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Underwater Acoustics
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Table of Contents

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

About the Author

RICHARD P. HODGES has forty years experience in sonar, operations analysis, modeling, and the simulation of military systems. He is currently working for Sonalysts, Inc as a principal analyst, and is a member of the Acoustic Society of America. He has taught courses at the Naval Underwater Warfare Center (NUWC) and elsewhere in naval analysis of sonar, acoustics, TMA, tactics, weapons, damage and kill mechanisms, C4I, non-acoustic sensors, platform dynamics weapons, tactics and on the use of NUWC's SIM II Naval Engagement Simulation.

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