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Capturing Hidden Geochemical Anomalies in Scarce Data by Fractal Analysis and Stochastic Modeling

Abstract

Fractal/multifractal modeling is a widely used geomathematical approach to capturing different populations in geochemical mapping. The rationale of this methodology is based on empirical frequency density functions attained from global or local distributions. This approach is quite popular because of its simplicity and versatility; it accounts for the frequency and spatial distribution of geochemical data considering self-similarity across a range of scales. Using this technique for detection of geochemical anomalies in scarce data, however, is problematic and can lead to systematic bias in the characterization of the underlying populations. In this paper, an innovative technique is presented that provides good results without a priori assumptions. A simulation approach is adopted for fractal analysis by generating different possible distribution scenarios for the variable under study to reveal the underlying populations that are frequently hidden due to lack of data. The proposed technique is called the global simulated size–number method, and it is validated in a case study with two synthetic datasets and another case study with real dataset from the Ushtagan gold deposit in northeast Kazakhstan.

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Acknowledgment

The first author acknowledges Nazarbayev University for funding this work via Social Policy Grant. The authors also appreciate Prof. Priscilla P. Nelson, head of the Department of Mining Engineering in Colorado School of Mines, for providing the data for real case study for this paper. The authors also appreciate Dr. Masoumeh Khalajmasoumi for her kind supports. The authors are appreciated the constructive comments from two anonymous reviewers, and also we are grateful to Dr. John Carranza for the valuable comments which substantially helped improving the final version of the manuscript.

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Correspondence to Nasser Madani.

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Madani, N., Sadeghi, B. Capturing Hidden Geochemical Anomalies in Scarce Data by Fractal Analysis and Stochastic Modeling. Nat Resour Res 28, 833–847 (2019). https://doi.org/10.1007/s11053-018-9421-4

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Keywords

  • Fractal modeling
  • Monte Carlo simulation
  • Kernel density function
  • Ushtagan gold deposit