New multidimensional classification scheme of altered igneous rocks from performance comparison of isometric and modified log-ratio transformations of major elements

Abstract

Nomenclature in any science is of fundamental importance. From performance comparison of isometric and modified or hybrid log-ratio transformations of major elements, we present a complete multidimensional classification scheme for altered igneous rocks for High-Mg rock varieties and magma and rock types. This scheme is efficiently applicable through a computer package called Multidimensional Igneous rock Classification System (MICSys) that encapsulates four new online computer modules (HMgClaMSys_ilr, MagClaMSys_mlr, and IgRoClaMSys_mlr and a robustness evaluation module). We used a major element database of multinormally distributed 33868 samples of relatively fresh igneous rocks and compared the performance of isometric log-ratio and modified log-ratio transformations, both of which were multinormally distributed in terms of the 9 log-transformed variables as confirmed by the DOMUDaF program. The system must be trained from only fresh rocks because the prior class assignment requires an efficient scheme accepted by all, which is available only for fresh rocks. The multivariate technique of linear discriminant analysis (LDA) and canonical analysis applied to the two transformations provided the same percent success or correct classification for the respective databases. With these findings, we reinforce the recently published work on the International Union of Geological Sciences (IUGS)-consistent multidimensional classification of altered igneous rocks. The numerous tests and applications documented earlier on multidimensional classification were applied in the present work. The mathematical properties of log-ratio transformations are no longer important, provided the multidimensional technique involves the LDA and canonical analysis. MICSys available for online application at the web portal http://tlaloc.ier.unam.mx , was successfully applied to 6 new tests and 11 new applications to illustrate the usefulness of our multidimensional classification system to igneous rocks altered from post-emplacement compositional changes. Robustness of the new scheme for altered igneous rock nomenclature as compared to the conventional IUGS procedure for fresh rock nomenclature was confirmed from simulation of post-emplacement alteration of all elements in 28 different rock compositions representative of all rock types. Even greater robustness was demonstrated against analytical uncertainty propagation in 14 geochemical reference materials issued from Canada (3), France (3), Japan (5), and the USA (3). The estimation of robustness against post-emplacement changes and uncertainty propagation was facilitated by the incorporation of a fourth module in MICSys. This work, therefore, clearly shows that, for altered rocks, the new multidimensional scheme should be used, instead of the conventional classification meant for fresh rocks only.