Log‐ratio transformed major element based multidimensional classification for altered High‐Mg igneous rocks

Abstract

A new multidimensional classification scheme consistent with the chemical classification of the International Union of Geological Sciences (IUGS) is proposed for the nomenclature of High‐Mg altered rocks. Our procedure is based on an extensive database of major element (SiO2, TiO2, Al2O3, Fe2 O3t, MnO, MgO, CaO, Na2O, K2O, and P2O5) compositions of a total of 33,868 (920 High‐Mg and 32,948 “Common”) relatively fresh igneous rock samples. The database consisting of these multinormally distributed samples in terms of their isometric log‐ratios was used to propose a set of 11 discriminant functions and 6 diagrams to facilitate High‐Mg rock classification. The multinormality required by linear discriminant and canonical analysis was ascertained by a new computer program DOMuDaF. One multidimensional function can distinguish the High‐Mg and Common igneous rocks with high percent success values of about 86.4% and 98.9%, respectively. Similarly, from 10 discriminant functions the High‐Mg rocks can also be classified as one of the four rock types (komatiite, meimechite, picrite, and boninite), with high success values of about 88%–100%. Satisfactory functioning of this new classification scheme was confirmed by seven independent tests. Five further case studies involving application to highly altered rocks illustrate the usefulness of our proposal. A computer program HMgClaMSys was written to efficiently apply the proposed classification scheme, which will be available for online processing of igneous rock compositional data. Monte Carlo simulation modeling and mass‐balance computations confirmed the robustness of our classification with respect to analytical errors and postemplacement compositional changes.

Using Major Element Logratios to Recognize Compositional Patterns of Basalt: Implications for Source Lithological and Compositional Heterogeneities

“…In the compositional data analysis field, some logratio transformations, including coordinates such as centered logratio (Clr), isometric logratio, and additive‐logratio (Alr; see Appendix A), have been shown to possess better statistical properties that can be used to identify the structure of compositional data (Aitchison, ; Egozcue et al, ). These coordinates have been recently explored in the petrochemical field and provide a powerful tool for capturing the nature of specific petrological issues (e.g., Rollinson, ; Verma et al, ). However, in this study, these coordinates are not directly selected to perform discriminant function analysis because of the following two reasons.…”

“…This contrast suggests that two populations of rocks and/or melts with different major element patterns in logratio space may show indistinguishable patterns in subcompositional space (i.e., Harker diagrams and simple major element ratios) owing chiefly to spurious correlations and the constant sum problem of compositional data, as noted by many statisticians (Aitchison, ; Aitchison & Egozcue, ; Egozcue et al, ; Pawlowsky‐Glahn & Egozcue, ); this observation can explain why melts of peridotite and mafic lithologies with low and high FCKANTMS, respectively, are difficult to distinguish in major element content‐ and ratio‐based analysis, as discussed in the above section. We note that FCKANTMS is a polynomial relationship of major element logratios, suggesting that logratios other than major element contents should be regarded as the appropriate independent variables for compositional pattern analysis, especially from a statistical perspective, which in effect has long been recognized in the compositional data analysis field but has received little attention in the petrology field (Aitchison, ; Aitchison & Egozcue, ; Egozcue et al, ; Pawlowsky‐Glahn & Egozcue, ; Rollinson, ; Verma et al, ). As suggested by many statisticians and mathematical geologists, for pattern recognition of major and trace elements, logratios are the best variables to use because many geological and petrological implications derived from major element content‐based analysis may suffer from geometrical illusion, as shown in Figure .…”

“…The essence of compositional data is ratios, because ratios do not change when compositional data are renormalized to 100% or considered in subcompositional space, and logratios would allow compositional data to freely range from −∞ to +∞, which can be analyzed using standard statistical techniques (Aitchison, ; Aitchison & Egozcue, ; Egozcue et al, ; Pawlowsky‐Glahn & Egozcue, ). The logratio method, however, has only just begun to be realized in petrological and geochemical fields in recent years (e.g., Cortés et al, ; Ó. Kovács et al, ; Rollinson, ; Verma et al, ; Yang & Zhou, ). Numerous studies involving pattern recognition of compositional data for rocks and minerals still focus on the raw concentration form.…”

Petrogenesis, geochemistry, and tectonic setting of a basaltic body within the Gercus Formation of northern Iraq: first record for Eocene anorogenic volcanic activity in the region

“…A number of online computer programs designed for the classification of altered igneous rocks, which are available at https://tlaloc.ier.unam.mx, have been applied on the highly altered Gercus Basalt. These programs are HMgClaMSys_mlr (Verma et al, 2016) and IgRoClaMSys_ ilr , used for identifying the rock type, and MagClaMSys_ilr to identify the type of magma.…”

APMdisc: An online computer program for the geochemical discrimination of siliciclastic sediments from active and passive margins

“…The computer program DOMuDaF (Verma et al, 2016b) was then used to obtain multinormally distributed samples in the ilr and mlr spaces separately for the two groups (active and passive margins). These multivariate data were tested to examine the statistical similarities and differences between the two groups from Wilks lambda and F tests (Tables AI-7 and AI-8).…”