Underwater Acoustics: Analysis, Design and Performance of Sonar

UNDERWATER
ACOUSTICS......Page 5
Contents......Page 7
About the Author......Page 15
Preface......Page 17
Acknowledgements......Page 19
1.1 Acoustic Waves......Page 21
1.1.1 Compressions and Rarefactions......Page 23
1.2 Speed of Propagation......Page 24
1.3 Acoustic Wave Parameters......Page 25
1.4 Doppler Shift......Page 29
1.5 Intensity, SPL, and Decibels......Page 30
1.6 Combining Acoustic Waves......Page 31
1.7 Comparative Parameter for Sound in Water and Air......Page 34
References......Page 35
2.1 Signal-to-Noise Ratio......Page 37
2.2 Active Sonar Equation......Page 38
2.4 Figure of Merit......Page 40
References......Page 41
3 Transducers, Directionality, and Arrays......Page 43
3.2 Beam Pattern Response......Page 45
3.3 Linear Arrays......Page 47
3.4 Rectangular Planar Array......Page 53
3.6 Continuous Arrays......Page 57
3.7 Volumetric Arrays......Page 61
3.8 Product Theorem......Page 64
3.10 Directivity and Array Gain......Page 65
3.11 Noise Cross-Correlation between Hydrophones......Page 67
3.12 Directivity of Line Arrays......Page 69
3.13 Directivity of Area Arrays......Page 71
3.14 Directivity of Volumetric Arrays......Page 72
3.15 Difference Arrays......Page 74
3.16 Multiplicative Arrays......Page 77
3.17 Sparsely Populated Arrays......Page 79
3.18 Adaptive Beamforming......Page 80
References......Page 82
4.1 Source Level......Page 83
4.2 Cavitation......Page 84
4.4 Explosive Sources......Page 87
4.5 Physics of Shock Waves in Water......Page 88
4.6 Bubble Pulses......Page 92
4.8 Parametric Acoustic Sources......Page 93
References......Page 94
5 Transmission Loss......Page 95
5.1 Sound Speed Profile in the Sea......Page 96
5.2 Snell’s Law and Transmission across an Interface......Page 97
5.3 Reflection and Transmission Coefficients......Page 99
5.4 Transmission through a Plate......Page 102
5.5 Ray Tracing......Page 104
5.6 Spreading Loss......Page 111
5.7.1 Mechanisms of Absorption......Page 112
References......Page 115
6.1 Sea State, Wind Speed, and Wave Height......Page 117
6.2 Pierson–Moskowitz Model for Fully Developed Seas......Page 119
6.3.1 Lloyd Mirror Interference......Page 121
6.3.2 Loss Due to Interaction with the Surface......Page 124
6.4 Bottom Loss......Page 132
6.4.3 Low-Frequency Bottom Loss (LFBL) Model: 50 to 1000 Hz......Page 133
6.4.4 High-Frequency Bottom Loss (HFBL) Model......Page 134
6.5 Leakage Out of a Duct, Low-Frequency Cutoff......Page 137
6.6.1 Ray Models......Page 140
6.6.2 Normal Modes......Page 141
6.6.3 Parabolic Equations......Page 142
6.6.4 U.S. Navy Standard Models......Page 143
References......Page 145
7.1 Ambient Noise Models......Page 147
7.2 Seismic Noise......Page 148
7.3 Ocean Turbulence......Page 150
7.7 Rain Noise......Page 151
7.10 Directionality of Noise......Page 153
7.11 Under Ice Noise......Page 157
7.12 Spatial Coherence of Ambient Noise......Page 158
References......Page 160
8.1.1 Surface and Bottom Scattering......Page 163
8.1.3 Bottom Scattering......Page 172
8.1.4 Reverberation Target Strength......Page 173
8.1.5 Calculation of Reverberation for Use in the Sonar Equation......Page 174
8.1.6 Volume Reverberation Level......Page 176
8.2 Reverberation Frequency Spread and Doppler Gain Potential......Page 177
8.2.1 Power Spectral Density of a CW Pulse......Page 179
8.2.3 Frequency Spreading Due to Transmitter and Receiver Motion......Page 181
8.2.4 Frequency Spreading Due to Target......Page 182
References......Page 184
9.1 Target Strength Definition......Page 187
9.2 Active Target Strength of a Large Sphere......Page 189
9.3 Active Target Strength of a Very Small Sphere......Page 190
9.5 Target Strength of Submarines......Page 193
9.6 The TAP Model......Page 194
9.8 Target Strength of Mines and Torpedoes......Page 196
9.9 Target Strength of Fish......Page 198
References......Page 201
10.1 General Characteristics of Ship Radiated Noise......Page 203
10.2 Propeller Radiated Noise......Page 204
10.3 Machinery Noise......Page 206
10.5 Hydrodynamic Noise......Page 207
10.7 Total Radiated Noise......Page 209
Reference......Page 212
11.1 Flow Noise......Page 213
11.2 Turbulent Noise Coherence......Page 218
References......Page 219
12.1 Introduction......Page 221
12.2 Case 1: Signal Is Known Exactly......Page 225
12.3 Case 2: Signal Is White Gaussian Noise......Page 230
12.3.1 Observations on Case 2......Page 233
References......Page 234
13 Methodology for Calculation of the Recognition Differential......Page 235
13.1 Continuous Broadband Signals (PBB)......Page 236
13.1.2 PBB Step 2: Correction for Noise Spectrum......Page 237
13.1.3 PBB Step 3: Correction for Processor Implementation......Page 240
13.1.4 PBB Step 4: Correction for Nonideal Signal Characteristics......Page 246
13.2 Continuous Narrowband Signals (PNB)......Page 247
13.2.1 PNB Step 1: Theoretical Narrowband Nrd......Page 249
13.2.2 PNB Step 2: Correction for Noise Spectrum......Page 250
13.2.3 PNB Step 3: Correction for Processor Implementation......Page 253
13.2.4 PNB Step 4: Correction for Nonideal Signal Characteristics (Signal Is Not a Perfect Sine Wave)......Page 259
13.2.5 PNB Step 5: Adjustment for Additional At-Sea Losses......Page 260
13.3 Active Sonar......Page 261
13.3.1 CW Active Pulse Active Step 1: Theoretical Nrd......Page 262
13.3.2 Active Step 2: Correction for Noise Spectrum......Page 273
13.3.3 Active Step 3: Correction for Processor Implementation......Page 275
13.3.5 Active Step 5: Adjustment for Additional At-Sea Losses......Page 277
13.4 Aural Detection......Page 278
13.5 Display Nomenclature......Page 281
References......Page 284
14.1 Sea Story......Page 285
14.3.1 Hypothesis Testing......Page 286
14.3.2 Probability Density Function......Page 287
14.3.3 Detection of Constant Level......Page 288
14.4 False Alarm Probability Calculation......Page 289
14.6 False Targets......Page 291
References......Page 292
15 Variability and Uncertainty......Page 293
15.2 Sources of Variability......Page 296
References......Page 301
16.1 Figure of Merit Range or R50 %......Page 303
16.2 Tactical Decision Aids......Page 307
References......Page 309
17.2 Discrete Glimpse and Continuous Looking......Page 311
17.3 Lambda–Sigma Jump Model......Page 312
17.5 What Are Appropriate Random Parameters?......Page 313
17.6 Approximation Method for Computation of the Cumulative Probability of Detection (CPD)......Page 316
References......Page 318
18.1.1 Amplitude Difference Method......Page 319
18.1.2 Phase Difference Method or Cross-Correlation Method......Page 320
18.2 General Principle of Tracking and Bearing Measurement......Page 321
18.3 Other Sources of Bearing Error for Area Arrays......Page 323
18.4 Additional Sources of Errors for Line Arrays......Page 325
18.6 Manual versus Automatic Tracking......Page 326
18.7.1 Localization......Page 327
18.7.2 Wave Front Curvature Ranging (WFCR)......Page 332
18.7.3 Multipath Ranging (MPR)......Page 334
18.7.5 Triangulation Ranging......Page 337
18.9 Four-Bearing TMA......Page 339
18.10 Ekelund Ranging......Page 341
18.11 Range and Bearing TMA......Page 342
18.12 Other Bearings Only TMA Methodologies......Page 343
References......Page 344
19.1 Choice of Frequency and Size......Page 345
19.2 Computational Requirements......Page 347
19.2.1 Beamforming......Page 348
19.3.1 Detection......Page 349
19.4 Active Pulse Choice......Page 350
19.5 Monostatic, Bistatic, and Multistatic Active Sonars......Page 352
19.7 Mine Hunting and Bottom Survey Sonars......Page 354
19.8 Echo Sounding and Fishing Sonars......Page 355
19.12 Communications......Page 356
References......Page 357
A.1 Definitions......Page 359
A.2 Parseval’s Theorem and Plancherel’s Theorem......Page 360
A.4 Localization or Uncertainty Property......Page 361
B Analysis of Errors Associated with a Least Squares Methodology......Page 363
Reference......Page 366
Index......Page 367