Abstract
Spatial variability is a ubiquitous feature of sedimentary rock. The physical properties of sedimentary formations are not smoothly varying functions of position, but are subject to abrupt changes of various magnitudes. These abrupt contrasts in rock properties affect the propagation and dispersion of seismic energy, with potentially important implications for geophysical studies. Spatial heterogeneity is also a dominant control on fluid and contaminant movement, thereby affecting the dynamics of groundwater aquifers and petroleum reservoirs.
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References
Agard, J., 1961, L’analyse statistique et probabiliste des sismogrammes, Revue de l’Institut Francais du Pétrole 16:1–85.
Dagan, G., 1989, Flow and Transport in Porous Formations, Springer-Verlag, New York.
Deutsch, C. V., and Journel, A. G., 1998, Geostatistical Software Library and User’s Guide, 2nd edition, Oxford University Press, New York.
Feller, W., 1971, An Introduction to Probability Theory and its Applications, Volume 2, Wiley, New York.
Gaynor, G. C., Chang, E. Y., Painter, S. L., and Paterson, L., 2000, Applications of Lévy random fractal simulation techniques in modeling reservoir mechanisms in the Kuparuk River field, North Slope, Alaska, SPE Reservoir Eval. and Eng. 3:263–271.
Gelhar, L. M., 1993, Stochastic Subsurface Hydrology, Prentice Hall, Englewood Cliffs, New Jersey.
Goff, J. A., and Holliger, K., 1999, Nature and origin of upper crustal velocity fluctuations and associated scaling properties: Combined stochastic analyses of KTB velocity and lithology logs, J. Geophys. Res. 104:13,169–13,182.
Goggin, D. J., Chandler, M. A., Kocurek, G., and Lake, L. W., 1992, Permeability transects of eolian sands and their use in generating random permeability fields, SPE Formation Evaluation 92:7–16.
Herrmann, F. J. 1998, Multiscale analysis of well and seismic data, in: Mathematical Methods in Geophysical Imaging V, (S. Hassanzadeh, ed), International Society of Optical Engineers, Bellingham, Washington, pp. 180–208.
Hewett, T. A., 1986, Fractal distributions of reservoir heterogeneity and their influence on fluid transport, in: Proceedings of the 6 1 st Annual Technical Conference of the Society of Petroleum Engineers, Rep. 15386, Society of Petroleum Engineers, Richardson, Texas.
Holliger, K., and Goff, J. A., A generic model for the 1/f-nature of seismic velocity fluctuations, this volume.
Hurst, H. E., 1957, A suggested statistical model of some time series which occur in nature, Nature 180:494.
Joumel, A. G., and Huijbregts, Ch. J., 1978, Mining Geostatistics, Academic Press, New York.
Krige, D. G., 1970, The role of mathematical statistics in improving ore valuation techniques in South African gold mines, in: Topics in Mathematical Geology (M. A. Romanova and O. V. Sarmanov, eds., Russian translations by J. P. Fitzsimmons), Consultants Bureau, New York, pp. 243–261.
Lévy, P., 1937, Théorie de l’Addition des Variables Aléatoires, Gauthier-Villars, Paris.
Liu, H. H., and Molz, F. J., 1997a, Comment on “Evidence for non-Gaussian scaling behavior in heterogeneous sedimentary formations” by Scott Painter, Water Resour. Res.
Liu, H. H., and Molz, F. J., 1997b, Multifractal analyses of hydraulic conductivity distributions, Water Resour. Res. 33:2483–2488.
Mandelbrot, B. B., 1982, The Fractal Geometry of Nature, Freeman, New York.
Mandelbrot, B. B., 1969, Robustness of the resealed range R/S in the measurement of noncyclic long run statistical dependence, Water Resour. Res. 5:967–988.
Mandelbrot, B. B., and Van Ness, J. W., 1968, Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10:422–437.
Marsan, D., and Bean, C. J., Multifractal analyses and modeling of crustal heterogeneity, this volume.
Molz, F. J., and Boman, G. K., 1993, A fractal-based stochastic interpolation scheme in subsurface hydrology, Water Resour. Res. 29:3769–3774.
Molz, F. J., and Boman, G. K., 1995, Further evidence of fractal structure in hydraulic conductivity distributions, Geophys. Res. Lett. 22:2545–2548.
Neuman, S. P., 1990, Universal scaling of hydraulic conductivities and dispersivities in geological media, Water Resour. Res. 26:1749–1758.
Neuman, S. P., 1994, Generalized scaling of permeability: Validation and effect of support scale, Geophys. Res. Lett. 21:349–352.
O’Doherty, R. F., and Anstey, N. A., 1971, Reflections on amplitudes, Geophys. Prosp. 19:440–458.
Painter, S., 1995, Random fractal models of heterogeneity: The Levy-stable approach, Math. Geol. 27:813–830.
Painter, S., 1996a, Evidence for non-Gaussian scaling behavior in heterogeneous sedimentary formations, Water Resour. Res. 32:1183–1195.
Painter, S., 1996b, Stochastic interpolation of aquifer properties using fractional Lévy motion, Water Resour. Res.32:1323–1332.
Painter, S., 1998, Numerical method for conditional simulation of Levy random fields, Math. Geol. 30:163–179.
Painter, S., 2001, Flexible scaling model for use in random field simulation of hydraulic conductivity, Water Resour. Res. 37:1155–1163.
Painter, S., and Paterson, L., 1994, Fractional Lévy motion as a model for spatial variability in sedimentary rock, Geophys. Res. Letts. 21:2857–2860.
Painter, S., Beresford, G., and Paterson, L., 1995, On the distribution of seismic reflection coefficients and seismic amplitudes, Geophysics 60:1187–1194.
Painter, S., Paterson, L., and Boult, P., 1997, Improved technique for stochastic interpolation of reservoir properties, Soc. Petr. Eng. J. 2:48–57.
Pilkington, M., and Todoeschuck, J. P., 1990, Stochastic inversion for scaling geology, Geophys. J. Int. 102:205–217.
Taqqu, M. S., 1987, Random processes with long-range dependence and high variability, J. Geophys. Res. 92:9683–9686.
Todoeschuck, J. P., and Jenson, O. G., 1988, Joseph geology and seismic deconvolution, Geophysics 53:1410–1414.
Tubman, K. M., and Crane, S. D. 1995, Vertical versus horizontal well log variability and application to fractal reservoir modeling, in: Fractals in Petroleum Geology and Earth Processes (C. C. Barton and P. R. La Pointe, eds.), Plenum Press, New York, pp.179–193.
Walden, A. T., and Hosken, J. W. J., 1985, An investigation of the spectral properties of primary reflection coefficients, Geophys. Prosp. 33:400–435.
Walden, A. T., and Hosken, J. W. J., 1986, The nature of the non-gaussianity of primary reflection coefficients and its significance for deconvolution, Geophys. Prosp. 34:1038–1066.
Zolotarev, V. M., 1986, One-Dimensional Stable Distributions, American Mathematical Society, Providence, Rhode Island.
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Painter, S. (2003). Statistical Characterization of Spatial Variability in Sedimentary Rock. In: Goff, J.A., Holliger, K. (eds) Heterogeneity in the Crust and Upper Mantle. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0103-9_7
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DOI: https://doi.org/10.1007/978-1-4615-0103-9_7
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