Abstract
Journel (1974) developed the turning-bands method which allows a three-dimensional data set with specified covariance to be obtained by the simulation of several one-dimensional realizations which have an intermediate covariance. The relationship between the threedimensional and one-dimensional covariance is straightforward and allows the one-dimensional covariance to be obtained immediately. In theory a dense uniform distribution of lines in three-dimensional space is required along which the one-dimensional realizations are generated; in practice most workers have been content to use the fifteen axes of the regular icosahedron. Many mining problems may be treated in two dimensions, and in this paper a turning-bands approach is developed to generate two-dimensional data sets with a specified covariance. By working in two dimensions, the area on which the data is simulated may be divided as finely as desired by the lines on which the one-dimensional realizations are first generated. The relationship between the two-dimensional and one-dimensional covariance is derived as a nontrivial integral equation. This is solved analytically for the onedimensional covariance. The method is applied to the generation of a two-dimensional data set with spherical covariance.
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References
Brooker, P. I. and Paul, C. J., 1982, Numerical simulation of a two dimensional orebody,in, Proceedings of the Fifth Biennial Conference of Simulation Society of Australia, p. 133–136.
Journel, A. G., 1974, Simulation conditionelle de gisements miniers—theorie et pratique: Thèse de Docteur Ingénieur, Université de Nancy.
Journel, A. G. and Huijbregts, C. T., 1978, Mining geostatistics: Academic Press, New York, 600 p.
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Brooker, P.I. Two-dimensional simulation by turning bands. Mathematical Geology 17, 81–90 (1985). https://doi.org/10.1007/BF01030369
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DOI: https://doi.org/10.1007/BF01030369