7/26/2019 TOC Applied Geostatistics

http://slidepdf.com/reader/full/toc-applied-geostatistics 1/7

C O N T E N T S

1

Introduction

3

The Walker Lake Data Set

4

Goals

of

the Case Studies

6

2

Univariate Description

1

Frequency Tables and Histograms

1

Cumulative Frequency Tables and Histograms

12

Normal and lognormal Probability Plots

13

Summary Statistics

16

Measures

of

Spread

2

Measures

of

Shape

2

Notes

21

Further Reading

23

3

Bivariate Description

24 

Comparing Two Distributions

24

Scatterplots

28

Correlation

3

Linear Regression

33

Conditional Expectation

35

Notes

38

Further Reading 39

4

Spatial Description 4

Data Postings

40

Contour Maps 41

Symbol Maps 43

Indicator Maps 44

Moving Window Statistics

46

7/26/2019 TOC Applied Geostatistics

http://slidepdf.com/reader/full/toc-applied-geostatistics 2/7

xiv

ONTENTS

Proport ional Effect

49

Spa t ia l Cont inu i ty 5

h Sca t t e rp lo t s 52

Cor relat ion Fun ct ions . Covariance Fun ct ions . and Vari

og rams 55

Cross h Scat terplots

60

Notes 64

Fur the r Read ing

65

5

The Exhaustive Data Set 67 

T he Di s t ri bu tion of V

67

T he Di s t ri bu tion

of

U

70

T he Di s t ri bu tion

of T

73

75

T h e

V U

Rela t ionship 76

Sp at ia l Descript ion of

V

78

Sp at ia l Descript ion of

U

80

Moving W indow Sta t i s t i cs 90

Notes

106 

Recognit ion

of T w o

Popula t ions

Spa t ia l Cont inu i ty 93

6 The Sample Data Set 1 7

D a t a Errors

109 

T h e Sampl ing Hi story 10

Un ivariate Descript ion of V 12

Un ivariate Descript ion of U 123

27

129

P r o p ort iona l Effect 136

Fur the r Read ing 138

T h e E f f e ct of t h e T T y p e

T h e

V U

Rela t ionship 27

S p a t a1 D esc rip t on

7

The Sample Data Set: Spatial Continuity

14

Sam ple h Sca t te rp lo ts and The i r Sum mar i es

1 4 1  

An Out l i ne of Spa t ia l C ont inu i ty Analysi s

43

Choos ing t he Di s t ance Paramete r s 146

49

Choo s ing the Di rect ional T olerance 154 

54

Finding the Anisotropy Axes

Sam ple V ar iograms

for U

Relat ive Variograms 163

7/26/2019 TOC Applied Geostatistics

http://slidepdf.com/reader/full/toc-applied-geostatistics 3/7

CONTENTS

x

Comparison

of

Relative Variograms 66 

T h e Covariance Function a nd the Correlogram 70 

Directional Covariance Functions for 173 

Cross Variograms 175 

S u m m ary

of

Spatial Continuity 177 

Notes 181 

Further R eading 182

E s t i m a t i o n 84 

Weighted Linear Combinations 85 

Global and Local Estimation 87 

Means and Complete Distributions

88

Point an d Block E st imates 90 

Notes 194 

Further R eading 194 

9

R a n d o m F u n c t i o n M o d e l s

196 

T h e Necessi ty

of

Modeling 196 

Deterministic Models 198 

Probabalistic Models 200

Random Variables 202 

Functions

of

Random Variables 04 

Parameters of a Random Variable 06 

Joint Random Variables 210

Marginal Distributions 11 

Conditional Distributions 212 

Parameters

of

Joint Random Variables 213 

W eighted Linear Com binations

of

Random Variables 215 

Random Funct ions 218 

Parameters

of a

Random Funct ion 221 

T h e U se

of

Random Function Models in Practice 226 

An Example

o

the Use

of a

Probabalistic Model 31 

Further R eading 236 

1

G l o b a l E s t i m a t i o n

237 

Polygonal Declustering 38 

Cell De clustering 241 

Comparison of Declustering M ethods 43 

Declustering Three Dimensional Data 247 

Further R eading 248 

7/26/2019 TOC Applied Geostatistics

http://slidepdf.com/reader/full/toc-applied-geostatistics 4/7

xvi

ONTENTS

11 Point Estimation

249 

Polygons

25

Tr iangula t ion

251 

Local Sam ple Mean

256

Inverse Dis tance M ethod s 57 

Search Neighborhoods

59 

Est ima t ion Cr i t e r ia

26

Case Studies

266

Notes

276 

Fur the r Read ing

277 

12 Ordinary Kriging

278

T h e L a g r ange P a r a m e t e r

84

Ordinary Kriging Using y

or

p

An Example of Ord inary Kr iging 9

An Intui t ive Look a t O rdinary K r iging

99

Variogram Model Parameters

1

Compar i son

of

Ordina ry Kr ig ing to O the r Es t ima t ion

M e t hods

313

Notes

321

Fur the r R ead ing

322

T h e Ran dom Func t ion Mode l and Unbiasedness

279

T h e R a n dom F unc ti on M ode l and Error Variance 81

Minimiza t ion

of

t h e

Error

Variance

86

89

Ordin ary Kr iging and th e Model

of

Spa t i a l Cont inu i ty

296

13

Block

Kriging 323 

Block E st imates Versus th e Averaging of Poin t Es t ima te s327

Varying th e Gr id

of

Point Loca t ions Within

a

Block

327

T h e Block Kr iging S ystem 24

A C a s e S t udy

33

1 4 Search S trategy 338

Search Neighborhoods

39

Quadrant Search

344

A re th e Nearb y Samples Relevant?

47

Relevance of Nearby Samples and Sta t ionary Models 349

Notes

349

7/26/2019 TOC Applied Geostatistics

http://slidepdf.com/reader/full/toc-applied-geostatistics 5/7

  ONTENT S xvii

5 Cross Validation

351 

Cross Validation

352

Cross Validation as a Qu ant i ta t ive Tool

52

Cross Validation as a Qual i ta t ive Tool

359

Cross Validation as a Goal Oriented Tool

64 

16 Modeling the Sample Variogram

369 

Rest r ic t ions on th e Var iogram Model

7

Positive Definite Variogram

Models 72

Models in O ne Direction

75

Models of Anisotropy

377

M a t r i x N o t a t ion

386

Coo rd ina te T rans forma t ion by Rota t ion

88

T h e Linear Model of Coregionalization

39

Models For th e T h e Walker Lake Samp le Var iograms

391

Notes

397

F ur t he r R e a d i ng

398

17 Cokriging 4

T h e Cokriging Sys tem

4 1

A C okr iging Examp le

5

A C a s e S t udy

4 7

Notes

16

F ur t he r R e a d ing

416

18 Estimating a Distribution

41

Cumula t ive Dis t r ibut ions

18

T he I na de qua cy of

a

Naive Dis t r ibut ion 19

T he I na de qua cy of Poin t Es t ima te s 2

Cu mu la t ive Di s t ribu t ions . Cou nt ing and Ind icato r s

21

Est im at ing a G lobal Cum ula t ive Dis t r ibut ion

24

Est ima t ing Oth e r Pa ram e te r s of th e G lobal D i s t r ibu t ion

428

Est imat ing Loca l Dis t r ibut ions

433

Choosing Ind ica tor Thresholds

435

Case S tud ie s

438

Indicator Var iograms

442

O rde r Relation Corrections

447

Case S tud y Resu l t s 448

Notes

456

Fur the r Read ing

457

7/26/2019 TOC Applied Geostatistics

http://slidepdf.com/reader/full/toc-applied-geostatistics 6/7

xviii

ONTEN T S

19

Change O f Support 458 

T he P r a c ti c a l I m por t anc e of the Su pp or t Ef fect 58

T h e Effect of Sup por t on Sum mary S ta t is t i c s 62

Correc t ing

For

th e S up po r t Effect 68

Trans forming One D is tr ibu t ion to Anothe r 69

Affine Correction 471

Indi rec t Logn ormal Cor rec tion 72

Dispersion Variance 476

Est ima ting Dispersion Var iances F rom

a

Variogram Model480

C a s e S t udy : G l obal C ha nge

of

S u p p o r t

83

Notes 486

Fur th e r Read ing 488

2 Assessing Uncertainty

489

Error and Uncer ta in ty 489

Repor t ing Uncer ta in ty 92

Ranking Unce r ta in ty 497

Case Stud y: Ran king Sample Da ta Configurat ions 99

Assigning Confidence Intervals 504

Case Study: Confidence Intervals for An Est imate

of

th e Globa l Mean 506

A Dubious Use o Cross Validation 14

Local Confidence Intervals 17

Case Study: Local Confidence Intervals f rom Relat ive

Variograms 519

Notes 523

Fur the r Read ing 524

21

Final Thoughts 5 2 5

Description an d D a ta Analysis 25 

Es t ima t ion 528

Globa l Es t ima t ion 528

Local Es t imat io n 528

Accom mod at ing Dif fe rent S amp le Su pp or t 30

Search St ra tegy 531 

Incorpora t ing

a

Trend 31 

Cross V alidation 533 

Modeling S amp le Var iograms 34

Using Other Variables 35

7/26/2019 TOC Applied Geostatistics

http://slidepdf.com/reader/full/toc-applied-geostatistics 7/7

  ONTENTS

xix

Estimating Distr ibut ions

36 

O the r Uses of ndica tors 36 

Bibliography

5 8

A The Walker Lake Dat a Sets 4

T h e Digita l Elevation M odel

42 

T he E xha us t i ve D a t a S et 45 

Art i fac ts

545 

B Continuous Random Variables 5 48 

T h e Pro bab i l i ty Dis tr ibut ion Funct ion

48 

Parame te r s

ofa

Cont inuous R andom Variab le

549

Join t R an do m Variables

5

M argina l Dis t r ibut ions

5

Con di t iona l Dis t r ibut ions

52 

Parame te r s

of

Join t R and om Variables

552 

Index 55