Introduction to geostatistics: applications to hydrogeology
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| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Ausgabe: | Reprinted |
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| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016526440&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XX, 249 S. graph. Darst. |
| ISBN: | 0521587476 0521583128 |
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| 100 | 1 | |a Kitanidis, Peter K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to geostatistics |b applications to hydrogeology |c P. K. Kitanidis |
| 250 | |a Reprinted | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2003 | |
| 300 | |a XX, 249 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Stanford-Cambridge program | |
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| DE-BY-TUM_call_number | 0003 GEO 325f 2009 L 267 0004 GEO 325f 2008 A 3244(2003) 0041 GEO 325f 2009 A 2097 0041 GEO 325f 2008 A 6745 |
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Jahrgang:
2003
Artikel: Autor:
Kitanidis, Peter K.
Artikel: Titel:
Introduction to geostatistics
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Contents
Preface
page
xix
/
Introduction
1
1.1
Introduction
1
1.2
A simple example
3
1.3
Statistics
7
1.4
Geostatistics
10
1.5
Key points of Chapter
1 11
2
Exploratory data analysis
12
2.1
Exploratory analysis scope
12
2.2
Experimental distribution
15
2.2.1
Histogram
16
2.2.2
Ogive
17
2.2.3
Summary statistics
19
2.2.4
The box plot
22
2.3
Transformations and outliers
24
2.3.1
Normality
24
2.3.2
Outliers
26
2.4
Normality tests and independence
26
2.5
Spatial structure
27
2.6
The experimental variogram
30
2.7
Meaning of experimental variogram
32
2.7.1
Scale
32
2.7.2
Near the origin
34
2.7.3
Large-scale behavior
39
2.8
Key points of Chapter
2 40
3
Intrinsic model
41
3.1
Methodology overview
41
3.2
Illustrative example
47
viu
Contents
3.3
Intrinsic
isotropie
model
51
3.4
Common models
54
3.4.1
Stationary models
54
3.4.2
Intrinsic nonstationary models
61
3.4.3
Model superposition
62
3.4.4
Special topic:
microstructura
64
3.5
Interpolation using kriging
65
3.6
Kriging system
67
3.7
Kriging with moving neighborhood
71
3.8
Nonnegativity
72
3.9
Derivation
72
3.10
The function estimate
74
3.11
Conditional realizations
76
3.11.1
Point simulation
76
3.11.2
Function simulation
77
3.12
Properties of kriging
77
3.13
Uniqueness
79
3.14
Kriging as exact interpolator
79
3.15
Generalized covariance functions
80
3.16
Key points of Chapter
3 82
4
Variogram fitting
83
4.1
The problem
83
4.2
Prior information
84
4.3
Experimental variogram
85
4.4
Residuals
86
4.4.1
The concept
86
4.4.2
Residuals in kriging
88
4.4.3
Distribution of residuals
89
4.5
Model validation
90
4.5.1
β
¡
statistic
91
4.5.2
Qi statistic
93
4.5.3
Normality
95
4.5.4
No correlation
96
4.5.5
Ordering
96
4.6
Variogram fitting
96
4.7
On modeling
99
4.8
Estimation simulator
101
4.8
Л
Synthetic realizations
101
4.8.2
Example
1
JO2
4.8.3
Example
2
1
05
4.9
Key points of Chapter
4
IQ9
Contents ix
5
Anisotropy
110
5.1
Examples of anisotropy HO
5.2
Overall approach
112
5.3
Directional variogram
113
5.4
Geoanisotropy
114
5.4.1
General
114
5.4.2
Two dimensions
116
5.4.3
Three dimensions
117
5.5
Practical considerations
118
5.6
Key points of Chapter
5 119
6
Variable mean
120
6.1
Limitations of constant mean
120
6.2
The linear model
123
6.3
Estimation with drift
125
6.4
Generalized covariance function
127
6.5
Illustration of the GCF concept
130
6.6
Polynomial GCF
133
6.7
Stationary-increment processes
134
6.8
Splines
135
6.9
Validation tests
136
6.10
Parameter estimation
139
6.11
On model selection
140
6.12
Data detrending
143
6.13
An application
143
6.14
Variance-ratio test
145
6.15
Key points of Chapter
6 148
7
More linear estimation
150
7.1
Overview
150
7.1.1
Kriging with known mean
151
7.1.2
Estimation of drift coefficients
151
7.1.3
Estimation of continuous part
15
1
7.1.4
Spatial averaging
152
7.2
Estimation with known mean
152
7.2.1
Known drift
152
7.2.2
Simple kriging
154
7.3
Estimation of drift coefficients
156
7.4
Continuous part
158
7.4.1
Rationale
158
7.4.2
Kriging equations
159
x
Contents
7.5
Spatial averaging 163
7.5.1
Stationary 163
7.5.2
Intrinsic 165
7.5.3
Variable
mean 166
7.6
Spatial
averaging implementation
166
7.6.1
Nugget effect 166
7.6.2
Numerical quadrature
167
7.6.3
Examples 168
7.7
Key points of Chapter
7
17
!
8
Multiple variables
172
8.1
Joint analysis
172
8.2
Second-moment characterization
173
8.3
Best linear unbiased estimation
175
8.4
Another cokriging example
177
8.5
Model selection
179
8.6
Method of auxiliary variables
180
8.7
Matrix form
182
8.7.1
Linear model
182
8.7.2
BLUE
182
8.7.3
Parameter estimation
183
8.8
Key points of Chapter
8 183
9
Estimation and GW models
184
9.1
Groundwater models
184
9.2
Using a mathematical model
187
9.2.1
Equations and conditions
187
9.2.2
Log-transmissivity
188
9.2.3
Derivation of joint moments
188
9.3
Monte Carlo simulations
189
9.3.1
The approach
189
9.3.2
Example
190
9.4
First-order approximation
196
9.4.1
The principle
196
9.4.2
Linearization
196
9.4.3
Moment derivation
198
9.5
Large-domain analytical solutions
205
9.6
Numerical small-perturbation method
212
9.7
An inverse problem
214
9.8
Key points of Chapter
9 219
9.9
Addendum
220
Contents xi
A Probability theory review
221
A.I Introduction
221
A.
1.1
Experiments
221
A.
1.2
Probability
222
A.
1.3
Random variables
222
A.2 Jointly distributed random variables
223
A.3 Expectation and moments
225
A.4 Functions of random variables
227
A.5 Further reading
228
A.6 Review exercises
228
В
Lagrange
multipliers
232
B.I The method
232
B.2 Explanation
233
С
Generation of realizations
235
C.I Background
235
C.2 Linear transformation
236
C.3 Random vector
237
C.4 Stationary random functions
238
References
239
Index
247
List of tables
1.1
Transmissivity data for example in this section
3
1.2
Porosity versus location (depth)
9
2.1
Head observations in a regional confined aquifer
14
2.2
TCE concentrations in groundwater in a vertical cross section
15
2.3
Summary statistics for transmissivity data of Table
1.1 21
2.4
Summary statistics for head data of Table
2.1 21
2.5
Summary statistics for concentration data of Table
2.2 22
4.1
The
0.025
and
0.975
percentiles of the Q2 distribution
94
4.2
Coefficients for the Filliben test for departures from normality
95
4.3
Optimizing the fit
107
6.1
Data for illustrative example
121
7.1
Data (observation and location)
162
7.2
Coordinates of the center of each element
170
9.1
Measured transmissivity and coordinates of observation points
214
9.2
Measured head and coordinates of observation points
214
xiu
List of figures
1.1
Location of transmissivity measurements (o) and unknown (x)
4
1.2
Distribution of nearly normal data
6
2.1
Plan view of aquifer showing location of head data
13
2.2
Vertical cross section with location of TCE measurements
14
2.3
Histogram of transmissivity data
16
2.4
Histogram of head data
17
2.5
Histogram of TCE concentration data
17
2.6
Ogive of transmissivity data
18
2.7
Ogive of head data
18
2.8
Ogive of concentration data
19
2.9
Box plot of transmissivity data
22
2.10
Box plot of head data
23
2.11
Box plot of TCE concentration data
23
2.12
Histogram and theoretical distribution of normal data
24
2.13
Box plot of the logarithm of the concentration data
25
2.14
Plot of data versus the first spatial coordinate
28
2.15
Plot of data versus the second spatial coordinate
29
2.16
Plot showing the location and relative magnitude of data
(o
<
median,
χ
>
median). When outliers are present, they
are indicated by
* 29
2.17
Draftsman s display of some three-dimensional data
30
2.18
Raw and experimental variogram of transmissivity data
31
2.19
Experimental variogram of the head data
32
2.20
Plot of the measurements for the discontinuous case
34
2.21
Experimental variogram for the discontinuous data
35
2.22
Plot of the data for the parabolic case
36
2.23
Plot of the slopes for the parabolic case
36
2.24
Experimental variogram for the parabolic case
37
xv
xvi
List of figures
2.25
The data for the linear case
2.26
Slope of data for linear case -30
2.27
Experimental variogram for linear case 39
2.28
Experimental variogram indicative of stationary and nonstationary
behavior
3.1
The interpolation problem. Observations are indicated by the
symbol o.
3.2
Five realizations from a family of z(x) functions
43
3.3
Five realizations from another family of functions
44
3.4
Five realizations from yet another family of functions
45
3.5
Plot of covariance function (periodic)
48
3.6
Five sample functions
4
3.7
Conditional mean, given z(0)
= 0.5 50
3.8
Conditional variance, given z(0)
= 0.5 50
3.9
Sample function and model for Gaussian variogram and
covariance function
55
3.10
Sample function and model for exponential variogram and
covariance function
57
3.11
Sample function and model for spherical variogram and
covariance function
58
3.12
Sample function and model for hole-effect variogram and
covariance function.
59
3.13
Sample function and model for nugget-effect variogram and
covariance function
60
3.14
Sample function for power variogram with exponent
0.4 62
3.15
Sample function for linear variogram
63
3.16
Experimental variogram and model
64
4.1
Variogram (continuous line) fitted to experimental variogram
(dashed line)
85
4.2
Fitting a straight line to data
87
4.3
Fitting a straight line to data that would better fit a quadratic
88
4.4
Probability density function of Q statistic for
η
= 20 92
4.5
Probability density function of Q2 for
η
= 20 94
4.6
Recommended procedure to estimate variogram parameters
99
4.7
List for checking the fit of the model
100
4.8
Plot of observations versus locations for Example
1 102
4.9
Experimental variogram and preliminary fit
ШЗ
4.10
Experimental variogram and fit from residuals
103
4.11
Experimental variogram and fitted model for Example
1 104
4.12
Data for Example
2 105
List of figures
xvii
4.13
Experimental variogram and preliminary fit for Example
2 106
4.14
Experimental variogram and preliminary fit for Example
2
using another discretization
Ш6
4.15
Experimental variogram and best fit estimate of variogram
107
4.16
Orthonormal
residuals pass normality test
108
4.17
Experimental variogram of residuals in nugget effect
108
5.1
Vertical cross section of alluvial formation
111
5.2
Variograms in horizontal and vertical directions
1
11
5.3
Streamlines and iso-concentration contour lines
112
5.4
Vertical dimension stretched by a factor
12 115
5.5
Rotation of coordinate system (new system is denoted by
*) 116
6.1
Experimental and model variogram for intrinsic case
122
6.2
Comparison of best estimates ]22
6.3
Comparison of mean square error of estimation
123
6.4
Interpolation through data (shown as o) using cubic and
thin-plate splines
136
6.5
How to proceed in developing a model with variable mean
137
6.6
Experimental (semi) variogram of original data. (Adapted
after
[83].) 144
6.7
Experimental (semi)variogram of detrended data. (Adapted
after
[83].) 144
6.8
Experimental variogram and fitted equation (exponential GCF)
using detrended data. (Adapted after
[83].) 145
7.1
Simple kriging lambda coefficient as function of distance from
observation
155
7.2
Mean square estimation error
156
7.3
Variogram of
z
versus variograms of zc and
η
159
7.4
Results from ordinary kriging
162
7.5
Results from continuous-part kriging
163
7.6
Map of area, showing subdivision into blocks and location of
observations
169
9.1
Example of a simple flow domain
187
9.2
Mean head from Monte Carlo simulations
192
9.3
Variance of head from Monte Carlo simulations
192
9.4
Correlation of head at
χ
with heat at
χ
= 0.25 193
9.5
Cross-covariance of head-log-conductivity at same location
193
9.6
Correlation of log-conductivity at
χ
with head at
χ
= 0.25 194
9.7
Log-conductivity variance from Monte Carlo simulations
194
9.8
Comparison of head variance from two sets, each with
400
realizations
195
xviii
List of figures
9.9
Comparison of head-log-conductivity covariance (same
location) from two sets, each with
400
realizations
195
9.10
Comparison for mean head
(σ2
= 1) 201
9.11
Comparison for head variance
(σ2
= 1) 201
9.12
Comparison of
0(0.25)
to
φ(χ)
correlation
(er2 = 1) 202
9.13
Comparison of cross-covariance
(σ2
= 1) 202
9.14
Comparison of
φ
(0.25)
to
У (де)
correlation
(σ2
=
I
) 203
9.15
Comparison of mean head
(σ2
= 2) 203
9.16
Comparison of head variance
(σ2
= 2) 204
9.17
Comparison of
φ
(0.25)
to
φ (χ)
correlation
(σ2 =
2) 204
9.18
Comparison of cross-covariance
(σ2
= 2) 205
9.19
Comparison of
0(0.25)
to Y(x) correlation
(σ2
= 2) 205
9.20
Influence function for one dimension. Positive
η
indicates
that the head fluctuation is downgradient of the log-conductivity
perturbation
207
9.21
Influence function in two dimensions
208
9.22
Contour plot of cross-covariance
209
9.23
The cross-covariance in the direction of flow
210
9.24
Уфф(г)
in the two principal directions.
r¡
is the distance in the
direction of flow
210
9.25
Contour plot of the variogram
211
9.26
Trae
transmissivity and location of transmissivity observations
215
9.27
True head and location of head observations
216
9.28
Location of transmissivity data and estimate of transmissivity
obtained using only these data
216
9.29
Location of head data and estimate of head obtained using
only these data
217
9.30
Estimate of transmissivity obtained from transmissivity and
head observations
218
9.31
Estimate of head obtained from transmissivity and
head observations
219
B.
1
Contour lines of constant
MSE
and the line of the constant
234
|
| any_adam_object | 1 |
| author | Kitanidis, Peter K. |
| author_facet | Kitanidis, Peter K. |
| author_role | aut |
| author_sort | Kitanidis, Peter K. |
| author_variant | p k k pk pkk |
| building | Verbundindex |
| bvnumber | BV023342698 |
| callnumber-first | G - Geography, Anthropology, Recreation |
| callnumber-label | GB1001 |
| callnumber-raw | GB1001.72.S7 |
| callnumber-search | GB1001.72.S7 |
| callnumber-sort | GB 41001.72 S7 |
| callnumber-subject | GB - Physical Geography |
| classification_rvk | RB 10103 SK 850 |
| classification_tum | GEO 325f |
| ctrlnum | (OCoLC)253826801 (DE-599)BVBBV023342698 |
| dewey-full | 551.49072 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 551 - Geology, hydrology, meteorology |
| dewey-raw | 551.49072 |
| dewey-search | 551.49072 |
| dewey-sort | 3551.49072 |
| dewey-tens | 550 - Earth sciences |
| discipline | Geologie / Paläontologie Mathematik Geographie |
| edition | Reprinted |
| format | Book |
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| genre | (DE-588)4056995-0 Statistik gnd-content |
| genre_facet | Statistik |
| id | DE-604.BV023342698 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:14:02Z |
| institution | BVB |
| isbn | 0521587476 0521583128 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016526440 |
| oclc_num | 253826801 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-91 DE-BY-TUM DE-824 |
| owner_facet | DE-19 DE-BY-UBM DE-91 DE-BY-TUM DE-824 |
| physical | XX, 249 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Stanford-Cambridge program |
| spellingShingle | Kitanidis, Peter K. Introduction to geostatistics applications to hydrogeology Geostatistik - Hydrogeologie - Anwendung Geostatistik - Lehrbuch Geostatistik (DE-588)4020279-3 gnd Hydrogeologie (DE-588)4026307-1 gnd |
| subject_GND | (DE-588)4020279-3 (DE-588)4026307-1 (DE-588)4056995-0 |
| title | Introduction to geostatistics applications to hydrogeology |
| title_auth | Introduction to geostatistics applications to hydrogeology |
| title_exact_search | Introduction to geostatistics applications to hydrogeology |
| title_full | Introduction to geostatistics applications to hydrogeology P. K. Kitanidis |
| title_fullStr | Introduction to geostatistics applications to hydrogeology P. K. Kitanidis |
| title_full_unstemmed | Introduction to geostatistics applications to hydrogeology P. K. Kitanidis |
| title_short | Introduction to geostatistics |
| title_sort | introduction to geostatistics applications to hydrogeology |
| title_sub | applications to hydrogeology |
| topic | Geostatistik - Hydrogeologie - Anwendung Geostatistik - Lehrbuch Geostatistik (DE-588)4020279-3 gnd Hydrogeologie (DE-588)4026307-1 gnd |
| topic_facet | Geostatistik - Hydrogeologie - Anwendung Geostatistik - Lehrbuch Geostatistik Hydrogeologie Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016526440&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kitanidispeterk introductiontogeostatisticsapplicationstohydrogeology |
Inhaltsverzeichnis
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Teilbibliothek Stammgelände, Lehrbuchsammlung
| Signatur: |
0003 GEO 325f 2009 L 267
Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 2 | Ausleihbar Am Standort |
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| Exemplar 4 | Ausleihbar Am Standort |
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| Exemplar 9 | Ausleihbar Am Standort |
| Exemplar 10 | Ausleihbar Am Standort |
Teilbibliothek Stammgelände
| Signatur: |
0004 GEO 325f 2008 A 3244(2003)
Lageplan |
|---|---|
| Exemplar 1 | Nicht ausleihbar Am Standort |
Handapparate (nicht verfügbar)
| Signatur: |
0041 GEO 325f 2008 A 6745
Lageplan 0041 GEO 325f 2009 A 2097 Lageplan |
|---|---|
| Exemplar 1 | Dauerhaft ausgeliehen Ausgeliehen – Rückgabe bis: 31.12.9999 |
| Exemplar 2 | Dauerhaft ausgeliehen Ausgeliehen – Rückgabe bis: 31.12.9999 |