Abstract
Sequential Gaussian simulation (sgsim), Gaussian truncated simulation (gtsim), and probability field simulation (pfsim) are three algorithms frequently used for conditional stochastic simulation. They were developed independently and are seen as different algorithms in applications. This paper establishes that gtsim and pfsim can be bridged by a simple quantile transform between Gaussian and uniform distributions. As for the sgsim algorithm, the normal score back-transform can be seen as a series of truncations of the simulated Gaussian field. All three algorithms are shown to be applicable to both continuous and categorical variables. In practice, gtsim can be most often replaced by the more CPU-efficient pfsim algorithm.
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REFERENCES
Bahar, A., and Kelkar, M., 1997, Integrated lithofacies and petrophysical properties simulation: SPE Paper 38261.
Cassiraga, E. F., 1999, Incorporacion de informacion blanda para la cuantificacion de la incertidumbre: aplicacion a la hidrogeologia: unpublished Ph.D. dissertation, Technical University of Valencia, Valencia, Spain, 331 p.
Deutsch, C. V., and Journel, A.G., 1998, GSLIB: Geostatistical software library and user's guide, 2nd ed.: Oxford University Press, New York, 369 p.
Fichtl, P., Fournier, F., and Royer, J. J., 1997, Cosimulation of lithofacies and associated reservoir properties using well and seismic data: SPE Paper 38680.
Froidevaux, R., 1992, Probability field simulation, in Soares, A. ed., Geostatistics Troia 1992, Vol. 1: Kluwer, Dordrecht, p. 73–84.
Gómez-Hernández, J. J., and Garcia, M., 1998, Analyse bibliographique des methodes geostatistiques adaptees a la caracterisation des aquiferes: ANDRA, report OFSS 98- 001/A, Paris.
Johann, P., Fournier, F., Souza, O., Jr., and Doligez, B., 1997, 3-D stochastic reservoir modeling: A non stationary approach guided by seismic data: SPE Paper 38997.
Journel, A. G., 1974, Geostatistics for conditional simulation of orebodies: Economic Geology, v. 69, p. 673–680.
Journel, A. G., and Isaaks, E. H., 1984, Conditional indicator simulation: Application to a Saskatchewan uranium deposit: Math. Geology, v. 16, no. 7, p. 685–718.
Matheron, G., Beucher, H., de Fouquet, H., Galli, A., Guerillot, D., and Ravenne, C., 1987, Conditional simulation of the geometry of fluvio-deltaic reservoirs: SPE Paper 16753.
Srivastava, R. M., 1992, Reservoir characterization with probability field simulation: SPE Paper 24753.
Xu, W., and Journel, A. G., 1993, GTSIM: Gaussian truncated simulations of reservoir units in a West Texas carbonate field: SPE Paper 27412.
Yao, T., 1998, Conditional spectral simulation with phase identification: Math. Geology, v. 30, no. 3, p. 285–308.
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Journel, A.G., Ying, Z. The Theoretical Links Between Sequential Gaussian Simulation, Gaussian Truncated Simulation, and Probability Field Simulation. Mathematical Geology 33, 31–40 (2001). https://doi.org/10.1023/A:1007558125766
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DOI: https://doi.org/10.1023/A:1007558125766