Wavelets in Geophysics (eBook)

Front Cover 1
Wavelets in Geophysics 4
Copyright Page 5
Table of Contents 8
Contributors 10
Preface 12
Chapter 1. Wavelet Analysis in Geophysics: An Introduction 16
§1. Prologue 16
§2. Time-Frequency Analysis 18
§3. Wavelets and Time-Scale Analysis 27
§4. Examples of One-Dimensional Wavelets 31
§5. Discrete Wavelet Transforms 34
§6. Two-Dimensional Wavelets 44
§7. Conclusions 48
References 54
Chapter 2. Applications of Structure Preserving Wavelet Decompositions to Intermittent Turbulence: A Case Study 60
§1. Introduction 61
§2. The Wavelet Transform 63
§3. Filtering Properties of Wavelets 69
§4. Applications to Atmospheric Data 82
§5. Summary and Conclusions 89
References 93
Chapter 3. Intermittency in Atmospheric Surface Layer Turbulence: The Orthonormal Wavelet Representation 96
§1. Introduction 96
§2. Analysis of Turbulence using Wavelet Transforms 98
§3. Experiment 101
§4. Wavelet Statistics 103
§5. Results and Discussion 110
§6. Summary and Conclusions 116
References 116
Chapter 4. An Adaptive Decomposition: Application to Turbulence 122
§1. Introduction 123
§2. Partitioning the Time Series 124
§4. Physical Interpretation 138
§5. Conclusion 140
References 141
Chapter 5. Wavelet Analysis of Diurnal and Nocturnal Turbulence Above a Maize Crop 144
§1. Introduction 144
§2. Experimental Procedures and Flow Characteristics 146
§3. Wavelet Variance and Covariance 149
§4. Jump Detection and Conditional Sampling 153
§5. Wavelet Decomposition 158
§6. Summary and Conclusions 161
References 163
Chapter 6. Wavelet Spectrum Analysis and Ocean Wind Waves 166
§1. Introduction 166
§2. Wavelet Spectrum 167
§3. Applications 170
§4. Concluding Remarks 179
References 180
Chapter 7. Wavelet Analysis of Seafloor Bathymetry: An Example 182
§1. Introduction 182
§2· 1-D Topographie Profile 183
§3. 2-D Bathymetry 184
§4. Conclusions 195
References 196
Chapter 8. Analysis of High Resolution Marine Seismic Data Using the Wavelet Transform 198
§1. Introduction 198
§2. Acoustic-Geotechnical Correlations: Physical and Historical Context 200
§3. The Wavelet Transform for Acoustic Soil Analysis 203
§4. Experimental Field Program 209
§5. Data Analysis 211
§6. Conclusion 221
References 223
Chapter 9. Including Multi-Scale Information in the Characterization of Hydraulic Conductivity Distributions 228
§1. Introduction 228
§2. Wavelet Based Interpolation 231
§3. Traditional Interpolation Methods 240
§4. Evaluation of Methods 243
§5. Conclusions and Recommendations 258
§6. Concluding Remarks 261
References 261
Chapter 10. Wavelet-Based Multifractal Analysis of Non-Stationary and/or Intermittent Geophysical Signals 264
§1. Introduction and Overview 264
§2. Preliminary Considerations on Stationarity, Ergodicity and Scale-Invariance 266
§3. Quantifying and Qualifying Non-Stationarity with Structure Functions 271
§4. Quantifying and Qualifying Intermittency with Singular Measures 280
§5. Summary and Bi-Multifractal Statistics 290
§6. Conclusions 293
References 308
Chapter 11. Simultaneous Noise Suppression and Signal Compression Using a Library of Orthonormal Bases and the Minimum Description Length Criterion 314
§1. Introduction 314
§2. A Library of Orthonormal Bases 315
§3. Problem Formulation 319
§4. The Minimum Description Length Principle 320
§5. A Simultaneous Noise Suppression and Signal Compression Algorithm 325
§6· Extension to Images 329
§7. Examples 330
§8. Discussions 334
§9. Conclusions 336
Acknowledgements 337
References 337
Chapter 12. Long-Memory Processes, the Allan Variance and Wavelets 340
§1. Introduction 340
§2. The Allan Variance and the Haar Wavelet 342
§3. The Wavelet Variance 346
§4. An Application to Vertical Shear Measurements 349
§5. Concluding Remarks 356
References 358
Bibliography 360
Subject Index 374
Detailed Table of Contents 382
WAVELET ANALYSIS AND ITS APPLICATIONS 388