Skip to main content
  • 1386 Accesses

Abstract

A combination of logratio transformation (additive logratio) and linear discriminant analysis (LDA) is a powerful experimental data-handling coherent multi-dimensional probability-based statistical technique, which is superior to the use of conventional bi-variate or ternary diagrams. Application of this procedure is illustrated with three subsets of compositional data for 2270 igneous rock samples from the central part of the Mexican Volcanic Belt (MVB). A combination of isometric logratio transformation and LDA will be used in future to test these and other sub-compositions on an updated worldwide compilation of geochemical data, which will enable us to achieve newer sets of more versatile, efficient, and coherent diagrams and related probability estimates.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

REFERENCES

  1. Verma, S.P., Pandarinath, K., Verma, S.K. and Agrawal, S.: Fifteen new discriminant-function-based multi-dimensional robust diagrams for acid rocks and their application to Precambrian rocks. Lithos, 168-169, 113–123 (2013)

    Google Scholar 

  2. Aitchison, J.: The statistical analysis of compositional data. Chapman and Hall, London (1986)

    Google Scholar 

  3. Egozcue, J.J., Pawlowsky-Glahn, V., Mateu-Figueras, G. and Barceló-Vidal, C.: Isometric logratio transformations for compositional data analysis. Math. Geol., 35, 279–300 (2003)

    Google Scholar 

  4. Verma, S.P., Guevara, M. and Agrawal, S.: Discriminating four tectonic settings: five new geochemical diagrams for basic and ultrabasic volcanic rocks based on log-ratio transformation of major-element data. J. Earth Sys. Sci., 115, 485–528 (2006)

    Google Scholar 

  5. Agrawal, S., Guevara, M. and Verma, S.P.: Tectonic discrimination of basic and ultrabasic rocks through log-transformed ratios of immobile trace elements. Int. Geol. Rev., 50, 1057–1079 (2008)

    Google Scholar 

  6. Verma, S.P. and Agrawal, S.: New tectonic discrimination diagrams for basic and ultrabasic volcanic rocks through log-transformed ratios of high field strength elements and implications for petrogenetic processes. Rev. Mex. Cienc. Geol., 28, 24–44 (2011)

    Google Scholar 

  7. Verma, S.P. and Verma, S.K.: First 15 probability-based multi-dimensional discrimination diagrams for intermediate magmas and their robustness against post-emplacement compositional changes and petrogenetic processes. Turk. J. Earth Sci., 22, 931–995 (2013)

    Google Scholar 

  8. Verma, S.K., Pandarinath, K. and Verma, S.P.: Statistical evaluation of tectonomagmatic discrimination diagrams for granitic rocks and proposal of new discriminant-function-based multi-dimensional diagrams for acid rocks. Int. Geol. Rev., 54, 325–347 (2012)

    Google Scholar 

  9. Verma, S.P.: Statistical evaluation of bivariate, ternary and discriminant function tectonomagmatic discrimination diagrams. Turk. J. Earth Sci., 19, 185–238 (2010)

    Google Scholar 

Download references

ACKNOWLEDGEMENTS

This work was supported by DGAPA-PAPIIT grant IN104813.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Srendra P. Verma .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Capital Publishing Company

About this paper

Cite this paper

Verma, S.P. (2016). Application of a Coherent Multi-Dimensional Technique to the Central Part of the Mexican Volcanic Belt. In: Raju, N. (eds) Geostatistical and Geospatial Approaches for the Characterization of Natural Resources in the Environment. Springer, Cham. https://doi.org/10.1007/978-3-319-18663-4_6

Download citation

Publish with us

Policies and ethics