Ainslie Principles of Sonar Performance Modelling

1. Auflage 2010
ISBN: 978-3-540-87662-5
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 707 Seiten

Reihe: Springer Praxis Books

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 3rd 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.

Autoren/Hrsg.

Ainslie, Michael

Inhaltsverzeichnis

1;Principles of Sonar Performance Modeling;2
1.1;Contents;4
1.2;Preface;12
1.3;Foreword;13
1.4;Acknowledgments;15
1.5;Figures;17
1.6;Tables;23
1.7;Part I Foundations;27
1.7.1;1 Introduction;28
1.7.1.1;1.1 WHAT IS SONAR?;28
1.7.1.2;1.2 PURPOSE, SCOPE, AND INTENDED READERSHIP;29
1.7.1.3;1.3 STRUCTURE;31
1.7.1.3.1;1.3.1 Part I: Foundations (Chapters 1–3);31
1.7.1.3.2;1.3.2 Part II: Thefour pillars (Chapters 4–7);31
1.7.1.3.3;1.3.3 Part III: Towards applications (Chapters 8–11);32
1.7.1.3.4;1.3.4 Appendices;32
1.7.1.4;1.4 A BRIEF HISTORY OF SONAR;32
1.7.1.4.1;1.4.1 Conception and birth of sonar (–1918);33
1.7.1.4.1.1;1.4.1.1 Discovery and ingenuity;33
1.7.1.4.1.2;1.4.1.2 The Titanic and the Fessenden oscillator;35
1.7.1.4.1.3;1.4.1.3 WW1: a sense of urgency;35
1.7.1.4.1.4;1.4.1.4 Origins of passive sonar;38
1.7.1.4.2;1.4.2 Sonar in its infancy (1918–1939);40
1.7.1.4.2.1;1.4.2.1 Fathometers and fish finders;40
1.7.1.4.2.2;1.4.2.2 National research laboratories;41
1.7.1.4.2.3;1.4.2.3 Temperature and the ‘‘afternoon effect’’;41
1.7.1.4.3;1.4.3 Sonar comes of age (1939–);42
1.7.1.4.3.1;1.4.3.1 WW2: a giant awakes;42
1.7.1.4.3.2;1.4.3.2 Passive sonar in Germany;42
1.7.1.4.3.3;1.4.3.3 The anomalous absorption of seawater;43
1.7.1.4.3.4;1.4.3.4 SOFAR, SOSUS, and the Roswell Incident;44
1.7.1.4.3.4.1;1.4.3.4.1 The speed of sound in seawater;44
1.7.1.4.3.4.2;1.4.3.4.2 Sound fixing and ranging: the SOFAR channel;45
1.7.1.4.3.4.3;1.4.3.4.3 The Sound Surveillance System (SOSUS);46
1.7.1.4.3.4.4;1.4.3.4.4 Project MOGUL and the Roswell Incident;46
1.7.1.4.3.5;1.4.3.5 Advances in detection theory and processing technology;46
1.7.1.4.3.5.1;1.4.3.5.1 Statistical detection theory;46
1.7.1.4.3.5.2;1.4.3.5.2 FM processing and electronic scanning;47
1.7.1.4.3.5.3;1.4.3.5.3 The computer era;47
1.7.1.4.3.6;1.4.4 Swords to ploughshares;47
1.7.1.4.3.6.1;1.4.4.1 Oceanographic instruments;47
1.7.1.4.3.6.2;1.4.4.2 Discovery of dolphin sonar and concern over the effects of anthropogenic sound;48
1.7.1.5;1.5 REFERENCES;48
1.7.2;2 Essential background;52
1.7.2.1;2.1 ESSENTIALS OF SONAR OCEANOGRAPHY;52
1.7.2.1.1;2.1.1 Acoustical properties of seawater;53
1.7.2.1.1.1;2.1.1.1 Speed of sound;53
1.7.2.1.1.2;2.1.1.2 Density;53
1.7.2.1.1.3;2.1.1.3 Attenuation of sound;53
1.7.2.1.2;2.1.2 Acoustical properties of air;55
1.7.2.2;2.2 ESSENTIALS OF UNDERWATER ACOUSTICS;55
1.7.2.2.1;2.2.1 What is sound?;55
1.7.2.2.2;2.2.2 Radiation of sound;56
1.7.2.2.2.1;2.2.2.1 Radiation from a point monopole source;56
1.7.2.2.2.1.1;2.2.2.1.1 Spherical spreading;56
1.7.2.2.2.1.2;2.2.2.1.2 Reflection from the sea surface;59
1.7.2.2.2.2;2.2.2.2 Radiation from an infinite sheet of uniformly distributed dipoles;62
1.7.2.2.3;2.2.3 Scattering of sound;65
1.7.2.2.3.1;2.2.3.1 Scattering from a small object;65
1.7.2.2.3.2;2.2.3.2 Scattering from a rough surface;66
1.7.2.3;2.3 ESSENTIALS OF SONAR SIGNAL PROCESSING;67
1.7.2.3.1;2.3.1 Temporal filter;67
1.7.2.3.2;2.3.2 Spatial filter (beamformer);69
1.7.2.4;2.4 ESSENTIALS OF DETECTION THEORY;72
1.7.2.4.1;2.4.1 Gaussian distribution;72
1.7.2.4.1.1;2.4.1.1 Noise only;74
1.7.2.4.1.2;2.4.1.2 Signal plus noise;74
1.7.2.4.2;2.4.2 Other distributions;76
1.7.2.4.2.1;2.4.2.1 Coherent processing (Rayleigh statistics);76
1.7.2.4.2.2;2.4.2.2 Incoherent processing (chi-squared statistics with many samples);76
1.7.2.5;2.5 REFERENCES;77
1.7.3;3 The sonar equations;78
1.7.3.1;3.1 INTRODUCTION;78
1.7.3.1.1;3.1.1 Objectives of sonar performance modeling;78
1.7.3.1.2;3.1.2 Concepts of ‘‘signal’’ and ‘‘noise’’;79
1.7.3.1.3;3.1.3 Generic deep-water scenario;80
1.7.3.1.4;3.1.4 Chapter organization;80
1.7.3.2;3.2 PASSIVE SONAR;81
1.7.3.2.1;3.2.1 Overview;81
1.7.3.2.2;3.2.2 Definition of standard terms (passive sonar);83
1.7.3.2.2.1;3.2.2.1 Mean square pressure, sound pressure level, and the decibel;83
1.7.3.2.2.2;3.2.2.2 Source level;85
1.7.3.2.2.3;3.2.2.3 Propagation loss;85
1.7.3.2.2.4;3.2.2.4 Noise spectrum level and array response;86
1.7.3.2.2.5;3.2.2.5 Signal-to-noise ratio, array gain, and directivity index;87
1.7.3.2.2.6;3.2.2.6 Signal gain and noise gain;88
1.7.3.2.2.7;3.2.2.7 Detection threshold and signal excess;88
1.7.3.2.3;3.2.3 Coherent processing: narrowband passive sonar;89
1.7.3.2.3.1;3.2.3.1 Signal (single hydrophone);89
1.7.3.2.3.2;3.2.3.2 Noise (single hydrophone);91
1.7.3.2.3.3;3.2.3.3 Signal-to-noise ratio, signal excess, and narrowband passive sonar equation;92
1.7.3.2.3.4;3.2.3.4 Array gain and directivity index for a horizontal line array;94
1.7.3.2.3.5;3.2.3.5 Probability of detection, detection threshold, and ROC curves;96
1.7.3.2.3.6;3.2.3.6 Probability of false alarm;97
1.7.3.2.3.7;3.2.3.7 Special case: low-frequency tonal in the broadside beam of a horizontal line array;98
1.7.3.2.3.8;3.2.3.8 Worked example;99
1.7.3.2.3.8.1;3.2.3.8.1 Part (i): source level SL;99
1.7.3.2.3.8.2;3.2.3.8.2 Part (ii): noise spectrum level NLf;100
1.7.3.2.3.8.3;3.2.3.8.3 Part (iii): AG, BW, and DT;100
1.7.3.2.3.8.4;3.2.3.8.4 Part (iv): figure of merit FOM;100
1.7.3.2.3.8.5;3.2.3.8.5 Part (v): propagation loss PL(r);100
1.7.3.2.3.8.6;3.2.3.8.6 Part (vi): signal level LS(r) and in-beam noise level LN;102
1.7.3.2.3.8.7;3.2.3.8.7 Part (vii): sensitivity to sonar parameters;103
1.7.3.2.4;3.2.4 Incoherent processing: broadband passive sonar;105
1.7.3.2.4.1;3.2.4.1 Signal (single hydrophone);105
1.7.3.2.4.2;3.2.4.2 Noise (single hydrophone);107
1.7.3.2.4.3;3.2.4.3 Signal-to-noise ratio, signal excess, and broadband passive sonar equation;109
1.7.3.2.4.4;3.2.4.4 Array gain;110
1.7.3.2.4.5;3.2.4.5 Probability of detection, detection threshold, and ROC curves;110
1.7.3.2.4.6;3.2.4.6 Probability of false alarm;112
1.7.3.2.4.7;3.2.4.7 Special case: broadband target in the broadside beam of a horizontal line array;112
1.7.3.2.4.8;3.2.4.8 Worked example;113
1.7.3.2.4.8.1;3.2.4.8.1 Part (i): source level SLf and noise spectrum level NLf;114
1.7.3.2.4.8.2;3.2.4.8.2 Part (ii): AGm and DT;115
1.7.3.2.4.8.3;3.2.4.8.3 Part (iii): detection range;115
1.7.3.2.4.8.4;3.2.4.8.4 Part (iv): halving detection range;118
1.7.3.2.4.8.5;3.2.4.8.5 Part (v): doubling transmitter depth;119
1.7.3.3;3.3 ACTIVE SONAR;119
1.7.3.3.1;3.3.1 Overview;119
1.7.3.3.2;3.3.2 Definition of standard terms (active sonar);120
1.7.3.3.2.1;3.3.2.1 Signal energy, energy source level, and total path loss;121
1.7.3.3.2.2;3.3.2.2 Background energy and background energy level;122
1.7.3.3.2.3;3.3.2.3 Signal-to-background ratio and array gain;123
1.7.3.3.2.4;3.3.2.4 Target strength;124
1.7.3.3.3;3.3.3 Coherent processing: CW pulseþDoppler filter;124
1.7.3.3.3.1;3.3.3.1 Signal (single hydrophone);125
1.7.3.3.3.2;3.3.3.2 Background (single hydrophone);125
1.7.3.3.3.3;3.3.3.3 Signal-to-background ratio, signal excess, and coherent narrowband activesonar equation;125
1.7.3.3.3.4;3.3.3.4 Array gain;127
1.7.3.3.3.5;3.3.3.5 Probability of detection, detection threshold, and ROC curves;128
1.7.3.3.3.6;3.3.3.6 Probability of false alarm;128
1.7.3.3.3.7;3.3.3.7 Special case: rigid spherical target in the broadside beam of a horizontal line array, CW pulse with Doppler processing;129
1.7.3.3.3.8;3.3.3.8 Worked example;130
1.7.3.3.3.8.1;3.3.3.8.1 Part (i): smallest detectable sphere;131
1.7.3.3.3.8.2;3.3.3.8.2 Part (ii): figure of merit;132
1.7.3.3.3.8.3;3.3.3.8.3 Part (iii): detection probability;132
1.7.3.3.3.8.4;3.3.3.8.4 Part (iv): best depth;136
1.7.3.3.4;3.3.4 Incoherent processing: CW pulseþenergy detector;137
1.7.3.3.4.1;3.3.4.1 Signal (single hydrophone);137
1.7.3.3.4.2;3.3.4.2 Background (single hydrophone);137
1.7.3.3.4.3;3.3.4.3 Signal-to-background ratio, signal excess, and incoherent active sonar equation;137
1.7.3.3.4.4;3.3.4.4 Array gain;139
1.7.3.3.4.5;3.3.4.5 Probability of detection, detection threshold, and ROC curves;140
1.7.3.3.4.6;3.3.4.6 Probability of false alarm;140
1.7.3.3.4.7;3.3.4.7 Special case: point target in the broadside beam of a horizontal line array, CW pulse with incoherent processing;141
1.7.3.3.4.8;3.3.4.8 Worked example;142
1.7.3.3.4.8.1;3.3.4.8.1 Part (i): signal, background, and detection threshold;142
1.7.3.3.4.8.2;3.3.4.8.2 Part (ii): detection range;142
1.7.3.3.4.8.3;3.3.4.8.3 Part (iii): detection probability;142
1.7.3.4;3.4 REFERENCES;147
1.8;Part II The Four Pillars;148
1.8.1;4 Sonar oceanography;149
1.8.1.1;4.1 PROPERTIES OF THE OCEAN VOLUME;150
1.8.1.1.1;4.1.1 Terrestrial and universal constants;150
1.8.1.1.2;4.1.2 Bathymetry;150
1.8.1.1.3;4.1.3 Factors affecting sound speed and attenuation in pure seawater;150
1.8.1.1.3.1;4.1.3.1 Density and static pressure;151
1.8.1.1.3.2;4.1.3.2 Temperature;152
1.8.1.1.3.3;4.1.3.3 Salinity;153
1.8.1.1.3.4;4.1.3.4 Acidity (pH);162
1.8.1.1.3.5;4.1.3.5 Viscosity;163
1.8.1.1.4;4.1.4 Speed of sound in pure seawater;163
1.8.1.1.5;4.1.5 Attenuation of sound in pure seawater;170
1.8.1.2;4.2 PROPERTIES OF BUBBLES AND MARINE LIFE;172
1.8.1.2.1;4.2.1 Properties of air bubbles in water;172
1.8.1.2.1.1;4.2.1.1 Properties of air under pressure;172
1.8.1.2.1.2;4.2.1.2 Properties of water that affect the behavior of a pulsating bubble;175
1.8.1.2.1.3;4.2.1.3 Properties of bubbly water;176
1.8.1.2.2;4.2.2 Properties of marine life;176
1.8.1.2.2.1;4.2.2.1 Basic physiological properties;176
1.8.1.2.2.1.1;4.2.2.1.1 Zooplankton;176
1.8.1.2.2.1.2;4.2.2.1.2 Fish;176
1.8.1.2.2.1.3;4.2.2.1.3 Marine mammals;177
1.8.1.2.2.2;4.2.2.2 Acoustical properties;177
1.8.1.2.2.2.1;4.2.2.2.1 Fish flesh;177
1.8.1.2.2.2.2;4.2.2.2.2 Whale tissue;180
1.8.1.2.2.2.3;4.2.2.2.3 Zooplankton;180
1.8.1.2.2.3;4.2.2.3 Population estimates;180
1.8.1.2.2.3.1;4.2.2.3.1 Fish in the North Sea: population density and case study;180
1.8.1.2.2.3.2;4.2.2.3.2 Marine mammals;183
1.8.1.3;4.3 PROPERTIES OF THE SEA SURFACE;183
1.8.1.3.1;4.3.1 Effect of wind;183
1.8.1.3.2;4.3.2 Surface roughness;190
1.8.1.3.2.1;4.3.2.1 Pierson–Moskowitz spectrum;190
1.8.1.3.2.2;4.3.2.2 Neumann–Pierson spectrum;191
1.8.1.3.3;4.3.3 Wind-generated bubbles;193
1.8.1.4;4.4 PROPERTIES OF THE SEABED;195
1.8.1.4.1;4.4.1 Unconsolidated sediments;196
1.8.1.4.1.1;4.4.1.1 Pure samples and porosity;196
1.8.1.4.1.2;4.4.1.2 Mixed samples and the ‘‘phi’’ scale;197
1.8.1.4.1.3;4.4.1.3 Near-surface (high-frequency) properties;199
1.8.1.4.1.4;4.4.1.4 Bulk (medium frequency) properties;199
1.8.1.4.1.5;4.4.1.5 Low-frequency properties;201
1.8.1.4.1.5.1;4.4.1.5.1 Deep water;201
1.8.1.4.1.5.2;4.4.1.5.2 Shallow water;203
1.8.1.4.2;4.4.2 Rocks;204
1.8.1.4.2.1;4.4.2.1 Wave speed—density correlation equations;204
1.8.1.4.2.2;4.4.2.2 Typical parameter values;206
1.8.1.4.3;4.4.3 Geoacoustic models;207
1.8.1.5;4.5 REFERENCES;208
1.8.2;5 Underwater acoustics;215
1.8.2.1;5.1 INTRODUCTION;215
1.8.2.2;5.2 THE WAVE EQUATIONS FOR FLUID AND SOLID MEDIA;216
1.8.2.2.1;5.2.1 Compressional waves in a fluid medium;216
1.8.2.2.1.1;5.2.1.1 Equations of motion;216
1.8.2.2.1.2;5.2.1.2 Bulk modulus and the acoustic wave equation;217
1.8.2.2.1.3;5.2.1.3 Compressional wave speed;217
1.8.2.2.2;5.2.2 Compressional waves and shear waves in a solid medium;218
1.8.2.2.2.1;5.2.2.1 Shear modulus and the wave equations for a solid;218
1.8.2.2.2.2;5.2.2.2 Lame´ parameters,Young’s modulus,and Poisson’s ratio;219
1.8.2.2.2.3;5.2.2.3 Compressional and shear wave speeds;220
1.8.2.3;5.3 REFLECTION OF PLANE WAVES;221
1.8.2.3.1;5.3.1 Reflection from and transmission through a simple fluid–fluid or fluid–solid boundary;222
1.8.2.3.1.1;5.3.1.1 Amplitude reflection coefficient;222
1.8.2.3.1.2;5.3.1.2 Amplitude transmission coefficients;223
1.8.2.3.1.3;5.3.1.3 Energy reflection and transmission coefficients;224
1.8.2.3.2;5.3.2 Reflection from a layered fluid boundary;225
1.8.2.3.3;5.3.3 Reflection from a layered solid boundary;228
1.8.2.3.4;5.3.4 Reflection from a perfectly reflecting rough surface;229
1.8.2.3.4.1;5.3.4.1 Perturbation theory (small Q);229
1.8.2.3.4.1.1;5.3.4.1.1 Near-grazing (kL sin2 << 1);230
1.8.2.3.4.1.2;5.3.4.1.2 Non-grazing (kL sin2 >> 1);232
1.8.2.3.4.2;5.3.4.2 Heuristic extension for large Q;232
1.8.2.3.5;5.3.5 Reflection from a partially reflecting rough surface;232
1.8.2.4;5.4 SCATTERING OFPLA NE WAVES;233
1.8.2.4.1;5.4.1 Scattering cross-sections and the far field;233
1.8.2.4.2;5.4.2 Backscattering from solid objects;234
1.8.2.4.2.1;5.4.2.1 Small rigid object of approximately spherical shape;234
1.8.2.4.2.2;5.4.2.2 Large rigid object;236
1.8.2.4.2.3;5.4.2.3 Rigid object of arbitrary size;237
1.8.2.4.2.4;5.4.2.4 Sand grains of irregular shape and arbitrary size;238
1.8.2.4.3;5.4.3 Backscattering from fluid objects;238
1.8.2.4.3.1;5.4.3.1 Small fluid object of arbitrary shape;238
1.8.2.4.3.2;5.4.3.2 Large fluid object;238
1.8.2.4.3.3;5.4.3.3 Fluid object of arbitrary size;239
1.8.2.4.3.4;5.4.3.4 Gas bubble;239
1.8.2.4.3.5;5.4.3.5 Dispersed bubbles;242
1.8.2.4.3.6;5.4.3.6 Single fish (with bladder);242
1.8.2.4.3.7;5.4.3.7 Single fish (without bladder);245
1.8.2.4.3.8;5.4.3.8 Dispersed fish (with bladder);246
1.8.2.4.3.9;5.4.3.9 Dispersed fish (without bladder);247
1.8.2.4.3.10;5.4.3.10 Aggregated fish (with bladder);247
1.8.2.4.3.11;5.4.3.11 Aggregated fish (without bladder);247
1.8.2.4.4;5.4.4 Scattering from rough boundaries;247
1.8.2.4.4.1;5.4.4.1 Non-specular term;248
1.8.2.4.4.2;5.4.4.2 Near-specular term;248
1.8.2.5;5.5 DISPERSION IN THE PRESENCE OFIMP URITIES;249
1.8.2.5.1;5.5.1 Wood’s model for sediments in dilute suspension;249
1.8.2.5.2;5.5.2 Buckingham’s model for saturated sediments with intergranular contact;250
1.8.2.5.3;5.5.3 Effect of bubbles or bladdered fish;251
1.8.2.5.3.1;5.5.3.1 Dispersion in bubbly water;252
1.8.2.5.3.2;5.5.3.2 Bulk modulus Bb(a,w);254
1.8.2.5.3.3;5.5.3.3 Effect of surface tension on small bubbles at low frequency;255
1.8.2.5.3.4;5.5.3.4 Bubble resonance;256
1.8.2.5.3.4.1;5.5.3.4.1 Polytropic index G;259
1.8.2.5.3.4.2;5.5.3.4.2 Resonance frequency;260
1.8.2.5.3.4.3;5.5.3.4.3 Resonant bubble radius;263
1.8.2.5.3.5;5.5.3.5 Damping factor;266
1.8.2.5.3.5.1;5.5.3.5.1 Thermal and viscous damping;266
1.8.2.5.3.5.2;5.5.3.5.2 Radiation and thermal damping;267
1.8.2.5.3.5.3;5.5.3.5.3 Total damping;267
1.8.2.5.3.5.4;5.5.3.5.4 Q-factors;268
1.8.2.5.3.6;5.5.3.6 Scattering,extin ction,an d absorption cross-sections;269
1.8.2.6;5.6 REFERENCES;271
1.8.3;6 Sonar signal processing;274
1.8.3.1;6.1 PROCESSING GAIN FOR PASSIVE SONAR;275
1.8.3.1.1;6.1.1 Beam patterns;275
1.8.3.1.1.1;6.1.1.1 Steered line array;275
1.8.3.1.1.1.1;6.1.1.1.1 Unshaded;276
1.8.3.1.1.1.2;6.1.1.1.2 Cosine shading (cosn);280
1.8.3.1.1.1.3;6.1.1.1.3 Cosine on a pedestal (Hamming family);281
1.8.3.1.1.1.4;6.1.1.1.4 Tukey shading (raised cosine spectrum);282
1.8.3.1.1.1.5;6.1.1.1.5 Summary;283
1.8.3.1.1.2;6.1.1.2 Unsteered planar arrays;284
1.8.3.1.1.2.1;6.1.1.2.1 Piston arrays;284
1.8.3.1.1.2.2;6.1.1.2.2 Rectangular arrays;289
1.8.3.1.2;6.1.2 Directivity index;289
1.8.3.1.2.1;6.1.2.1 Steered line array;290
1.8.3.1.2.2;6.1.2.2 Unsteered planar array;293
1.8.3.1.3;6.1.3 Array gain;294
1.8.3.1.3.1;6.1.3.1 Definition;294
1.8.3.1.3.2;6.1.3.2 Special cases (noise gain for horizontal line array);296
1.8.3.1.3.2.1;6.1.3.2.1 Noise gain for isotropic noise;296
1.8.3.1.3.2.2;6.1.3.2.2 Noise gain for horizontal isotropic noise;297
1.8.3.1.3.2.3;6.1.3.2.3 Noise gain for a uniform sheet of dipole noise sources;298
1.8.3.1.3.2.4;6.1.3.2.4 Noise gain for multiple point sources of noise;301
1.8.3.1.4;6.1.4 BB application;301
1.8.3.1.5;6.1.5 Time domain processing;302
1.8.3.1.5.1;6.1.5.1 Coherent averaging;302
1.8.3.1.5.2;6.1.5.2 Incoherent averaging;302
1.8.3.2;6.2 PROCESSING GAIN FOR ACTIVE SONAR;302
1.8.3.2.1;6.2.1 Signal carrier and envelope;303
1.8.3.2.1.1;6.2.1.1 Intuitive concept;303
1.8.3.2.1.2;6.2.1.2 Formal methodology: analytic signals and the Hilbert transform;304
1.8.3.2.2;6.2.2 Simple envelopes and their spectra;305
1.8.3.2.2.1;6.2.2.1 CW spectra;309
1.8.3.2.2.2;6.2.2.2 LFM spectra;310
1.8.3.2.2.2.1;6.2.2.2.1 Gaussian envelope;310
1.8.3.2.2.2.2;6.2.2.2.2 Rectangular envelope;311
1.8.3.2.2.2.3;6.2.2.2.3 Method of stationary phase;312
1.8.3.2.2.3;6.2.2.3 HFM spectra;314
1.8.3.2.2.3.1;6.2.2.3.1 Gaussian envelope;316
1.8.3.2.2.3.2;6.2.2.3.2 Rectangular envelope;316
1.8.3.2.2.3.3;6.2.2.3.3 Synthesis of HFM envelopes;317
1.8.3.2.2.4;6.2.2.4 Hybrid spectra;317
1.8.3.2.3;6.2.3 Autocorrelation and cross-correlation functions and the matched filter;319
1.8.3.2.3.1;6.2.3.1 Autocorrelation function;319
1.8.3.2.3.2;6.2.3.2 Cross-correlation and the matched filter;320
1.8.3.2.3.3;6.2.3.3 Doppler processing;320
1.8.3.2.4;6.2.4 Ambiguity function;323
1.8.3.2.4.1;6.2.4.1 CW pulse;324
1.8.3.2.4.2;6.2.4.2 LFM pulse;327
1.8.3.2.4.3;6.2.4.3 HFM pulse;328
1.8.3.2.5;6.2.5 Matched filter gain for perfect replica;329
1.8.3.2.6;6.2.6 Matched filter gain for imperfect replica (coherence loss);330
1.8.3.2.7;6.2.7 Array gain and total processing gain (active sonar);331
1.8.3.3;6.3 REFERENCES;332
1.8.4;7 Statistical detection theory;334
1.8.4.1;7.1 SINGLE KNOWN PULSE IN GAUSSIAN NOISE,COHERENT PROCESSING;335
1.8.4.1.1;7.1.1 False alarm probability for Gaussian-distributed noise;335
1.8.4.1.2;7.1.2 Detection probability for signal with random phase;336
1.8.4.1.2.1;7.1.2.1 Signal with non-fluctuating amplitude (Dirac distribution);337
1.8.4.1.2.1.1;7.1.2.1.1 Marcum Q-function;337
1.8.4.1.2.1.2;7.1.2.1.2 Albersheim approximation;338
1.8.4.1.2.1.3;7.1.2.1.3 Limit of large SNR;339
1.8.4.1.2.2;7.1.2.2 Signal with Rayleigh fading;340
1.8.4.1.2.3;7.1.2.3 Signal with Rician fading;341
1.8.4.1.2.4;7.1.2.4 Signal with one-dominant-plus-Rayleigh distribution;345
1.8.4.1.2.5;7.1.2.5 Summary table;348
1.8.4.1.3;7.1.3 Detection threshold;349
1.8.4.1.4;7.1.4 Application to other waveforms;350
1.8.4.2;7.2 MULTIPLE KNOWN PULSES IN GAUSSIAN NOISE, INCOHERENT PROCESSING;350
1.8.4.2.1;7.2.1 False alarm probability for Rayleigh-distributed noise amplitude;351
1.8.4.2.2;7.2.2 Detection probability for incoherently processed pulse train;352
1.8.4.2.2.1;7.2.2.1 Signal with non-fluctuating amplitude;352
1.8.4.2.2.1.1;7.2.2.1.1 General case;352
1.8.4.2.2.1.2;7.2.2.1.2 Special case M = 1;356
1.8.4.2.2.1.3;7.2.2.1.3 Limit of large M;358
1.8.4.2.2.2;7.2.2.2 Signal with Rayleigh amplitude distribution (Swerling II);363
1.8.4.2.2.2.1;7.2.2.2.1 General case;363
1.8.4.2.2.2.2;7.2.2.2.2 Special case M = 1;364
1.8.4.2.2.2.3;7.2.2.2.3 Limit of large M;364
1.8.4.2.2.3;7.2.2.3 Signal with one-dominant-plus-Rayleigh amplitude distribution (Swerling IV);365
1.8.4.2.2.3.1;7.2.2.3.1 General case;365
1.8.4.2.2.3.2;7.2.2.3.2 Special case M = 1;365
1.8.4.2.2.3.3;7.2.2.3.3 Limit of large M;366
1.8.4.3;7.3 APPLICATION TO SONAR;367
1.8.4.3.1;7.3.1 Active sonar;367
1.8.4.3.2;7.3.2 Passive sonar;367
1.8.4.3.3;7.3.3 Decision strategies and the detection threshold;369
1.8.4.4;7.4 MULTIPLE LOOKS;371
1.8.4.4.1;7.4.1 Introduction;371
1.8.4.4.2;7.4.2 AND and OR operations;373
1.8.4.4.2.1;7.4.2.1 AND operation for Rayleigh statistics;373
1.8.4.4.2.2;7.4.2.2 OR operation for Rayleigh statistics;374
1.8.4.4.2.3;7.4.2.3 Summary table for Rayleigh statistics;375
1.8.4.4.2.4;7.4.2.4 Simulations with Rayleigh and non-Rayleigh signal statistics;375
1.8.4.4.3;7.4.3 Multiple OR operations;377
1.8.4.4.4;7.4.4 ‘‘M out of N ’’ operations;379
1.8.4.5;7.5 REFERENCES;380
1.9;Part III Towards Applications;382
1.9.1;8 Sources and scatterers of sound;383
1.9.1.1;8.1 REFLECTION AND SCATTERING FROM OCEAN BOUNDARIES;383
1.9.1.1.1;8.1.1 Reflection from the sea surface;384
1.9.1.1.1.1;8.1.1.1 Theoretical prediction for an isotropic surface wave spectrum;384
1.9.1.1.1.1.1;8.1.1.1.1 Coherent reflection coefficient;384
1.9.1.1.1.1.2;8.1.1.1.2 Pierson–Moskowitz surface wave spectrum;384
1.9.1.1.1.1.3;8.1.1.1.3 Neumann–Pierson surface wave spectrum;385
1.9.1.1.1.1.4;8.1.1.1.4 Effect of anisotropy;386
1.9.1.1.1.2;8.1.1.2 Semi-empirical surface reflection loss models;386
1.9.1.1.1.2.1;8.1.1.2.1 Low-frequency surface loss model;387
1.9.1.1.1.2.2;8.1.1.2.2 High-frequency surface loss model;389
1.9.1.1.2;8.1.2 Scattering from the sea surface;391
1.9.1.1.2.1;8.1.2.1 Theoretical prediction for Pierson–Moskowitz surface wave spectrum;391
1.9.1.1.2.1.1;8.1.2.1.1 Non-specular scattering (perturbation theory);391
1.9.1.1.2.1.2;8.1.2.1.2 Near-specular scattering (facet-scattering theory);392
1.9.1.1.2.2;8.1.2.2 Semi-empirical surface-scatteringstreng th models;393
1.9.1.1.2.2.1;8.1.2.2.1 Low-frequency model;393
1.9.1.1.2.2.2;8.1.2.2.2 High-frequency model (APL);394
1.9.1.1.3;8.1.3 Reflection from the seabed;397
1.9.1.1.3.1;8.1.3.1 Theoretical prediction for uniform unconsolidated sediment;397
1.9.1.1.3.1.1;8.1.3.1.1 Fluid sediment;397
1.9.1.1.3.1.2;8.1.3.1.2 Effect of a small non-zero shear speed;401
1.9.1.1.3.2;8.1.3.2 Theoretical prediction for layered unconsolidated sediment (1–100 kHz);402
1.9.1.1.3.3;8.1.3.3 Theoretical prediction for layered solid seabed (<1 kHz);406
1.9.1.1.4;8.1.4 Scattering from the seabed;413
1.9.1.1.4.1;8.1.4.1 Theoretical prediction for a fluid seabed with a rough boundary and a uniform distribution of embedded scatterers;414
1.9.1.1.4.1.1;8.1.4.1.1 Non-specular scattering from rough boundary (perturbation theory);414
1.9.1.1.4.1.2;8.1.4.1.2 Scattering from sediment volume;415
1.9.1.1.4.1.3;8.1.4.1.3 Near-specular scattering (facet-scattering theory);417
1.9.1.1.4.2;8.1.4.2 Empirical and semi-empirical seabed scatteringstre ngth models;417
1.9.1.1.4.2.1;8.1.4.2.1 Diffuse scattering model (empirical);418
1.9.1.1.4.2.2;8.1.4.2.2 Ellis–Crowe (semi-empirical) scattering strength model;420
1.9.1.1.4.2.3;8.1.4.2.3 McKinney–Anderson (empirical);421
1.9.1.2;8.2 TARGET STRENGTH, VOLUME BACKSCATTERING STRENGTH, AND VOLUME ATTENUATION COEFFICIENT;421
1.9.1.2.1;8.2.1 Target strength of point-like scatterers;422
1.9.1.2.1.1;8.2.1.1 Marine organisms with a gas enclosure;422
1.9.1.2.1.1.1;8.2.1.1.1 Bladdered fish;423
1.9.1.2.1.1.2;8.2.1.1.2 Marine mammals;424
1.9.1.2.1.1.3;8.2.1.1.3 Human divers;424
1.9.1.2.1.2;8.2.1.2 Miscellaneous marine organisms, mostly without a gas enclosure;426
1.9.1.2.1.2.1;8.2.1.2.1 Animals with a pronounced elongated shape;426
1.9.1.2.1.2.2;8.2.1.2.2 Miscellaneous animals with irregular shapes;427
1.9.1.2.1.3;8.2.1.3 Man-made objects;430
1.9.1.2.2;8.2.2 Volume backscattering strength and attenuation coefficient of distributed scatterers;431
1.9.1.2.2.1;8.2.2.1 Low-frequency VBS (mainly due to large fish);431
1.9.1.2.2.2;8.2.2.2 High-frequency VBS (partly due to small fish);433
1.9.1.2.2.3;8.2.2.3 Volume attenuation coefficient due to bubbles and bladdered fish;433
1.9.1.2.2.3.1;8.2.2.3.1 Bubbles;433
1.9.1.2.2.3.2;8.2.2.3.2 Dispersed fish with swimbladder;433
1.9.1.2.3;8.2.3 Column strength and wake strength of extended volume scatterers;434
1.9.1.2.3.1;8.2.3.1 Column strength and the deep scattering layer;434
1.9.1.2.3.2;8.2.3.2 Wake strength;435
1.9.1.3;8.3 SOURCES OF UNDERWATER SOUND;436
1.9.1.3.1;8.3.1 Shipping source spectrum level measurements;439
1.9.1.3.1.1;8.3.1.1 Conversion from far-field measurements;440
1.9.1.3.1.2;8.3.1.2 Industrial and commercial shipping(indi vidual ships);442
1.9.1.3.1.3;8.3.1.3 Commercial shipping(averag ed source spectra);443
1.9.1.3.1.4;8.3.1.4 Effect of ship speed and acceleration;445
1.9.1.3.2;8.3.2 Distributed sources on the sea surface;446
1.9.1.3.2.1;8.3.2.1 Wind noise source level;446
1.9.1.3.2.1.1;8.3.2.1.1 High-frequency wind noise (APL model);446
1.9.1.3.2.1.2;8.3.2.1.2 Low-frequency wind noise (Kuperman–Ferla measurements);447
1.9.1.3.2.1.3;8.3.2.1.3 Proposed composite wind noise model;448
1.9.1.3.2.2;8.3.2.2 Rain noise source level;448
1.9.1.3.2.3;8.3.2.3 Shippingnoise source level;449
1.9.1.3.2.3.1;8.3.2.3.1 Monopole density;450
1.9.1.3.2.3.2;8.3.2.3.2 Dipole density;450
1.9.1.3.3;8.3.3 Distributed sources on the seabed (crustacea);451
1.9.1.3.3.1;8.3.3.1 Snappingshri mp;451
1.9.1.3.3.2;8.3.3.2 Other crustaceans;452
1.9.1.4;8.4 REFERENCES;453
1.9.2;9 Propagation of underwater sound;461
1.9.2.1;9.1 PROPAGATION LOSS;462
1.9.2.1.1;9.1.1 Effect of the seabed in isovelocity water;462
1.9.2.1.1.1;9.1.1.1 Deep water;462
1.9.2.1.1.1.1;9.1.1.1.1 Lloyd mirror;465
1.9.2.1.1.1.2;9.1.1.1.2 Bottom-reflected paths;465
1.9.2.1.1.1.3;9.1.1.1.3 Bottom-refracted paths;467
1.9.2.1.1.2;9.1.1.2 Shallow water;471
1.9.2.1.1.2.1;9.1.1.2.1 Multipath propagation;474
1.9.2.1.1.2.2;9.1.1.2.2 Spherical and cylindrical spreading regions;474
1.9.2.1.1.2.3;9.1.1.2.3 Mode-stripping region;475
1.9.2.1.1.2.4;9.1.1.2.4 Single-mode region;479
1.9.2.1.1.2.5;9.1.1.2.5 Cut-off frequency;480
1.9.2.1.1.2.6;9.1.1.2.6 Depth dependence;480
1.9.2.1.2;9.1.2 Effect of a sound speed profile;481
1.9.2.1.2.1;9.1.2.1 Deep water;481
1.9.2.1.2.1.1;9.1.2.1.1 Examples for the northwest Pacific Ocean;484
1.9.2.1.2.1.2;9.1.2.1.2 Surface duct (upward refraction);484
1.9.2.1.2.1.3;9.1.2.1.3 Convergence zones;496
1.9.2.1.2.1.4;9.1.2.1.4 Lloyd mirror with downward refraction;496
1.9.2.1.2.2;9.1.2.2 Shallow water;500
1.9.2.1.2.2.1;9.1.2.2.1 Surface–bottom multipaths (‘‘V-duct’’);500
1.9.2.1.2.2.2;9.1.2.2.2 Surface or bottom duct propagation (‘‘U-duct’’);505
1.9.2.1.2.2.3;9.1.2.2.3 Total (VD+UD);505
1.9.2.2;9.2 NOISE LEVEL;505
1.9.2.2.1;9.2.1 Deep water;506
1.9.2.2.1.1;9.2.1.1 Typical spectra for wind, shipping, and thermal noise;506
1.9.2.2.1.1.1;9.2.1.1.1 Shipping noise;507
1.9.2.2.1.1.2;9.2.1.1.2 Thermal noise;507
1.9.2.2.1.2;9.2.1.2 Effect of rain rate and wind speed;507
1.9.2.2.1.3;9.2.1.3 Depth dependence of surface-generated noise;510
1.9.2.2.2;9.2.2 Shallow water;511
1.9.2.2.3;9.2.3 Noise maps;512
1.9.2.3;9.3 SIGNAL LEVEL (ACTIVE SONAR);513
1.9.2.3.1;9.3.1 The reciprocity principle;514
1.9.2.3.2;9.3.2 Calculation of echo level;515
1.9.2.3.3;9.3.3 V-duct propagation (isovelocity case);516
1.9.2.3.4;9.3.4 U-duct propagation (linear profile);516
1.9.2.4;9.4 REVERBERATION LEVEL;517
1.9.2.4.1;9.4.1 Isovelocity water;519
1.9.2.4.1.1;9.4.1.1 General power law scattering coefficient;519
1.9.2.4.1.2;9.4.1.2 Application to a reference problem with Lambert’s rule (RMW11);520
1.9.2.4.2;9.4.2 Effect of refraction;522
1.9.2.4.2.1;9.4.2.1 V-duct propagation;522
1.9.2.4.2.2;9.4.2.2 U-duct propagation;523
1.9.2.4.2.3;9.4.2.3 Application to a reference problem with Lambert’s rule (RMW12);525
1.9.2.5;9.5 SIGNAL-TO-REVERBERATION RATIO (ACTIVE SONAR);530
1.9.2.5.1;9.5.1 V-duct (isovelocity case);530
1.9.2.5.2;9.5.2 U-duct (linear profile);531
1.9.2.6;9.6 REFERENCES;532
1.9.3;10 Transmitter and receiver characteristics;535
1.9.3.1;10.1 TRANSMITTER CHARACTERISTICS;536
1.9.3.1.1;10.1.1 Of man-made systems;537
1.9.3.1.1.1;10.1.1.1 Continuous sources;537
1.9.3.1.1.1.1;10.1.1.1.1 Single-beam echo sounders;537
1.9.3.1.1.1.2;10.1.1.1.2 Sidescan sonar;537
1.9.3.1.1.1.3;10.1.1.1.3 Multibeam echo sounders;538
1.9.3.1.1.1.4;10.1.1.1.4 Sub-bottom profilers;538
1.9.3.1.1.1.5;10.1.1.1.5 Fisheries sonar;541
1.9.3.1.1.1.6;10.1.1.1.6 Military search sonar;541
1.9.3.1.1.1.7;10.1.1.1.7 Minesweeping sonar;542
1.9.3.1.1.1.8;10.1.1.1.8 Acoustic deterrent devices;545
1.9.3.1.1.1.9;10.1.1.1.9 Underwater communications systems and transponders;545
1.9.3.1.1.1.10;10.1.1.1.10 High-frequency imaging sonar;545
1.9.3.1.1.1.11;10.1.1.1.11 Research instruments (global oceanography);545
1.9.3.1.1.2;10.1.1.2 Impulsive sources;547
1.9.3.1.1.2.1;10.1.1.2.1 General characteristics;547
1.9.3.1.1.2.2;10.1.1.2.2 Seismic survey sources;556
1.9.3.1.1.2.3;10.1.1.2.3 Explosives;560
1.9.3.1.2;10.1.2 Of marine mammals;564
1.9.3.1.2.1;10.1.2.1 Continuous vocalizations;564
1.9.3.1.2.2;10.1.2.2 Impulsive sources;564
1.9.3.2;10.2 RECEIVER CHARACTERISTICS;567
1.9.3.2.1;10.2.1 Of man-made sonar;567
1.9.3.2.1.1;10.2.1.1 Hydrophone sensitivity and non-acoustic noise;567
1.9.3.2.1.1.1;10.2.1.1.1 Sensitivity;567
1.9.3.2.1.1.2;10.2.1.1.2 Molecular thermal noise;571
1.9.3.2.1.1.3;10.2.1.1.3 Flow noise;571
1.9.3.2.1.2;10.2.1.2 Array directivity;571
1.9.3.2.2;10.2.2 Of marine mammals, amphibians, human divers, and fish;571
1.9.3.2.2.1;10.2.2.1 The intensity of underwater sound: typical orders of magnitude;572
1.9.3.2.2.2;10.2.2.2 Measured audiograms;573
1.9.3.2.2.2.1;10.2.2.2.1 Of cetaceans;573
1.9.3.2.2.2.2;10.2.2.2.2 Of pinnipeds (seals, sea lions, and walruses);573
1.9.3.2.2.2.3;10.2.2.2.3 Of sirenians;576
1.9.3.2.2.2.4;10.2.2.2.4 Of human divers;576
1.9.3.2.2.2.5;10.2.2.2.5 Of fish;577
1.9.3.2.2.3;10.2.2.3 Discrimination against background noise;579
1.9.3.2.2.3.1;10.2.2.3.1 Critical bandwidth;579
1.9.3.2.2.3.2;10.2.2.3.2 Critical ratio;580
1.9.3.2.2.4;10.2.2.4 Hearingimpairm ent and behavioral effects;580
1.9.3.2.2.4.1;10.2.2.4.1 Sound exposure thresholds for hearing impairment to mammals and fish;582
1.9.3.2.2.4.2;10.2.2.4.2 Peak sound pressure thresholds for hearing impairment to mammals and fish;585
1.9.3.2.2.4.3;10.2.2.4.3 Thresholds for behavioral effects;585
1.9.3.3;10.3 REFERENCES;587
1.9.4;11 The sonar equations revisited;594
1.9.4.1;11.1 INTRODUCTION;594
1.9.4.2;11.2 PASSIVE SONAR WITH COHERENT PROCESSING: TONAL DETECTOR;595
1.9.4.2.1;11.2.1 Sonar equation;595
1.9.4.2.2;11.2.2 Source level (SL);596
1.9.4.2.3;11.2.3 Narrowband propagation loss (PL);597
1.9.4.2.4;11.2.4 Noise spectrum level (NLf );599
1.9.4.2.4.1;11.2.4.1 Background noise;599
1.9.4.2.4.2;11.2.4.2 Foreground noise;599
1.9.4.2.4.3;11.2.4.3 Non-acoustic noise;599
1.9.4.2.4.4;11.2.4.4 Self-noise and ambient noise;600
1.9.4.2.4.4.1;11.2.4.4.1 Self-noise, including platform noise;600
1.9.4.2.4.4.2;11.2.4.4.2 Ambient noise;600
1.9.4.2.5;11.2.5 Bandwidth (BW);600
1.9.4.2.6;11.2.6 Array gain (AG) and directivity index (DI);601
1.9.4.2.7;11.2.7 Detection threshold (DT);602
1.9.4.2.7.1;11.2.7.1 Calculation of DT for given pfa;602
1.9.4.2.7.2;11.2.7.2 Estimation of pfa;603
1.9.4.2.8;11.2.8 Worked example;604
1.9.4.2.8.1;11.2.8.1 Propagation loss and signal excess;604
1.9.4.2.8.2;11.2.8.2 What is the detection range?;606
1.9.4.2.8.3;11.2.8.3 Alternative performance measures;608
1.9.4.2.8.3.1;11.2.8.3.1 Detection volume (radius of equivalent volume sphere);608
1.9.4.2.8.3.2;11.2.8.3.2 Detection area (radius of equivalent area circle);611
1.9.4.3;11.3 PASSIVE SONAR WITH INCOHERENT PROCESSING: ENERGY DETECTOR;612
1.9.4.3.1;11.3.1 Sonar equation;612
1.9.4.3.2;11.3.2 Source level (SL);613
1.9.4.3.3;11.3.3 Broadband propagation loss (PL);613
1.9.4.3.4;11.3.4 Broadband noise level (NL);614
1.9.4.3.5;11.3.5 Processing gain (PG);614
1.9.4.3.5.1;11.3.5.1 Array gain (AG) and directivity index (DI);615
1.9.4.3.5.2;11.3.5.2 Filter gain (FG);615
1.9.4.3.5.2.1;11.3.5.2.1 Filter gain for a white signal spectrum;616
1.9.4.3.5.2.2;11.3.5.2.2 Filter gain for a colored signal spectrum;617
1.9.4.3.6;11.3.6 Broadband detection threshold (DT);618
1.9.4.3.6.1;11.3.6.1 Calculation of DT for given pfa;618
1.9.4.3.6.2;11.3.6.2 Estimation of false alarm probability;619
1.9.4.3.7;11.3.7 Worked example;620
1.9.4.3.7.1;11.3.7.1 Propagation loss;620
1.9.4.3.7.2;11.3.7.2 Signal-to-noise ratio;620
1.9.4.3.7.3;11.3.7.3 Detection threshold and signal excess;623
1.9.4.3.7.4;11.3.7.4 Effect of filter gain;626
1.9.4.3.7.5;11.3.7.5 Effect of rainfall;626
1.9.4.4;11.4 ACTIVE SONAR WITH COHERENT PROCESSING: MATCHED FILTER;627
1.9.4.4.1;11.4.1 Sonar equation;627
1.9.4.4.2;11.4.2 Echo level (EL), target strength (TS), and equivalent target strength (TSeq);628
1.9.4.4.2.1;11.4.2.1 Outward propagation loss (PLTx) and sonar source level (SL);629
1.9.4.4.2.2;11.4.2.2 Return propagation loss (PLRx);629
1.9.4.4.2.3;11.4.2.3 Special case: separable target cross-section;630
1.9.4.4.3;11.4.3 Background level (BL);631
1.9.4.4.4;11.4.4 Processing gain (PG);631
1.9.4.4.4.1;11.4.4.1 Array gain (AG) and directivity index (DI);632
1.9.4.4.4.2;11.4.4.2 Matched filter gain (MG);633
1.9.4.4.5;11.4.5 Detection threshold (DT);633
1.9.4.4.5.1;11.4.5.1 Calculation of DT from pfa;633
1.9.4.4.5.2;11.4.5.2 Estimation of pfa;633
1.9.4.4.6;11.4.6 Worked example;634
1.9.4.4.6.1;11.4.6.1 Part (i) maximum audibility range (no background);636
1.9.4.4.6.1.1;11.4.6.1.1 Echo level (EL);636
1.9.4.4.6.1.2;11.4.6.1.2 Hearing threshold (HT);640
1.9.4.4.6.1.3;11.4.6.1.3 Maximum audibility range;640
1.9.4.4.6.2;11.4.6.2 Part (ii) detection range for low wind speed (noise-limited);642
1.9.4.4.6.2.1;11.4.6.2.1 Noise level (NL);642
1.9.4.4.6.2.2;11.4.6.2.2 Array gain (AG);643
1.9.4.4.6.2.3;11.4.6.2.3 Detection threshold (DT);644
1.9.4.4.6.2.4;11.4.6.2.4 Signal excess (SE) and detection range;644
1.9.4.4.6.3;11.4.6.3 Part (iii) detection range for high wind speed (noise-limited);644
1.9.4.4.6.4;11.4.6.4 Part (iv) effect of reverberation (for high wind speed);645
1.9.4.4.6.4.1;11.4.6.4.1 Background level (BL);646
1.9.4.4.6.4.2;11.4.6.4.2 Processing gain (PG);649
1.9.4.4.6.4.3;11.4.6.4.3 Signal excess and detection range;650
1.9.4.5;11.5 THE FUTURE OF SONAR PERFORMANCE MODELING;651
1.9.4.5.1;11.5.1 Advances in signal processing and oceanographic modeling;651
1.9.4.5.2;11.5.2 Autonomous platforms;652
1.9.4.5.3;11.5.3 Environmental impact of anthropogenic sound;652
1.9.4.6;11.6 REFERENCES;653
1.10;Appendix A Special functions and mathematical operations;655
1.10.1;A.1 DEFINITIONS AND BASIC PROPERTIES OF SPECIAL FUNCTIONS;655
1.10.1.1;A.1.1 Heaviside step function, sign function, and rectangle function;655
1.10.1.2;A.1.2 Sine cardinal and sinh cardinal functions;656
1.10.1.3;A.1.3 Dirac delta function;656
1.10.1.4;A.1.4 Fresnel integrals;656
1.10.1.5;A.1.5 Error function, complementary error function, and right-tail probability function;657
1.10.1.6;A.1.6 Exponential integrals and related functions;659
1.10.1.6.1;A.1.6.1 Definition of the exponential integral;659
1.10.1.6.2;A.1.6.2 Exponential integral of first order (imaginary argument);659
1.10.1.6.3;A.1.6.3 Exponential integral of third order (real argument);659
1.10.1.6.4;A.1.6.4 Sine and cosine integral functions;660
1.10.1.7;A.1.7 Gamma function and incomplete gamma functions;660
1.10.1.7.1;A.1.7.1 Gamma function;660
1.10.1.7.1.1;A.1.7.1.1 Definition and important values;660
1.10.1.7.1.2;A.1.7.1.2 Approximations;661
1.10.1.7.1.3;A.1.7.1.3 Use of the gamma function;662
1.10.1.7.2;A.1.7.2 Incomplete gamma functions;662
1.10.1.8;A.1.8 Marcum Q functions;664
1.10.1.9;A.1.9 Elliptic integrals;664
1.10.1.10;A.1.10 Bessel and related functions;665
1.10.1.10.1;A.1.10.1 Bessel function of the first kind;665
1.10.1.10.2;A.1.10.2 Modified Bessel function;666
1.10.1.10.3;A.1.10.3 Airy functions;668
1.10.1.11;A.1.11 Hypergeometric functions;668
1.10.1.11.1;A.1.11.1 Gauss’s hypergeometricfunc tion;668
1.10.1.11.2;A.1.11.2 Confluent hypergeometricfunc tion of the first kind;669
1.10.2;A.2 FOURIER TRANSFORMS AND RELATED INTEGRALS;669
1.10.2.1;A.2.1 Forward and inverse Fourier transforms;669
1.10.2.2;A.2.2 Cross-correlation;670
1.10.2.3;A.2.3 Convolution;671
1.10.2.4;A.2.4 Discrete Fourier transform;671
1.10.2.5;A.2.5 Plancherel’s theorem;672
1.10.3;A.3 STATIONARY PHASE METHOD FOR EVALUATION OF INTEGRALS;672
1.10.3.1;A.3.1 Stationary phase approximation;672
1.10.3.2;A.3.2 Derivation;673
1.10.4;A.4 SOLUTION TO QUADRATIC, CUBIC, AND QUARTIC EQUATIONS;675
1.10.4.1;A.4.1 Quadratic equation;675
1.10.4.2;A.4.2 Cubic equation;675
1.10.4.3;A.4.3 Quartic and higher order equations;676
1.10.5;A.5 REFERENCES;676
1.11;Appendix B Units and nomenclature;678
1.11.1;B.1 UNITS;678
1.11.1.1;B.1.1 SI units;678
1.11.1.2;B.1.2 Non-SI units;678
1.11.1.3;B.1.3 Logarithmic units;678
1.11.1.3.1;B.1.3.1 Base-10 logarithmic units;679
1.11.1.3.1.1;B.1.3.1.1 Bel and decibel;679
1.11.1.3.1.2;B.1.3.1.2 pH (acidity measure);683
1.11.1.3.1.3;B.1.3.1.3 Decade;683
1.11.1.3.2;B.1.3.2 Base-e logarithmic unit (neper);684
1.11.1.3.3;B.1.3.3 Base-2 logarithmic units;684
1.11.1.3.3.1;B.1.3.3.1 Octave;684
1.11.1.3.3.2;B.1.3.3.2 Phi;684
1.11.2;B.2 NOMENCLATURE;684
1.11.2.1;B.2.1 Notation;684
1.11.2.2;B.2.2 Abbreviations and acronyms;685
1.11.2.3;B.2.3 Names of fish and marine mammals;685
1.11.3;B.3 REFERENCES;690
1.12;Appendix C Fish and their swimbladders;692
1.12.1;C.1 TABLES OF FISH AND BLADDER TYPES;692
1.12.2;C.2 REFERENCES;713
1.13;Index;714