Abstract
We derive the bias and sampling variation of the harmonic average. These expressions, based on the lognormal distribution, are validated using Monte Carlo and jackknife analysis of field data. The average has a positive bias. The sampling variation results suggest that, for moderate to large sample sizes, the harmonic average is no more variable than the arithmetic average if the medium is appropriately sampled.
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References
Barakat, R., 1976, Sums of independent lognormally distributed random variables: J. Opt. Soc. Am., v. 66, no. 3, p. 211–216.
Corbett, P. W. M., and Jensen, J. L., 1992, Estimating the mean permeability: How many mea- surements do you need?: First Break, v. 10, no. 3, p. 89–94.
Desbarats, A. J., and Dimitrakopoulos, R., 1990, Geostatistical modeling of transmissibility for 2D reservoir studies: SPE Form. Eval., v. 5, no. 4, p. 437–443.
Hald, A., 1952, Statistical theory with engineering applications: John Wiley & Sons, New York, 783 p.
Haldorsen, H. H., and Chang, D. M., 1986, Notes on stochastic shales: from outcrop to simulation model,in Lake, L. W., and Carroll, H. B., eds., Reservoir characterization: Academic Press, Orlando, Florida, p. 445–486.
Hurst, A., and Rosvoll, K. J., 1991, Permeability variations in sandstones and their relationship to sedimentary structures,in Lake, L. W., Carroll, H. B., and Wesson, T. C. eds., Reservoir characterization II: Academic Press, Orlando, Florida, p. 166–196.
Jacobsen, T., and Rendall, H., 1991, Permeability patterns of some fluvial sandstones. An outcrop study from Yorkshire, North East England,in Lake, L. W., and Carroll, H. B., eds., Reservoir characterization: Academic Press, Orlando, Florida, p. 315–338.
Johnson, N. L., and Kotz, S., 1970, Continuous univariate distributions-1: John Wiley & Sons, New York, 300 p.
Kittridge, M. G., Lake, L. W., and Lucia, F. J., and Fogg, G. E., 1990, Outcrop/subsurface comparisons of heterogeneity in the San Andres Formation: SPE Form. Eval., v. 5, no. 3, p. 233–240.
Muskat, M., 1937, The flow of homogeneous fluids through porous media: McGraw-Hill Book Co., New York, 763 p.
Thomas, S. D., Corbett, P. W. M., and Jensen, J. L., 1996, Permeability and permeability ani- sotropy characterisation in the near well-bore: a numerical model using probe permeability and formation micro-resistivity data,in Proc. SPWLA 37th Ann. Symposium (New Orleans, Lou- isiana), Paper JJJ, 14 p.
Weber, K. J., 1987, Computation of initial well productivities in aeolian sandstone on the basis of a geological model, Leman Gas Field, U. K.,in Tillman, R. W., and Weber, K. J., eds., Reservoir sedimentology: Soc. Econ. Paleontologists and Mineralogists Spec. Publ. 40, p. 333–354.
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Jensen, J.L., Thomas, S.D. & Corbett, P.W.M. On the bias and sampling variation of the harmonic average. Math Geol 29, 267–276 (1997). https://doi.org/10.1007/BF02769632
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DOI: https://doi.org/10.1007/BF02769632