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Cover image for Imaging of complex media with acoustic and seismic waves
Title:
Imaging of complex media with acoustic and seismic waves
Series:
Topics in applied physics ; 82
Publication Information:
Berlin : Springer, 2002
ISBN:
9783540416678
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30000010045497 TA1770 I52 2002 Open Access Book Book
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Summary

Summary

In this interdisciplinary book, leading experts in underwater acoustics, seismology, acoustic medical imaging and non-destructive testing present basic concepts as well as the recent advances in imaging. The different subjects tackled show significant similarities.


Table of Contents

Roel SniederMat has FinkWilliam A. Kuperman and Darrel R. JacksonJames H. RoseClaire PradaJ0rgen A. JensenJean-Paul MontagnerBruce R. ThompsonMostafa Fatemi and James F. GreenleafTravis E. Ol and Richard L. Ehman and James F. GreenleafPhil and Satish C. SinghShamita Das
Time-Reversal Invariance and the Relation between Wave Chaos and Classical Chaosp. 1
1 Time-Reversal Invariance of the Laws of Naturep. 1
2 Wave Chaos and Particle Chaosp. 4
3 Instability of Particle Trajectoriesp. 6
4 Instability of Wave Propagationp. 7
4 Numerical Examplesp. 10
6 Discussionp. 14
Acoustic Time-Reversal Mirrorsp. 17
1 Introductionp. 17
2 Time-Reversal Cavities and Mirrorsp. 17
2.1 The Time-Reversal Cavityp. 18
2.2 The Time-Reversal Mirrorp. 20
3 Time-Reversal Experimentsp. 21
3.1 Time Reversal through Random Mediap. 21
3.2 Time Reversal in Waveguidesp. 27
3.3 Time Reversal in Chaotic Cavitiesp. 32
4 Applications of Time-Reversal Mirrorsp. 37
5 Conclusionp. 40
Ocean Acoustics, Matched-Field Processing and Phase Conjugationp. 43
1 Review of Ocean Acousticsp. 43
1.1 Qualitative Description of Ocean Sound Propagationp. 43
1.2 Sound Propagation Modelsp. 49
1.3 Quantitative Description of Propagationp. 53
2 Matched-Field Processingp. 56
3 Phase Conjugation in the Oceanp. 60
3.1 Basic Properties of Phase Conjugationp. 60
3.2 Background Theory and Simulation for Phase Conjugation/Time-Reversal Mirror in the Oceanp. 65
3.3 Implementation of a Time-Reversal Mirror in the Oceanp. 71
3.4 Summary of Time-Reversal Mirror Experimentsp. 75
4 The Range-Dependent Ocean Waveguidep. 75
5 The Effect of Ocean Fluctuations on Phase Conjugationp. 83
5.1 Time-Independent Volume Scatteringp. 83
5.2 Time-Dependent Scattering by Surface Wavesp. 85
5.3 Time-Dependent Scattering by Internal Wavesp. 87
6 Conclusionsp. 90
7 Appendix A: Parabolic Equation (PE) Modelp. 91
7.1 Standard Parabolic Equation Split-Step Algorithmp. 91
7.2 Generalized or Higher-Order Parabolic Equation Methodsp. 92
8 Appendix B: Unitsp. 93
Time Reversal, Focusing and Exact Inverse Scatteringp. 97
1 Introductionp. 97
2 Direct and Inverse Scattering Problemsp. 98
2.1 The Forward Problemp. 99
2.2 Inverse Scattering Problemp. 100
3 Physics of the Newton-Marchenko Equationp. 100
4 Discussion and Summaryp. 104
Detection and Imaging in Complex Media with the D.O.R.T. Method

p. 107

1 Introductionp. 107
2 Basic Principle of the D.O.R.T. Methodp. 109
2.1 The Transfer Matrixp. 109
2.2 Invariants of the Time-Reversal Process and Decomposition of the Transfer Matrixp. 110
2.3 Transfer Matrix for Point-Like Scatterersp. 111
2.4 Decomposition of K for Well-Resolved Scatterersp. 112
2.5 The D.O.R.T. Method in Practicep. 113
3 Selective Focusing Through an Inhomogeneous Medium with the D.O.R.T. Methodp. 114
4 Highly Resolved Detection and Selective Focusing in a Waveguidep. 116
4.1 Selective Highly Resolved Focusing in a Waveguidep. 118
4.2 Detection Near the Interfacep. 120
4.3 Detection in a Nonstationary Waveguidep. 121
5 Inverse-Scattering Analysis and Target Resonancep. 122
5.1 Experimentp. 123
5.2 Invariants of the Time-Reversal Processp. 125
5.3 Resonance Frequencies of the Shellp. 127
6 The D.O.R.T. Method in the Time Domainp. 128
6.1 Construction of the Temporal Green's Functionsp. 129
6.2 Selective Focusing in the Pulse Modep. 131
7 Conclusionp. 132
Ultrasound Imaging and Its Modelingp. 135
1 Fundamental Ultrasound Imagingp. 135
2 Imaging with Arraysp. 138
3 Focusingp. 142
4 Ultrasound Fieldsp. 144
4.1 Derivation of the Fourier Relationp. 144
4.2 Beam Patternsp. 146
5 Spatial Impulse Responsesp. 149
5.1 Fields in Linear Acoustic Systemsp. 149
5.2 Basic Theoryp. 150
5.3 Geometric Considerationsp. 153
5.4 Calculationof Spatial Impulse Responsesp. 154
5.5 Examples of Spatial Impulse Responsesp. 156
5.6. Pulse-Echo Fields

p. 157

6 Fields from Array Transducersp. 159
7 Examples of Ultrasound Fieldsp. 161
8 Summaryp. 164
Nondestructive Acoustic Imaging Techniquesp. 167
1 Introductionp. 167
2 The Nondestructive Testing Taskp. 168
3 The Inverse Problemp. 170
4 Special Features of SAFTp. 172
4.1 Lateral Resolutionp. 173
4.2 Signal-to-Noise Ratio Improvement by SAFTp. 175
4.3 Localization Accuracyp. 175
4.4 Pulse-Echo/Pitch-and-Catch Reconstructionp. 177
4.4 Acoustic Imaging in a 3-dimensional CAD Environmentp. 180
5 Imaging in Transversally Isotropic Material - Ray Tracingp. 183
5.1 Sound Propagation Through a V Weld with Defectsp. 184
5.2 A 10-Layer Approximated Austenitic Weldp. 185
6 Summaryp. 188
Seismic Anisotropy Tomographyp. 191
1 Introductionp. 191
2 The Anatomy of Seismogramsp. 192
2.1 Progress in Instrumentationp. 192
2.2 Body Waves, Surface Waves and Normal Modesp. 195
2.3 Normal-Mode Theoryp. 198
3 An Anisotropic Earthp. 202
3.1 Seismic Anisotropy at All Scalesp. 202
3.2 First-Order Perturbation Theory in the Planar Casep. 205
4 Tomography of Anisotropyp. 212
4.1 Forward Problemp. 212
4.2 Inverse Problemp. 216
4.3 Practical Implementationp. 218
4.4 Geophysical Applicationsp. 218
5 Conclusionsp. 224
Elastic-Wave Propagation in Random Polycrystals: Fundamentals and Application to Nondestructive Evaluationp. 233
1 Introductionp. 233
2 Simple Polycrystalsp. 235
2.1 Backgroundp. 235
2.2 Theoryp. 236
2.3 Randomly Oriented, Equi-axed Polycrystalsp. 240
2.4 Equi-axed Polycrystals with Preferred Orientationp. 241
2.4 Randomly Oriented Polycrystals with Grain Elongationp. 243
2.6. Polycrystals with Both Preferred Orientation and Grain Elongation

p. 244

3 Complex Microstructuresp. 244
3.1 Backgroundp. 244
4 Effects on Imagingp. 251
5 Conclusionsp. 253
Imaging the Viscoelastic Properties of Tissuep. 257
1 Introductionp. 257
2 Theory of the Radiation Forcep. 260
3 Radiation-Force Methodsp. 261
3.1 Transient Methodp. 262
3.2 Shear-Wave Methodsp. 262
3.3 Vibro-Acoustographyp. 263
4 Capabilities and Limitationsp. 272
5 Summaryp. 274
Estimation of Complex-Valued Stiffness Using Acoustic Waves Measured with Magnetic Resonancep. hant
1 Introductionp. 277
2 Measurement Modelp. 278
2.1 Acoustic Modelp. 278
2.2 Displacement Measurement with Magnetic Resonancep. 281
3 Estimating Material Propertiesp. 284
3.1 Algebraic Inversion of the Differential Equation (AIDE)p. 285
3.2 Other Inversion Methodsp. 287
4 Examplesp. 289
4.1 Experimental Phantomp. 289
5 Conclusionp. 292
A New Approach for Traveltime Tomography and Migration Without Ray Tracingpe O. Ecoublet
1 Introductionp. 295
2 The Traveltime Functionp. 296
2.1 Traveltime as a Series Expansionp. 298
2.2 The Eikonal Equationp. 299
2.3 The Equations of Constraintp. 300
3 Tomographyp. 301
3.1 The Misfit Functionp. 301
3.2 The Initial Modelp. 302
3.3 Optimizationp. 302
3.4 Slowness Image Reconstructionp. 302
4 Error and Resolution Analysesp. 303
5 Prestack Depth Migrationp. 303
5.1 Computation of the Incidence Angle of the Rayp. 304
6 Conclusionsp. 305
Simple Models in the Mechanics of Earthquake Rupturep. 311
1 Introductionp. 311
2 Brief Derivation of the Underlying Equationsp. 312
3 The Finite Circular Shear Faultp. 321
4 Spontaneous Faultsp. 322
4.1 Fracture Criterionp. 324
Indexp. 333
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