UNDERWATER ACOUSTIC MODELING and SIMULATION

Paul C. Etter

CRC Press Taylor & Francis Croup Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Croup, an informa business Contents

Preface xv Preface to the Third Edition xvii

Preface to the Second Edition xix

Preface to the First Edition xxi Acknowledgments xxiii

Author xxv

Chapter 1 Introduction 1 1.1 Background 1 1.1.1 Setting 1 1.1.2 Framework 2 1.2 Measurements and Prediction 4 1.3 Developments in Modeling 8 1.4 Advances in Simulation 10 1.5 Operational Challenges 11 1.5.1 Naval Operations 12 1.5.2 Offshore Industries 14 1.5.3 Operational Oceanography 16 1.6 Inverse Acoustic Sensing of the Oceans 16 1.7 Standard Definitions 19

Chapter 2 Acoustical Oceanography 21

2.1 Background 21 2.2 Physical and Chemical Properties 21 2.2.1 Temperature Distribution 23 2.2.2 Salinity Distribution 23 2.2.3 Water Masses... 25 2.3 Sound Speed 27 2.3.1 Calculation and Measurements 27 2.3.2 Sound-Speed Distribution 30 2.4 Boundaries 35 2.4.1 Sea Surface 35 2.4.2 Ice Cover 41 2.4.3 Sea Floor 42 2.5 Dynamic Features 45 2.5.1 Large-Scale Features 45 2.5.2 Mesoscale Features 46 2.5.2.1 Fronts and Eddies 47 2.5.2.2 Internal Waves 54

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2.5.3 Fine-Scale Features 56 2.5.3.1 Thermohaline Staircases 56 2.5.3.2 Langmuir Circulation 58 2.6 Biologies 60

Chapter 3 Propagation I: Observations and Physical Models 61

3.1 Background 61 3.2 Nature of Measurements 62 3.3 Basic Concepts 63 3.4 Sea-Surface Boundary 69 3.4.1 Forward Scattering and Reflection Loss 69 3.4.2 Image Interference and Frequency Effects 70 3.4.3 Turbidity and Bubbles 72 3.4.3.1 Open Ocean 72 3.4.3.2 Coastal Ocean 73 3.4.4 Ice Interaction 74 3.4.5 Measurements 75 3.5 Sea-Floor Boundary 76 3.5.1 Forward Scattering and Reflection Loss 77 3.5.1.1 Acoustic Interaction with the Sea Floor 77 3.5.1.2 Boundary Conditions and Modeling 77 3.5.1.3 Geoacoustic Models 79 3.5.2 Interference and Frequency Effects 81 3.5.3 Attenuation by Sediments 81 3.5.4 Measurements 82 3.6 Attenuation and Absorption in Sea Water 83 3.7 Surface Ducts 86 3.7.1 Mixed-Layer Distribution 86 3.7.2 General Propagation Features 90 3.7.3 Low-Frequency Cutoff 95 3.8 Deep Sound Channel 96 3.9 Convergence Zones 97 3.10 Reliable Acoustic Path 98 3.11 Shallow-Water Ducts 98 3.12 Arctic Half-Channel 100 3.13 Coherence 102

Chapter 4 Propagation II: Mathematical Models (Part One) 103

4.1 Background 103 4.2 Theoretical Basis for Propagation Modeling 104 4.2.1 Wave Equation 104 4.2.2 Classification of Modeling Techniques 106 4.3 Ray-Theory Models 107 4.3.1 Basic Theory 107 4.3.2 Caustics 110 Contents *

4.3.3 Gaussian Beam Tracing Ill 4.3.4 Range Dependence 111 4.3.5 Arrival Structure 114 4.3.6 Beam Displacement 115 4.3.7 Waveguide Invariant 117 4.3.8 Energy-Flux Models 118 4.3.9 Advanced Algorithms 119 4.4 Normal-Mode Models 120 4.4.1 Basic Theory 120 4.4.2 Normal-Mode Solution 121 4.4.3 Dispersion Effects 123 4.4.4 Experimental Measurements 123 4.4.5 Range Dependence 124 4.4.6 High-Frequency Adaptations 126 4.4.7 Wedge Modes 127 4.5 Multipath Expansion Models 127 4.6 Fast-Field Models 129 4.7 Parabolic Equation Models 130 4.7.1 Basic Theory 130 4.7.2 Numerical Techniques.... 134 4.7.3 Wide-Angle and 3D Adaptations 136 4.7.4 Range-Refraction Corrections 137 4.7.5 High-Frequency Adaptations 138 4.7.6 Time-Domain Applications 138 4.8 RAYMODE Model: A Specific Example 138 4.9 Numerical Model Summaries 145

Chapter 5 Propagation II: Mathematical Models (Part Two) 163

5.1 Background 163 5.2 Surface Duct Models 163 5.2.1 Ray-Theory Models 163 5.2.2 Wave-Theory Models 165 5.2.3 Oceanographic Mixed-Layer Models 166 5.3 Shallow-Water Duct Models 168 5.3.1 Shallow-Water Propagation Characteristics 168 5.3.2 Optimum Frequency of Propagation 172 5.3.3 Numerical Models 172 5.3.3.1 Upslope Propagation 177 5.3.3.2 Downslope Propagation 178 5.3.4 Empirical Models 178 5.3.4.1 Rogers Model 179 5.3.4.2 Marsh-Schulkin Model 180 5.3.5 Field Experiments 183 5.3.5.1 SWAT Experiments in the South China Sea 183 X Contents

5.3.5.2 SWARM Experiment in the Atlantic Ocean 184 5.3.5.3 Littoral Acoustic Demonstration Center.... 184 5.3.5.4 Shallow Water '06 184 5.4 Arctic Models 184 5.4.1 Arctic Environmental Models 184 5.4.2 Arctic Propagation Models 185 5.4.3 Numerical Models 185 5.4.4 Empirical Models 187 5.4.4.1 Marsh-Mellen Model 187 5.4.4.2 Buck Model 187 5.5 Data Support Requirements 188 5.5.1 Sound-Speed Profile Synthesis 189 5.5.1.1 Segmented Constant Gradient 190 5.5.1.2 Curvilinear or Continuous Gradient 190 5.5.2 Earth Curvature Corrections 192 5.5.3 Merging Techniques 193

Chapter 6 Special Applications and Inverse Techniques 195

6.1 Background 195 6.2 Stochastic Modeling 196 6.3 Broadband Modeling 197 6.4 Matched-Field Processing 199 6.5 Transmutation Approaches 201 6.6 Nonlinear Acoustics and Chaos 201 6.7 Three-Dimensional Modeling 203 6.8 Ocean Fronts, Eddies, and Internal Waves 204 6.8.1 Fronts and Eddies 205 6.8.2 Internal Waves 206 6.9 Coupled Ocean-Acoustic Modeling 210 6.10 Acoustic Tomography 211 6.11 Phase Conjugation and Time-Reversal Mirrors 216 6.12 Deductive Geoacoustic Inversion 217 6.12.1 Navigating Parameter Landscapes 220 6.12.2 Tabu Search 221 6.13 Prediction Uncertainties in Complex Environments 221 6.14 Rapid Environmental Assessments 223 6.15 Underwater Acoustic Networks and Vehicles 223 6.15.1 Channel Models 223 6.15.2 Localization Methods 227 6.15.2.1 Range-Based Schemes 227 6.15.2.2 Range-Free Schemes 228 6.15.3 Vehicles 228 6.16 Marine-Mammal Protection 229 6.16.1 Regulatory Initiatives and Measurement Programs....230 Contents xi

6.16.2 Rising Levels of Underwater Noise 231 6.16.2.1 Increased Shipping Levels 231 6.16.2.2 Ocean Acidification 231 6.16.2.3 Windfarm Development 232 6.16.3 Seismic Operations and Protection of Whales 233 6.16.4 Modeling Efforts 234 6.16.4.1 Acoustic Integration Model 234 6.16.4.2 Effects of Sound on the Marine Environment 235 6.16.4.3 Marine-Mammal Movement Models 235 6.16.4.4 Collision Avoidance 236 6.16.5 ASW Training Ranges and Mitigation Techniques.... 236 6.16.5.1 Environmentally Adaptive Sonars 237 6.16.5.2 Frequency Diversity 237 6.17 Through-the-Sensor Parameter Estimation 237 6.18 Seismo-Acoustic Inversion 238

Chapter 7 Noise I: Observations and Physical Models 239

7.1 Background 239 7.2 Noise Sources and Spectra 239 7.2.1 Seismo-Acoustic Noise 241 7.2.2 Shipping Noise 242 7.2.3 Bioacoustic Noise 243 7.2.4 Wind and Rain Noise 244 7.3 Depth Dependence 247 7.4 Directionality 247 7.5 Surf Noise 249 7.6 Arctic Ambient Noise 250 7.7 Acoustic Daylight 252 7.8 Geoacoustic Inversion 253 7.9 Acoustic Rain Gauges 254

Chapter 8 Noise II: Mathematical Models 255

8.1 Background 255 8.2 Theoretical Basis for Noise Modeling 255 8.3 Ambient-Noise Models 257 8.4 RANDI Model: A Specific Example 259 8.4.1 Transmission Loss 260 8.4.2 Noise Sources and Spectra 260 8.4.3 Directionality 260 8.4.4 Recent Developments 261 8.5 Noise Notch 262 8.6 Beam-Noise Statistics Models 266 8.7 Data Support Requirements 267 8.8 Numerical Model Summaries 267 xj; Contents

Chapter 9 Reverberation I: Observations and Physical Models 275

9.1 Background 275 9.2 Volume Reverberation 276 9.2.1 Deep Scattering Layer 277 9.2.2 Column or Integrated Scattering Strength 278 9.2.3 Vertical-Scattering Plumes 279 9.3 Boundary Reverberation 279 9.3.1 Sea-Surface Reverberation 279 9.3.2 Under-Ice Reverberation 284 9.3.3 Sea-Floor Reverberation 284 9.4 Inversion Techniques 288

Chapter 10 Reverberation II: Mathematical Models 291

10.1 Background 291 10.2 Theoretical Basis for Reverberation Modeling 291 10.2.1 Basic Approaches 291 10.2.2 Advanced Developments 293 10.3 Cell-Scattering Models 296 10.3.1 Volume-Reverberation Theory 297 10.3.2 Boundary-Reverberation Theory 298 10.4 REVMOD Model: A Specific Example 299 10.5 Bistatic Reverberation 304 10.5.1 Computational Considerations 304 10.5.2 Bistatic Acoustic Model: A Specific Example 305 10.6 Point-Scattering Models 307 10.6.1 Computational Considerations 307 10.6.2 Under-Ice Reverberation Simulation Model: A Specific Example 307 10.7 Numerical Model Summaries 309

Chapter 11 Sonar Performance Models 315

11.1 Background 315 11.2 Sonar Equations 316 11.2.1 Monostatic Sonars 316 11.2.2 Bistatic Sonars 319 11.2.3 Multistatic Sonars 321 11.3 NISSM Model: A Specific Example 322 11.3.1 Propagation 322 11.3.2 Reverberation 325 11.3.3 Target Echo 327 11.3.4 Noise 327 11.3.5 Signal-to-Noise Ratio 327 11.3.6 Probability of Detection 329 11.3.7 Model Outputs 329 Contents xiii

11.4 Model Operating Systems 331 11.4.1 System Architecture 332 11.4.2 Sonar Modeling Functions 334 11.4.3 System Usage 337 11.4.4 Generic Sonar Model: A Specific Example 338 11.4.5 Comprehensive Acoustic System Simulation: A Specific Example 338 11.5 Advanced Signal Processing Issues 339 11.5.1 Background 339 11.5.2 Adjoint Methods 340 11.5.3 Stochastic Resonance 341 11.5.4 Pulse Propagation 341 11.5.5 Multiple-Input/Multiple-Output 342 11.5.6 Clutter Environments 343 11.5.7 Vectors and Clusters 343 11.5.7.1 Replica Vectors 343 11.5.7.2 Ray Clusters 344 11.5.8 High-Frequency Acoustics 345 11.6 Data Sources and Availability 345 11.7 Numerical Model Summaries 350

Chapter 12 Model Evaluation 359

12.1 Background 359 12.2 Past Evaluation Efforts 360 12.3 Analytical Benchmark Solutions 362 12.4 Quantitative Accuracy Assessments 364 12.5 POSSM Experience: A Specific Example 368 12.6 Evaluation Guidelines 372 12.6.1 Documentation 372 12.6.2 Verification 372 12.6.3 Validity 373 12.6.4 Maintainability..... 373 12.6.5 Usability 373 12.7 Documentation Standards 374

Chapter 13 Simulation 379

13.1 Background 379 13.2 Hierarchical Levels 380 13.2.1 Engineering 380 13.2.2 Engagement 381 13.2.3 Mission 382 13.2.4 Theater 382 13.3 Simulation Infrastructure 382 13.4 High-Level Architecture 383 13.5 Testbeds 384 xiv Contents

13.6 Applications 385 13.6.1 Systems Engineering 386 13.6.2 Simulation-Based Acquisition 387 13.6.3 Operations Analysis 390 13.6.4 Training 391

Appendix A: Abbreviations and Acronyms 395

Appendix B: Glossary of Terms 413

Appendix C: Websites 421

Appendix D: Problem Sets 425

References 431

Subject Index 493

Author Index 513