Underwater Acoustics: Analysis, Design and Performance of Sonar

About the Author xiii

Preface xv

Acknowledgements xvii

1 Introduction to Sonar 1

1.1 Acoustic Waves 1

1.1.1 Compressions and Rarefactions 3

1.2 Speed of Propagation 4

1.3 Acoustic Wave Parameters 5

1.4 Doppler Shift 9

1.5 Intensity, SPL, and Decibels 10

1.6 Combining Acoustic Waves 11

1.7 Comparative Parameter for Sound in Water and Air 14

References 15

2 The Sonar Equations 17

2.1 Signal-to-Noise Ratio 17

2.2 Active Sonar Equation 18

2.3 Signal Excess 20

2.4 Figure of Merit 20

References 21

3 Transducers, Directionality, and Arrays 23

3.1 Transducer Response 25

3.2 Beam Pattern Response 25

3.3 Linear Arrays 27

3.3.1 Triplet Towed Array 33

3.3.2 Multiline Towed Arrays 33

3.4 Rectangular Planar Array 33

3.5 Amplitude Shading 37

3.6 Continuous Arrays 37

3.7 Volumetric Arrays 41

3.8 Product Theorem 44

3.9 Broadband Beam Patterns 45

3.10 Directivity and Array Gain 45

3.11 Noise Cross-Correlation between Hydrophones 47

3.12 Directivity of Line Arrays 49

3.13 Directivity of Area Arrays 51

3.14 Directivity of Volumetric Arrays 52

3.15 Difference Arrays 54

3.16 Multiplicative Arrays 57

3.17 Sparsely Populated Arrays 59

3.18 Adaptive Beamforming 60

References 62

4 Active Sonar Sources 63

4.1 Source Level 63

4.2 Cavitation 64

4.3 Near-Field Interactions 67

4.4 Explosive Sources 67

4.5 Physics of Shock Waves in Water 68

4.6 Bubble Pulses 72

4.7 Pros and Cons of Explosive Charges 73

4.8 Parametric Acoustic Sources 73

References 74

5 Transmission Loss 75

5.1 Sound Speed Profile in the Sea 76

5.2 Snell’s Law and Transmission across an Interface 77

5.3 Reflection and Transmission Coefficients 79

5.4 Transmission through a Plate 82

5.5 Ray Tracing 84

5.6 Spreading Loss 91

5.7 Absorption of Sound in the Ocean 92

5.7.1 Mechanisms of Absorption 92

References 95

6 Transmission Loss: Interaction with Boundaries 97

6.1 Sea State, Wind Speed, and Wave Height 97

6.2 Pierson–Moskowitz Model for Fully Developed Seas 99

6.3 Sea Surface Interaction 101

6.3.1 Lloyd Mirror Interference 101

6.3.2 Loss Due to Interaction with the Surface 104

6.4 Bottom Loss 112

6.4.1 Simple Rayleigh Bottom Loss Model 113

6.4.2 U.S. Navy OAML Approved Models of Bottom Loss 113

6.4.3 Low-Frequency Bottom Loss (LFBL) Model: 50 to 1000 Hz 113

6.4.4 High-Frequency Bottom Loss (HFBL) Model 114

6.4.5 High-Frequency Environment Acoustic (HFEVA) Model 117

6.5 Leakage Out of a Duct, Low-Frequency Cutoff 117

6.6 Propagation Loss Model Descriptions 120

6.6.1 Ray Models 120

6.6.2 Normal Modes 121

6.6.3 Parabolic Equations 122

6.6.4 U.S. Navy Standard Models 123

References 125

7 Ambient Noise 127

7.1 Ambient Noise Models 127

7.2 Seismic Noise 128

7.3 Ocean Turbulence 130

7.4 Shipping Noise 131

7.5 Wave Noise 131

7.6 Thermal Noise 131

7.7 Rain Noise 131

7.8 Temporal Variability of Ambient Noise 133

7.9 Depth Effects on Noise 133

7.10 Directionality of Noise 133

7.11 Under Ice Noise 137

7.12 Spatial Coherence of Ambient Noise 138

References 140

8 Reverberation 143

8.1 Scattering, Backscattering Strength, and Target Strength 143

8.1.1 Surface and Bottom Scattering 143

8.1.2 Volume Scattering 152

8.1.3 Bottom Scattering 152

8.1.4 Reverberation Target Strength 153

8.1.5 Calculation of Reverberation for Use in the Sonar Equation 154

8.1.6 Volume Reverberation Level 156

8.2 Reverberation Frequency Spread and Doppler Gain Potential 157

8.2.1 Power Spectral Density of a CW Pulse 159

8.2.2 Environmental Frequency Spreading 161

8.2.3 Frequency Spreading Due to Transmitter and Receiver Motion 161

8.2.4 Frequency Spreading Due to Target 162

8.3 Important Observation with Respect to Reverberation 164

References 164

9 Active Target Strength 167

9.1 Target Strength Definition 167

9.2 Active Target Strength of a Large Sphere 169

9.3 Active Target Strength of a Very Small Sphere 170

9.4 Target Strengths of Simple Geometric Forms 173

9.5 Target Strength of Submarines 173

9.6 The TAP Model 174

9.7 Target Strength of Surface Ships 176

9.8 Target Strength of Mines and Torpedoes 176

9.9 Target Strength of Fish 178

References 181

10 Radiated Noise 183

10.1 General Characteristics of Ship Radiated Noise 183

10.2 Propeller Radiated Noise 184

10.3 Machinery Noise 186

10.4 Resonance Noise 187

10.5 Hydrodynamic Noise 187

10.6 Platform Quieting 189

10.7 Total Radiated Noise 189

Reference 192

11 Self Noise 193

11.1 Flow Noise 193

11.2 Turbulent Noise Coherence 198

11.3 Strumming Noise 199

References 199

12 Statistical Detection Theory 201

12.1 Introduction 201

12.2 Case 1: Signal Is Known Exactly 205

12.2.1 Observations on Case 1 210

12.3 Case 2: Signal Is White Gaussian Noise 210

12.3.1 Observations on Case 2 213

References 214

13 Methodology for Calculation of the Recognition Differential 215

13.1 Continuous Broadband Signals (PBB) 216

13.1.1 PBB Step 1: Theoretical Broadband Nrd 217

13.1.2 PBB Step 2: Correction for Noise Spectrum 217

13.1.3 PBB Step 3: Correction for Processor Implementation 220

13.1.4 PBB Step 4: Correction for Nonideal Signal Characteristics 226

13.1.5 PBB Step 5: Adjustment for Additional At-Sea Losses 227

13.2 Continuous Narrowband Signals (PNB) 227

13.2.1 PNB Step 1: Theoretical Narrowband Nrd 229

13.2.2 PNB Step 2: Correction for Noise Spectrum 230

13.2.3 PNB Step 3: Correction for Processor Implementation 233

13.2.4 PNB Step 4: Correction for Nonideal Signal Characteristics (Signal Is Not a Perfect Sine Wave) 239

13.2.5 PNB Step 5: Adjustment for Additional At-Sea Losses 240

13.2.6 Nrd Calculation Example 241

13.3 Active Sonar 241

13.3.1 CW Active Pulse Active Step 1: Theoretical Nrd 242

13.3.2 Active Step 2: Correction for Noise Spectrum 253

13.3.3 Active Step 3: Correction for Processor Implementation 255

13.3.4 Active Step 4: Correction for Nonideal Signal Characteristics 257

13.3.5 Active Step 5: Adjustment for Additional At-Sea Losses 257

13.3.6 Nrd Calculation Examples 258

13.4 Aural Detection 258

13.5 Display Nomenclature 261

References 264

14 False Alarms, False Contacts, and False Targets 265

14.1 Sea Story 265

14.2 Failure to Detect 266

14.3 Detection Theory 266

14.3.1 Hypothesis Testing 266

14.3.2 Probability Density Function 267

14.3.3 Detection of Constant Level 268

14.4 False Alarm Probability Calculation 269

14.5 False/Nonthreat Contacts 271

14.6 False Targets 271

14.7 Summary and Conclusions 272

References 272

15 Variability and Uncertainty 273

15.1 Random Variability of a Sonar 276

15.2 Sources of Variability 276

References 281

16 Modeling Detection and Tactical Decision Aids 283

16.1 Figure of Merit Range or R50 % 283

16.2 Tactical Decision Aids 287

References 289

17 Cumulative Probability of Detection 291

17.1 Why is CPD Important? 291

17.2 Discrete Glimpse and Continuous Looking 291

17.3 Lambda–Sigma Jump Model 292

17.4 Nonjump Processes 293

17.5 What Are Appropriate Random Parameters? 293

17.6 Approximation Method for Computation of the Cumulative Probability of Detection (CPD) 296

References 298

18 Tracking, Target Motion Analysis, and Localization 299

18.1 Bearing Trackers 299

18.1.1 Amplitude Difference Method 299

18.1.2 Phase Difference Method or Cross-Correlation Method 300

18.2 General Principle of Tracking and Bearing Measurement 301

18.3 Other Sources of Bearing Error for Area Arrays 303

18.4 Additional Sources of Errors for Line Arrays 305

18.5 Bottom Bounce 306

18.6 Manual versus Automatic Tracking 306

18.7 Localization and Target Motion Analysis 307

18.7.1 Localization 307

18.7.2 Wave Front Curvature Ranging (WFCR) 312

18.7.3 Multipath Ranging (MPR) 314

18.7.4 Depression/Elevation (D/E) Ranging 317

18.7.5 Triangulation Ranging 317

18.8 Bearings Only Methodologies 319

18.9 Four-Bearing TMA 319

18.10 Ekelund Ranging 321

18.11 Range and Bearing TMA 322

18.12 Other Bearings Only TMA Methodologies 323

18.13 Other TMA and Localization Schemes 324

References 324

19 Design and Evaluation of Sonars 325

19.1 Choice of Frequency and Size 325

19.2 Computational Requirements 327

19.2.1 Beamforming 328

19.3 Signal Processing after Beamformer 329

19.3.1 Detection 329

19.4 Active Pulse Choice 330

19.5 Monostatic, Bistatic, and Multistatic Active Sonars 332

19.6 Ambiguity Functions 334

19.7 Mine Hunting and Bottom Survey Sonars 334

19.8 Echo Sounding and Fishing Sonars 335

19.9 Navigation 336

19.10 Vehicle Location and At-Sea Rescue 336

19.11 Intercept Receivers 336

19.12 Communications 336

19.13 Marine Mammals and Active Sonar 337

References 337

A Fourier Transforms 339

A.1 Definitions 339

A.2 Parseval’s Theorem and Plancherel’s Theorem 340

A.3 Properties of Fourier Transforms 341

A.4 Localization or Uncertainty Property 341

B Analysis of Errors Associated with a Least Squares Methodology 343

Reference 346

Index 347