Multivariate geostatistics: an introduction with applications ; with 5 tables
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kon
Springer
1998
|
| Ausgabe: | 2., completely rev. edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 265 - 283 |
| Beschreibung: | XIV, 291 S. graph. Darst. |
| ISBN: | 354064721X |
Internformat
MARC
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| 245 | 1 | 0 | |a Multivariate geostatistics |b an introduction with applications ; with 5 tables |c Hans Wackernagel |
| 250 | |a 2., completely rev. edition | ||
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kon |b Springer |c 1998 | |
| 300 | |a XIV, 291 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 265 - 283 | ||
| 650 | 0 | 7 | |a Multivariate Analyse |0 (DE-588)4040708-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geostatistik |0 (DE-588)4020279-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Geostatistik |0 (DE-588)4020279-3 |D s |
| 689 | 0 | 1 | |a Multivariate Analyse |0 (DE-588)4040708-1 |D s |
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Datensatz im Suchindex
| _version_ | 1804126774189096960 |
|---|---|
| adam_text | Contents
1 Introduction
A From Statistics to Geostatistics 5
2 Mean, Variance, Covariance 7
The mean: center of mass......................... 7
Distribution function............................ 9
Expectation................................. 10
Variance................................... 11
Covariance.................................. 12
3 Linear Regression and Simple Kriging 13
Experimental covariance.......................... 13
Linear regression.............................. 15
Variance-covariance matrix......................... 18
Multiple linear regression.......................... 19
Simple kriging................................ 22
4 Kriging the Mean 25
Arithmetic mean and its estimation variance............... 25
Estimating the mean with spatial correlation............... 26
No systematic bias............................. 27
Variance of the estimation error...................... 28
Minimal estimation variance........................ 28
Kriging equations.............................. 29
Case of no correlation ........................... 30
B Geostatistics 33
5 Regionalized Variable and Random Function 37
Multivariate time/space data ....................... 37
Regionalized variable............................ 38
Random variable and regionalized value ................. 39
Random function.............................. 40
Probability distributions.......................... 41
Strict stationarity.............................. 41
Stationarity of first two moments..................... 42
6 Variogram Cloud 43
Dissimilarity versus separation....................... 43
Experimental variogram.......................... 45
Replacing the experimental by a theoretical variogram......... 47
7 Variogram and Covariance Function 48
Regional variogram............................. 48
Theoretical variogram ........................... 48
Covariance function............................. 50
Positive definite function.......................... 51
Conditionally negative definite function.................. 51
Fitting the variogram with a covariance function............. 53
8 Examples of Covariance Functions 55
Nugget-effect model ............................ 55
Exponential covariance function...................... 55
Spherical model............................... 56
Derivation of the spherical covariance................... 57
9 Anisotropy 60
Geometric Anisotropy ........................... 60
Rotating and dilating an ellipsoid..................... 60
Exploring 3D space for anisotropy..................... 62
Zonal anisotropy.............................. 63
Nonlinear deformations of space...................... 63
10 Extension and Dispersion Variance 64
Support................................... 64
Extension variance............................. 65
Dispersion variance............................. 66
Krige s relation............................... 67
Change of support effect.......................... 68
Application: acoustic data......................... 70
Comparison of sampling designs...................... 72
11 Measures and Plots of Dispersion 76
Tonnage, recovered quantity, investment and profit ........... 76
Selectivity.................................. 78
Recovered quantity as a function of tonnage............... 80
Time series in environmental monitoring................. 81
12 Ordinary Kriging 83
Ordinary kriging problem......................... 83
Simple kriging of increments........................ 85
Block kriging................................ 86
Simple kriging with an estimated mean.................. 88
Kriging the residual............................. 89
Cross validation............................... 90
Kriging with known measurement error variance............. 91
13 Kriging Weights 93
Geometry.................................. 93
Geometric anisotropy............................ 95
Relative position of samples........................ 95
Screen effect................................. 96
Factorizable covariance functions..................... 97
Negative kriging weights.......................... 99
14 Mapping with Kriging 100
Kriging for spatial interpolation......................100
Neighborhood................................101
15 Linear Model of Regionalization 105
Spatial anomalies.............................. 105
Nested variogram model.......................... 106
Decomposition of the random function.................. 107
Second-order stationary regionalization.................. 108
Intrinsic regionalization .......................... 109
Intrinsic regionalization with mostly stationary components ...... 109
Locally stationary regionalization..................... 110
16 Kriging Spatial Components 111
Kriging of the intrinsic component ....................Ill
Kriging of a second-order stationary component.............112
Filtering...................................114
Application: kriging spatial components of arsenic data.........115
17 The Smoothness of Kriging 117
Kriging with irregularly spaced data ...................117
Sensitivity to choice of variogram model.................120
Application: kriging topographic data ..................121
C Multivariate Analysis 125
18 Principal Component Analysis 127
Transformation into factors ........................127
Maximization of the variance of a factor.................128
Interpretation of the factor variances...................129
Correlation of the variables with the factors...............130
19 Canonical Analysis 136
Factors in two groups of variables.....................136
Intermezzo: singular value decomposition.................137
Maximization of the correlation......................137
20 Correspondence Analysis 139
Disjunctive table.............................. 139
Contingency table.............................. 139
Canonical analysis of disjunctive tables.................. 140
Coding of a quantitative variable..................... 140
Contingencies between two quantitative variables............ 140
Continuous correspondence analysis.................... 141
D Multivariate Geostatistics 143
21 Direct and Cross Covariances 145
Cross covariance function .........................145
Delay effect.................................146
Cross variograrn...............................147
Pseudo cross variogram...........................150
Difficult characterization of the cross covariance function........150
22 Covariance Function Matrices 152
Covariance function matrix ........................152
Cramer s theorem..............................152
Spectral densities..............................153
Phase shift .................................154
23 Intrinsic Multivariate Correlation 155
Intrinsic correlation model.........................155
Linear model................................156
Codispersion coefficients..........................157
24 Heterotopic Cokriging 159
Isotopy and heterotopy...........................159
Ordinary cokriging.............................160
Simple cokriging ..............................162
Collocated simple cokriging........................164
Collocated ordinary cokriging.......................165
Xlll
25 Isotopic Cokriging 167
Cokriging with isotopic data........................167
Autokrigeability...............................168
Bivariate ordinary cokriging........................170
26 Multivariate Nested Variogram 172
Linear model of coregionalization.....................172
Bivariate fit of the experimental variograms...............174
Multivariate fit...............................175
The need for an analysis of the coregionalization.............178
27 Coregionalization Analysis 181
Regionalized principal component analysis................181
Generalizing the analysis..........................182
Regionalized canonical and redundancy analysis.............183
Cokriging regionalized factors.......................183
Regionalized multivariate analysis.....................184
28 Kriging a Complex Variable 187
Coding directional data as a complex variable.............. 187
Complex covariance function........................187
Complex kriging .............................. 188
Cokriging of the real and imaginary parts ................ 189
Complex kriging and cokriging versus a separate kriging........ 190
Complex covariance function modeling.................. 191
29 Bilinear Coregionalization Model 194
Complex linear model of coregionalization................194
Bilinear model of coregionalization....................195
E Non-Stationary Geostatistics 197
30 External Drift 199
Depth measured with drillholes and seismic............... 199
Estimating with a shape function..................... 200
Estimating external drift coefficients................... 202
Cross validation with external drift.................... 203
Regularity of the external drift function ................. 209
31 Universal Kriging 210
Universal kriging system..........................210
Estimation of the drift...........................212
Underlying variogram and estimated residuals..............213
From universal to intrinsic kriging.....................216
XIV
32 Translation Invariant Drift 218
Exponential-polynomial basis functions.................. 218
Intrinsic random functions of order k................... 219
Generalized covariance function...................... 219
Intrinsic kriging............................... 221
Trigonometric temporal drift........................ 222
Filtering trigonometric temporal drift................... 222
Dual kriging................................. 223
Splines.................................... 224
APPENDIX 227
Matrix Algebra 229
Linear Regression Theory 239
Covariance and Variogram Models 244
Additional Exercices 247
Solutions to Exercises 249
References and Software 260
Bibliography 265
Index 285
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 550 - Earth sciences |
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| discipline | Geowissenschaften Geologie / Paläontologie Mathematik Geographie |
| edition | 2., completely rev. edition |
| format | Book |
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| id | DE-604.BV012162838 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:22:48Z |
| institution | BVB |
| isbn | 354064721X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008239288 |
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| physical | XIV, 291 S. graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
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| spelling | Wackernagel, Hans 1955- Verfasser (DE-588)1228015775 aut Multivariate geostatistics an introduction with applications ; with 5 tables Hans Wackernagel 2., completely rev. edition Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kon Springer 1998 XIV, 291 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 265 - 283 Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Geostatistik (DE-588)4020279-3 gnd rswk-swf Geostatistik (DE-588)4020279-3 s Multivariate Analyse (DE-588)4040708-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008239288&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wackernagel, Hans 1955- Multivariate geostatistics an introduction with applications ; with 5 tables Multivariate Analyse (DE-588)4040708-1 gnd Geostatistik (DE-588)4020279-3 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4020279-3 |
| title | Multivariate geostatistics an introduction with applications ; with 5 tables |
| title_auth | Multivariate geostatistics an introduction with applications ; with 5 tables |
| title_exact_search | Multivariate geostatistics an introduction with applications ; with 5 tables |
| title_full | Multivariate geostatistics an introduction with applications ; with 5 tables Hans Wackernagel |
| title_fullStr | Multivariate geostatistics an introduction with applications ; with 5 tables Hans Wackernagel |
| title_full_unstemmed | Multivariate geostatistics an introduction with applications ; with 5 tables Hans Wackernagel |
| title_short | Multivariate geostatistics |
| title_sort | multivariate geostatistics an introduction with applications with 5 tables |
| title_sub | an introduction with applications ; with 5 tables |
| topic | Multivariate Analyse (DE-588)4040708-1 gnd Geostatistik (DE-588)4020279-3 gnd |
| topic_facet | Multivariate Analyse Geostatistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008239288&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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