Skip to main content
SpringerLink
Log in

Co-simulated Size Number: An Elegant Novel Algorithm for Identification of Multivariate Geochemical Anomalies

  • Original Paper
  • Published:
Natural Resources Research Aims and scope Submit manuscript

Abstract

Identification of geochemical anomalies is of particular importance for tracing the footprints of anomalies. This can be implemented by advanced techniques of exploratory data analysis, such as fractal/multi-fractal approaches based on priori or posteriori distribution of geochemical elements. The latter workflow involves analysis of 2D/3D produced maps, which can be mostly obtained by geostatistical algorithms. There are two challenging issues for such an analysis. The first one corresponds to handling the cross-correlation structures among the data, and the second one relates to the compositional nature of data. To tackle these problems, this paper investigates the application of Gaussian co-simulation for modeling the cross-correlated compositional data in order to recognize the multivariate geochemical anomalies in integration with fractal analysis. In this context, an innovative algorithm, namely co-simulated size number (CoSS-N), is introduced for this purpose. The compositional nature of data is addressed by additive log-ratio transformation of original data while the Gaussian co-simulation handles the reproduction of cross-correlation among the components. The co-simulated outputs are then taken into account for capturing different geochemical populations, showing different levels of backgrounds and anomalies. The algorithm is illustrated via a real case study located in Philippine wherever seven geochemical components are required to be considered. The accuracy of results is examined by statistical validation techniques, indicating the capability of the CoSS-N algorithm for multivariate identification of geochemical anomalies.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14

Similar content being viewed by others

References

  • Abildin, Y., Madani, N., & Topal, E. (2019). A hybrid approach for joint simulation of geometallurgical variables with inequality constraint. Minerals,9(1), 24.

    Google Scholar 

  • Adeli, A., Emery, X., & Dowd, P. (2018). Geological modelling and validation of geological interpretations via simulation and classification of quantitative covariates. Minerals,8(1), 7.

    Google Scholar 

  • Afzal, P., Fadakar Alghalandis, Y., Khakzad, A., Moarefvand, P., & Rashidnejad Omran, N. (2011). Delineation of mineralization zones in porphyry Cu deposits by fractal concentration–volume modeling. Journal of Geochemical Exploration,108, 220–232.

    Google Scholar 

  • Afzal, P., Khakzad, A., Moarefvand, P., Rashidnejad Omran, N., Esfandiari, B., & Fadakar Alghalandis, Y. (2010). Geochemical anomaly separation by multifractal modeling in Kahang (Gor Gor) porphyry system. Central Iran. Journal of Geochemical Exploration,104, 34–46.

    Google Scholar 

  • Afzal, P., Madani, N., Shahbeik, Sh, & Yasrebi, A. B. (2015). Multi-Gaussian kriging: a practice to enhance delineation of mineralized zones by concentration–volume fractal model in Dardevey iron ore deposit, SE Iran. Journal of Geochemical Exploration,158, 10–21.

    Google Scholar 

  • Agterberg, F. P. (1995). Multifractal modeling of the sizes and grades of giant and supergiant deposits. International Geology Review,37(1), 1–8.

    Google Scholar 

  • Aitchison, J. (1982). The statistical analysis of compositional data. Journal of the Royal Statistical Society: Series B (Methodological),44(2), 139–177. (with discussion).

    Google Scholar 

  • Aitchison, J. (1986). The statistical analysis of compositional data. Monographs on statistics and applied probability. London: Chapman & Hall Ltd. (Reprinted in 2003 with additional material by The Blackburn Press).

    Google Scholar 

  • Aitchison, J., & Shen, S. M. (1980). Logistic-normal distributions. Some properties and uses. Biometrika,67(2), 261–272.

    Google Scholar 

  • Almeida, A. S., & Journel, A. G. (1994). Joint simulation of multiple variables with a Markov-type coregionalization model. Mathematical Geology,26(5), 565–588.

    Google Scholar 

  • Battalgazy, N., & Madani, N. (2019). Categorization of mineral resources based on different geostatistical simulation algorithms: A case study from an iron ore deposit. Natural Resources Research. https://doi.org/10.1007/s11053-019-09474-9.

    Article  Google Scholar 

  • Buccianti, A., & Pawlowsky-Glahn, V. (2005). New perspectives on water chemistry and compositional data analysis. Mathematical Geology,37(7), 703–727.

    Google Scholar 

  • Carr, J. R., & Myers, D. E. (1985). COSIM: A FORTRAN IV program for coconditional simulation. Computers & Geosciences,11(6), 675–705.

    Google Scholar 

  • Carranza, E. J. M. (2008). Geochemical anomaly and mineral prospectivity mapping in GIS. Handbook of exploration and environmental geochemistry (Vol. 11). Amsterdam: Elsevier.

    Google Scholar 

  • 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,25, 383–400.

    Google Scholar 

  • Carranza, E. J. M. (2010a). Catchment basin modelling of stream sediment anomalies revisited: incorporation of EDA and fractal analysis. Geochemistry: Exploration, Environment, Analysis,10, 365–381.

    Google Scholar 

  • Carranza, E. J. M. (2010b). Mapping of anomalies in continuous and discrete fields of stream sediment geochemical landscapes. Geochemistry: Exploration, Environment, Analysis,10, 171–187.

    Google Scholar 

  • 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.

    Google Scholar 

  • Chen, G., & Cheng, Q. (2018). Fractal-based wavelet filter for separating geophysical or geochemical anomalies from background. Mathematical Geosciences,50(3), 249–272.

    Google Scholar 

  • Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration,122, 55–70.

    Google Scholar 

  • Cheng, Q., Agterberg, F. P., & Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration,51, 109–130.

    Google Scholar 

  • Cheng, Q., Agterberg, F. P., & Bonham-Carter, G. F. (1996). A spatial analysis method for geochemical anomaly separation. Journal of Geochemical Exploration,56(3), 183–195.

    Google Scholar 

  • Cheng, Q., Xu, Y. & Grunsky, E. (1999). Integrated spatial and spectral analysis for geochemical anomaly separation. In: S. J. Lippard, A. Naess, & R. Sinding-Larsen (Eds.), Proceedings of the conference of the international association for mathematical geology (Vol. 1, pp. 87–92). Trondheim.

  • Cheng, Q., Xu, Y., & Grunsky, E. C. (2000). Integrated spatial and spectrum method for geochemical anomaly separation. Natural Resources Research,9, 43–52.

    Google Scholar 

  • Chilès, J. P., & Delfiner, P. (2012). Geostatistics: Modeling spatial uncertainty (2nd ed.). New York: Wiley.

    Google Scholar 

  • Deutsch, C. V., & Journel, A. G. (1998). GSLIB: Geostatistical software library and user’s guide. New York: Oxford University Press.

    Google Scholar 

  • Egozcue, J., Pawlowsky-Glahn, V., Mateu-Figueras, G., & Barceló-Vidal, B. (2003). Isometric logratio transformations for compositional data analysis. Mathematical Geology,35(3), 279–300.

    Google Scholar 

  • Emery, X. (2004). Testing the correctness of the sequential algorithm for simulating Gaussian random fields. Stochastic Environmental Research and Risk Assessment A,18(6), 401–413.

    Google Scholar 

  • Emery, X. (2005). Variograms of order ω: A tool to validate a bivariate distribution model. Mathematical Geology,37(2), 163–181.

    Google Scholar 

  • Emery, X. (2007). Conditioning simulations of Gaussian random fields by ordinary kriging. Mathematical Geology,39(6), 607–623.

    Google Scholar 

  • Emery, X. (2008). A turning bands program for conditional co-simulation of cross-correlated Gaussian random fields. Computers & Geosciences,34(12), 1850–1862.

    Google Scholar 

  • Emery, X. (2010). Iterative algorithms for fitting a linear model of coregionalization. Computers & Geoscience,36(9), 1150–1160.

    Google Scholar 

  • Emery, X., & Lantuéjoul, C. (2006). TBSIM: A computer program for conditional simulation of three-dimensional Gaussian random fields via the turning bands method. Computer & Geoscience,32(10), 1615–1628.

    Google Scholar 

  • Eze, P. N., Madani, N., & Adoko, A. C. (2019). Multivariate mapping of heavy metals spatial contamination in a Cu–Ni exploration field (Botswana) using turning bands co-simulation algorithm. Natural Resources Researches,28(1), 109–124.

    Google Scholar 

  • Feder, J. (1988). Fractals (p. 283). New York: Plenum Press.

    Google Scholar 

  • Filzmoser, P., Hron, K., & Reimann, C. (2009). Principal components analysis for compositional data with outliers. Environmetrics,20, 621–632.

    Google Scholar 

  • Gneiting, T. (1999). The correlation bias for two-dimensional simulations by turning bands. Mathematical Geology,31(2), 195–211.

    Google Scholar 

  • Gómez-Hernández, J. J., & Journel, A. G. (1993). Joint sequential simulation of multigaussian fields. In A. Soares (Ed.), Geostatistics Tróia’92 (Vol. 1, pp. 85–94). Dordrecht: Springer.

  • Goovaerts, P. (1997). Geostatistics for natural resources evaluation. New York: Oxford University Press.

    Google Scholar 

  • Goovaerts, P. (1999). Impact of the simulation algorithm, magnitude of ergodic fluctuations and number of realizations on the spaces of uncertainty of flow properties. Stochastic Environmental Research and Risk Assessment,13(3), 161–182.

    Google Scholar 

  • He, J., Yao, S., Zhang, Z., & You, G. (2013). Complexity and productivity differentiation models of metallogenic indicator elements in rocks and supergene media around Daijiazhuang Pb–Zn deposit in Dangchang County, Gansu Province. Natural Resources Research,22, 19–36.

    Google Scholar 

  • Hogg, R. V., McKean, J., & Craig, A. T. (2012). Introduction to mathematical statistics (7th ed.). Harlow: Pearson Education Ltd.

    Google Scholar 

  • Hosseini, S. A., & Asghari, O. (2019). Multivariate geostatistical simulation on block-support in the presence of complex multivariate relationships: Iron ore deposit case study. Natural Resources Research,28, 125–144.

    Google Scholar 

  • JICA-MMAJ. (1986). Report on mineral exploration, mineral deposits and tectonics of two contrasting geologic environments in the Republic of the Philippines, Phase II (Masbate and Leyte Areas). Tokyo: Japan International Cooperating Agency and Metal Mining Agency of Japan.

    Google Scholar 

  • Job, M. (2010). Application of logratios for compositional data. Centre for Computational Geostatistics Report 12, 307. University of Alberta, Canada.

  • Journel, A. B., & Huijbregts, C. J. (1978). Mining geostatistics. New York: Academic.

    Google Scholar 

  • Lantuéjoul, C. (1994). Non conditional simulation of stationary isotropic multigaussian random functions. In M. Armstrong & P. A. Dowd (Eds.), Geostatistical simulations (pp. 147–177). Dordrecht: Kluwer.

    Google Scholar 

  • Lantuéjoul, C. (2002). Geostatistical simulation: Models and algorithms. Berlin: Springer.

    Google Scholar 

  • Leuangthong, O., McLennan, J. A., & Deutsch, C. V. (2004). Minimum acceptance criteria for geostatistical realizations. Natural Resources Research,13, 131–141.

    Google Scholar 

  • Li, C., Xu, Y., & Jiang, X. (1994). The fractal model of mineral deposits. Geology of Zhejiang,10, 25–32. (in Chinese with English abstract).

    Google Scholar 

  • Luz, F., Mateus, A., Matos, J. X., & Gonçalves, M. A. (2014). Cu- and Zn-soil anomalies in the NE border of the South Portuguese Zone (Iberian Variscides, Portugal) identified by multifractal and geostatistical analyses. Natural Resources Research,23, 195–215.

    Google Scholar 

  • Madani, N., & Emery, X. (2019). A comparison of search strategies to design the cokriging neighborhood for predicting coregionalized variables. Stochastic Environmental Research and Risk Assessment,33(1), 183–199.

    Google Scholar 

  • Madani, N., & Sadeghi, B. (2019). Capturing hidden geochemical anomalies in scarce data by fractal analysis and stochastic modeling. Natural Resources Research,28(3), 833–847.

    Google Scholar 

  • Mandelbrot, B. B. (1983). The fractal geometry of nature. San Fransisco: W. H. Freeman.

    Google Scholar 

  • Matheron, G. (1973). The intrinsic random functions and their applications. Advances in Applied Probability,5(3), 439–468. https://doi.org/10.2307/1425829.

    Article  Google Scholar 

  • Mery, N., Emery, X., Cáceres, A., Ribeiro, D., & Cunha, E. (2017). Geostatistical modeling of the geological uncertainty in an iron ore deposit. Ore Geology Reviews,88, 336–351.

    Google Scholar 

  • Mitchell, A. H. G., & Leach, T. M. (1991). Epithermal gold in the Philippines: Island arc metallogenesis. Geothermal Systems and Geology. London: Academic Press.

    Google Scholar 

  • Monecke, T., Monecke, J., Herzig, P. M., Gemmell, J. B., & Monch, W. (2005). Truncated fractal frequency distribution of element abundance data: A dynamic model for the metasomatic enrichment of base and precious metals. Earth Planetary Science Letters,232, 363–378.

    Google Scholar 

  • Mueller, U., Tolosana-Delgado, R., & van den Boogaart, K. G. (2014). Simulation of compositional data: A nickel laterite case study. In R. Dimitrakopoulos (Ed.), Advances in orebody modelling and strategic mine planning. Melbourne: AusIMM.

    Google Scholar 

  • Myers, D. E. (1989). Vector conditional simulation. In M. Armstrong (Ed.), Geostatistics (pp. 283–293). Dordrecht: Springer.

    Google Scholar 

  • Olea, R. A., Luppens, J. A., Egozcue, J. J., & Pawlowsky-Glahn, V. (2016). Calorific value and compositional ultimate analysis with a case study of a Texas lignite. International Journal of Coal Geology,162, 27–33.

    Google Scholar 

  • Paravarzar, S., Emery, X., & Madani, N. (2015). Comparing sequential Gaussian and turning bands algorithms for cosimulating grades in multi-element deposits. Comptes Rendus Geoscience,347(2), 84–93.

    Google Scholar 

  • Pawlowsky-Glahn, V. (1984). On spurious spatial covariance between variables of constant sum. Science de la Terre Information Géologie,21, 107–113.

    Google Scholar 

  • Pawlowsky, V., & Burger, H. (1992). Spatial structure analysis of regionalized compositions. Mathematical Geology,24, 675–691.

    Google Scholar 

  • Pawlowsky-Glahn, V. (2003). Statistical modelling on coordinates. In S. Thió-Henestrosa & J. A. Martín-Fernández (Eds.), Proceedings of CoDaWork’03, the 1st compositional data analysis workshop. Girona (E): Universitat de Girona. ISBN 84–8458-111-X. Retrieved April 18, 2019 from http://ima.udg.es/Activitats/CoDaWork2003/.

  • Pawlowsky-Glahn, V., & Egozcue, J. J. (2016). Spatial analysis of compositional data: A historical review. Journal of Geochemical Exploration,164, 28–32.

    Google Scholar 

  • Pawlowsky-Glahn, V., Egozcue, J. J., & Tolosana-Delgado, R. (2015). Modelling and analysis of compositional data. New York: Wiley.

    Google Scholar 

  • Pawlowsky-Glahn, V., & Olea, R. A. (2004). Geostatistical analysis of compositional data. Studies in mathematical geology (Vol. 7). Oxford: Oxford University Press.

    Google Scholar 

  • Pebesma, E. J. (2004). Multivariable geostatistics in S: The gstat package. Computers & Geosciences,30(7), 683–691.

    Google Scholar 

  • Reimann, C., Filzmoser, P., Garrett, R. G., & Dutter, R. (2008). Statistical data analysis explained: Applied environmental statistics with R (No. Sirsi) i9780470985816. Chichester: Wiley.

    Google Scholar 

  • Rivoirard, J. (1994). Introduction to disjunctive kriging and nonlinear geostatistics. Oxford: Oxford University Press.

    Google Scholar 

  • Rossi, M. E., & Deutsch, C. V. (2014). Mineral resource estimation. Dordrecht: Springer.

    Google Scholar 

  • Rubio, R. H., Costa, J. F. C. L., & Bassani, M. A. A. (2016). A geostatistical framework for estimating compositional data avoiding bias in back-transformation. Rem: Revista Escola de Minas,69(2), 219–226.

    Google Scholar 

  • Sadeghi, B., Madani, N., & Carranza, E. J. M. (2015). Combination of geostatistical simulation and fractal modeling for mineral resource classification. Journal of Geochemical Exploration,149, 59–73.

    Google Scholar 

  • Sadeghi, B., Moarefvand, P., Afzal, P., Yasrebi, A. B., & Saein, L. D. (2012). Application of fractal models to outline mineralized zones in the Zaghia iron ore deposit, Central Iran. Journal of Geochemical Exploration,122, 9–19.

    Google Scholar 

  • Shi, J., & Wang, C. (1998). Fractal analysis of gold deposits in China: Implication for giant deposit exploration. Earth Sciences Journal of China University of Geosciences,23, 616–618. (in Chinese with English abstract).

    Google Scholar 

  • Talebi, H., Mueller, U., & Tolosana-Delgado, R. (2019). Joint simulation of compositional and categorical data via direct sampling technique—Application to improve mineral resource confidence. Computer & Geosciences,122, 87–102.

    Google Scholar 

  • Tolosana-Delgado, R. (2006). Geostatistics for constrained variables: Positive data, compositions and probabilities. Application to environmental hazard monitoring. Retrieved April 18, 2019 from http://www.tesisenxarxa.net/TDX-0123106-122444/index_an.html.

  • Tolosana-Delgado, R., Mueller, U., & van den Boogaart, K. G. (2018). Geostatistics for compositional data: An overview. Mathematical Geosciences. https://doi.org/10.1007/s11004-018-9769-3.

    Article  Google Scholar 

  • Tolosana-Delgado, R., Otero, N., & Pawlowsky-Glahn, V. (2005). Some basic concepts of compositional geometry. Mathematical Geology,37(7), 673–680.

    Google Scholar 

  • Tolosana-Delgado, R., & van den Boogaart, K. G. (2013). Joint consistent mapping of high-dimensional geochemical surveys. Mathematical Geosciences,45, 983–1004.

    Google Scholar 

  • Turcotte, D. L. (1996). Fractals and chaos in geophysics (2nd edn) (pp. 81–99). Cambridge: Cambridge University Press.

    Google Scholar 

  • Van den Boogaart, K. G., Mueller, U., & Tolosana-Delgado, R. (2017). An affine equivariant multivariate normal score transform for compositional data. Mathematical Geosciences,49, 231–251.

    Google Scholar 

  • Wackernagel, H. (2003). Multivariate geostatistics: An introduction with applications. Berlin: Springer.

    Google Scholar 

  • Zuo, R., Cheng, Q., & Xia, Q. (2009). Application of fractal models to characterization of vertical distribution of geochemical element concentration. Journal of Geochemical Exploration,102, 37–43.

    Google Scholar 

  • Zuo, R., & Wang, J. (2016). Fractal/multifractal modeling of geochemical data: A review. Journal of Geochemical Exploration,164, 33–41.

    Google Scholar 

Download references

Acknowledgments

The first author acknowledges the Nazarbayev University for supporting this work through Faculty Development Competitive Research Grants for 2018–2020 under Contract No. 090118FD5336.

Author information

Authors and Affiliations

  1. School of Mining and Geosciences, Nazarbayev University, Nur-Sultan, Kazakhstan

    Nasser Madani

  2. University of KwaZulu-Natal, Westville Campus, Durban, South Africa

    Emmanuel John M. Carranza

Authors
  1. Nasser Madani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Emmanuel John M. Carranza
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nasser Madani.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Madani, N., Carranza, E.J.M. Co-simulated Size Number: An Elegant Novel Algorithm for Identification of Multivariate Geochemical Anomalies. Nat Resour Res 29, 13–40 (2020). https://doi.org/10.1007/s11053-019-09547-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11053-019-09547-9

Keywords

Search

Navigation