LEADER 05609nam 22007333u 450 001 9911006600803321 005 20230802010932.0 010 $a0-486-16091-2 010 $a1-62198-600-4 035 $a(CKB)2550000001188910 035 $a(EBL)1890406 035 $a(SSID)ssj0001002773 035 $a(PQKBManifestationID)12472981 035 $a(PQKBTitleCode)TC0001002773 035 $a(PQKBWorkID)11027803 035 $a(PQKB)10025063 035 $a(MiAaPQ)EBC1890406 035 $a(Au-PeEL)EBL1890406 035 $a(CaONFJC)MIL568232 035 $a(OCoLC)868965766 035 $a(EXLCZ)992550000001188910 100 $a20141222d2012|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRandom Field Models in Earth Sciences 205 $a1st ed. 210 $aNewburyport $cDover Publications$d2012 215 $a1 online resource (864 p.) 225 1 $aDover Earth Science 300 $aDescription based upon print version of record. 311 08$a0-486-43872-4 311 08$a1-306-36981-9 327 $aTitle Page; Copyright Page; Dedication; Table of Contents; Foreword; Preface; 1 - Prolegomena; 1. The Science of the Probable and the Random Field Model; 2. The Physical Significance of the Random Field Model; 3. The Mathematics of Random Fields; 4. The Philosophical Theses of the Stochastic Research Program; 5. The Practice of the Stochastic Research Program and the Spectrum of Its Applications; 2 - The Spatial Random Field Model; 1. Introduction; 2. Basic Notions; 3. Characterization of Spatial Random Fields by Means of Their Second-Order Statistical Moments-Correlation Theory 327 $a4. Certain Geometrical Properties of Spatial Random Fields5. Spectral Characteristics of Spatial Random Fields; 6. Auxiliary Hypotheses; 7. Homogeneous Spatial Random Fields; 8. Isotropic Spatial Random Fields; 9. Scales of Spatial Correlation; 10. Relationships between the Spatial and the Frequency Domains-The Uncertainty Principle; 11. Spatial Random Fields with Homogeneous Increments; 12. On the Ergodicity Hypotheses of Spatial Random Fields; 13. Information and Entropy of Spatial Random Fields; 3 - The Intrinsic Spatial Random Field Model; 1. Introduction 327 $a2. Generalized Spatial Random Fields3. Spatial Random Fields with Space Homogeneous Increments or Intrinsic Spatial Random Fields; 4. Discrete Linear Representations of Spatial Random Fields; 5. Stochastic Differential and Difference Equations; 4 - The Factorable Random Field Model; 1. Introduction; 2. The Theory of Factorable Random Fields; 3. Nonlinear Transformations of Factorable Random Fields; 4. Construction of Factorable Random Fields; 5. The Nonlinear State-Nonlinear Observation System; 5 - The Spatiotemporal Random Field Model; 1. Introduction 327 $a2. Spatiotemporal Natural Processes-A Review3. Ordinary Spatiotemporal Random Fields; 4. Generalized Spatiotemporal Random Fields; 5. Spatiotemporal Random Fields of Order ?/?, (Ordinary and Generalized); 6. Stochastic Partial Differential Equations; 7. Discrete Linear Representations of Spatiotemporal Random Fields; 6 - Space Transformations of Random Fields; 1. Introduction; 2. Space Transformations; 3. Space Transformation Representations of Spatial Random Fields; 4. Stochastic Differential Equation Models; 5. Criteria of Permissibility; 7 - Random Field Modeling of Natural Processes 327 $a1. Introduction2. Descriptive Features of Natural Processes and the Basic Working Hypotheses; 3. Duality Relations between the Natural Process and the Spatial Random Field Model-Examples from the Geosciences; 4. Certain Practical Aspects of Spatial and Temporal Variability Characterization; 5. Qualitative (Soft) Information; 6. Some Final Comments about the Stochastic Research Program; 8 - Simulation of Natural Processes; 1. Introduction; 2. The Physical Significance of Simulation; 3. Simulation of Random Fields; 4. Simulation of Spatial Random Field by Space Transformations-Examples 327 $a5. Techniques of One-Dimensional Simulation 330 $a This graduate-level text surveys the problems of earth and environmental sciences by means of theoretical models that have as an essential basis a purely random element. In addition to introducing students to spatiotemporal modeling as a fundamental methodology in the earth sciences, this volume illustrates the role of spatiotemporal modeling in the general framework of the scientific method.Starting with discussions of the science of the probable, the various theories of probability, and the physical significance of the random field model, the text explores a variety of problems in earth sci 410 0$aDover Earth Science 606 $aEarth sciences$xMathematical models 606 $aRandom fields$xMathematical models 606 $aStochastic processes$xMathematical models 606 $aGeology$2HILCC 606 $aEarth & Environmental Sciences$2HILCC 606 $aGeology - General$2HILCC 615 0$aEarth sciences$xMathematical models. 615 0$aRandom fields$xMathematical models. 615 0$aStochastic processes$xMathematical models. 615 7$aGeology 615 7$aEarth & Environmental Sciences 615 7$aGeology - General 676 $a550/.1/5118 700 $aChristakos$b George$0283759 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9911006600803321 996 $aRandom field models in earth sciences$9764210 997 $aUNINA