This fully revised third edition introduces geostatistics by emphasising the multivariate aspects for scientists, engineers and statisticians. Geostatistics offers a variety of models, methods and techniques for the analysis, estimation and display of multivariate data distributed in space or time. The text contains a brief review of statistical concepts, a detailed introduction to linear geostatistics, and an account of 3 basic methods of multivariate analysis. Applications from different areas of science, as well as exercises with solutions, are provided to help convey the general ideas. The introductory chapter has been divided into two separate sections for clarity. The final section deals with non-stationary geostatistics.
Introducing geostatistics from a multivariate perspective is the main aim of this book. The idea took root while teaching geostatistics at the Centre de Geostatis tique (Ecole des Mines de Paris) over the past ten years in the two postgraduate programs DEA and CFSG. A first script of lecture notes in French originated from this activity. A specialized course on Multivariate and Exploratory Geostatistics held in September 1993 in Paris (organized in collaboration with the Department of Statistics of Trinity College Dublin) was the occasion to test some of the mate rial on a pluridisciplinary audience. Another important opportunity arose last year when giving a lecture on Spatial Statistics during the summer term at the Department of Statistics of the University of Washington at Seattle, where part of this manuscript was distributed in an early version. Short accounts were also given during COMETT and TEMPUS courses on geostatistics for environment al studies in Fontainebleau, Freiberg, Rome and Prague, which were sponsored by the European Community. I wish to thank the participants of these various courses for their stimulating questions and comments. Among the organizers of these courses, I particularly want to acknowledge the support received from Georges Matheron, Pierre Chau vet, Margaret Armstrong, John Haslett and Paul Sampson. Michel Grzebyk has made valuable comments on Chapters 26 and 27, which partly summarize some of his contributions to the field.
This unique book presents a learn-by-doing introduction to geostatistics. Geostatistics provides the essential numerical tools for addressing research problems that are encountered in fields of study such as geology, engineering, and the earth sciences. Illustrating key methods through both theoretical and practical exercises, Solved Problems in Geostatistics is a valuable and well-organized collection of worked-out problems that allow the reader to master the statistical techniques for modeling data in the geological sciences. The book's scope of coverage begins with the elements from statistics and probability that form the foundation of most geostatistical methodologies, such as declustering, debiasing methods, and Monte Carlo simulation. Next, the authors delve into three fundamental areas in conventional geostatistics: covariance and variogram functions; kriging; and Gaussian simulation. Finally, special topics are introduced through problems involving utility theory, loss functions, and multiple-point geostatistics. Each topic is treated in the same clearly organized format. First, an objective presents the main concepts that will be established in the section. Next, the background and assumptions are outlined, supplying the comprehensive foundation that is necessary to begin work on the problem. A solution plan demonstrates the steps and considerations that have to be taken when working with the exercise, and the solution allows the reader to check their work. Finally, a remarks section highlights the overarching principles and noteworthy aspects of the problem. Additional exercises are available via a related Web site, which also includes data related to the book problems and software programs that facilitate their resolution. Enforcing a truly hands-on approach to the topic, Solved Problems in Geostatistics is an indispensable supplement for courses on geostatistics and spatial statistics a the upper-undergraduate and graduate levels.It also serves as an applied reference for practicing professionals in the geosciences.
An International Forum in Honour of Michel David’s Contribution to Geostatistics, Montreal, 1993
Author: Roussos Dimitrakopoulos
This book contains selected contributions from the International Forum on `Geostatistics for the Next Century', organized in honour of Michel David in Montreal, June 1993. In order to present current problems and concerns, disseminate new significant results and futuristic ideas, as well as to promote dialogue and critique, the book includes contributions from leading researchers and practitioners as well as comments by participants and replies by authors. Notable new advances and ideas featured in this volume include: developments in dealing with uncertainty, advances in sampling, fuzzy set and Bayesian frameworks, fractal and multifractal approaches, neural network based simulation, optimization based conditional simulations, spatiotemporal modelling, issues of support change and upscaling, new stochastic fluid flow related formulations. For researchers and practitioners working in quantitative modelling in earth sciences and engineering, including mining, petroleum, environmental sciences, hydrogeology, geotechnics, applied statistics and renewable resources.
Estimates of average annual precipitation (AAP) are-needed for hydrologic modeling at Yucca Mtn., Nevada, site of a proposed, high-level nuclear waste repository. Historical precipitation data and station elevation were obtained for stations in southern Nevada and southeastern California. Elevations for 1,531 additional locations were obtained from topographic maps. The sample direct-variogram for the transformed variable TAAP = ln(AAP) * 1000 was fit with an isotropic, spherical model with a small nugget and a range of 190,000 ft. The sample direct-variogram for elevation was fit with an isotropic model with four nested structures (nugget, Gaussian, spherical, and linear) with ranges between 0 and 270,000 ft. There was a significant (p = 0.05, r = 0.75) linear correlation between TAAP and station elevation. The sample cross-variogram for TAAP and elevation was fit with two nested structures (Gaussian, spherical) with ranges from 55,000 to 355,000 ft. Alternate model structures and parameters were compared using cross-validation. Isohyetal maps for average annual precipitation (AAP) were prepared from estimates obtained by kriging and cokriging using the selected models. Isohyets based on the kriging estimates were very smooth, increasing gradually from the southwest to the northeast. Isohyets based on the cokriging estimates and the spatial correlation between AAP and elevation were more irregular and displayed known orographic effects. Indirect confirmation of the cokriging estimates were obtained by comparing isohyets prepared with the cokriging estimates to the boundaries of more densely vegetated and/or forested zones. Estimates for AAP at the repository site were 145 and 165 mm for kriging and cokriging, respectively. Cokriging reduced estimation variances at the repository site by 55% relative to kriging. The effectiveness of an existing network of stations for measuring AAP is evaluated and recommendations are made for optimal locations for additional stations.
Praise for the First Edition ". . . a readable, comprehensive volume that . . . belongs onthe desk, close at hand, of any serious researcher orpractitioner." —Mathematical Geosciences The state of the art in geostatistics Geostatistical models and techniques such as kriging andstochastic multi-realizations exploit spatial correlations toevaluate natural resources, help optimize their development, andaddress environmental issues related to air and water quality, soilpollution, and forestry. Geostatistics: Modeling SpatialUncertainty, Second Edition presents a comprehensive, up-to-datereference on the topic, now featuring the latest developments inthe field. The authors explain both the theory and applications ofgeostatistics through a unified treatment that emphasizesmethodology. Key topics that are the foundation of geostatisticsare explored in-depth, including stationary and nonstationarymodels; linear and nonlinear methods; change of support;multivariate approaches; and conditional simulations. The SecondEdition highlights the growing number of applications ofgeostatistical methods and discusses three key areas of growth inthe field: New results and methods, including kriging very large datasets;kriging with outliers; nonse??parable space-time covariances;multipoint simulations; pluri-gaussian simulations; gradualdeformation; and extreme value geostatistics Newly formed connections between geostatistics and otherapproaches such as radial basis functions, Gaussian Markov randomfields, and data assimilation New perspectives on topics such as collocated cokriging, krigingwith an external drift, discrete Gaussian change-of-support models,and simulation algorithms Geostatistics, Second Edition is an excellent book for courseson the topic at the graduate level. It also serves as an invaluablereference for earth scientists, mining and petroleum engineers,geophysicists, and environmental statisticians who collect andanalyze data in their everyday work.
A field study was conducted to determine the applicability of multivariate geostatistical methods to the problem of estimating and simulating pesticide concentrations in groundwater from measured concentrations of nitrate and pesticide, when pesticide is undersampled. Prior to this study, no published attempt had been made to apply multivariate geostatistics to groundwater contamination. The study was divided into two complementary aspects of geostatistics: estimation and simulation. The use of kriging and cokriging to estimate nitrate and the herbicide dimethyl tetrachloroterepthalate (DCPA) contaminant densities is described in Chapter I. Measured concentrations of nitrate and the DCPA were obtained for 42 wells in a shallow unconfined alluvial and basin-fill aquifer in a 16.5 km2 agricultural area in eastern Oregon. The correlation coefficient between log(nitrate) and log(DCPA) was 0.74. Isotropic, spherical models were fitted to experimental direct- and cross-semivariograms with correlation ranges and sliding neighborhoods of 4 km. The relative gain for estimates obtained by cokriging ranged from 14 to 34%. Additional sample locations were selected for nitrate and DCPA using the fictitious point method. A simple economic analysis demonstrated that additional nitrate samples would be more beneficial in reducing estimation variances than additional DCPA samples, unless the costs of nitrate and DCPA analysis were identical. These estimates are by definition, the Best Linear Unbiased Estimates (i.e., the estimates with minimized estimation variance), however the requirement of minimized variance smoothes the variability of contaminant values. The application of conditional simulations to groundwater contamination is described in Chapter 11. Conditional simulation allows the degree of fluctuation of nitrate and DCPA between sample points to be assesed. With knowledge of both the 'best' estimates and the of the variability between sample points, nitrate and DCPA groundwater contamination in the study area can be characterized Based on the semivariogram models found in Chapter I, univariate and multivariate conditional simulations of nitrate and DCPA were generated using the turning bands method and the kriging or cokriging system. Kriging was used to condition the univariate simulations, while cokriging was used to cross-correlate and condition the multivariate simulations. The mean of 25 conditional and coconditional simulations at 8 different locations in the study area were generated and compared to kriging and cokriging estimates and 95% confidence intervals. Both conditional and coconditional simulation of the DCPA and nitrate contaminant densities showed large variations when values in different simulations were compared. The fluctuation in values demonstrate the uncertainties in the contaminant distributions when sample sizes are small. As a result of this unkown component, simulated values vary widely. Coconditional simulation displayed the cross-correlation imposed by using the cokriging system to condition the simulations. After 25 simulations, the mean remained unstable indicating that more simulations would be required to enable comparisons with kriging and cokriging estimates.
Papers from a recent symposium present work in traditional areas of mineral exploration, geostatistics, production planning, and scheduling, as well as the emerging areas of information technology, e-commerce, neural networks, and geological information systems. Contributors reflect the efforts of i