Teacher's Aide Variogram Interpretation and Modeling
Tóm tắt
The variogram is a critical input to geostatistical studies: (1) it is a tool to investigate and quantify the spatial variability of the phenomenon under study, and (2) most geostatistical estimation or simulation algorithms require an analytical variogram model, which they will reproduce with statistical fluctuations. In the construction of numerical models, the variogram reflects some of our understanding of the geometry and continuity of the variable, and can have a very important impact on predictions from such numerical models. The principles of variogram modeling are developed and illustrated with a number of practical examples. A three-dimensional interpretation of the variogram is necessary to fully describe geologic continuity. Directional continuity must be described simultaneously to be consistent with principles of geological deposition and for a legitimate measure of spatial variability for geostatistical modeling algorithms. Interpretation principles are discussed in detail. Variograms are modeled with particular functions for reasons of mathematical consistency. Used correctly, such variogram models account for the experimental data, geological interpretation, and analogue information. The steps in this essential data integration exercise are described in detail through the introduction of a rigorous methodology.
Tài liệu tham khảo
Armstrong, M., 1984, Improving the estimation and modeling of the variogram, in G. Verly and others, eds., Geostatistics for Natural Resources Characterization: Reidel, Dordrecht, Holland, p. 1–20.
Barnes, R. J., 1991, The variogram sill and the sample variance: Math. Geology, v. 23, no. 4, p. 673–678.
Benkendorfer, J. P., Deutsch, C. V., LaCroix, P. D., Landis, L. H., Al-Askar, Y. A., and Cole, J., 1995, Integrated reservoir modelling of a major Arabian carbonate reservoir, SPE Paper 29869, in Proceedings of SPE Middle East Oil Show, Bahrain, p. 311–326.
Christakos, G., 1984,On the problem of permissible covariance and variogram models: Water Resources Res. v. 20, no. 2, p. 251–265.
Cressie, N., 1985, Fitting variogram models by weighted least squares: Math Geology, v. 17, p. 563–586.
Cressie, N., 1993, Statistics for spatial data, Wiley, New York, 900 p.
Cressie, N., and Hawkins, D. M., 1980, Robust estimation of the variogram, I: Math. Geology, v. 12, no. 2, p. 115–125.
Deutsch, C. V., and Journel, A. G., 1997, GSLIB: Geostatistical software library and user's guide, 2nd Edition: Oxford University Press, New York, 369 p.
Genton, M. G., 1998a, Highly robust variogram estimation: Math Geology, v. 30, no. 2, p. 213–221.
Genton, M. G., 1998b, Variogram fitting by generalized least squares using an explicit formula for the covariance structure: Math Geology, v. 30, no. 4, p. 323–345.
Goovaerts, P., 1997, Geostatistics for natural resources evaluation: Oxford University Press, New York, 483 p.
Gringarten, A. G., 1986, Computer-aided well test analysis, SPE Paper 14099, in Proceedings of the 1986 International Meeting on Petroleum Engineering, Beijing, China, March 17-20.
Journel, A. G., 1991, The Amoco data set: Exploratory data analysis, Stanford Center for Reservoir Forecasting, Report 4.
Journel, A. G., and Huijbregts, Ch. J. 1978. Mining geostatistics: Academic Press, New York, 600 p.
Myers, D. E. 1991, Pseudo-cross variograms, positive-definiteness, and cokriging, Math Geology, v. 23, no. 6, p. 805–816.
Olea, R. A., 1995, Fundamentals of semivariogram estimation, modeling, and usage in J. M. Yarus and R. L. Chambers, eds., Stochastic modeling and geostatistics: Principles, methods, and case studies, AAPG Computer Applications in Geology, no. 3, p. 27–36.
Omre, H., 1984, The Variogram and its estimation, in G. Verly and others, eds., Geostatistics for natural resources charcterization, Reidel, Dordrecht, Holland, v. 1, p. 107–125.
Scholle, P. A., and Spearing, D., 1982, Sandstone depositional environments: American Association of Petroleum Geologists, Tulsa, Oklahoma, 648 p.