Clear separation of models, from methods and algorithms
Coherent overview of the subject
This book deals with the estimation of natural resources using the Monte Carlo methodology. It includes a set of tools to describe the morphological, statistical and stereological properties of spatial random models. Furthermore, the author presents a wide range of spatial models, including random sets and functions, point processes and object populations applicable to the geosciences. The text is based on a series of courses given in the USA and Latin America to civil, mining and petroleum engineers as well as graduate students in statistics. It is the first book to discuss the geostatistical simulation techniques in such a specific way.|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.
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.
Within the geoscience community the estimation of natural resources is a challenging topic. The difficulties are threefold: Intitially, the design of appropriate models to take account of the complexity of the variables of interest and their interactions. This book discusses a wide range of spatial models, including random sets and functions, point processes and object populations. Secondly,the construction of algorithms which reproduce the variability inherent in the models. Finally, the conditioning of the simulations for the data, which can considerably reduce their variability. Besides the classical algorithm for gaussian random functions, specific algorithms based on markovian iterations are presented for conditioning a wide range of spatial models (boolean model, Voronoi tesselation, substitution random function etc.) This volume is the result of a series of courses given in the USA and Latin America to civil, mining and petroleum engineers, as well as to gradute students is statistics. It is the first book to discuss geostatistical simulation techniques in such a systematic way.
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)
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.
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)
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.
Klappentext
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.
Clear separation of models, from methods and algorithms
Coherent overview of the subject
Includes supplementary material: sn.pub/extras
