Garnier J. Passive imaging with ambient noise (Cambridge; New York, 2016). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаGarnier J. Passive imaging with ambient noise / J.Garnier, G.Paranicolaou. - Cambridge; New York: Cambridge university press, 2016. - xii, 294 p.: ill. - Bibliogr.: p.285-292. - Ind.: p.293-294. - ISBN 978-1-107-13563-5
Шифр: (И/Д-G20) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
Preface ........................................................ xi

1    Introduction and overview of the book ...................... 1
1.1  Why passive, correlation-based imaging? .................... 1
     1.1.1  Travel time estimation .............................. 2
     1.1.2  Applications of travel time estimation .............. 3
     1.1.3  Reflector imaging ................................... 4
     1.1.4  Auxiliary array or virtual source imaging ........... 6
     1.1.5  Passive synthetic aperture imaging .................. 8
     1.1.6  Imaging with intensity cross correlations ........... 9
1.2  Chapter-by-chapter description of the book ................ 10

2    Green's function estimation from noise cross
     correlations .............................................. 17
2.1  The scalar wave equation and its Green's function ......... 17
     2.1.1  The Sommerfeld radiation condition ................. 19
     2.1.2  Reciprocity ........................................ 20
     2.1.3  The Helmholtz-Kirchhoff identity ................... 21
     2.1.4  Application to time reversal ....................... 23
2.2  The scalar wave equation with noise sources ............... 25
2.3  Green's function estimation with a uniform distribution 
     of sources in a homogeneous open medium ................... 29
2.4  Green's function estimation with an extended distribution
     of sources in an inhomogeneous open medium ................ 31
2.5  Green's function estimation with an extended 
     distribution of sources in an inhomogeneous cavity ........ 34
2.6  Green's function estimation with a limited distribution
     of sources in a one-dimensional inhomogeneous medium ...... 38
     2.6.1  The one-dimensional wave equation .................. 39
     2.6.2  Reflection seismology .............................. 43
     2.6.3  Daylight imaging ................................... 45
2.7  Conclusion ................................................ 48
     Appendix: the covariance of the empirical cross
     correlation ............................................... 48

3    Travel time estimation from noise cross correlations 
     using stationary phase .................................... 51
3.1  High-frequency wave propagation ........................... 52
3.2  High-frequency asymptotic analysis of the Green's 
     function in a homogeneous medium .......................... 53
3.3  High-frequency asymptotic analysis of the Green's 
     function in a smoothly varying medium ..................... 53
     3.3.1  An introduction to geometrical optics .............. 53
     3.3.2  Ray solution of the eikonal equation ............... 55
     3.3.3  Fermat's principle for the travel time ............. 57
     3.3.4  Properties of the travel time ...................... 58
3.4  High-frequency asymptotic analysis of the cross 
     correlation ............................................... 60
3.5  Conclusion ................................................ 67

4    Overview of conventional sensor array imaging ............. 68  
4.1  Passive  array imaging of sources ......................... 68
     4.1.1  Data acquisition ................................... 68
     4.1.2  Imaging function ................................... 69
     4.1.3  The linear forward operator ........................ 69
     4.1.4  The adjoint operator ............................... 70
     4.1.5  Least squares inversion ............................ 71
     4.1.6  The reverse-time imaging function .................. 73
     4.1.7  Kirchhoff migration (or travel-time migration) ..... 74
4.2  Passive  array imaging of sources: resolution analysis .... 74
     4.2.1  Full-aperture array ................................ 75
     4.2.2  Partial-aperture array ............................. 75
     4.2.3  Summary of resolution analysis for passive source
           imaging ............................................. 83
4.3  Active array imaging of reflectors ........................ 84
     4.3.1  Data acquisition ................................... 84
     4.3.2  Source and reflector array imaging: comparison ..... 85
     4.3.3  Modeling ........................................... 85
     4.3.4  Nonlinear inversion ................................ 86
     4.3.5  Linearization of the forward problem ............... 86
     4.3.6  Linearized inversion ............................... 88
     4.3.7  The reverse-time imaging function .................. 89
     4.3.8  Kirchhoff migration (or travel-time migration) ..... 91
     4.3.9  Summary of resolution analysis for active 
            reflector imaging .................................. 91
4.4  A remark about time-reversal experiments .................. 92
4.5  Conclusion ................................................ 92

5    Passive array imaging of reflectors using ambient noise 
     illumination .............................................. 94
5.1  Imaging configurations of noise sources, sensors, and 
     reflectors ................................................ 94
5.2  Stationary phase analysis of the cross correlation with 
     reflectors ................................................ 96
5.3  Migration imaging of cross correlations ................... 99
     5.3.1  Migration imaging with daylight illumination ...... 100
     5.3.2  Migration imaging with backlight illumination ..... 101
     5.3.3  Migration imaging with surround light 
            illumination ...................................... 103
5.4  Conclusion ............................................... 105

6    Resolution analysis for passive array imaging using 
     ambient noise illumination ............................... 106
6.1  A comparison of reflector imaging with active and 
     passive arrays ........................................... 107
6.2  Imaging by cross correlation of signals generated by
     ambient noise sources .................................... 108
     6.2.1  The wave equation with noise sources .............. 108
     6.2.2  Statistical stability of the cross correlation 
            function .......................................... 108
     6.2.3  Passive sensor imaging ............................ 109
     6.2.4  Hypothesis of small decoherence time and 
            correlation radius for the noise sources .......... 110
6.3  Structure of the cross correlations in a homogeneous 
     medium ................................................... 111
     6.3.1  The background Green's function ................... 111
     6.3.2  The peaks of the cross correlation in the 
            presence of a reflector ........................... 111
6.4  Resolution analysis of correlation-based imaging ......... 115
     6.4.1  The daylight imaging function ..................... 115
     6.4.2  The backlight imaging function .................... 122
     6.4.3  Numerical simulations ............................. 124
     6.4.4  Role of illumination diversity .................... 125
6.5  Conclusion ............................................... 126
     6.A Appendix: Proof of Proposition 6.2 ................... 126
     6.В Appendix: Proof of Propositions 6.4-6.5 .............. 128
     6.C Appendix: Proof of Proposition 6.6 ................... 132

7    Travel time estimation using ambient noise in weakly 
     scattering media ......................................... 136
7.1  Role of scattering in travel time estimation with 
     cross correlations ....................................... 136
7.2  A model for the scattering medium ........................ 138
7.3  Signal-to-noise ratio reduction and enhanced resolution 
     due to scattering ........................................ 140
7.4  Use of fourth-order cross correlations ................... 142
7.5  Conclusion ............................................... 145
     7.A Appendix: Complete expression of the average cross 
         correlation .......................................... 146
     7.В Appendix: Proof of Proposition 7.1 ................... 148
     7.C Appendix: Proof of Proposition 7.2 ................... 149

8    Correlation-based reflector imaging using ambient 
     noise in weakly scattering media ......................... 152
8.1  Role of scattering in correlation-based imaging .......... 152
8.2  Passive sensor imaging in a randomly scattering medium ... 154
     8.2.1  A model for the scattering medium ................. 155
     8.2.2  The differential cross correlation ................ 156
     8.2.3  Expansion of the clutter Green's function ......... 157
     8.2.4  Expansion of the differential cross correlation ... 159
     8.2.5  Statistical analysis of the differential cross 
            correlation ....................................... 160
     8.2.6  On the trade-off between resolution enhancement
            and signal-to-noise ratio reduction ............... 164
     8.2.7  Numerical simulation of migration imaging with 
            cross correlations in the presence of
            scatterers ........................................ 164
8.3  Passive sensor imaging with a reflecting interface ....... 165
     8.3.1  Stationary phase analysis of the cross 
            correlation with a reflecting interface ........... 166
     8.3.2  Numerical simulations of migration imaging with 
            cross correlations in the presence of an 
            interface ......................................... 168
8.4  Iterated cross correlations for passive imaging in 
     a randomly scattering medium ............................. 170
     8.4.1  The coda cross correlation ........................ 170
     8.4.2  Numerical simulations of migration imaging with
            coda cross correlations ........................... 172
8.5  Conclusion ............................................... 172
     8.A Appendix: Proof of Proposition 8.1 ................... 174
     8.В Appendix: Proof of Proposition 8.2 ................... 178
         8.B.1 First group .................................... 178
         8.B.2 Second group ................................... 180
     8.C Appendix: Statistical analysis of the cross 
         correlations ......................................... 182
         8.C.1 The cross correlation at the difference of 
               travel times ................................... 182
         8.C.2 The cross correlation at the sum of travel
               times .......................................... 184
     8.D Appendix: Proof of Proposition 8.3 ................... 185

9    Virtual source imaging in homogeneous media .............. 187
9.1  Introduction to virtual source imaging ................... 187
9.2  Ideal virtual source imaging with an infinite source 
     array .................................................... 190
9.3  High-frequency analysis in a homogeneous background 
     with a limited source array .............................. 191
     9.3.1  Direct scattering problem ......................... 191
     9.3.2  High-frequency analysis of the cross 
            correlations ...................................... 192
     9.3.3  High-frequency analysis of the imaging function ... 195
9.4  Passive synthetic aperture imaging in a homogeneous 
     background ............................................... 197
     9.4.1  High-frequency analysis of the imaging function ... 198
     9.4.2  Comparison with classical synthetic aperture 
            imaging ........................................... 199
9.5  Conclusion ............................................... 201
     9.A Appendix: Proof of Proposition 9.2 ................... 202
     9.B Appendix: Proof of Proposition 9.3 ................... 203

10   Virtual source imaging in scattering media ............... 206
10.1 The auxiliary array imaging setup ........................ 206
10.2 Time-reversal interpretation of virtual source imaging ... 208
10.3 The paraxial approximation in random media ............... 209 
     10.3.1 The main results in the paraxial approximation .... 210
     10.3.2 Validity of the paraxial approximation in 
            random media ...................................... 211
10.4 Analysis of virtual source imaging in the random 
     paraxial regime .......................................... 212
     10.4.1 The cross correlation of the recorded field ....... 212
     10.4.2 Migration of cross correlations ................... 216
10.5 Numerical simulations .................................... 218
10.6 Passive synthetic aperture imaging in random media ....... 219
10.7 Conclusion ............................................... 222
     10.A Appendix: Proofs of Propositions 10.1-10.2 .......... 223
     10.B Appendix: Proofs of Propositions 10.3-10.4 .......... 227

11   Imaging with intensity cross correlations ................ 228
11.1 The ghost imaging setup .................................. 228
11.2 The intensity correlation function ....................... 231
     11.2.1 The empirical and statistical correlations ........ 231
     11.2.2 Paraxial regime ................................... 233
     11.2.3 Time-reversal interpretation ...................... 235
     11.2.4 Averaging with respect to the random medium ....... 236
11.3 Resolution analysis ...................................... 237
     11.3.1 Resolution analysis for the fully incoherent
            case .............................................. 237
     11.3.2 Resolution analysis for the partially coherent
            case .............................................. 240
11.4 Conclusion ............................................... 242
     11.A Appendix: The fields in the white-noise paraxial
          regime .............................................. 243

12   A review of wave propagation in random media ............. 245
12.1 The random travel time model ............................. 245
     12.1.1 Domain of validity ................................ 245
     12.1.2 Statistics of the amplitude and phase 
            perturbations ..................................... 247
     12.1.3 The moments of the Green's function ............... 250
12.2 The random paraxial model ................................ 253
     12.2.1 The random paraxial regime ........................ 253
     12.2.2 The random paraxial wave equation ................. 254
     12.2.3 The moments of the fundamental solution ........... 255
12.3 The randomly layered model ............................... 258
     12.3.1 The scaling regime ................................ 258
     12.3.2 Review of wave propagation in randomly layered 
            media ............................................. 260
     12.3.3 Statistics of the Green's function ................ 261
12.4 Conclusion ............................................... 262
     12.A Appendix: Proof of Lemma 12.1 ....................... 262
     12.В Appendix: Proof of Proposition 12.6 ................. 264
     12.С Appendix: Proof of Proposition 12.8 ................. 267

13   Appendix: Basic facts from analysis and probability ...... 269
13.1 Fourier identities ....................................... 269
13.2 Divergence theorem ....................................... 270
13.3 Stationary phase method .................................. 270
13.4 Sampling theorem ......................................... 272
13.5 Random processes ......................................... 274
     13.5.1 Random variables .................................. 274
     13.5.2 Random vectors .................................... 275
     13.5.3 Gaussian random vectors ........................... 276
     13.5.4 Random processes .................................. 277
     13.5.5 Ergodic processes ................................. 278
     13.5.6 Mean square theory ................................ 279
     13.5.7 Gaussian processes ................................ 281
     13.5.8 Stationary Gaussian processes ..................... 282
     13.5.9 Vector-and complex-valued Gaussian processes ...... 283

References .................................................... 285
Index ......................................................... 293

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