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Multivariate analysis of log-ratio transformed data and its priority in mining science: Porphyry and polymetallic vein deposits case studies

Yıl 2019, Cilt: 159 Sayı: 159, 185 - 200, 15.08.2019
https://doi.org/10.19111/bulletinofmre.456958

Öz

Each mineralization style is
characterized by typical signature associations between elements due to
elemental interactions, therefore the coherence and closure effects problem
must be overcome in geochemical processing. The coherence indicates the ratios
between two components (rows or columns) remains the same whether they are
considered in a subcomposition or in the full composition. The log-ratio
transformation (LRT) has recognized as a standard procedure to support
subcompositional coherence. The log-transformed data is applicable for
geochemical data to unveil such associations, prior to applying the
multivariate analysis like correspondence analysis (CA) and principal component
analysis (PCA). At the present study, subcompositional coherence is overcome by
inverse iso-metric log-ratio transformation for geochemical compositional data
at two polymetallic and porphyry deposits. Based on Ilr-transformed data, Ag,
Au, As, Pb, Te, Mo and rather S, W, Cu are enriched as polymetallic elements at
Glojeh, while Au-Cu-(Mo) compositions indicate a porphyry deposit occurred in
Dalli deposit. The ability to handle zero values in the data matrix and
determining an elemental eccentricity from the center of each axis based on
Euclidean distances are the advantages of CA method, with compression to LRT.
Whereas, loading factors which spread in every direction and providing
subcompositional coherence are the competitive advantages of PCA based on LRT,
for both case studies. Results with these techniques show significant ability
to draw an inference in such geochemical data, and in improving the performance
of multivariate techniques using LRT.



 

Teşekkür

The authors are grateful to the Iranian Mines and Mining Industries Development and Renovation Organization (IMIDRO) for their permission to have access to Glojeh deposit dataset. The authors are also thankful to Mr. Fattahi and Mr. Hemmati for their encouragement and valuable help hugely.

Kaynakça

  • Abdi, H., Valentin, D. 2007. Multiple correspondence analysis. Encyclopedia of measurement and statistics, 651-657.
  • Abdi, H., Williams, L. J., Valentin, D. 2013. Multiple factor analysis: Principal component analysis for multi- table and multi-block data sets. Computational Statistics 5, 149-179.
  • Aitchison, J. 1982. The statistical analysis of compositional data. Journal of the Royal Statistical Society. Series B (Methodological), 139-177.
  • Aitchison, J. 1983. Principal component analysis of compositional data. Biometrika, 57-65.
  • Aitchison, J. 1986. The statistical analysis of compositional data. Monographs on Statistics and Applied Probability, 416 p.
  • Aitchison, J. 1990. Relative variation diagrams for describing patterns of compositional variability. Mathematical Geology 22, 487-511.
  • Aitchison, J., Greenacre, M. 2002. Biplots of compositional data. Journal of the Royal Statistical Society: Series C (Applied Statistics) 51, 375-392.
  • Akbarpour, A., Gholami, N., Azizi, H., Torab, F. M. 2013. Cluster and R-mode factor analyses on soil geochemical data of Masjed-Daghi exploration area, northwestern Iran. Arabian Journal of Geosciences 6, 3397-3408.
  • Bitner-Mathé, B. C., Klaczko, L. B. 1999. Heritability, phenotypic and genetic correlations of size and shape of Drosophila mediopunctata wings. Heredity 83, 688-696.
  • Carranza, E. J. M. 2009. Controls on mineral deposit occurrence inferred from analysis of their spatial pattern and spatial association with geological features. Ore Geology Reviews 35, 383-400.
  • Carranza, E. J. M. 2011. Analysis and mapping of geochemical anomalies using logratio- transformed stream sediment data with censored values. Journal of Geochemical Exploration 110, 167-185.
  • Carranza, E. J. M. 2017. Geochemical Mineral Exploration: Should We Use Enrichment Factors or Log- Ratios? Natural Resources Research 26, 411-428.
  • Collins, M., Ovalles, F. 1988. Variability of northwest Florida soils by principal component analysis. Soil Science Society of America Journal 52, 1430-1435.
  • Croux, C., Haesbroeck, G. 2000. Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies. Biometrika 87, 603- 618.
  • Darabi-Golestan, F., Ghavami-Riabi, R., Asadi- Harooni, H. 2013a. Alteration, zoning model, and mineralogical structure considering lithogeochemical investigation in Northern Dalli Cu–Au porphyry. Arabian Journal of Geosciences 6, 4821-4831.
  • Darabi-Golestan, F., Ghavami-Riabi, R., Khalokakaie, R., Asadi-Haroni, H., Seyedrahimi-Nyaragh, M. 2013b. Interpretation of lithogeochemical and geophysical data to identify the buried mineralized area in Cu-Au porphyry of Dalli-Northern Hill. Arabian Journal of Geosciences 6, 4499-4509.
  • Darabi-Golestan, F., Hezarkhani, A. 2016. High precision analysis modeling by backward elimination with attitude on interaction effects on Au (Ag)- polymetallic mineralization of Glojeh, Iran. Journal of African Earth Sciences 124, 505-516.
  • Darabi-Golestan, F., Hezarkhani, A. 2017. R- and Q-mode multivariate analysis to sense spatial mineralization rather than uni-elemental fractal modeling in polymetallic vein deposits. Geosystem Engineering, 1-10.
  • Darabi-Golestan, F., Hezarkhani, A. 2018. Evaluation of elemental mineralization rank using fractal and multivariate techniques and improving the performance by log-ratio transformation. Journal of Geochemical Exploration 189, 11-24.
  • Darabi-Golestan, F., Hezarkhani, A., Zare, M. 2017. Assessment of 226 Ra, 238 U, 232 Th, 137 Cs and 40 K activities from the northern coastline of Oman Sea (water and sediments). Marine Pollution Bulletin 118, 197-205.
  • David, M., Campiglio, C., Darling, R. 1974. Progresses in R-and Q-mode analysis: correspondence analysis and its application to the study of geological processes. Canadian Journal of Earth Sciences 11, 131-146.
  • Diday, E., Noirhomme-Fraiture, M. 2008. Symbolic data analysis and the SODAS software, Wiley Online Library, Namur, Belgium.
  • Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G., Barcelo-Vidal, C. 2003. Isometric logratio transformations for compositional data analysis. Mathematical Geology 35, 279-300.
  • Fávaro, D., Damatto, S., Moreira, E., Mazzilli, B., Campagnoli, F. 2007. Chemical characterization and recent sedimentation rates in sediment cores from Rio Grande reservoir, SP, Brazil. Journal of Radioanalytical and Nuclear Chemistry 273, 451- 463.
  • Filzmoser, P., Hron, K. 2008. Outlier detection for compositional data using robust methods. Mathematical Geosciences 40, 233-248.
  • Filzmoser, P., Hron, K., Reimann, C. 2009a. Principal component analysis for compositional data with outliers. Environmetrics 20, 621-632.
  • Filzmoser, P., Hron, K., Reimann, C. 2009b. Univariate statistical analysis of environmental (compositional) data: problems and possibilities. Science of the Total Environment 407, 6100- 6108.
  • Filzmoser, P., Hron, K., Reimann, C., Garrett, R. 2009c. Robust factor analysis for compositional data. Computers ve Geosciences 35, 1854-1861.
  • Filzmoser, P., Hron, K., Reimann, C. 2010. The bivariate statistical analysis of environmental (compositional) data. Science of the Total Environment 408, 4230-4238.
  • García-Izquierdo, M., Ríos-Rísquez, M. I. 2012. The relationship between psychosocial job stress and burnout in emergency departments: an exploratory study. Nursing outlook 60, 322-329.
  • Golestan, F. D., Hezarkhani, A., Zare, M. 2013. Interpretation of the Sources of Radioactive Elements and Relationship between them by Using Multivariate Analyses in Anzali Wetland Area. Geoinformatics & Geostatistics: An Overview 1, 1-10.
  • Greenacre, M. 2007. “Correspondence analysis in practice,” CRC press.
  • Greenacre, M. 2010. Log-ratio analysis is a limiting case of correspondence analysis. Mathematical Geosciences 42, 129-134.
  • Greenacre, M. 2011. Measuring subcompositional incoherence. Mathematical Geosciences 43, 681- 693.
  • Greenacre, M., Blasius, J. 2006. “Multiple correspondence analysis and related methods,” CRC press.
  • Greenacre, M. J. 1984. “Theory and applications of correspondence analysis.”
  • Gu, X., Liu, C., Wang, S., Zhao, C. 2015. Feature extraction using adaptive slow feature discriminant analysis. Neurocomputing 154, 139-148.
  • Hayton, J. C., Allen, D. G., Scarpello, V. 2004. Factor retention decisions in exploratory factor analysis: A tutorial on parallel analysis. Organizational research methods 7, 191-205.
  • Jeong, D. H., Ziemkiewicz, C., Fisher, B., Ribarsky, W., Chang, R. 2009. iPCA: An Interactive System for PCA-based Visual Analytics. In “Computer Graphics Forum”, Vol. 28, pp. 767-774. Wiley Online Library.
  • Ji, H., Zhu, Y., Wu, X. 1995. Correspondence cluster analysis and its application in exploration geochemistry. Journal of geochemical Exploration 55, 137-144.
  • Ji, H., Zeng, D., Shi, Y., Wu, Y., Wu, X. 2007. Semi- hierarchical correspondence cluster analysis and regional geochemical pattern recognition. Journal of Geochemical Exploration 93, 109-119.
  • Karamanis, D., Ioannides, K., Stamoulis, K. 2009. Environmentalassessment of natural radionuclides and heavy metals in waters discharged from a lignite-fired power plant. Fuel 88, 2046-2052.
  • Kazmierczak, J. 1985. Analyse logarithmique: deux exemples d’application. Revue de statistique appliquée 33, 13-24.
  • Liu, Y., Cheng, Q., Zhou, K., Xia, Q., Wang, X. 2016. Multivariate analysis for geochemical process identification using stream sediment geochemical data: A perspective from compositional data. Geochemical Journal 50, 293-314.
  • Março, P. H., Scarminio, I. S. 2007. Q-mode curve resolution of UV–vis spectra for structural transformation studies of anthocyanins in acidic solutions. Analytica chimica acta 583, 138-146.
  • Maronna, R., Martin, R. D., Yohai, V. 2006. “Robust statistics: Theory and Methods,” John Wiley & Sons, Chichester. ISBN.
  • Martín-Fernández, J. A., Barceló-Vidal, C., Pawlowsky- Glahn, V. 2003. Dealing with zeros and missing values in compositional data sets using nonparametric imputation. Mathematical Geology 35, 253-278.
  • Olofsson, T., Andersson, S., Sjögren, J.-U. 2009. Building energy parameter investigations based on multivariate analysis. Energy and Buildings 41, 71-80.
  • Pawlowsky-Glahn, V., Egozcue, J. J. 2006. Compositional data and their analysis: an introduction. Geological Society, London, Special Publications 264, 1-10.
  • Pawlowsky-Glahn, V., Buccianti, A. 2011. “Compositional data analysis: Theory and applications,” John Wiley & Sons.
  • Pawlowsky-Glahn, V., Egozcue, J. J., Tolosana Delgado, R. 2007. Lecture notes on compositional data analysis.
  • Pommer, L., Fick, J., Sundell, J., Nilsson, C., Sjöström, M., Stenberg, B., Andersson, B. 2004. Class separation of buildings with high and low prevalence of SBS by principal component analysis. Indoor Air 14, 16-23.
  • Ramasamy, V., Sundarrajan, M., Paramasivam, K., Meenakshisundaram, V., Suresh, G. 2013. Assessment of spatial distribution and radiological hazardous nature of radionuclides in high background radiation area, Kerala, India. Applied Radiation and Isotopes 73, 21-31.
  • Reimann, C., Filzmoser, P., Garrett, R., Dutter, R. 2011. “Statistical data analysis explained: applied environmental statistics with R,” John Wiley & Sons.
  • Reimann, C., Filzmoser, P., Fabian, K., Hron, K., Birke, M., Demetriades, A., Dinelli, E., Ladenberger, A., Team, T. G. P. 2012. The concept of compositional data analysis in practice—total major element concentrations in agricultural and grazing land soils of Europe. Science of the total environment 426, 196-210.
  • Silverman, J. D., Washburne, A., Mukherjee, S., David, L. A. 2016. A phylogenetic transform enhances analysis of compositional microbiota data. bioRxiv, 072413.
  • Stanley, C. R. 2006. On the special application of Thompson– Howarth error analysis to geochemical variables exhibiting a nugget effect. Geochemistry: Exploration, Environment, Analysis 6, 357-368.
  • Templ, M., Filzmoser, P., Reimann, C. 2008. Cluster analysis applied to regional geochemical data: problems and possibilities. Applied Geochemistry 23, 2198-2213.
  • Thió-Henestrosa, S., Martín-Fernández, J. 2005. Dealing with compositional data: the freeware CoDaPack. Mathematical Geology 37, 773-793.
  • Thompson, M., Howarth, R. J. 1976. Duplicate analysis in geochemical practice. Part I. Theoretical approach and estimation of analytical reproducibility. Analyst 101, 690-698.
  • Tokatlı, C., Köse, E., Çiçek, A. 2014. Assessment of the effects of large borate deposits on surface water quality by multi statistical approaches: A case study of Seydisuyu Stream (Turkey). Polish Journal of Environmental Studies 23, 1741-1751.
  • Zhu, Y., An, F., Tan, J. 2011. Geochemistry of hydrothermal gold deposits: a review. Geoscience Frontiers 2, 367-374.
  • Zuo, R., Xia, Q., Wang, H. 2013. Compositional data analysis in the study of integrated geochemical anomalies associated with mineralization. Applied geochemistry 28, 202-211.
Yıl 2019, Cilt: 159 Sayı: 159, 185 - 200, 15.08.2019
https://doi.org/10.19111/bulletinofmre.456958

Öz

 

Kaynakça

  • Abdi, H., Valentin, D. 2007. Multiple correspondence analysis. Encyclopedia of measurement and statistics, 651-657.
  • Abdi, H., Williams, L. J., Valentin, D. 2013. Multiple factor analysis: Principal component analysis for multi- table and multi-block data sets. Computational Statistics 5, 149-179.
  • Aitchison, J. 1982. The statistical analysis of compositional data. Journal of the Royal Statistical Society. Series B (Methodological), 139-177.
  • Aitchison, J. 1983. Principal component analysis of compositional data. Biometrika, 57-65.
  • Aitchison, J. 1986. The statistical analysis of compositional data. Monographs on Statistics and Applied Probability, 416 p.
  • Aitchison, J. 1990. Relative variation diagrams for describing patterns of compositional variability. Mathematical Geology 22, 487-511.
  • Aitchison, J., Greenacre, M. 2002. Biplots of compositional data. Journal of the Royal Statistical Society: Series C (Applied Statistics) 51, 375-392.
  • Akbarpour, A., Gholami, N., Azizi, H., Torab, F. M. 2013. Cluster and R-mode factor analyses on soil geochemical data of Masjed-Daghi exploration area, northwestern Iran. Arabian Journal of Geosciences 6, 3397-3408.
  • Bitner-Mathé, B. C., Klaczko, L. B. 1999. Heritability, phenotypic and genetic correlations of size and shape of Drosophila mediopunctata wings. Heredity 83, 688-696.
  • Carranza, E. J. M. 2009. Controls on mineral deposit occurrence inferred from analysis of their spatial pattern and spatial association with geological features. Ore Geology Reviews 35, 383-400.
  • Carranza, E. J. M. 2011. Analysis and mapping of geochemical anomalies using logratio- transformed stream sediment data with censored values. Journal of Geochemical Exploration 110, 167-185.
  • Carranza, E. J. M. 2017. Geochemical Mineral Exploration: Should We Use Enrichment Factors or Log- Ratios? Natural Resources Research 26, 411-428.
  • Collins, M., Ovalles, F. 1988. Variability of northwest Florida soils by principal component analysis. Soil Science Society of America Journal 52, 1430-1435.
  • Croux, C., Haesbroeck, G. 2000. Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies. Biometrika 87, 603- 618.
  • Darabi-Golestan, F., Ghavami-Riabi, R., Asadi- Harooni, H. 2013a. Alteration, zoning model, and mineralogical structure considering lithogeochemical investigation in Northern Dalli Cu–Au porphyry. Arabian Journal of Geosciences 6, 4821-4831.
  • Darabi-Golestan, F., Ghavami-Riabi, R., Khalokakaie, R., Asadi-Haroni, H., Seyedrahimi-Nyaragh, M. 2013b. Interpretation of lithogeochemical and geophysical data to identify the buried mineralized area in Cu-Au porphyry of Dalli-Northern Hill. Arabian Journal of Geosciences 6, 4499-4509.
  • Darabi-Golestan, F., Hezarkhani, A. 2016. High precision analysis modeling by backward elimination with attitude on interaction effects on Au (Ag)- polymetallic mineralization of Glojeh, Iran. Journal of African Earth Sciences 124, 505-516.
  • Darabi-Golestan, F., Hezarkhani, A. 2017. R- and Q-mode multivariate analysis to sense spatial mineralization rather than uni-elemental fractal modeling in polymetallic vein deposits. Geosystem Engineering, 1-10.
  • Darabi-Golestan, F., Hezarkhani, A. 2018. Evaluation of elemental mineralization rank using fractal and multivariate techniques and improving the performance by log-ratio transformation. Journal of Geochemical Exploration 189, 11-24.
  • Darabi-Golestan, F., Hezarkhani, A., Zare, M. 2017. Assessment of 226 Ra, 238 U, 232 Th, 137 Cs and 40 K activities from the northern coastline of Oman Sea (water and sediments). Marine Pollution Bulletin 118, 197-205.
  • David, M., Campiglio, C., Darling, R. 1974. Progresses in R-and Q-mode analysis: correspondence analysis and its application to the study of geological processes. Canadian Journal of Earth Sciences 11, 131-146.
  • Diday, E., Noirhomme-Fraiture, M. 2008. Symbolic data analysis and the SODAS software, Wiley Online Library, Namur, Belgium.
  • Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G., Barcelo-Vidal, C. 2003. Isometric logratio transformations for compositional data analysis. Mathematical Geology 35, 279-300.
  • Fávaro, D., Damatto, S., Moreira, E., Mazzilli, B., Campagnoli, F. 2007. Chemical characterization and recent sedimentation rates in sediment cores from Rio Grande reservoir, SP, Brazil. Journal of Radioanalytical and Nuclear Chemistry 273, 451- 463.
  • Filzmoser, P., Hron, K. 2008. Outlier detection for compositional data using robust methods. Mathematical Geosciences 40, 233-248.
  • Filzmoser, P., Hron, K., Reimann, C. 2009a. Principal component analysis for compositional data with outliers. Environmetrics 20, 621-632.
  • Filzmoser, P., Hron, K., Reimann, C. 2009b. Univariate statistical analysis of environmental (compositional) data: problems and possibilities. Science of the Total Environment 407, 6100- 6108.
  • Filzmoser, P., Hron, K., Reimann, C., Garrett, R. 2009c. Robust factor analysis for compositional data. Computers ve Geosciences 35, 1854-1861.
  • Filzmoser, P., Hron, K., Reimann, C. 2010. The bivariate statistical analysis of environmental (compositional) data. Science of the Total Environment 408, 4230-4238.
  • García-Izquierdo, M., Ríos-Rísquez, M. I. 2012. The relationship between psychosocial job stress and burnout in emergency departments: an exploratory study. Nursing outlook 60, 322-329.
  • Golestan, F. D., Hezarkhani, A., Zare, M. 2013. Interpretation of the Sources of Radioactive Elements and Relationship between them by Using Multivariate Analyses in Anzali Wetland Area. Geoinformatics & Geostatistics: An Overview 1, 1-10.
  • Greenacre, M. 2007. “Correspondence analysis in practice,” CRC press.
  • Greenacre, M. 2010. Log-ratio analysis is a limiting case of correspondence analysis. Mathematical Geosciences 42, 129-134.
  • Greenacre, M. 2011. Measuring subcompositional incoherence. Mathematical Geosciences 43, 681- 693.
  • Greenacre, M., Blasius, J. 2006. “Multiple correspondence analysis and related methods,” CRC press.
  • Greenacre, M. J. 1984. “Theory and applications of correspondence analysis.”
  • Gu, X., Liu, C., Wang, S., Zhao, C. 2015. Feature extraction using adaptive slow feature discriminant analysis. Neurocomputing 154, 139-148.
  • Hayton, J. C., Allen, D. G., Scarpello, V. 2004. Factor retention decisions in exploratory factor analysis: A tutorial on parallel analysis. Organizational research methods 7, 191-205.
  • Jeong, D. H., Ziemkiewicz, C., Fisher, B., Ribarsky, W., Chang, R. 2009. iPCA: An Interactive System for PCA-based Visual Analytics. In “Computer Graphics Forum”, Vol. 28, pp. 767-774. Wiley Online Library.
  • Ji, H., Zhu, Y., Wu, X. 1995. Correspondence cluster analysis and its application in exploration geochemistry. Journal of geochemical Exploration 55, 137-144.
  • Ji, H., Zeng, D., Shi, Y., Wu, Y., Wu, X. 2007. Semi- hierarchical correspondence cluster analysis and regional geochemical pattern recognition. Journal of Geochemical Exploration 93, 109-119.
  • Karamanis, D., Ioannides, K., Stamoulis, K. 2009. Environmentalassessment of natural radionuclides and heavy metals in waters discharged from a lignite-fired power plant. Fuel 88, 2046-2052.
  • Kazmierczak, J. 1985. Analyse logarithmique: deux exemples d’application. Revue de statistique appliquée 33, 13-24.
  • Liu, Y., Cheng, Q., Zhou, K., Xia, Q., Wang, X. 2016. Multivariate analysis for geochemical process identification using stream sediment geochemical data: A perspective from compositional data. Geochemical Journal 50, 293-314.
  • Março, P. H., Scarminio, I. S. 2007. Q-mode curve resolution of UV–vis spectra for structural transformation studies of anthocyanins in acidic solutions. Analytica chimica acta 583, 138-146.
  • Maronna, R., Martin, R. D., Yohai, V. 2006. “Robust statistics: Theory and Methods,” John Wiley & Sons, Chichester. ISBN.
  • Martín-Fernández, J. A., Barceló-Vidal, C., Pawlowsky- Glahn, V. 2003. Dealing with zeros and missing values in compositional data sets using nonparametric imputation. Mathematical Geology 35, 253-278.
  • Olofsson, T., Andersson, S., Sjögren, J.-U. 2009. Building energy parameter investigations based on multivariate analysis. Energy and Buildings 41, 71-80.
  • Pawlowsky-Glahn, V., Egozcue, J. J. 2006. Compositional data and their analysis: an introduction. Geological Society, London, Special Publications 264, 1-10.
  • Pawlowsky-Glahn, V., Buccianti, A. 2011. “Compositional data analysis: Theory and applications,” John Wiley & Sons.
  • Pawlowsky-Glahn, V., Egozcue, J. J., Tolosana Delgado, R. 2007. Lecture notes on compositional data analysis.
  • Pommer, L., Fick, J., Sundell, J., Nilsson, C., Sjöström, M., Stenberg, B., Andersson, B. 2004. Class separation of buildings with high and low prevalence of SBS by principal component analysis. Indoor Air 14, 16-23.
  • Ramasamy, V., Sundarrajan, M., Paramasivam, K., Meenakshisundaram, V., Suresh, G. 2013. Assessment of spatial distribution and radiological hazardous nature of radionuclides in high background radiation area, Kerala, India. Applied Radiation and Isotopes 73, 21-31.
  • Reimann, C., Filzmoser, P., Garrett, R., Dutter, R. 2011. “Statistical data analysis explained: applied environmental statistics with R,” John Wiley & Sons.
  • Reimann, C., Filzmoser, P., Fabian, K., Hron, K., Birke, M., Demetriades, A., Dinelli, E., Ladenberger, A., Team, T. G. P. 2012. The concept of compositional data analysis in practice—total major element concentrations in agricultural and grazing land soils of Europe. Science of the total environment 426, 196-210.
  • Silverman, J. D., Washburne, A., Mukherjee, S., David, L. A. 2016. A phylogenetic transform enhances analysis of compositional microbiota data. bioRxiv, 072413.
  • Stanley, C. R. 2006. On the special application of Thompson– Howarth error analysis to geochemical variables exhibiting a nugget effect. Geochemistry: Exploration, Environment, Analysis 6, 357-368.
  • Templ, M., Filzmoser, P., Reimann, C. 2008. Cluster analysis applied to regional geochemical data: problems and possibilities. Applied Geochemistry 23, 2198-2213.
  • Thió-Henestrosa, S., Martín-Fernández, J. 2005. Dealing with compositional data: the freeware CoDaPack. Mathematical Geology 37, 773-793.
  • Thompson, M., Howarth, R. J. 1976. Duplicate analysis in geochemical practice. Part I. Theoretical approach and estimation of analytical reproducibility. Analyst 101, 690-698.
  • Tokatlı, C., Köse, E., Çiçek, A. 2014. Assessment of the effects of large borate deposits on surface water quality by multi statistical approaches: A case study of Seydisuyu Stream (Turkey). Polish Journal of Environmental Studies 23, 1741-1751.
  • Zhu, Y., An, F., Tan, J. 2011. Geochemistry of hydrothermal gold deposits: a review. Geoscience Frontiers 2, 367-374.
  • Zuo, R., Xia, Q., Wang, H. 2013. Compositional data analysis in the study of integrated geochemical anomalies associated with mineralization. Applied geochemistry 28, 202-211.
Toplam 63 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Farshad Darabı-golestan Bu kişi benim 0000-0002-4648-152X

Ardeshir Hezarkhanı Bu kişi benim 0000-0002-1149-3440

Yayımlanma Tarihi 15 Ağustos 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 159 Sayı: 159

Kaynak Göster

APA Darabı-golestan, F., & Hezarkhanı, A. (2019). Multivariate analysis of log-ratio transformed data and its priority in mining science: Porphyry and polymetallic vein deposits case studies. Bulletin of the Mineral Research and Exploration, 159(159), 185-200. https://doi.org/10.19111/bulletinofmre.456958
AMA Darabı-golestan F, Hezarkhanı A. Multivariate analysis of log-ratio transformed data and its priority in mining science: Porphyry and polymetallic vein deposits case studies. Bull.Min.Res.Exp. Ağustos 2019;159(159):185-200. doi:10.19111/bulletinofmre.456958
Chicago Darabı-golestan, Farshad, ve Ardeshir Hezarkhanı. “Multivariate Analysis of Log-Ratio Transformed Data and Its Priority in Mining Science: Porphyry and Polymetallic Vein Deposits Case Studies”. Bulletin of the Mineral Research and Exploration 159, sy. 159 (Ağustos 2019): 185-200. https://doi.org/10.19111/bulletinofmre.456958.
EndNote Darabı-golestan F, Hezarkhanı A (01 Ağustos 2019) Multivariate analysis of log-ratio transformed data and its priority in mining science: Porphyry and polymetallic vein deposits case studies. Bulletin of the Mineral Research and Exploration 159 159 185–200.
IEEE F. Darabı-golestan ve A. Hezarkhanı, “Multivariate analysis of log-ratio transformed data and its priority in mining science: Porphyry and polymetallic vein deposits case studies”, Bull.Min.Res.Exp., c. 159, sy. 159, ss. 185–200, 2019, doi: 10.19111/bulletinofmre.456958.
ISNAD Darabı-golestan, Farshad - Hezarkhanı, Ardeshir. “Multivariate Analysis of Log-Ratio Transformed Data and Its Priority in Mining Science: Porphyry and Polymetallic Vein Deposits Case Studies”. Bulletin of the Mineral Research and Exploration 159/159 (Ağustos 2019), 185-200. https://doi.org/10.19111/bulletinofmre.456958.
JAMA Darabı-golestan F, Hezarkhanı A. Multivariate analysis of log-ratio transformed data and its priority in mining science: Porphyry and polymetallic vein deposits case studies. Bull.Min.Res.Exp. 2019;159:185–200.
MLA Darabı-golestan, Farshad ve Ardeshir Hezarkhanı. “Multivariate Analysis of Log-Ratio Transformed Data and Its Priority in Mining Science: Porphyry and Polymetallic Vein Deposits Case Studies”. Bulletin of the Mineral Research and Exploration, c. 159, sy. 159, 2019, ss. 185-00, doi:10.19111/bulletinofmre.456958.
Vancouver Darabı-golestan F, Hezarkhanı A. Multivariate analysis of log-ratio transformed data and its priority in mining science: Porphyry and polymetallic vein deposits case studies. Bull.Min.Res.Exp. 2019;159(159):185-200.

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