Overview

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.

Full Product Details

Author:   Christian Lantuejoul
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Dimensions:   Width: 15.20cm , Height: 1.40cm , Length: 22.90cm
Weight:   0.639kg
ISBN:  

9783540422020

ISBN 10:   3540422021
Pages:   256
Publication Date:   09 October 2001
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

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.

Reviews

From the reviews of the first edition: <p> Geostatistical simulations have mainly been developed during the last decade. a ] this is the first book that is entirely dedicated to this subject. a ] it has been a good initiative by C. LantuA(c)joul to compile this book and it will become a basic reference work, partly because it is the first work dedicated entirely to this new subject of geostatistics. a ] The book mainly aims at researchers who are using geostatistical simulations and who would like to know more about the theoretical background a ] . (AndrA(c) Vervoort, Geologica Belgica, Vol. 7 (3-4), 2004) <p> The author has dedicated the book to Georges Matheron, founder of modern geostatistics. Well organized is the book in three parts, namely (i) the tools, (ii) the algorithm and (iii) the models. a ] It certainly fills a gap and is therefore welcome to the geostatistics market. (Erik W. Grafarend, Zentralblatt MATH, Vol. 990 (15), 2002)

From the reviews of the first edition: Geostatistical simulations have mainly been developed during the last decade. ... this is the first book that is entirely dedicated to this subject. ... it has been a good initiative by C. Lantuejoul to compile this book and it will become a basic reference work, partly because it is the first work dedicated entirely to this new subject of geostatistics. ... The book mainly aims at researchers who are using geostatistical simulations and who would like to know more about the theoretical background ... . (Andre Vervoort, Geologica Belgica, Vol. 7 (3-4), 2004) The author has dedicated the book to Georges Matheron, founder of modern geostatistics. Well organized is the book in three parts, namely (i) the tools, (ii) the algorithm and (iii) the models. ... It certainly fills a gap and is therefore welcome to the geostatistics market. (Erik W. Grafarend, Zentralblatt MATH, Vol. 990 (15), 2002)

"From the reviews of the first edition: ""Geostatistical simulations have mainly been developed during the last decade. … this is the first book that is entirely dedicated to this subject. … it has been a good initiative by C. Lantuéjoul to compile this book and it will become a basic reference work, partly because it is the first work dedicated entirely to this new subject of geostatistics. … The book mainly aims at researchers who are using geostatistical simulations and who would like to know more about the theoretical background … ."" (André Vervoort, Geologica Belgica, Vol. 7 (3-4), 2004) ""The author has dedicated the book to Georges Matheron, founder of modern geostatistics. Well organized is the book in three parts, namely (i) the tools, (ii) the algorithm and (iii) the models. … It certainly fills a gap and is therefore welcome to the geostatistics market."" (Erik W. Grafarend, Zentralblatt MATH, Vol. 990 (15), 2002)"

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