Abstract
Realizations generated by conditional simulation techniques must honor as much data as possible to be reliable numerical models of the attribute under study. The application of optimization methods such as simulated annealing to stochastic simulation has the potential to honor more data than conventional geostatistical simulation techniques. The essential feature of this approach is the formulation of stochastic imaging as an optimization problem with some specified objective function. The data to be honored by the stochastic images are coded as components in a global objective function. This paper describes the basic algorithm and then addresses a number of practical questions: (1) what are the criteria for adding a component to the global objective function? (2) what perturbation mechanism should be employed in the annealing simulation? (3) when should the temperature be lowered in the annealing procedure? (4) how are edge/border nodes handled? (5) how are local conditioning data handled? and (6) how are multiple components weighted in the global objective function?
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aarts, E., and Korst, J., 1989,Simulated Annealing and Boltzmann Machines: John Wiley & Sons, New York.
Deutsch, C., 1992a, Annealing Techniques Applied to Reservoir Modeling and the Integration of Geological and Engineering (Well Test) Data: Ph.D. thesis, Stanford University, Stanford, California, 1992.
Deutsch, C., 1992b, Conditioning reservoir models to well test information: Fourth International Geostatistics Congress, Troia, September.
Deutsch, C., and Journel, A., 1991, The application of simulated annealing to stochastic reservoir modeling: J. Pet. Technol., submitted.
Deutsch, C., and Journel, A., 1992,GSLIB: Geostatistical Software Library and User's Guide: Oxford University Press, New York.
Doyen, P., 1988, Porosity from seismic data: A geostatistical approach: Geophysics, v. 53, n. 10, p. 1263–1275.
Doyen, P., and Guidish, T., 1990, Seismic discrimination of lithology: A Bayesian approach: Geostatistics Symposium, Calgary, Alberta, May.
Farmer, C., 1992, Numerical rocks,in P. King (Ed.),The Mathematical Generation of Reservoir Geology: Clarendon Press, Oxford, 1992 (Proceedings of a conference held at Robinson College, Cambridge, 1989).
Geman, S., and Geman, D., 1984, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images: IEEE Trans. Pattern Anal. Machine Intell. PAMI, v. 6, n. 6, p. 721–741.
Haldorsen, H., and Damsleth, E., 1990, Stochastic modeling: J. Pet. Technol., p. 404–412.
Kirkpatrick, S., Gelatt, C., Jr., and Vecchi, M., 1983, Optimization by simulated annealing: Science, v. 220, n. 4598, p. 671–680.
Marechal, A., Kriging seismic data in presence of faults,in G. Verly et al. (Ed.),Geostatistics for Natural Resources Characterization: Reidel, Dordrecht, Holland, p. 271–294.
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E., 1953, Equation of state calculations by fast computing machines: J. Chem. Phys., v. 21, n. 6, p. 1087–1092.
Press, W., Flannery B., Teukolsky, S., and Vetterling, W., 1986,Numerical Recipes: Cambridge University Press, New York.
Zhu, H., 1991, Modeling Mixture of Spatial Distributions with Integration of Soft Data: Ph.D. thesis, Stanford University, Stanford, California, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Deutsch, C.V., Cockerham, P.W. Practical considerations in the application of simulated annealing to stochastic simulation. Math Geol 26, 67–82 (1994). https://doi.org/10.1007/BF02065876
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02065876