2020; Spencer et al., 2020; Cavazos-Tovar et al., 2020), and petrography, allowing the generation of large databases that can be properly interpreted to reconstruct the evolution of sedimentary basins through the Earth history (Garzanti, 2016; Martini et al., 2020).

Multi-sample analyses of U–Pb zircon geochronology are presently a quite common achievement (Park et al., 2010; Nie et al., 2014; Solari et al., 2014). While the traditional age-signature comparison made by visually comparing probability density plots (PDPs) and Kernel density estimators (KDEs) are useful when working with two or a few samples, the management and visualization of a large amount of data become a subjective and cumber some challenge. An alternative, objective method for visualization and quantitative measurement of the inter-sample dissimilarity of a large data set should be adopted (Vermeesch and Garzanti, 2015). Multidimensional Scaling (MDS), a subset of principal component analysis (Sircombe, 2000), is a technique largely used in many scientific fields to compare and weight data of different nature, from ecology (Kenkel and Orlóci, 1986) to psychology (Jaworska and Chupetlovska-Anastasova, 2009). In provenance analysis, this technique was introduced to the community by Vermeesch (2013; 2018a) and was implemented in a series of software packages that facilitate its use (e.g., Vermeesch, 2018b).

Since more than 50% of the stratigraphic record of Mexico is characterized by sedimentary successions, more than a half of which is made up of clastic deposits spanning from Paleozoic to recent time (Sánchez-Zavala et al., 1999; Martini and Ortega-Gutiérrez, 2018; Fitz-Diaz et al., 2018; Juárez-Arriaga et al., 2019a; Silva-Romo et al., 2019; Ortega-Flores et al., 2020), MDS is a key tool for reconstructing the evolution of regional-scale tectonic events that shaped the Mexican territory, such as the assembly and breakup of Pangea and the development of the North American Cordilleran Orogeny, among others. In this work, we apply the MDS analysis to three specific geological cases for which U–Pb detrital data are available, with the aim to test and amend previous interpretations on the tectono-sedimentary setting and evolution. In particular, we will focus on:1) the submarine single-fan versus multi-fan scenarios proposed for the Upper Triassic successions of the Mexican Pacific margin (Centeno-García, 2005; Ortega-Flores et al., 2014); 2) the Paleozoic–lower Mesozoic Ayú-Acatlán complexes dichotomy (e.g., Helbig et al., 2012a; 2012b); and 3) the change from a heterogeneous to a more homogeneous provenance associated with the change from extensional to compressive tectonics across the southernmost North American Pacific margin during Late Jurassic–Cretaceous time (Centeno-García et al., 2011; Martini et al., 2014).

Section snippets

Study case 1: Upper Triassic fluvial to deep-marine systems of Mexico

Exposures of Upper Triassic sedimentary rocks are scattered in Mexico (Fig. 1). In northwestern Mexico, Upper Triassic fluvial to deep-marine successions are grouped into the Santa Clara, Antimonio, and Río Asunción formations (e.g., González-León et al., 2009, Fig. 1). These successions represent the stratigraphic record of the Antimonio-Barranca forearc basin (Dickinson et al., 2010, Fig. 1), which received detrital contribution from the adjacent Permian–Triassic arc, Proterozoic igneous and

Methods

The detrital zircon ages in Supplementary Table ST1 from previously published works are modeled employing MDS, a statistical tool that uses the dissimilarity matrix of the Kolmogorov-Smirnov test to create a map of distances indicative of the dissimilarity between the age distributions (Vermeesch, 2013). Non-metric MDS maps, best suited to compare large data sets (e.g., Vermeesch, 2013), are used to visualize similarities between the age distributions of Upper Triassic fluvial to deep-marine

Study case 1: Upper Triassic fluvial to deep-marine systems of Mexico

The MDS plot (Fig. 5A) shows that all samples are interconnected. However, two large dissimilarities separate samples with a pronounced detrital signature affinity with Laurencia and those with an evident affinity with Gondwana. Most samples show a detrital signature affinity with peri-Gondwanan blocks and the Carboniferous-Middle Triassic granitoid belt, and they are more similar to each other, although they have well defined specific clusters. These similarities suggest that, although most of

Conclusions

The quantitative approach through MDS statistical analysis in detrital geochronology represents a potential tool to compare and visualize, in a simplified way, large multi-sample sets of rocks involved in determined geologic events. As other techniques for visualization provenance data, it has advantages and limitations. One of its advantages is that, being a measurement of dissimilarities between samples, it allows to group and quickly visualize which samples share certain attributes. As the

Author statement

The author state that all authors have seen and approved the final version of the manuscript being submitted. The authors warrant that the article is the authors' original work, hasn't received prior publication and isn't under consideration for publication elsewhere.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The concepts behind this paper benefitted from funds of PAPIIT-DGAPA grants IA100320 to BOF, IN101520 to LAS, and IN104018 to MM. We thank the opportunity to share this work in the Journal of South American Earth Sciences special volume dedicated to the career of Profr. Tim F. Lawton in Mexico. The authors want to thank Dr. Carlos Ortega-Obregón at CGEO, UNAM, for U–Pb data analysis and instrumental maintenance. We would like to thank the reviewers Carita Augustsson and Igor Ishi Rubio-Cisneros

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