Geostatistical Simulation

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Beschreibung

1. 1 Simulation versus estimation The following problem was raised by Alfaro (1979). A submarine cable has to be laid across the straits of Gibraltar. How can its length be predicted if the depth of the sea floor has been measured sparsely along its trajectory? Fig. 1. 1. Part of the actual trajectory and sample data points An exact determination of the length requires knowledge of the depth at each point of the trajectory. But these are mostly unknown. In a geostatistical set ting, they are considered as random and can be estimated by linear regression starting from the available data points. This suggests estimating the actual length as the length of the estimated trajectory. The results turn out to be disappointing. The length of the trajectory is seriously underestimated (see Figure 1. 2). Clearly, the estimated trajectory is much smoother than the actual one. Fig. 1. 2. Part of the actual trajectory and its estimate from linear regression. In this particular example, the estimated trajectory is piecewise linear because the linear regression has been carried out using an exponential covariance function 2 1. Introduction What is really questionable in this procedure is not the construction of an estimator for the length starting from the depth estimator, but the depth estimator itself. Linear regression estimation requires only the mean and the covariance function. But the covariance function does not tell us much about the length of the trajectories. Figure 1.

Zusammenfassung

Clear separation of models, from methods and algorithms

Coherent overview of the subject

Includes supplementary material: [...]

Inhaltsverzeichnis

1. Introduction.- 2. Investigating stochastic models.- 3. Variographic tools.- 4. The integral range.- 5. Basic morphological concepts.- 6. Stereology: some basic notions.- 7. Basics about simulations.- 8. Iterative algorithms for simulation.- 9. Rate of convergence of iterative algorithms.- 10. Exact simulations.- 11. Point processes.- 12. Tessellations.- 13. Boolean model.- 14. Object based models.- 15. Gaussian random function.- 16. Gaussian variations.- 17. Substitution random functions.

Erscheinungsjahr:	2001
Fachbereich:	Geologie
Genre:	Geowissenschaften , Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xiii 256 S. 156 s/w Illustr. 76 farbige Illustr. 256 p. 232 illus. 76 illus. in color.
ISBN-13:	9783540422020
ISBN-10:	3540422021
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Lantuejoul, Christian
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 22 mm
Von/Mit:	Christian Lantuejoul
Erscheinungsdatum:	09.10.2001
Gewicht:	0,639 kg

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