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Statistical Analysis of Geoscience Data

  • Y. Z. Ma
Chapter

Abstract

This chapter presents statistical methods and their applications to geoscience data analysis. These include descriptive statistics and change of scale problem in characterizing rock and petrophysical properties, and mitigations of sampling bias in exploration and production.

Some geoscientists consider statistical applications to geosciences as part of geostatistics. For a historic reason, geostatistics is more focused on spatial aspects of statistics, while classical statistics are mainly applications and extensions of probability theory. However, geostatistics still follows the rules of probability and statistics. Hence, this and the next three chapters have two purposes: applications of statistical analytics to geoscience data and providing basic mathematical foundations for geostatistics.

References

  1. Bertin, E., & Clusel, M. (2006). Generalized extreme value statistics and sum of correlated variables. Journal of Physics A: Mathematical and General, 39, 7607–7619.MathSciNetCrossRefGoogle Scholar
  2. Chiles, J. P., & Delfiner, P. (2012). Geostatistics: Modeling spatial uncertainty. New York: John Wiley & Sons, 699p.CrossRefGoogle Scholar
  3. Ghilani, C. D. (2018). Adjustment computations (6th ed.). New York: Wiley.Google Scholar
  4. Gotway, C. A., & Young, L. J. (2002). Combining incompatible spatial data. Journal of the American Statistical Association, 97(458), 632–648.MathSciNetCrossRefGoogle Scholar
  5. Isaaks, E. H., & Srivastava, R. M. (1989). An introduction to applied geostatistics. New York: Oxford University Press.Google Scholar
  6. Journel, A. (1983). Nonparametric estimation of spatial distribution. Mathematical Geology, 15(3), 445–468.MathSciNetCrossRefGoogle Scholar
  7. Journel, A. G., & Huijbregts, C. J. (1978). Mining geostatistics. New York: Academic Press.Google Scholar
  8. Kaminski, M. (2007). Central limit theorem for certain classes of dependent random variables. Theory of Probability and Its Applications, 51(2), 335–342.MathSciNetCrossRefGoogle Scholar
  9. Lake, L. W., & Jensen, J. L. (1989). A review of heterogeneity measures used in reservoir characterization (SPE paper 20156). Society of Petroleum Engineers.Google Scholar
  10. Lantuejoul, C. (2002). Geostatistical simulation: Models and algorithms. Berlin: Springer.CrossRefGoogle Scholar
  11. Lindley, D. (2004). Bayesian thoughts or a life in statistics. Significance June 2004:73–75.MathSciNetCrossRefGoogle Scholar
  12. Liu, K. L., & Meng, X. (2014). Comment: A fruitful resolution to Simpson’s paradox via multi-resolution inference. The American Statistician, 68(1), 17–29.MathSciNetCrossRefGoogle Scholar
  13. Louhichi, S. (2002). Rates of convergence in the CLT for some weakly dependent random variables. Theory of Probability and Its Applications, 46(2), 297–315.MathSciNetCrossRefGoogle Scholar
  14. Ma, Y. Z. (2009a). Simpson’s paradox in natural resource evaluation. Mathematical Geosciences, 41(2), 193–213.  https://doi.org/10.1007/s11004-008-9187-z.CrossRefzbMATHGoogle Scholar
  15. Ma, Y. Z. (2009b). Propensity and probability in depositional facies analysis and modeling. Mathematical Geosciences, 41, 737–760.  https://doi.org/10.1007/s11004-009-9239-z.CrossRefzbMATHGoogle Scholar
  16. Ma, Y. Z. (2010). Error types in reservoir characterization and management. Journal of Petroleum Science and Engineering, 72(3–4), 290–301.  https://doi.org/10.1016/j.petrol.2010.03.030.CrossRefGoogle Scholar
  17. Ma, Y. Z., Gomez, E., & Luneau, B. (2017). Integrations of seismic and well-log data using statistical and neural network methods. The Leading Edge, 36(4, April), 324–329.CrossRefGoogle Scholar
  18. Manchuk, J. G., Leuangthong, O., & Deutsch, C. V. (2009). The proportional effect. Mathematical Geosciences, 41(7), 799–816.MathSciNetCrossRefGoogle Scholar
  19. Matheron, G. (1984). Change of support for diffusion-type random function. Mathematical Geology, 1(2), 137–165.MathSciNetCrossRefGoogle Scholar
  20. Popper, K. R. (1959). The propensity interpretation of probability. British Journal for Philosophy of Science, 10, 25–42.CrossRefGoogle Scholar
  21. Robinson, W. (1950). Ecological correlation and behaviors of individuals. American Sociological Review, 15(3), 351–357.  https://doi.org/10.2307/2087176.CrossRefGoogle Scholar
  22. Squire, P. (1988). Why the 1936 Literary Digest poll failed. Public Opinion Quarterly, 52, 125–133.CrossRefGoogle Scholar
  23. Xu, C., Bayer, W. S., Wunderle, M., & Bansal, A. (2016). Normalizing gamma-ray logs acquired from a mixture of vertical and horizontal Wells in the Haynesville Shale. Petrophysics, 57, 638–643.Google Scholar
  24. Yule, G. U., & Kendall, M. G. (1968). An introduction to the theory of statistics (14th ed.). New York: Hafner Pub. Co, Revised and Enlarged, Fifth Impression.zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Y. Z. Ma
    • 1
  1. 1.SchlumbergerDenverUSA

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