Principles of Sonar Performance Modelling (eBook)

Michael Ainslie (Autor)

eBook Download: PDF

2010 | 2010
XXVIII, 707 Seiten
Springer Berlin (Verlag)
978-3-540-87662-5 (ISBN)

Infos

Sonar performance modelling (SPM) is concerned with the prediction of quantitative measures of sonar performance, such as probability of detection. It is a multi-disciplinary subject, requiring knowledge and expertise in the disparate fields of underwater acoustics, acoustical oceanography, sonar signal processing and statistical detection theory. No books have been published on this subject, however, since the 3^rd edition of Urick's classic work 25 years ago and so Dr Ainslie's book will fill a much-needed gap in the market. Currently, up-to-date information can only be found, in different forms and often with conflicting information, in various journals, conference and textbook publications.

Dr Michael Ainslie is eminently qualified to write this unique book. He has worked on sonar performance modeling problems since 1983. He has written many peer reviewed research articles and conference papers related to sonar performance modeling, making contributions in the fields of sound propagation and detection theory.

Inhalt

Principles of Sonar Performance Modeling 2
Contents 4
Preface 12
Foreword 13
Acknowledgments 15
Figures 17
Tables 23
Part I Foundations 27
1 Introduction 28
1.1 WHAT IS SONAR? 28
1.2 PURPOSE, SCOPE, AND INTENDED READERSHIP 29
1.3 STRUCTURE 31
1.3.1 Part I: Foundations (Chapters 1–3) 31
1.3.2 Part II: Thefour pillars (Chapters 4–7) 31
1.3.3 Part III: Towards applications (Chapters 8–11) 32
1.3.4 Appendices 32
1.4 A BRIEF HISTORY OF SONAR 32
1.4.1 Conception and birth of sonar (–1918) 33
1.4.1.1 Discovery and ingenuity 33
1.4.1.2 The Titanic and the Fessenden oscillator 35
1.4.1.3 WW1: a sense of urgency 35
1.4.1.4 Origins of passive sonar 38
1.4.2 Sonar in its infancy (1918–1939) 40
1.4.2.1 Fathometers and fish finders 40
1.4.2.2 National research laboratories 41
1.4.2.3 Temperature and the ‘‘afternoon effect’’ 41
1.4.3 Sonar comes of age (1939–) 42
1.4.3.1 WW2: a giant awakes 42
1.4.3.2 Passive sonar in Germany 42
1.4.3.3 The anomalous absorption of seawater 43
1.4.3.4 SOFAR, SOSUS, and the Roswell Incident 44
1.4.3.4.1 The speed of sound in seawater 44
1.4.3.4.2 Sound fixing and ranging: the SOFAR channel 45
1.4.3.4.3 The Sound Surveillance System (SOSUS) 46
1.4.3.4.4 Project MOGUL and the Roswell Incident 46
1.4.3.5 Advances in detection theory and processing technology 46
1.4.3.5.1 Statistical detection theory 46
1.4.3.5.2 FM processing and electronic scanning 47
1.4.3.5.3 The computer era 47
1.4.4 Swords to ploughshares 47
1.4.4.1 Oceanographic instruments 47
1.4.4.2 Discovery of dolphin sonar and concern over the effects of anthropogenic sound 48
1.5 REFERENCES 48
2 Essential background 52
2.1 ESSENTIALS OF SONAR OCEANOGRAPHY 52
2.1.1 Acoustical properties of seawater 53
2.1.1.1 Speed of sound 53
2.1.1.2 Density 53
2.1.1.3 Attenuation of sound 53
2.1.2 Acoustical properties of air 55
2.2 ESSENTIALS OF UNDERWATER ACOUSTICS 55
2.2.1 What is sound? 55
2.2.2 Radiation of sound 56
2.2.2.1 Radiation from a point monopole source 56
2.2.2.1.1 Spherical spreading 56
2.2.2.1.2 Reflection from the sea surface 59
2.2.2.2 Radiation from an infinite sheet of uniformly distributed dipoles 62
2.2.3 Scattering of sound 65
2.2.3.1 Scattering from a small object 65
2.2.3.2 Scattering from a rough surface 66
2.3 ESSENTIALS OF SONAR SIGNAL PROCESSING 67
2.3.1 Temporal filter 67
2.3.2 Spatial filter (beamformer) 69
2.4 ESSENTIALS OF DETECTION THEORY 72
2.4.1 Gaussian distribution 72
2.4.1.1 Noise only 74
2.4.1.2 Signal plus noise 74
2.4.2 Other distributions 76
2.4.2.1 Coherent processing (Rayleigh statistics) 76
2.4.2.2 Incoherent processing (chi-squared statistics with many samples) 76
2.5 REFERENCES 77
3 The sonar equations 78
3.1 INTRODUCTION 78
3.1.1 Objectives of sonar performance modeling 78
3.1.2 Concepts of ‘‘signal’’ and ‘‘noise’’ 79
3.1.3 Generic deep-water scenario 80
3.1.4 Chapter organization 80
3.2 PASSIVE SONAR 81
3.2.1 Overview 81
3.2.2 Definition of standard terms (passive sonar) 83
3.2.2.1 Mean square pressure, sound pressure level, and the decibel 83
3.2.2.2 Source level 85
3.2.2.3 Propagation loss 85
3.2.2.4 Noise spectrum level and array response 86
3.2.2.5 Signal-to-noise ratio, array gain, and directivity index 87
3.2.2.6 Signal gain and noise gain 88
3.2.2.7 Detection threshold and signal excess 88
3.2.3 Coherent processing: narrowband passive sonar 89
3.2.3.1 Signal (single hydrophone) 89
3.2.3.2 Noise (single hydrophone) 91
3.2.3.3 Signal-to-noise ratio, signal excess, and narrowband passive sonar equation 92
3.2.3.4 Array gain and directivity index for a horizontal line array 94
3.2.3.5 Probability of detection, detection threshold, and ROC curves 96
3.2.3.6 Probability of false alarm 97
3.2.3.7 Special case: low-frequency tonal in the broadside beam of a horizontal line array 98
3.2.3.8 Worked example 99
3.2.3.8.1 Part (i): source level SL 99
3.2.3.8.2 Part (ii): noise spectrum level NLf 100
3.2.3.8.3 Part (iii): AG, BW, and DT 100
3.2.3.8.4 Part (iv): figure of merit FOM 100
3.2.3.8.5 Part (v): propagation loss PL(r) 100
3.2.3.8.6 Part (vi): signal level LS(r) and in-beam noise level LN 102
3.2.3.8.7 Part (vii): sensitivity to sonar parameters 103
3.2.4 Incoherent processing: broadband passive sonar 105
3.2.4.1 Signal (single hydrophone) 105
3.2.4.2 Noise (single hydrophone) 107
3.2.4.3 Signal-to-noise ratio, signal excess, and broadband passive sonar equation 109
3.2.4.4 Array gain 110
3.2.4.5 Probability of detection, detection threshold, and ROC curves 110
3.2.4.6 Probability of false alarm 112
3.2.4.7 Special case: broadband target in the broadside beam of a horizontal line array 112
3.2.4.8 Worked example 113
3.2.4.8.1 Part (i): source level SLf and noise spectrum level NLf 114
3.2.4.8.2 Part (ii): AGm and DT 115
3.2.4.8.3 Part (iii): detection range 115
3.2.4.8.4 Part (iv): halving detection range 118
3.2.4.8.5 Part (v): doubling transmitter depth 119
3.3 ACTIVE SONAR 119
3.3.1 Overview 119
3.3.2 Definition of standard terms (active sonar) 120
3.3.2.1 Signal energy, energy source level, and total path loss 121
3.3.2.2 Background energy and background energy level 122
3.3.2.3 Signal-to-background ratio and array gain 123
3.3.2.4 Target strength 124
3.3.3 Coherent processing: CW pulseþDoppler filter 124
3.3.3.1 Signal (single hydrophone) 125
3.3.3.2 Background (single hydrophone) 125
3.3.3.3 Signal-to-background ratio, signal excess, and coherent narrowband activesonar equation 125
3.3.3.4 Array gain 127
3.3.3.5 Probability of detection, detection threshold, and ROC curves 128
3.3.3.6 Probability of false alarm 128
3.3.3.7 Special case: rigid spherical target in the broadside beam of a horizontal line array, CW pulse with Doppler processing 129
3.3.3.8 Worked example 130
3.3.3.8.1 Part (i): smallest detectable sphere 131
3.3.3.8.2 Part (ii): figure of merit 132
3.3.3.8.3 Part (iii): detection probability 132
3.3.3.8.4 Part (iv): best depth 136
3.3.4 Incoherent processing: CW pulseþenergy detector 137
3.3.4.1 Signal (single hydrophone) 137
3.3.4.2 Background (single hydrophone) 137
3.3.4.3 Signal-to-background ratio, signal excess, and incoherent active sonar equation 137
3.3.4.4 Array gain 139
3.3.4.5 Probability of detection, detection threshold, and ROC curves 140
3.3.4.6 Probability of false alarm 140
3.3.4.7 Special case: point target in the broadside beam of a horizontal line array, CW pulse with incoherent processing 141
3.3.4.8 Worked example 142
3.3.4.8.1 Part (i): signal, background, and detection threshold 142
3.3.4.8.2 Part (ii): detection range 142
3.3.4.8.3 Part (iii): detection probability 142
3.4 REFERENCES 147
Part II The Four Pillars 148
4 Sonar oceanography 149
4.1 PROPERTIES OF THE OCEAN VOLUME 150
4.1.1 Terrestrial and universal constants 150
4.1.2 Bathymetry 150
4.1.3 Factors affecting sound speed and attenuation in pure seawater 150
4.1.3.1 Density and static pressure 151
4.1.3.2 Temperature 152
4.1.3.3 Salinity 153
4.1.3.4 Acidity (pH) 162
4.1.3.5 Viscosity 163
4.1.4 Speed of sound in pure seawater 163
4.1.5 Attenuation of sound in pure seawater 170
4.2 PROPERTIES OF BUBBLES AND MARINE LIFE 172
4.2.1 Properties of air bubbles in water 172
4.2.1.1 Properties of air under pressure 172
4.2.1.2 Properties of water that affect the behavior of a pulsating bubble 175
4.2.1.3 Properties of bubbly water 176
4.2.2 Properties of marine life 176
4.2.2.1 Basic physiological properties 176
4.2.2.1.1 Zooplankton 176
4.2.2.1.2 Fish 176
4.2.2.1.3 Marine mammals 177
4.2.2.2 Acoustical properties 177
4.2.2.2.1 Fish flesh 177
4.2.2.2.2 Whale tissue 180
4.2.2.2.3 Zooplankton 180
4.2.2.3 Population estimates 180
4.2.2.3.1 Fish in the North Sea: population density and case study 180
4.2.2.3.2 Marine mammals 183
4.3 PROPERTIES OF THE SEA SURFACE 183
4.3.1 Effect of wind 183
4.3.2 Surface roughness 190
4.3.2.1 Pierson–Moskowitz spectrum 190
4.3.2.2 Neumann–Pierson spectrum 191
4.3.3 Wind-generated bubbles 193
4.4 PROPERTIES OF THE SEABED 195
4.4.1 Unconsolidated sediments 196
4.4.1.1 Pure samples and porosity 196
4.4.1.2 Mixed samples and the ‘‘phi’’ scale 197
4.4.1.3 Near-surface (high-frequency) properties 199
4.4.1.4 Bulk (medium frequency) properties 199
4.4.1.5 Low-frequency properties 201
4.4.1.5.1 Deep water 201
4.4.1.5.2 Shallow water 203
4.4.2 Rocks 204
4.4.2.1 Wave speed—density correlation equations 204
4.4.2.2 Typical parameter values 206
4.4.3 Geoacoustic models 207
4.5 REFERENCES 208
5 Underwater acoustics 215
5.1 INTRODUCTION 215
5.2 THE WAVE EQUATIONS FOR FLUID AND SOLID MEDIA 216
5.2.1 Compressional waves in a fluid medium 216
5.2.1.1 Equations of motion 216
5.2.1.2 Bulk modulus and the acoustic wave equation 217
5.2.1.3 Compressional wave speed 217
5.2.2 Compressional waves and shear waves in a solid medium 218
5.2.2.1 Shear modulus and the wave equations for a solid 218
5.2.2.2 Lame´ parameters,Young’s modulus,and Poisson’s ratio 219
5.2.2.3 Compressional and shear wave speeds 220
5.3 REFLECTION OF PLANE WAVES 221
5.3.1 Reflection from and transmission through a simple fluid–fluid or fluid–solid boundary 222
5.3.1.1 Amplitude reflection coefficient 222
5.3.1.2 Amplitude transmission coefficients 223
5.3.1.3 Energy reflection and transmission coefficients 224
5.3.2 Reflection from a layered fluid boundary 225
5.3.3 Reflection from a layered solid boundary 228
5.3.4 Reflection from a perfectly reflecting rough surface 229
5.3.4.1 Perturbation theory (small Q) 229
5.3.4.1.1 Near-grazing (kL sin2 < <
5.3.4.1.2 Non-grazing (kL sin2 > >
5.3.4.2 Heuristic extension for large Q 232
5.3.5 Reflection from a partially reflecting rough surface 232
5.4 SCATTERING OFPLA NE WAVES 233
5.4.1 Scattering cross-sections and the far field 233
5.4.2 Backscattering from solid objects 234
5.4.2.1 Small rigid object of approximately spherical shape 234
5.4.2.2 Large rigid object 236
5.4.2.3 Rigid object of arbitrary size 237
5.4.2.4 Sand grains of irregular shape and arbitrary size 238
5.4.3 Backscattering from fluid objects 238
5.4.3.1 Small fluid object of arbitrary shape 238
5.4.3.2 Large fluid object 238
5.4.3.3 Fluid object of arbitrary size 239
5.4.3.4 Gas bubble 239
5.4.3.5 Dispersed bubbles 242
5.4.3.6 Single fish (with bladder) 242
5.4.3.7 Single fish (without bladder) 245
5.4.3.8 Dispersed fish (with bladder) 246
5.4.3.9 Dispersed fish (without bladder) 247
5.4.3.10 Aggregated fish (with bladder) 247
5.4.3.11 Aggregated fish (without bladder) 247
5.4.4 Scattering from rough boundaries 247
5.4.4.1 Non-specular term 248
5.4.4.2 Near-specular term 248
5.5 DISPERSION IN THE PRESENCE OFIMP URITIES 249
5.5.1 Wood’s model for sediments in dilute suspension 249
5.5.2 Buckingham’s model for saturated sediments with intergranular contact 250
5.5.3 Effect of bubbles or bladdered fish 251
5.5.3.1 Dispersion in bubbly water 252
5.5.3.2 Bulk modulus Bb(a,w) 254
5.5.3.3 Effect of surface tension on small bubbles at low frequency 255
5.5.3.4 Bubble resonance 256
5.5.3.4.1 Polytropic index G 259
5.5.3.4.2 Resonance frequency 260
5.5.3.4.3 Resonant bubble radius 263
5.5.3.5 Damping factor 266
5.5.3.5.1 Thermal and viscous damping 266
5.5.3.5.2 Radiation and thermal damping 267
5.5.3.5.3 Total damping 267
5.5.3.5.4 Q-factors 268
5.5.3.6 Scattering,extin ction,an d absorption cross-sections 269
5.6 REFERENCES 271
6 Sonar signal processing 274
6.1 PROCESSING GAIN FOR PASSIVE SONAR 275
6.1.1 Beam patterns 275
6.1.1.1 Steered line array 275
6.1.1.1.1 Unshaded 276
6.1.1.1.2 Cosine shading (cosn) 280
6.1.1.1.3 Cosine on a pedestal (Hamming family) 281
6.1.1.1.4 Tukey shading (raised cosine spectrum) 282
6.1.1.1.5 Summary 283
6.1.1.2 Unsteered planar arrays 284
6.1.1.2.1 Piston arrays 284
6.1.1.2.2 Rectangular arrays 289
6.1.2 Directivity index 289
6.1.2.1 Steered line array 290
6.1.2.2 Unsteered planar array 293
6.1.3 Array gain 294
6.1.3.1 Definition 294
6.1.3.2 Special cases (noise gain for horizontal line array) 296
6.1.3.2.1 Noise gain for isotropic noise 296
6.1.3.2.2 Noise gain for horizontal isotropic noise 297
6.1.3.2.3 Noise gain for a uniform sheet of dipole noise sources 298
6.1.3.2.4 Noise gain for multiple point sources of noise 301
6.1.4 BB application 301
6.1.5 Time domain processing 302
6.1.5.1 Coherent averaging 302
6.1.5.2 Incoherent averaging 302
6.2 PROCESSING GAIN FOR ACTIVE SONAR 302
6.2.1 Signal carrier and envelope 303
6.2.1.1 Intuitive concept 303
6.2.1.2 Formal methodology: analytic signals and the Hilbert transform 304
6.2.2 Simple envelopes and their spectra 305
6.2.2.1 CW spectra 309
6.2.2.2 LFM spectra 310
6.2.2.2.1 Gaussian envelope 310
6.2.2.2.2 Rectangular envelope 311
6.2.2.2.3 Method of stationary phase 312
6.2.2.3 HFM spectra 314
6.2.2.3.1 Gaussian envelope 316
6.2.2.3.2 Rectangular envelope 316
6.2.2.3.3 Synthesis of HFM envelopes 317
6.2.2.4 Hybrid spectra 317
6.2.3 Autocorrelation and cross-correlation functions and the matched filter 319
6.2.3.1 Autocorrelation function 319
6.2.3.2 Cross-correlation and the matched filter 320
6.2.3.3 Doppler processing 320
6.2.4 Ambiguity function 323
6.2.4.1 CW pulse 324
6.2.4.2 LFM pulse 327
6.2.4.3 HFM pulse 328
6.2.5 Matched filter gain for perfect replica 329
6.2.6 Matched filter gain for imperfect replica (coherence loss) 330
6.2.7 Array gain and total processing gain (active sonar) 331
6.3 REFERENCES 332
7 Statistical detection theory 334
7.1 SINGLE KNOWN PULSE IN GAUSSIAN NOISE,COHERENT PROCESSING 335
7.1.1 False alarm probability for Gaussian-distributed noise 335
7.1.2 Detection probability for signal with random phase 336
7.1.2.1 Signal with non-fluctuating amplitude (Dirac distribution) 337
7.1.2.1.1 Marcum Q-function 337
7.1.2.1.2 Albersheim approximation 338
7.1.2.1.3 Limit of large SNR 339
7.1.2.2 Signal with Rayleigh fading 340
7.1.2.3 Signal with Rician fading 341
7.1.2.4 Signal with one-dominant-plus-Rayleigh distribution 345
7.1.2.5 Summary table 348
7.1.3 Detection threshold 349
7.1.4 Application to other waveforms 350
7.2 MULTIPLE KNOWN PULSES IN GAUSSIAN NOISE, INCOHERENT PROCESSING 350
7.2.1 False alarm probability for Rayleigh-distributed noise amplitude 351
7.2.2 Detection probability for incoherently processed pulse train 352
7.2.2.1 Signal with non-fluctuating amplitude 352
7.2.2.1.1 General case 352
7.2.2.1.2 Special case M = 1 356
7.2.2.1.3 Limit of large M 358
7.2.2.2 Signal with Rayleigh amplitude distribution (Swerling II) 363
7.2.2.2.1 General case 363
7.2.2.2.2 Special case M = 1 364
7.2.2.2.3 Limit of large M 364
7.2.2.3 Signal with one-dominant-plus-Rayleigh amplitude distribution (Swerling IV) 365
7.2.2.3.1 General case 365
7.2.2.3.2 Special case M = 1 365
7.2.2.3.3 Limit of large M 366
7.3 APPLICATION TO SONAR 367
7.3.1 Active sonar 367
7.3.2 Passive sonar 367
7.3.3 Decision strategies and the detection threshold 369
7.4 MULTIPLE LOOKS 371
7.4.1 Introduction 371
7.4.2 AND and OR operations 373
7.4.2.1 AND operation for Rayleigh statistics 373
7.4.2.2 OR operation for Rayleigh statistics 374
7.4.2.3 Summary table for Rayleigh statistics 375
7.4.2.4 Simulations with Rayleigh and non-Rayleigh signal statistics 375
7.4.3 Multiple OR operations 377
7.4.4 ‘‘M out of N ’’ operations 379
7.5 REFERENCES 380
Part III Towards Applications 382
8 Sources and scatterers of sound 383
8.1 REFLECTION AND SCATTERING FROM OCEAN BOUNDARIES 383
8.1.1 Reflection from the sea surface 384
8.1.1.1 Theoretical prediction for an isotropic surface wave spectrum 384
8.1.1.1.1 Coherent reflection coefficient 384
8.1.1.1.2 Pierson–Moskowitz surface wave spectrum 384
8.1.1.1.3 Neumann–Pierson surface wave spectrum 385
8.1.1.1.4 Effect of anisotropy 386
8.1.1.2 Semi-empirical surface reflection loss models 386
8.1.1.2.1 Low-frequency surface loss model 387
8.1.1.2.2 High-frequency surface loss model 389
8.1.2 Scattering from the sea surface 391
8.1.2.1 Theoretical prediction for Pierson–Moskowitz surface wave spectrum 391
8.1.2.1.1 Non-specular scattering (perturbation theory) 391
8.1.2.1.2 Near-specular scattering (facet-scattering theory) 392
8.1.2.2 Semi-empirical surface-scatteringstreng th models 393
8.1.2.2.1 Low-frequency model 393
8.1.2.2.2 High-frequency model (APL) 394
8.1.3 Reflection from the seabed 397
8.1.3.1 Theoretical prediction for uniform unconsolidated sediment 397
8.1.3.1.1 Fluid sediment 397
8.1.3.1.2 Effect of a small non-zero shear speed 401
8.1.3.2 Theoretical prediction for layered unconsolidated sediment (1–100 kHz) 402
8.1.3.3 Theoretical prediction for layered solid seabed (< 1 kHz)
8.1.4 Scattering from the seabed 413
8.1.4.1 Theoretical prediction for a fluid seabed with a rough boundary and a uniform distribution of embedded scatterers 414
8.1.4.1.1 Non-specular scattering from rough boundary (perturbation theory) 414
8.1.4.1.2 Scattering from sediment volume 415
8.1.4.1.3 Near-specular scattering (facet-scattering theory) 417
8.1.4.2 Empirical and semi-empirical seabed scatteringstre ngth models 417
8.1.4.2.1 Diffuse scattering model (empirical) 418
8.1.4.2.2 Ellis–Crowe (semi-empirical) scattering strength model 420
8.1.4.2.3 McKinney–Anderson (empirical) 421
8.2 TARGET STRENGTH, VOLUME BACKSCATTERING STRENGTH, AND VOLUME ATTENUATION COEFFICIENT 421
8.2.1 Target strength of point-like scatterers 422
8.2.1.1 Marine organisms with a gas enclosure 422
8.2.1.1.1 Bladdered fish 423
8.2.1.1.2 Marine mammals 424
8.2.1.1.3 Human divers 424
8.2.1.2 Miscellaneous marine organisms, mostly without a gas enclosure 426
8.2.1.2.1 Animals with a pronounced elongated shape 426
8.2.1.2.2 Miscellaneous animals with irregular shapes 427
8.2.1.3 Man-made objects 430
8.2.2 Volume backscattering strength and attenuation coefficient of distributed scatterers 431
8.2.2.1 Low-frequency VBS (mainly due to large fish) 431
8.2.2.2 High-frequency VBS (partly due to small fish) 433
8.2.2.3 Volume attenuation coefficient due to bubbles and bladdered fish 433
8.2.2.3.1 Bubbles 433
8.2.2.3.2 Dispersed fish with swimbladder 433
8.2.3 Column strength and wake strength of extended volume scatterers 434
8.2.3.1 Column strength and the deep scattering layer 434
8.2.3.2 Wake strength 435
8.3 SOURCES OF UNDERWATER SOUND 436
8.3.1 Shipping source spectrum level measurements 439
8.3.1.1 Conversion from far-field measurements 440
8.3.1.2 Industrial and commercial shipping(indi vidual ships) 442
8.3.1.3 Commercial shipping(averag ed source spectra) 443
8.3.1.4 Effect of ship speed and acceleration 445
8.3.2 Distributed sources on the sea surface 446
8.3.2.1 Wind noise source level 446
8.3.2.1.1 High-frequency wind noise (APL model) 446
8.3.2.1.2 Low-frequency wind noise (Kuperman–Ferla measurements) 447
8.3.2.1.3 Proposed composite wind noise model 448
8.3.2.2 Rain noise source level 448
8.3.2.3 Shippingnoise source level 449
8.3.2.3.1 Monopole density 450
8.3.2.3.2 Dipole density 450
8.3.3 Distributed sources on the seabed (crustacea) 451
8.3.3.1 Snappingshri mp 451
8.3.3.2 Other crustaceans 452
8.4 REFERENCES 453
9 Propagation of underwater sound 461
9.1 PROPAGATION LOSS 462
9.1.1 Effect of the seabed in isovelocity water 462
9.1.1.1 Deep water 462
9.1.1.1.1 Lloyd mirror 465
9.1.1.1.2 Bottom-reflected paths 465
9.1.1.1.3 Bottom-refracted paths 467
9.1.1.2 Shallow water 471
9.1.1.2.1 Multipath propagation 474
9.1.1.2.2 Spherical and cylindrical spreading regions 474
9.1.1.2.3 Mode-stripping region 475
9.1.1.2.4 Single-mode region 479
9.1.1.2.5 Cut-off frequency 480
9.1.1.2.6 Depth dependence 480
9.1.2 Effect of a sound speed profile 481
9.1.2.1 Deep water 481
9.1.2.1.1 Examples for the northwest Pacific Ocean 484
9.1.2.1.2 Surface duct (upward refraction) 484
9.1.2.1.3 Convergence zones 496
9.1.2.1.4 Lloyd mirror with downward refraction 496
9.1.2.2 Shallow water 500
9.1.2.2.1 Surface–bottom multipaths (‘‘V-duct’’) 500
9.1.2.2.2 Surface or bottom duct propagation (‘‘U-duct’’) 505
9.1.2.2.3 Total (VD+UD) 505
9.2 NOISE LEVEL 505
9.2.1 Deep water 506
9.2.1.1 Typical spectra for wind, shipping, and thermal noise 506
9.2.1.1.1 Shipping noise 507
9.2.1.1.2 Thermal noise 507
9.2.1.2 Effect of rain rate and wind speed 507
9.2.1.3 Depth dependence of surface-generated noise 510
9.2.2 Shallow water 511
9.2.3 Noise maps 512
9.3 SIGNAL LEVEL (ACTIVE SONAR) 513
9.3.1 The reciprocity principle 514
9.3.2 Calculation of echo level 515
9.3.3 V-duct propagation (isovelocity case) 516
9.3.4 U-duct propagation (linear profile) 516
9.4 REVERBERATION LEVEL 517
9.4.1 Isovelocity water 519
9.4.1.1 General power law scattering coefficient 519
9.4.1.2 Application to a reference problem with Lambert’s rule (RMW11) 520
9.4.2 Effect of refraction 522
9.4.2.1 V-duct propagation 522
9.4.2.2 U-duct propagation 523
9.4.2.3 Application to a reference problem with Lambert’s rule (RMW12) 525
9.5 SIGNAL-TO-REVERBERATION RATIO (ACTIVE SONAR) 530
9.5.1 V-duct (isovelocity case) 530
9.5.2 U-duct (linear profile) 531
9.6 REFERENCES 532
10 Transmitter and receiver characteristics 535
10.1 TRANSMITTER CHARACTERISTICS 536
10.1.1 Of man-made systems 537
10.1.1.1 Continuous sources 537
10.1.1.1.1 Single-beam echo sounders 537
10.1.1.1.2 Sidescan sonar 537
10.1.1.1.3 Multibeam echo sounders 538
10.1.1.1.4 Sub-bottom profilers 538
10.1.1.1.5 Fisheries sonar 541
10.1.1.1.6 Military search sonar 541
10.1.1.1.7 Minesweeping sonar 542
10.1.1.1.8 Acoustic deterrent devices 545
10.1.1.1.9 Underwater communications systems and transponders 545
10.1.1.1.10 High-frequency imaging sonar 545
10.1.1.1.11 Research instruments (global oceanography) 545
10.1.1.2 Impulsive sources 547
10.1.1.2.1 General characteristics 547
10.1.1.2.2 Seismic survey sources 556
10.1.1.2.3 Explosives 560
10.1.2 Of marine mammals 564
10.1.2.1 Continuous vocalizations 564
10.1.2.2 Impulsive sources 564
10.2 RECEIVER CHARACTERISTICS 567
10.2.1 Of man-made sonar 567
10.2.1.1 Hydrophone sensitivity and non-acoustic noise 567
10.2.1.1.1 Sensitivity 567
10.2.1.1.2 Molecular thermal noise 571
10.2.1.1.3 Flow noise 571
10.2.1.2 Array directivity 571
10.2.2 Of marine mammals, amphibians, human divers, and fish 571
10.2.2.1 The intensity of underwater sound: typical orders of magnitude 572
10.2.2.2 Measured audiograms 573
10.2.2.2.1 Of cetaceans 573
10.2.2.2.2 Of pinnipeds (seals, sea lions, and walruses) 573
10.2.2.2.3 Of sirenians 576
10.2.2.2.4 Of human divers 576
10.2.2.2.5 Of fish 577
10.2.2.3 Discrimination against background noise 579
10.2.2.3.1 Critical bandwidth 579
10.2.2.3.2 Critical ratio 580
10.2.2.4 Hearingimpairm ent and behavioral effects 580
10.2.2.4.1 Sound exposure thresholds for hearing impairment to mammals and fish 582
10.2.2.4.2 Peak sound pressure thresholds for hearing impairment to mammals and fish 585
10.2.2.4.3 Thresholds for behavioral effects 585
10.3 REFERENCES 587
11 The sonar equations revisited 594
11.1 INTRODUCTION 594
11.2 PASSIVE SONAR WITH COHERENT PROCESSING: TONAL DETECTOR 595
11.2.1 Sonar equation 595
11.2.2 Source level (SL) 596
11.2.3 Narrowband propagation loss (PL) 597
11.2.4 Noise spectrum level (NLf ) 599
11.2.4.1 Background noise 599
11.2.4.2 Foreground noise 599
11.2.4.3 Non-acoustic noise 599
11.2.4.4 Self-noise and ambient noise 600
11.2.4.4.1 Self-noise, including platform noise 600
11.2.4.4.2 Ambient noise 600
11.2.5 Bandwidth (BW) 600
11.2.6 Array gain (AG) and directivity index (DI) 601
11.2.7 Detection threshold (DT) 602
11.2.7.1 Calculation of DT for given pfa 602
11.2.7.2 Estimation of pfa 603
11.2.8 Worked example 604
11.2.8.1 Propagation loss and signal excess 604
11.2.8.2 What is the detection range? 606
11.2.8.3 Alternative performance measures 608
11.2.8.3.1 Detection volume (radius of equivalent volume sphere) 608
11.2.8.3.2 Detection area (radius of equivalent area circle) 611
11.3 PASSIVE SONAR WITH INCOHERENT PROCESSING: ENERGY DETECTOR 612
11.3.1 Sonar equation 612
11.3.2 Source level (SL) 613
11.3.3 Broadband propagation loss (PL) 613
11.3.4 Broadband noise level (NL) 614
11.3.5 Processing gain (PG) 614
11.3.5.1 Array gain (AG) and directivity index (DI) 615
11.3.5.2 Filter gain (FG) 615
11.3.5.2.1 Filter gain for a white signal spectrum 616
11.3.5.2.2 Filter gain for a colored signal spectrum 617
11.3.6 Broadband detection threshold (DT) 618
11.3.6.1 Calculation of DT for given pfa 618
11.3.6.2 Estimation of false alarm probability 619
11.3.7 Worked example 620
11.3.7.1 Propagation loss 620
11.3.7.2 Signal-to-noise ratio 620
11.3.7.3 Detection threshold and signal excess 623
11.3.7.4 Effect of filter gain 626
11.3.7.5 Effect of rainfall 626
11.4 ACTIVE SONAR WITH COHERENT PROCESSING: MATCHED FILTER 627
11.4.1 Sonar equation 627
11.4.2 Echo level (EL), target strength (TS), and equivalent target strength (TSeq) 628
11.4.2.1 Outward propagation loss (PLTx) and sonar source level (SL) 629
11.4.2.2 Return propagation loss (PLRx) 629
11.4.2.3 Special case: separable target cross-section 630
11.4.3 Background level (BL) 631
11.4.4 Processing gain (PG) 631
11.4.4.1 Array gain (AG) and directivity index (DI) 632
11.4.4.2 Matched filter gain (MG) 633
11.4.5 Detection threshold (DT) 633
11.4.5.1 Calculation of DT from pfa 633
11.4.5.2 Estimation of pfa 633
11.4.6 Worked example 634
11.4.6.1 Part (i) maximum audibility range (no background) 636
11.4.6.1.1 Echo level (EL) 636
11.4.6.1.2 Hearing threshold (HT) 640
11.4.6.1.3 Maximum audibility range 640
11.4.6.2 Part (ii) detection range for low wind speed (noise-limited) 642
11.4.6.2.1 Noise level (NL) 642
11.4.6.2.2 Array gain (AG) 643
11.4.6.2.3 Detection threshold (DT) 644
11.4.6.2.4 Signal excess (SE) and detection range 644
11.4.6.3 Part (iii) detection range for high wind speed (noise-limited) 644
11.4.6.4 Part (iv) effect of reverberation (for high wind speed) 645
11.4.6.4.1 Background level (BL) 646
11.4.6.4.2 Processing gain (PG) 649
11.4.6.4.3 Signal excess and detection range 650
11.5 THE FUTURE OF SONAR PERFORMANCE MODELING 651
11.5.1 Advances in signal processing and oceanographic modeling 651
11.5.2 Autonomous platforms 652
11.5.3 Environmental impact of anthropogenic sound 652
11.6 REFERENCES 653
Appendix A Special functions and mathematical operations 655
A.1 DEFINITIONS AND BASIC PROPERTIES OF SPECIAL FUNCTIONS 655
A.1.1 Heaviside step function, sign function, and rectangle function 655
A.1.2 Sine cardinal and sinh cardinal functions 656
A.1.3 Dirac delta function 656
A.1.4 Fresnel integrals 656
A.1.5 Error function, complementary error function, and right-tail probability function 657
A.1.6 Exponential integrals and related functions 659
A.1.6.1 Definition of the exponential integral 659
A.1.6.2 Exponential integral of first order (imaginary argument) 659
A.1.6.3 Exponential integral of third order (real argument) 659
A.1.6.4 Sine and cosine integral functions 660
A.1.7 Gamma function and incomplete gamma functions 660
A.1.7.1 Gamma function 660
A.1.7.1.1 Definition and important values 660
A.1.7.1.2 Approximations 661
A.1.7.1.3 Use of the gamma function 662
A.1.7.2 Incomplete gamma functions 662
A.1.8 Marcum Q functions 664
A.1.9 Elliptic integrals 664
A.1.10 Bessel and related functions 665
A.1.10.1 Bessel function of the first kind 665
A.1.10.2 Modified Bessel function 666
A.1.10.3 Airy functions 668
A.1.11 Hypergeometric functions 668
A.1.11.1 Gauss’s hypergeometricfunc tion 668
A.1.11.2 Confluent hypergeometricfunc tion of the first kind 669
A.2 FOURIER TRANSFORMS AND RELATED INTEGRALS 669
A.2.1 Forward and inverse Fourier transforms 669
A.2.2 Cross-correlation 670
A.2.3 Convolution 671
A.2.4 Discrete Fourier transform 671
A.2.5 Plancherel’s theorem 672
A.3 STATIONARY PHASE METHOD FOR EVALUATION OF INTEGRALS 672
A.3.1 Stationary phase approximation 672
A.3.2 Derivation 673
A.4 SOLUTION TO QUADRATIC, CUBIC, AND QUARTIC EQUATIONS 675
A.4.1 Quadratic equation 675
A.4.2 Cubic equation 675
A.4.3 Quartic and higher order equations 676
A.5 REFERENCES 676
Appendix B Units and nomenclature 678
B.1 UNITS 678
B.1.1 SI units 678
B.1.2 Non-SI units 678
B.1.3 Logarithmic units 678
B.1.3.1 Base-10 logarithmic units 679
B.1.3.1.1 Bel and decibel 679
B.1.3.1.2 pH (acidity measure) 683
B.1.3.1.3 Decade 683
B.1.3.2 Base-e logarithmic unit (neper) 684
B.1.3.3 Base-2 logarithmic units 684
B.1.3.3.1 Octave 684
B.1.3.3.2 Phi 684
B.2 NOMENCLATURE 684
B.2.1 Notation 684
B.2.2 Abbreviations and acronyms 685
B.2.3 Names of fish and marine mammals 685
B.3 REFERENCES 690
Appendix C Fish and their swimbladders 692
C.1 TABLES OF FISH AND BLADDER TYPES 692
C.2 REFERENCES 713
Index 714

Produkt-Details

• Erscheint lt. Verlag: 14.9.2010
• Reihe/Serie: Geophysical Sciences
• Reihe/Serie: Geophysical Sciences
• Reihe/Serie: Springer Praxis Books
• Reihe/Serie: Springer Praxis Books
• Zusatzinfo: XXVIII, 707 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: acoustics • Modeling • Modelling • ocean • Oceanography • Sonar • Sound • Sound navigation • underwater acoustics
• ISBN-10: 3-540-87662-6 / 3540876626
• ISBN-13: 978-3-540-87662-5 / 9783540876625