Solving petrological problems through machine learning: the study case of tectonic discrimination using geochemical and isotopic data

Maurizio Petrelli* and Diego Perugini

Department of Physics and Geology, University of Perugia, Piazza Università, 06100, Perugia (Italy)

*Corresponding Author:
E-mail: maurizio.petrelli@unipg.it Tel.: +39 075 5852607 Fax: +39 075 5852630

2 Abstract Machine learning methods are evaluated to study the intriguing and debated topic of discrimination among different tectonic environments using geochemical and isotopic data. Volcanic rocks characterized by a whole geochemical signature of major elements (SiO2, TiO2, Al2O3, Fe2O3T, CaO, MgO, Na2O, K2O), selected trace elements (Sr, Ba, Rb, Zr, Nb, La, Ce, Nd, Hf, Sm, Gd, Y, Yb, Lu, Ta, Th) and isotopes (206Pb/204Pb, 207Pb/204Pb, 208Pb/204Pb, 87Sr/86Sr and 143Nd/144Nd) have been extracted from open-access and comprehensive petrological databases (i.e. PetDB and GEOROC). The obtained dataset has been analyzed using support vector machines, a set of supervised machine learning methods, which are considered particularly powerful in classification problems. Results from the application of the machine learning methods show that the combined use of major, trace elements and isotopes allow associating the geochemical composition of rocks to the relative tectonic setting with high classification scores (93%, on average). The lowest scores are recorded from volcanic rocks deriving from back-arc basins (65%). All the other tectonic settings display higher classification scores, with oceanic islands reaching values up to 99%. Results of this study could have a significant impact in other petrological studies potentially opening new perspectives for petrologists and geochemists. Other examples of applications include the development of more robust geo-thermometers and geo-barometers and the recognition of volcanic sources for tephra layers in tephro-chronological studies.

Keywords: Machine Learning, Large Petrological Databases, Tectonic Discrimination, Major and Trace Elements, Isotopes.

3 Introduction Machine learning (ML) entails the use of algorithms and techniques to detect patterns from large datasets and to exploit the uncovered patterns to predict future trends, classify, or perform other kind of strategic decisions (Murphy 2012). The field of ML has progressed dramatically over the past two decades, developing from a “numerical curiosity” to a practical technology with widespread scientific and commercial use (Jordan and Mitchell 2015). For example, ML is now successfully utilized in several fields like computer vision, speech recognition, natural language processing and robot control (Jordan and Mitchell 2015). In principle, each complex problem characterized by a large enough number of input samples is well suited for ML applications (Jordan and Mitchell 2015). It is notable that the application of ML techniques has been quite extensively tested in the Earth Sciences (Huang et al. 2002; Petrelli et al. 2003; Masotti et al. 2006; Cannata et al. 2011; Zuo and Carranza 2011; Abedi et al. 2012; Goldstein and Coco 2014) but, surprisingly, their use is still virtually unexplored with regards to the solution of petrological problems. One intriguing and debated petrological application, potentially well-suited for the investigation by ML, is the tectonic discrimination of magmas using geochemical data (Li et al. 2015).
Trace element discrimination diagrams were introduced in the 1970s as a method for identifying the tectonic setting of basalts and other volcanic rocks (Pearce and Cann 1973). At that time, classification diagrams utilized only a few elements plotted as binary or triangular diagrams (Pearce and Cann 1973; Pearce 1976; Pearce and Norry 1979; Wood 1980; Shervais 1982; Meschede 1986; Grimes et al. 2015). This approach is still widely used; to date the work by Pierce and Cann (1973) received about 2082 citations (more than 400 only in the last 5 years; source: Scopus,

4 August 2016) testifying for the popularity of this approach in the petrological community (Li et al. 2015).
In 2006, Snow (2006) demonstrated that the success of these diagrams is mainly hindered by their limited dimensionality due to visualization requirements. Snow (2006) proposed alternative probabilistic methods and reported single analysis classification success rates for volcanic rocks from island arcs, ocean islands and mid- ocean ridges environments of about 83%, 75% and 76%, respectively.
In addition, Vermeesch (2006a) firstly proposed the application of two dimensional linear discriminant analysis (LDA, Vermeesch 2006a) and the application of classification trees (Vermeesch 2006b) to statistically determine the tectonic affinity of oceanic basalts. LDA has also been implemented by other authors (Agrawal et al. 2004; Agrawal et al. 2008; Ver

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