Probabilistic Analytics for Geoscience Data

  • Y. Z. Ma


Geological processes and reservoir properties are not random; why should one use probabilistic analytics in geosciences? Probability is a useful theory not just for dealing with randomness but also for dealing with non randomness and uncertainty. Many geoscience problems are indeterministic, meaning that it is impossible to perfectly describe them by a deterministic function. This is due to the complexity of physical processes that took place in geological time and limited data, which leads to uncertainties in their analysis and prediction.

This chapter presents probability for geoscience data analytics and uncertainty analysis, including examples in geological facies mapping and lithofacies classification. Other uses of probability for statistical and geostatistical applications, including stochastic modeling, hydrocarbon volumetrics and their uncertainty quantifications, are presented in later chapters. The presentation emphasizes intuitive conceptualization, analytics, and geoscience applications, while minimizing the use of equations.


  1. Aitchison, J. (1986). The Statistical Analysis of Compositional Data. Chapman and Hall: London.Google Scholar
  2. Billingsley, P. (1995). Probability and measure (3rd ed.). New York: Wiley Interscience Pub.zbMATHGoogle Scholar
  3. Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (2008). Time series analysis: Forecasting and control. Hoboken: Wiley, 784p.CrossRefGoogle Scholar
  4. Caers, J., & Scheidt, C. (2011). Integration of engineering and geological uncertainty for reservoir performance prediction using a distance-based approach. In Y. Z. Ma, & P. R. La Pointe (Eds.), Uncertainty analysis and reservoir modeling: AAPG Memoir (Vol. 96, pp. 191–202). Tulsa: AAPG.Google Scholar
  5. Darwin, C. (1901). The structure and distribution of coral reefs (3rd ed.). New York: Appleton and Co, 366p.Google Scholar
  6. De Finetti, B. (1974). Theory of probability: A critical introductory treatment. Hoboken: Wiley.zbMATHGoogle Scholar
  7. Feller, W. (1968). An introduction to probability theory and its applications, volume I (3rd ed.). New York: Wiley.zbMATHGoogle Scholar
  8. Gill, R. (2011). The Monty Hall problem is not a probability puzzle (it’s a challenge in mathematical modelling). Statistica Neerlandica, 65, 58–71.MathSciNetCrossRefGoogle Scholar
  9. Gillies, D. (2000). Philosophical theories of probability. London/New York: Routledge, 223p.Google Scholar
  10. Grana, D., Fjeldstad, T., & Omre, H. (2017). Bayesian Gaussian mixture linear inversion for geophysical inverse problems. Mathematical Geosciences, 49(4), 493–515. Scholar
  11. Hajek, A. (2007). Interpretations of probability, Stanford Encyclopedia of Philosophy.
  12. Jaynes, E. T. (2003). Probability theory: The logic of science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  13. Journel, A. G., & Huijbregts, C. J. (1978). Mining geostatistics. New York: Academic.Google Scholar
  14. Keynes, J. M. (1973). A treatise on probability (4th ed.). New York: St Martin’s Press.CrossRefGoogle Scholar
  15. Ma, Y. Z. (2009). Propensity and probability in depositional facies analysis and modeling. Mathematical Geosciences, 41, 737–760. Scholar
  16. Ma, Y. Z. (2011). Uncertainty analysis in reservoir characterization and management: How much should we know about what we don’t know? In Y. Z. Ma, & P. R. LaPointe (Eds.), Uncertainty analysis and reservoir modeling: AAPG Memoir (Vol. 96, pp. 1–15). Tulsa: AAPG.Google Scholar
  17. Ma, Y. Z. (2015). Simpson’s paradox in GDP and per capita GDP growths. Empirical Economics, 49(4), 1301–1315.CrossRefGoogle Scholar
  18. Ma, Y. Z., Seto, A., & Gomez, E. (2009). Depositional facies analysis and modeling of Judy Creek reef complex of the Late Devonian Swan Hills, Alberta, Canada. AAPG Bulletin, 93(9), 1235–1256. Scholar
  19. Ma, Y. Z., Wang, H., Sitchler, J., et al. (2014). Mixture decomposition and lithofacies clustering using wireline logs. Journal of Applied Geophysics, 102, 10–20. Scholar
  20. Matheron, G. (1989). Estimating and choosing – An essay on probability in practice. Berlin: Springer-Verlag.CrossRefGoogle Scholar
  21. McLachlan, G. J., & Peel, D. (2000). Finite mixture models. New York: Wiley, 419p.CrossRefGoogle Scholar
  22. Middleton, G. V. (1973). Johannes Walther’s Law of the correlation of facies. GSA Bulletin, 84(3), 979–988.CrossRefGoogle Scholar
  23. Moore, W. R., Ma, Y. Z., Urdea, J., & Bratton, T. (2011). Uncertainty analysis in well-log and petrophysical interpretations. In Y. Z. Ma, & P. R. La Pointe (Eds.), Uncertainty analysis and reservoir modeling: AAPG Memoir (Vol. 96, pp. 17–28). Tulsa: AAPG.Google Scholar
  24. Murphy, K. P. (2012). Machine learning: A probabilistic perspective. Cambridge, MA: The MIT Press.zbMATHGoogle Scholar
  25. Popper, K. R. (1959). The propensity interpretation of probability. British Journal for the Philosophy of Science, 10, 25–42.CrossRefGoogle Scholar
  26. Rosenhouse, J. (2009). The Monty Hall Problem: The remarkable story of math’s most contentious brain teaser. Oxford: Oxford University Press.zbMATHGoogle Scholar
  27. Scott, D. W. (1992). Multivariate density estimation. New York: Wiley, 317p.CrossRefGoogle Scholar
  28. Silverman, B. W. (1986). Density estimation for statistics and data analysis. London: Chapman and Hall, 175p.CrossRefGoogle Scholar
  29. Thompson, E. L., & Shumann, E. L. (1987). Interpretation of statistical evidence in criminal trials: The Prosecutor’s Fallacy and the Defence Attorney’s Fallacy. Law and Human Behavior, 2(3), 167. Scholar
  30. Tierney, J. (1991). Behind Monty Hall’s doors: Puzzles, debate and answer? The New York Times, 1991-07-21.Google Scholar
  31. Tolosana-Delgado, R., & van den Boogaart, K. G. (2013). Joint consistent mapping of high-dimensional geochemical surveys. Mathematical Geosciences, 45, 983–1004.CrossRefGoogle Scholar
  32. Wasserman, L. (2004). All of statistics. New York: Springer.CrossRefGoogle Scholar
  33. Woodward, W. A., Gray, H. L., & Elliott, A. C. (2011). Applied time series analysis. Boca Raton: CRC Press, 564p.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

Personalised recommendations