Skip to main content

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.

Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write

H. G. Wells

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 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
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

  • Bertin, E., & Clusel, M. (2006). Generalized extreme value statistics and sum of correlated variables. Journal of Physics A: Mathematical and General, 39, 7607–7619.

    Article  MathSciNet  Google Scholar 

  • Chiles, J. P., & Delfiner, P. (2012). Geostatistics: Modeling spatial uncertainty. New York: John Wiley & Sons, 699p.

    Book  Google Scholar 

  • Ghilani, C. D. (2018). Adjustment computations (6th ed.). New York: Wiley.

    Google Scholar 

  • Gotway, C. A., & Young, L. J. (2002). Combining incompatible spatial data. Journal of the American Statistical Association, 97(458), 632–648.

    Article  MathSciNet  Google Scholar 

  • Isaaks, E. H., & Srivastava, R. M. (1989). An introduction to applied geostatistics. New York: Oxford University Press.

    Google Scholar 

  • Journel, A. (1983). Nonparametric estimation of spatial distribution. Mathematical Geology, 15(3), 445–468.

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  • Kaminski, M. (2007). Central limit theorem for certain classes of dependent random variables. Theory of Probability and Its Applications, 51(2), 335–342.

    Article  MathSciNet  Google Scholar 

  • 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 

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

    Book  Google Scholar 

  • Lindley, D. (2004). Bayesian thoughts or a life in statistics. Significance June 2004:73–75.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Manchuk, J. G., Leuangthong, O., & Deutsch, C. V. (2009). The proportional effect. Mathematical Geosciences, 41(7), 799–816.

    Article  MathSciNet  Google Scholar 

  • Matheron, G. (1984). Change of support for diffusion-type random function. Mathematical Geology, 1(2), 137–165.

    Article  MathSciNet  Google Scholar 

  • Popper, K. R. (1959). The propensity interpretation of probability. British Journal for Philosophy of Science, 10, 25–42.

    Article  Google Scholar 

  • Robinson, W. (1950). Ecological correlation and behaviors of individuals. American Sociological Review, 15(3), 351–357. https://doi.org/10.2307/2087176.

    Article  Google Scholar 

  • Squire, P. (1988). Why the 1936 Literary Digest poll failed. Public Opinion Quarterly, 52, 125–133.

    Article  Google Scholar 

  • 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 

  • 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.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ma, Y.Z. (2019). Statistical Analysis of Geoscience Data. In: Quantitative Geosciences: Data Analytics, Geostatistics, Reservoir Characterization and Modeling. Springer, Cham. https://doi.org/10.1007/978-3-030-17860-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-17860-4_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-17859-8

  • Online ISBN: 978-3-030-17860-4

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics