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2023 | OriginalPaper | Buchkapitel

9. Geostatistische Simulation – Grundlagen und Methoden

verfasst von : Jörg Benndorf

Erschienen in: Angewandte Geodatenanalyse und -Modellierung

Verlag: Springer Fachmedien Wiesbaden

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Zusammenfassung

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Literatur
Zurück zum Zitat Alabert, F. G. (1987). Stochastic imaging of spatial distribution using hard and soft information. Unpubl. Msc thesis, Stanford University, Stanford, California. Alabert, F. G. (1987). Stochastic imaging of spatial distribution using hard and soft information. Unpubl. Msc thesis, Stanford University, Stanford, California.
Zurück zum Zitat Anderson, T.W. (1984). An introduction to multivariate statistical analysis. John Wiley & Sons, Inc., New York. Anderson, T.W. (1984). An introduction to multivariate statistical analysis. John Wiley & Sons, Inc., New York.
Zurück zum Zitat Aprat, G. B. & Cears, J. (2007). Conditional simulation with patterns. Mathematical Geology, v. 39, no. 2, pp. 177–203. Aprat, G. B. & Cears, J. (2007). Conditional simulation with patterns. Mathematical Geology, v. 39, no. 2, pp. 177–203.
Zurück zum Zitat Benndorf, J. & Dimitrakopoulos, R. (2018). New efficient methods for conditional simulations of large orebodies. In Advances in applied strategic mine planning (pp. 353–369). Springer, Cham. Benndorf, J. & Dimitrakopoulos, R. (2018). New efficient methods for conditional simulations of large orebodies. In Advances in applied strategic mine planning (pp. 353–369). Springer, Cham.
Zurück zum Zitat Beucher, H. & Renard, D. (2016). Truncated Gaussian and derived methods. Comptes Rendus Geoscience, 348(7), 510–519.CrossRef Beucher, H. & Renard, D. (2016). Truncated Gaussian and derived methods. Comptes Rendus Geoscience, 348(7), 510–519.CrossRef
Zurück zum Zitat Caers, J. (2000). Direct sequential indicator simulation. In Kleinegeld, W. J. and Krige, D. G., eds., Geostatistics 2000 Cape Town, South Africa, v. 1, pp. 39–48. Caers, J. (2000). Direct sequential indicator simulation. In Kleinegeld, W. J. and Krige, D. G., eds., Geostatistics 2000 Cape Town, South Africa, v. 1, pp. 39–48.
Zurück zum Zitat Caers, J. (2005). Petroleum geostatistics (p. 104). Richardson, TX: Society of Petroleum Engineers.CrossRef Caers, J. (2005). Petroleum geostatistics (p. 104). Richardson, TX: Society of Petroleum Engineers.CrossRef
Zurück zum Zitat Chiles, J. P. & Delfiner, P. (2012). Geostatistics: modeling spatial uncertainty (Vol. 497), 2nd edition. John Wiley & Sons. Chiles, J. P. & Delfiner, P. (2012). Geostatistics: modeling spatial uncertainty (Vol. 497), 2nd edition. John Wiley & Sons.
Zurück zum Zitat David, M. (1977). Geostatistical Ore Reserve Estimation. Elsevier Scientific Publishing Company. David, M. (1977). Geostatistical Ore Reserve Estimation. Elsevier Scientific Publishing Company.
Zurück zum Zitat Davis, M. D. (1987). Production of conditional simulations via the LU triangular decomposition of the covariance matrix. Mathematical Geology, v. 19, no. 2, pp. 91–98. Davis, M. D. (1987). Production of conditional simulations via the LU triangular decomposition of the covariance matrix. Mathematical Geology, v. 19, no. 2, pp. 91–98.
Zurück zum Zitat Deutsch, C. V. & Journel, A. G., (1997). GSLIB Geostatistical Software Library and User’s Guide, Oxford University Press, New York, second edition. 369 pages. Deutsch, C. V. & Journel, A. G., (1997). GSLIB Geostatistical Software Library and User’s Guide, Oxford University Press, New York, second edition. 369 pages.
Zurück zum Zitat Dietrich, C. R. & Newsam, G. N. (1993). A fast and efficient method for multi-dimensional Gaussian stochastic simulations. Water Resources Research, v. 29, no. 8, pp. 2861–2868. Dietrich, C. R. & Newsam, G. N. (1993). A fast and efficient method for multi-dimensional Gaussian stochastic simulations. Water Resources Research, v. 29, no. 8, pp. 2861–2868.
Zurück zum Zitat Dimitrakopoulos, R. & Luo, X. (2004). Generalised sequential Gaussian simulation on group size ν and screen – effect approximations for large field simulations. Mathematical Geology, v. 36, no. 5, pp. 567–591. Dimitrakopoulos, R. & Luo, X. (2004). Generalised sequential Gaussian simulation on group size ν and screen – effect approximations for large field simulations. Mathematical Geology, v. 36, no. 5, pp. 567–591.
Zurück zum Zitat Dimitrakopoulos, R. (Ed.). (2018). Advances in applied strategic mine planning. Springer. Dimitrakopoulos, R. (Ed.). (2018). Advances in applied strategic mine planning. Springer.
Zurück zum Zitat Emery, X. (2007). Conditioning Simulations of Gaussian Random Fields by Ordinary Kriging. Mathematical Geology, v. 39, no. 6, pp. 607–623. Emery, X. (2007). Conditioning Simulations of Gaussian Random Fields by Ordinary Kriging. Mathematical Geology, v. 39, no. 6, pp. 607–623.
Zurück zum Zitat Farmer, C. L. (1992). Numerical rocks. In King P.R., ed., Mathematics of Oil Recovery. Oxford University Press, Oxford, pp. 437–447. Farmer, C. L. (1992). Numerical rocks. In King P.R., ed., Mathematics of Oil Recovery. Oxford University Press, Oxford, pp. 437–447.
Zurück zum Zitat Fenton, G. A. & Griffiths, D. V. (2008). Risk assessment in geotechnical engineering (Vol. 461). New York: John Wiley & Sons. Fenton, G. A. & Griffiths, D. V. (2008). Risk assessment in geotechnical engineering (Vol. 461). New York: John Wiley & Sons.
Zurück zum Zitat Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on PAMI, v. 6, no. 6, pp. 721–741. Geman, S. & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on PAMI, v. 6, no. 6, pp. 721–741.
Zurück zum Zitat Goovaerts, P. (1997). Geostatistics for natural resources evaluation. Oxford University Press, New York. Goovaerts, P. (1997). Geostatistics for natural resources evaluation. Oxford University Press, New York.
Zurück zum Zitat Guardiano, F. & Srivastava, R. M. (1992). Multivariate geostatistics: beyond bivariate moments. In Soares, A., ed., Geostat Troia 1992, Kluwer Publication, Dordtrecht, pp. 133–144. Guardiano, F. & Srivastava, R. M. (1992). Multivariate geostatistics: beyond bivariate moments. In Soares, A., ed., Geostat Troia 1992, Kluwer Publication, Dordtrecht, pp. 133–144.
Zurück zum Zitat Isaaks, E. H. (1990). The application of Monte Carlo methods to the analysis of spatially correlated data. Unpubl. PhD dissertation, Department of Applied Earth Sciences, Stanford University, Stanford, California. Isaaks, E. H. (1990). The application of Monte Carlo methods to the analysis of spatially correlated data. Unpubl. PhD dissertation, Department of Applied Earth Sciences, Stanford University, Stanford, California.
Zurück zum Zitat Journel, A. G., (1974). Geostatistics for conditional simulation of ore bodies. Economic Geology, v. 69, pp. 673–678. Journel, A. G., (1974). Geostatistics for conditional simulation of ore bodies. Economic Geology, v. 69, pp. 673–678.
Zurück zum Zitat Journel, A. G. (1994). Modelling uncertainty: some conceptual thoughts. In Dimitrakopoulos, R., ed., Geostatistics for the Next Century, Kluwer Academic Publishers, Dordtrecht, The Netherlands, pp. 30–43.CrossRef Journel, A. G. (1994). Modelling uncertainty: some conceptual thoughts. In Dimitrakopoulos, R., ed., Geostatistics for the Next Century, Kluwer Academic Publishers, Dordtrecht, The Netherlands, pp. 30–43.CrossRef
Zurück zum Zitat Journel A. G. & Huijbregts, C. J. (2004). Mining Geostatistics. The Blackburn Press. Journel A. G. & Huijbregts, C. J. (2004). Mining Geostatistics. The Blackburn Press.
Zurück zum Zitat Kolmogorov, A. N. (1950). Foundations of the theory of probability. Chelsa, New York. Kolmogorov, A. N. (1950). Foundations of the theory of probability. Chelsa, New York.
Zurück zum Zitat Leuangthong, O., McLennan, J. A. & Deutsch, C. V. (2004). Minimum acceptance criteria for geostatistical realizations. In Natural Resources Research. v13, no.3, pp. 131–141. Leuangthong, O., McLennan, J. A. & Deutsch, C. V. (2004). Minimum acceptance criteria for geostatistical realizations. In Natural Resources Research. v13, no.3, pp. 131–141.
Zurück zum Zitat Mariethoz, G., & Caers, J. (2014). Multiple-point geostatistics: stochastic modeling with training images. John Wiley & Sons.CrossRef Mariethoz, G., & Caers, J. (2014). Multiple-point geostatistics: stochastic modeling with training images. John Wiley & Sons.CrossRef
Zurück zum Zitat Matheron, G. (1973). The intrinsic random functions and their application. Advances in Applied Probability, v. 5, pp. 439–468. Matheron, G. (1973). The intrinsic random functions and their application. Advances in Applied Probability, v. 5, pp. 439–468.
Zurück zum Zitat Meier, S. & Keller, W. (1990). Geostatistik. Springer-Verlag, New York.CrossRef Meier, S. & Keller, W. (1990). Geostatistik. Springer-Verlag, New York.CrossRef
Zurück zum Zitat Menz, J. & Wälder, K. (2000). Cut-off-Überschreitungswahrscheinlichkeiten aus bedingter Simulation oder aus Indikatorkriging? In J. Menz (ed.): Angewandte Geostatistik in Bergbau, Geologie, Geophysik, Geodäsie und Umwelt9schutz. Mathematische Geologie, Band 5, pp. 205 – 213. Menz, J. & Wälder, K. (2000). Cut-off-Überschreitungswahrscheinlichkeiten aus bedingter Simulation oder aus Indikatorkriging? In J. Menz (ed.): Angewandte Geostatistik in Bergbau, Geologie, Geophysik, Geodäsie und Umwelt9schutz. Mathematische Geologie, Band 5, pp. 205 – 213.
Zurück zum Zitat Nowak, M. & Verly, G. (2007). A practical process for geostatistical simulation with emphasis on gaussian methods. In Orebody Modelling and strategic mine planning, The Australasian Institute of Mining and Metallurgy, Spectrum Series, vol. 14, 2nd Edition, pp. 69–78. Nowak, M. & Verly, G. (2007). A practical process for geostatistical simulation with emphasis on gaussian methods. In Orebody Modelling and strategic mine planning, The Australasian Institute of Mining and Metallurgy, Spectrum Series, vol. 14, 2nd Edition, pp. 69–78.
Zurück zum Zitat Osterholt, V. & Dimitrakopoulos, R. (2018). Simulation of Orebody Geology with Multiple-Point Geostatistics—Application at Yandi Channel Iron Ore Deposit, WA, and Implications for Resource Uncertainty. In: Dimitrakopoulos, R. (eds) Advances in Applied Strategic Mine Planning. Springer, Cham. https://doi.org/10.1007/978-3-319-69320-0_22 Osterholt, V. & Dimitrakopoulos, R. (2018). Simulation of Orebody Geology with Multiple-Point Geostatistics—Application at Yandi Channel Iron Ore Deposit, WA, and Implications for Resource Uncertainty. In: Dimitrakopoulos, R. (eds) Advances in Applied Strategic Mine Planning. Springer, Cham. https://​doi.​org/​10.​1007/​978-3-319-69320-0_​22
Zurück zum Zitat Pardo-Iguzquiza, E. & Chica-Olmo, M. (1993). The Fourier integral method: an efficient spectral method for simulation of random fields. Mathematical Geology, v. 25, no. 2, pp. 177–217. Pardo-Iguzquiza, E. & Chica-Olmo, M. (1993). The Fourier integral method: an efficient spectral method for simulation of random fields. Mathematical Geology, v. 25, no. 2, pp. 177–217.
Zurück zum Zitat Pyrcz, M. J. & Deutsch C. V. (2001). Two artifacts of probability field simulation. Mathematical Geology, v. 33, no. 7, p. 775–795. Pyrcz, M. J. & Deutsch C. V. (2001). Two artifacts of probability field simulation. Mathematical Geology, v. 33, no. 7, p. 775–795.
Zurück zum Zitat Ravenscroft, P. J. (1992). Risk analysis for mine scheduling by conditional simulation. Transactions of the Institute of Mining and Metallurgy, Section A, v.101, pp. A104-A108. Ravenscroft, P. J. (1992). Risk analysis for mine scheduling by conditional simulation. Transactions of the Institute of Mining and Metallurgy, Section A, v.101, pp. A104-A108.
Zurück zum Zitat Rosenblatt, M. (1952). Remarks on multivariate transformation. Annals of Mathematical Statistics, v. 23, pp. 470–472. Rosenblatt, M. (1952). Remarks on multivariate transformation. Annals of Mathematical Statistics, v. 23, pp. 470–472.
Zurück zum Zitat Schafmeister, M. T. (2013). Geostatistik für die hydrogeologische Praxis. Springer-Verlag. Schafmeister, M. T. (2013). Geostatistik für die hydrogeologische Praxis. Springer-Verlag.
Zurück zum Zitat Scheuer, E. M. & Stoller, D. S. (1962). On the generation of normal random vectors. Technotronics, v. 4, no. 5, pp. 278–281. Scheuer, E. M. & Stoller, D. S. (1962). On the generation of normal random vectors. Technotronics, v. 4, no. 5, pp. 278–281.
Zurück zum Zitat Shinozuka, M. & Jan, C.-M. (1972). Digital simulation of random prozesses and its applications. Journal of sound and vibration 1972. Shinozuka, M. & Jan, C.-M. (1972). Digital simulation of random prozesses and its applications. Journal of sound and vibration 1972.
Zurück zum Zitat Soares, A. (2001). Direct sequential simulation and co-simulation. Mathematical Geology, v. 33, no. 8, pp. 911–926. Soares, A. (2001). Direct sequential simulation and co-simulation. Mathematical Geology, v. 33, no. 8, pp. 911–926.
Zurück zum Zitat Srivastava, M. R. (1992). Reservoir characterization with probability field simulation. 1992 SPE annual technical conference and exhibition., Society of Petroleum Engineers, Washington, DC, pp. 927–938. Srivastava, M. R. (1992). Reservoir characterization with probability field simulation. 1992 SPE annual technical conference and exhibition., Society of Petroleum Engineers, Washington, DC, pp. 927–938.
Zurück zum Zitat Strebelle, S. (2002). Conditional simulation of complex geological structures using multi-point statistics. Mathematical Geology, v. 34, no. 1, pp. 1–21. Strebelle, S. (2002). Conditional simulation of complex geological structures using multi-point statistics. Mathematical Geology, v. 34, no. 1, pp. 1–21.
Zurück zum Zitat Tonn, F. (1996). Anwendung der geostatistischen Simulation zur computergestützten Generierung praxisnaher Erkundungsdaten. Unveröffentlichte Dissertation an der TU Bergakademie Freiberg, Institut für Markscheidewesen und Geodäsie; Freiberg. Tonn, F. (1996). Anwendung der geostatistischen Simulation zur computergestützten Generierung praxisnaher Erkundungsdaten. Unveröffentlichte Dissertation an der TU Bergakademie Freiberg, Institut für Markscheidewesen und Geodäsie; Freiberg.
Zurück zum Zitat Wackernagel, H. (2003). Multivariate geostatistics: an introduction with applications. Springer Science & Business Media.CrossRefMATH Wackernagel, H. (2003). Multivariate geostatistics: an introduction with applications. Springer Science & Business Media.CrossRefMATH
Zurück zum Zitat Wameling, A. (2002). Räumliche Genauigkeit geostatistischer Interpolationsverfahren in Forst-und Umweltwissenschaften. Cuvillier Verlag. Wameling, A. (2002). Räumliche Genauigkeit geostatistischer Interpolationsverfahren in Forst-und Umweltwissenschaften. Cuvillier Verlag.
Zurück zum Zitat Wang, L. (1995). Modelling complex reservoir geometries with multiple point statistics. Report 8, Stanford Center for Reservoir Forecasting (SCRF), Stanford University, Stanford, California, pp. 1–41. Wang, L. (1995). Modelling complex reservoir geometries with multiple point statistics. Report 8, Stanford Center for Reservoir Forecasting (SCRF), Stanford University, Stanford, California, pp. 1–41.
Zurück zum Zitat Yaglom, A. M. (1987). Correlation theory of stationary and related random functions. Springer-Verlag, New York.CrossRefMATH Yaglom, A. M. (1987). Correlation theory of stationary and related random functions. Springer-Verlag, New York.CrossRefMATH
Zurück zum Zitat Yao, T. (1998). Conditional spectral simulation with phase identification. Mathematical Geology, v. 30, no. 3, pp. 285–308. Yao, T. (1998). Conditional spectral simulation with phase identification. Mathematical Geology, v. 30, no. 3, pp. 285–308.
Zurück zum Zitat Yao, T., Calvert, G., Jones, T., Bishop, G., Ma, Y. & Lincoln, F. (2006). Spectral Simulation and Conditioning to Local Continuity Trends in Geologic Modeling. Mathematical Geology, v. 38, no. 1, pp. 51–62. Yao, T., Calvert, G., Jones, T., Bishop, G., Ma, Y. & Lincoln, F. (2006). Spectral Simulation and Conditioning to Local Continuity Trends in Geologic Modeling. Mathematical Geology, v. 38, no. 1, pp. 51–62.
Metadaten
Titel
Geostatistische Simulation – Grundlagen und Methoden
verfasst von
Jörg Benndorf
Copyright-Jahr
2023
DOI
https://doi.org/10.1007/978-3-658-39981-8_9