Microgeometry II: Testing for homogeneity in Berea sandstone



Geological sample characterizations rely on statistical assumptions of homogeneity and isotropy. There is also a tacit assumption of homogeneity at some size scale in theoretical geophysics predicated on power spectra or ensemble averaging, for example, acoustics (Devaney and Levine, 1980)or electromagnetics (Lee, 1979).Discussion is presented of a homogeneity test performed on Berea sandstone to develop methods for assessing homogeneity and for delimiting the scale at which homogeneity can be assumed. The Wilcoxon sum-of-ranks and signed-ranks tests are applied to scanning electron microscope image data. Anisotropy is found at some scales, and not at other scales. The homogeneity assumption for Berea sandstone is supported by agreement between estimates which depend for accuracy on homogeneity and values obtained by other independent methods such as bulk measurements or calculations from “run-lengths.”

Key words

Homogeneity nonparametric statistics image analysis 


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  1. DeHoff, R., and Rhines, F., 1968, Quantitative metallography: New York, McGraw-Hill.Google Scholar
  2. Devaney, A. and Levine, H., 1980, Effective elastic parameters of random composites: Appl. Phys. Lett., v. 37, p. 377–379.Google Scholar
  3. Ehrlich, R. and Weinberg, B., 1970, An exact method for characterization of grain shape: J. Sed. Petr., v. 40, p. 205–212.Google Scholar
  4. Ehrlich, R., Brown, P., Yarus, J., and Przygocki, R., 1980, The origin of shape frequency distributions and the relationship between size and shape: J. Sed. Petr., v. 50, p. 475–484.Google Scholar
  5. Hogg, R. and Craig, A., 1978, Introduction to mathematical statistics: New York, Macmillan.Google Scholar
  6. Langley, R., 1968, Practical statistics, New York, Dover.Google Scholar
  7. Lee, T., 1979, Transient electromagnetic waves applied to prospecting: Proc. IEEE, v. 67, p. 1016–1021.Google Scholar
  8. Lin, C., 1982, Microgeometry I: Autocorrelation and rock microstructure: Jour. Math. Geol., v. 14, p. 343–360.Google Scholar
  9. Lin, C. and Cohen, M. H., 1981, Quantitative methods for microgeometric modeling, submitted to J. Appl. Phys.Google Scholar
  10. Perez-Rosales, C., 1969, Simultaneous determination of basic geometric characteristics of porous media: SPEJ, v. 9, p. 413–416.Google Scholar
  11. Plona, T. and Tsang, L., 1979, Characterization of the average microscopic dimension in granular media using ultrasonic pulses—theory and experiments: Geophy., v. 44, p. 334.Google Scholar
  12. Preston, F. and Davis, J., 1976, Sedimentary porous materials as a realization of a stochastic process,in Merriam, D. F., (ed.), Random processes in geology, New York/Germany, Springer-Verlag, p. 63–86.Google Scholar
  13. Rink, M. and Schopper, J., 1978, On the application of image analysis to formation evaluation: Log Anal., v. 19, p. 12–22.Google Scholar
  14. Scheidegger, A., 1957, The physics of flow through porous media: New York, Macmillan.Google Scholar
  15. Serra, J., 1974, Theoretical bases of the Leitz texture analysis system: Leitz Sci. Tech. Inform., Supplement 1, 4, p. 125–136.Google Scholar
  16. Serra, J., 1978, One, two, three, ⋯, infinity,in J. L. Chernant (Ed.), Quantitative analysis of microstructures in materials science, biology, and medicine: Stuttgart, Germany, Riederer-Verlag GmbH.Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • C. Lin
    • 1
  1. 1.Schlumberger-Doll ResearchRidgefieldUSA

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