Foufoula-Georgiou / Kumar MD / Kumar Wavelets in Geophysics

1. Auflage 2014
ISBN: 978-0-08-052087-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 4, 373 Seiten, Web PDF

Reihe: Wavelet Analysis and Its Applications

Applications of wavelet analysis to the geophysical sciences grew from Jean Morlet's work on seismic signals in the 1980s. Used to detect signals against noise, wavelet analysis excels for transients or for spatiallylocalized phenomena. In this fourth volume in the renown WAVELET ANALYSIS AND ITS APPLICATIONS Series, Efi Foufoula-Georgiou and Praveen Kumar begin with a self-contained overview of the nature, power, and scope of wavelet transforms. The eleven originalpapers that follow in this edited treatise show how geophysical researchers are using wavelets to analyze such diverse phenomena as intermittent atmospheric turbulence, seafloor bathymetry, marine and other seismic data, and flow in aquifiers. Wavelets in Geophysics will make informative reading for geophysicists seeking an up-to-date account of how these tools are being used as well as for wavelet researchers searching for ideas for applications, or even new points of departure. - Includes twelve original papers written by experts in the geophysical sciences - Provides a self-contained overview of the nature, power, and scope of wavelet transforms - Presents applications of wavelets to geophysical phenomena such as: The sharp events of seismic data, Long memory processes, such as fluctuation in the level of the Nile, A structure preserving decomposition of turbulence signals

Autoren/Hrsg.

Foufoula-Georgiou, Efi

Kumar MD, Praveen

Kumar, Praveen

Inhaltsverzeichnis

1;Front Cover;1
2;Wavelets in Geophysics;4
3;Copyright Page;5
4;Table of Contents;8
5;Contributors;10
6;Preface;12
7;Chapter 1. Wavelet Analysis in Geophysics: An Introduction;16
7.1;§1. Prologue;16
7.2;§2. Time-Frequency Analysis;18
7.3;§3. Wavelets and Time-Scale Analysis;27
7.4;§4. Examples of One-Dimensional Wavelets;31
7.5;§5. Discrete Wavelet Transforms;34
7.6;§6. Two-Dimensional Wavelets;44
7.7;§7. Conclusions;48
7.8;References;54
8;Chapter 2. Applications of Structure Preserving Wavelet Decompositions to Intermittent Turbulence: A Case Study;60
8.1;§1. Introduction;61
8.2;§2. The Wavelet Transform;63
8.3;§3. Filtering Properties of Wavelets;69
8.4;§4. Applications to Atmospheric Data;82
8.5;§5. Summary and Conclusions;89
8.6;References;93
9;Chapter 3. Intermittency in Atmospheric Surface Layer Turbulence: The Orthonormal Wavelet Representation;96
9.1;§1. Introduction;96
9.2;§2. Analysis of Turbulence using Wavelet Transforms;98
9.3;§3. Experiment;101
9.4;§4. Wavelet Statistics;103
9.5;§5. Results and Discussion;110
9.6;§6. Summary and Conclusions;116
9.7;References;116
10;Chapter 4. An Adaptive Decomposition: Application to Turbulence;122
10.1;§1. Introduction;123
10.2;§2. Partitioning the Time Series;124
10.3;§4. Physical Interpretation;138
10.4;§5. Conclusion;140
10.5;References;141
11;Chapter 5. Wavelet Analysis of Diurnal and Nocturnal Turbulence Above a Maize Crop;144
11.1;§1. Introduction;144
11.2;§2. Experimental Procedures and Flow Characteristics;146
11.3;§3. Wavelet Variance and Covariance;149
11.4;§4. Jump Detection and Conditional Sampling;153
11.5;§5. Wavelet Decomposition;158
11.6;§6. Summary and Conclusions;161
11.7;References;163
12;Chapter 6. Wavelet Spectrum Analysis and Ocean Wind Waves;166
12.1;§1. Introduction;166
12.2;§2. Wavelet Spectrum;167
12.3;§3. Applications;170
12.4;§4. Concluding Remarks;179
12.5;References;180
13;Chapter 7. Wavelet Analysis of Seafloor Bathymetry: An Example;182
13.1;§1. Introduction;182
13.2;§2· 1-D Topographie Profile;183
13.3;§3. 2-D Bathymetry;184
13.4;§4. Conclusions;195
13.5;References;196
14;Chapter 8. Analysis of High Resolution Marine Seismic Data Using the Wavelet Transform;198
14.1;§1. Introduction;198
14.2;§2. Acoustic-Geotechnical Correlations: Physical and Historical Context;200
14.3;§3. The Wavelet Transform for Acoustic Soil Analysis;203
14.4;§4. Experimental Field Program;209
14.5;§5. Data Analysis;211
14.6;§6. Conclusion;221
14.7;References;223
15;Chapter 9. Including Multi-Scale Information in the Characterization of Hydraulic Conductivity Distributions;228
15.1;§1. Introduction;228
15.2;§2. Wavelet Based Interpolation;231
15.3;§3. Traditional Interpolation Methods;240
15.4;§4. Evaluation of Methods;243
15.5;§5. Conclusions and Recommendations;258
15.6;§6. Concluding Remarks;261
15.7;References;261
16;Chapter 10. Wavelet-Based Multifractal Analysis of Non-Stationary and/or Intermittent Geophysical Signals;264
16.1;§1. Introduction and Overview;264
16.2;§2. Preliminary Considerations on Stationarity, Ergodicity and Scale-Invariance;266
16.3;§3. Quantifying and Qualifying Non-Stationarity with Structure Functions;271
16.4;§4. Quantifying and Qualifying Intermittency with Singular Measures;280
16.5;§5. Summary and Bi-Multifractal Statistics;290
16.6;§6. Conclusions;293
16.7;References;308
17;Chapter 11. Simultaneous Noise Suppression and Signal Compression Using a Library of Orthonormal Bases and the Minimum Description Length Criterion;314
17.1;§1. Introduction;314
17.2;§2. A Library of Orthonormal Bases;315
17.3;§3. Problem Formulation;319
17.4;§4. The Minimum Description Length Principle;320
17.5;§5. A Simultaneous Noise Suppression and Signal Compression Algorithm;325
17.6;§6· Extension to Images;329
17.7;§7. Examples;330
17.8;§8. Discussions;334
17.9;§9. Conclusions;336
17.10;Acknowledgements;337
17.11;References;337
18;Chapter 12. Long-Memory Processes, the Allan Variance and Wavelets;340
18.1;§1. Introduction;340
18.2;§2. The Allan Variance and the Haar Wavelet;342
18.3;§3. The Wavelet Variance;346
18.4;§4. An Application to Vertical Shear Measurements;349
18.5;§5. Concluding Remarks;356
18.6;References;358
19;Bibliography;360
20;Subject Index;374
21;Detailed Table of Contents;382
22;WAVELET ANALYSIS AND ITS APPLICATIONS;388