Principles of sonar performance modeling 2010

Principles of Sonar Performance Modeling

Michael A. Ainslie
Principles of Sonar
Performance Modeling
Published in association with
PPraxisraxis PPublishingublishing
Chichester, UK

Dr Michael A. Ainslie
TNO, Sonar Department
The Hague
The Netherlands
SPRINGER–PRAXIS BOOKS IN GEOPHYSICAL SCIENCES
SUBJECT ADVISORY EDITOR: Philippe Blondel, C.Geol., F.G.S., Ph.D., M.Sc., F.I.O.A., Senior Scientist,
Department of Physics, University of Bath, Bath, UK
ISBN 978-3-540-87661-8 e-ISBN 978-3-540-87662-5
DOI 10.1007/978-3-540-87662-5
Springer Heidelberg Dordrecht London New York
Library of Congress Control Number: 2010921914
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Foreword. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
List of ﬁgures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
List of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv
PART I FOUNDATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 What is sonar? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Purpose, scope, and intended readership . . . . . . . . . . . . . . . . 4
1.3 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 Part I: Foundations (Chapters 1–3) . . . . . . . . . . . . . . 6
1.3.2 Part II: The four pillars (Chapters 4–7) . . . . . . . . . . . 6
1.3.3 Part III: Towards applications (Chapters 8–11) . . . . . . 7
1.3.4 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 A brief history of sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.1 Conception and birth of sonar (–1918) . . . . . . . . . . . . 8
1.4.2 Sonar in its infancy (1918–1939) . . . . . . . . . . . . . . . . 15
1.4.3 Sonar comes of age (1939–) . . . . . . . . . . . . . . . . . . . 17
1.4.4 Swords to ploughshares . . . . . . . . . . . . . . . . . . . . . . 22
1.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 Essential background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.1 Essentials of sonar oceanography . . . . . . . . . . . . . . . . . . . . . 27
2.1.1 Acoustical properties of seawater . . . . . . . . . . . . . . . 28
2.1.2 Acoustical properties of air . . . . . . . . . . . . . . . . . . . 30

2.2 Essentials of underwater acoustics. . . . . . . . . . . . . . . . . . . . . 30
2.2.1 What is sound? . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2 Radiation of sound . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.3 Scattering of sound . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3 Essentials of sonar signal processing . . . . . . . . . . . . . . . . . . 42
2.3.1 Temporal filter . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.3.2 Spatial filter (beamformer) . . . . . . . . . . . . . . . . . . . . 44
2.4 Essentials of detection theory . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.1 Gaussian distribution . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.2 Other distributions . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3 The sonar equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.1.1 Objectives of sonar performance modeling . . . . . . . . . . 53
3.1.2 Concepts of ‘‘signal’’ and ‘‘noise’’ . . . . . . . . . . . . . . . 54
3.1.3 Generic deep-water scenario . . . . . . . . . . . . . . . . . . . 55
3.1.4 Chapter organization . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 Passive sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.1 Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.2 Definition of standard terms (passive sonar). . . . . . . . . 58
3.2.3 Coherent processing: narrowband passive sonar . . . . . . 64
3.2.4 Incoherent processing: broadband passive sonar . . . . . . 80
3.3 Active sonar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.3.2 Definition of standard terms (active sonar) . . . . . . . . . 95
3.3.3 Coherent processing: CW pulse þ Doppler filter. . . . . . . 99
3.3.4 Incoherent processing: CW pulse þ energy detector . . . . 112
3.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
PART II THE FOUR PILLARS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
4 Sonar oceanography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.1 Properties of the ocean volume . . . . . . . . . . . . . . . . . . . . . . 126
4.1.1 Terrestrial and universal constants . . . . . . . . . . . . . . . 126
4.1.2 Bathymetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.1.3 Factors affecting sound speed and attenuation in pure
seawater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.1.4 Speed of sound in pure seawater . . . . . . . . . . . . . . . . 139
4.1.5 Attenuation of sound in pure seawater . . . . . . . . . . . . 146
4.2 Properties of bubbles and marine life . . . . . . . . . . . . . . . . . . 148
4.2.1 Properties of air bubbles in water . . . . . . . . . . . . . . . 148
4.2.2 Properties of marine life . . . . . . . . . . . . . . . . . . . . . 152
vi Contents

4.3 Properties of the sea surface . . . . . . . . . . . . . . . . . . . . . . . . 159
4.3.1 Effect of wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
4.3.2 Surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . 166
4.3.3 Wind-generated bubbles . . . . . . . . . . . . . . . . . . . . . 169
4.4 Properties of the seabed . . . . . . . . . . . . . . . . . . . . . . . . . . 171
4.4.1 Unconsolidated sediments . . . . . . . . . . . . . . . . . . . . 172
4.4.2 Rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
4.4.3 Geoacoustic models . . . . . . . . . . . . . . . . . . . . . . . . 183
4.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
5 Underwater acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.2 The wave equations for fluid and solid media . . . . . . . . . . . . . 192
5.2.1 Compressional waves in a fluid medium . . . . . . . . . . . 192
5.2.2 Compressional waves and shear waves in a solid medium 194
5.3 Reflection of plane waves . . . . . . . . . . . . . . . . . . . . . . . . . . 197
5.3.1 Reflection from and transmission through a simple fluid–
fluid or fluid–solid boundary . . . . . . . . . . . . . . . . . . 198
5.3.2 Reflection from a layered fluid boundary . . . . . . . . . . 201
5.3.3 Reflection from a layered solid boundary . . . . . . . . . . 204
5.3.4 Reflection from a perfectly reflecting rough surface . . . . 205
5.3.5 Reflection from a partially reflecting rough surface . . . . 208
5.4 Scattering of plane waves . . . . . . . . . . . . . . . . . . . . . . . . . . 209
5.4.1 Scattering cross-sections and the far field . . . . . . . . . . 209
5.4.2 Backscattering from solid objects . . . . . . . . . . . . . . . 210
5.4.3 Backscattering from fluid objects . . . . . . . . . . . . . . . . 214
5.4.4 Scattering from rough boundaries . . . . . . . . . . . . . . . 223
5.5 Dispersion in the presence of impurities . . . . . . . . . . . . . . . . . 225
5.5.1 Wood’s model for sediments in dilute suspension . . . . . 225
5.5.2 Buckingham’s model for saturated sediments with inter-
granular contact . . . . . . . . . . . . . . . . . . . . . . . . . . 226
5.5.3 Effect of bubbles or bladdered fish . . . . . . . . . . . . . . 227
5.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
6 Sonar signal processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
6.1 Processing gain for passive sonar . . . . . . . . . . . . . . . . . . . . . 252
6.1.1 Beam patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
6.1.2 Directivity index . . . . . . . . . . . . . . . . . . . . . . . . . . 266
6.1.3 Array gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
6.1.4 BB application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
6.1.5 Time domain processing . . . . . . . . . . . . . . . . . . . . . 279
6.2 Processing gain for active sonar . . . . . . . . . . . . . . . . . . . . . . 279
6.2.1 Signal carrier and envelope . . . . . . . . . . . . . . . . . . . 280
6.2.2 Simple envelopes and their spectra . . . . . . . . . . . . . . 282
Contents vii

6.2.3 Autocorrelation and cross-correlation functions and the
matched filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
6.2.4 Ambiguity function . . . . . . . . . . . . . . . . . . . . . . . . 300
6.2.5 Matched filter gain for perfect replica . . . . . . . . . . . . 306
6.2.6 Matched filter gain for imperfect replica (coherence loss) 307
6.2.7 Array gain and total processing gain (active sonar) . . . 308
6.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
7 Statistical detection theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
7.1 Single known pulse in Gaussian noise, coherent processing . . . . 312
7.1.1 False alarm probability for Gaussian-distributed noise . 312
7.1.2 Detection probability for signal with random phase . . . 313
7.1.3 Detection threshold . . . . . . . . . . . . . . . . . . . . . . . . 326
7.1.4 Application to other waveforms . . . . . . . . . . . . . . . . 327
7.2 Multiple known pulses in Gaussian noise, incoherent processing 327
7.2.1 False alarm probability for Rayleigh-distributed noise
amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
7.2.2 Detection probability for incoherently processed pulse
train . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
7.3 Application to sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
7.3.1 Active sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
7.3.2 Passive sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
7.3.3 Decision strategies and the detection threshold . . . . . . 346
7.4 Multiple looks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
7.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
7.4.2 AND and OR operations . . . . . . . . . . . . . . . . . . . . 350
7.4.3 Multiple OR operations . . . . . . . . . . . . . . . . . . . . . 354
7.4.4 ‘‘M out of N ’’ operations . . . . . . . . . . . . . . . . . . . . 356
7.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
PART III TOWARDS APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . 359
8 Sources and scatterers of sound . . . . . . . . . . . . . . . . . . . . . . . . . . 361
8.1 Reflection and scattering from ocean boundaries . . . . . . . . . . . 361
8.1.1 Reflection from the sea surface . . . . . . . . . . . . . . . . . 362
8.1.2 Scattering from the sea surface . . . . . . . . . . . . . . . . . 369
8.1.3 Reflection from the seabed . . . . . . . . . . . . . . . . . . . 375
8.1.4 Scattering from the seabed . . . . . . . . . . . . . . . . . . . 391
8.2 Target strength, volume backscattering strength, and volume
attenuation coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
8.2.1 Target strength of point-like scatterers . . . . . . . . . . . . 400
8.2.2 Volume backscattering strength and attenuation coeffi-
cient of distributed scatterers . . . . . . . . . . . . . . . . . . 409
8.2.3 Column strength and wake strength of extended volume
scatterers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
viii Contents

8.3 Sources of underwater sound . . . . . . . . . . . . . . . . . . . . . . . 414
8.3.1 Shipping source spectrum level measurements . . . . . . . 417
8.3.2 Distributed sources on the sea surface . . . . . . . . . . . . 424
8.3.3 Distributed sources on the seabed (crustacea) . . . . . . . 429
8.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
9 Propagation of underwater sound. . . . . . . . . . . . . . . . . . . . . . . . . . 439
9.1 Propagation loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
9.1.1 Effect of the seabed in isovelocity water . . . . . . . . . . . 440
9.1.2 Effect of a sound speed profile . . . . . . . . . . . . . . . . . 459
9.2 Noise level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
9.2.1 Deep water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
9.2.2 Shallow water . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
9.2.3 Noise maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
9.3 Signal level (active sonar) . . . . . . . . . . . . . . . . . . . . . . . . . 491
9.3.1 The reciprocity principle . . . . . . . . . . . . . . . . . . . . . 492
9.3.2 Calculation of echo level . . . . . . . . . . . . . . . . . . . . . 493
9.3.3 V-duct propagation (isovelocity case) . . . . . . . . . . . . . 494
9.3.4 U-duct propagation (linear profile) . . . . . . . . . . . . . . 494
9.4 Reverberation level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
9.4.1 Isovelocity water . . . . . . . . . . . . . . . . . . . . . . . . . . 497
9.4.2 Effect of refraction . . . . . . . . . . . . . . . . . . . . . . . . . 500
9.5 Signal-to-reverberation ratio (active sonar) . . . . . . . . . . . . . . 508
9.5.1 V-duct (isovelocity case) . . . . . . . . . . . . . . . . . . . . . 508
9.5.2 U-duct (linear profile) . . . . . . . . . . . . . . . . . . . . . . . 509
9.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510
10 Transmitter and receiver characteristics. . . . . . . . . . . . . . . . . . . . . . 513
10.1 Transmitter characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 514
10.1.1 Of man-made systems . . . . . . . . . . . . . . . . . . . . . . . 515
10.1.2 Of marine mammals . . . . . . . . . . . . . . . . . . . . . . . . 542
10.2 Receiver characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545
10.2.1 Of man-made sonar . . . . . . . . . . . . . . . . . . . . . . . . 545
10.2.2 Of marine mammals, amphibians, human divers, and fish 549
10.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
11 The sonar equations revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573
11.2 Passive sonar with coherent processing: tonal detector . . . . . . . 574
11.2.1 Sonar equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 574
11.2.2 Source level (SL) . . . . . . . . . . . . . . . . . . . . . . . . . . 575
11.2.3 Narrowband propagation loss (PL) . . . . . . . . . . . . . . 576
11.2.4 Noise spectrum level (NLf ) . . . . . . . . . . . . . . . . . . . 578
11.2.5 Bandwidth (BW) . . . . . . . . . . . . . . . . . . . . . . . . . . 579
11.2.6 Array gain (AG) and directivity index (DI) . . . . . . . . . 580
Contents ix

11.2.7 Detection threshold (DT) . . . . . . . . . . . . . . . . . . . . . 581
11.2.8 Worked example . . . . . . . . . . . . . . . . . . . . . . . . . . 583
11.3 Passive sonar with incoherent processing: energy detector . . . . . 591
11.3.1 Sonar equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
11.3.2 Source level (SL) . . . . . . . . . . . . . . . . . . . . . . . . . . 592
11.3.3 Broadband propagation loss (PL) . . . . . . . . . . . . . . . 592
11.3.4 Broadband noise level (NL) . . . . . . . . . . . . . . . . . . . 593
11.3.5 Processing gain (PG) . . . . . . . . . . . . . . . . . . . . . . . 593
11.3.6 Broadband detection threshold (DT) . . . . . . . . . . . . . 597
11.3.7 Worked example . . . . . . . . . . . . . . . . . . . . . . . . . . 599
11.4 Active sonar with coherent processing: matched ﬁlter . . . . . . . 606
11.4.1 Sonar equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
11.4.2 Echo level (EL), target strength (TS), and equivalent
target strength (TSeq). . . . . . . . . . . . . . . . . . . . . . . . 607
11.4.3 Background level (BL) . . . . . . . . . . . . . . . . . . . . . . . 610
11.4.4 Processing gain (PG) . . . . . . . . . . . . . . . . . . . . . . . 610
11.4.5 Detection threshold (DT) . . . . . . . . . . . . . . . . . . . . . 612
11.4.6 Worked example . . . . . . . . . . . . . . . . . . . . . . . . . . 613
11.5 The future of sonar performance modeling . . . . . . . . . . . . . . 630
11.5.1 Advances in signal processing and oceanographic model-
ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
11.5.2 Autonomous platforms . . . . . . . . . . . . . . . . . . . . . . 631
11.5.3 Environmental impact of anthropogenic sound . . . . . . . 631
11.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 632
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
A Special functions and mathematical operations . . . . . . . . . . . . . . . . . 635
A.1 Deﬁnitions and basic properties of special functions . . . . . . . . 635
A.1.1 Heaviside step function, sign function, and rectangle
function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
A.1.2 Sine cardinal and sinh cardinal functions . . . . . . . . . . 636
A.1.3 Dirac delta function . . . . . . . . . . . . . . . . . . . . . . . . 636
A.1.4 Fresnel integrals . . . . . . . . . . . . . . . . . . . . . . . . . . 636
A.1.5 Error function, complementary error function, and right-
tail probability function . . . . . . . . . . . . . . . . . . . . . 637
A.1.6 Exponential integrals and related functions . . . . . . . . . 639
A.1.7 Gamma function and incomplete gamma functions . . . . 640
A.1.8 Marcum Q functions . . . . . . . . . . . . . . . . . . . . . . . . 644
A.1.9 Elliptic integrals . . . . . . . . . . . . . . . . . . . . . . . . . . 644
A.1.10 Bessel and related functions . . . . . . . . . . . . . . . . . . . 645
A.1.11 Hypergeometric functions . . . . . . . . . . . . . . . . . . . . 648
A.2 Fourier transforms and related integrals . . . . . . . . . . . . . . . . 649
A.2.1 Forward and inverse Fourier transforms . . . . . . . . . . 649
A.2.2 Cross-correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 650
x Contents

A.2.3 Convolution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651
A.2.4 Discrete Fourier transform . . . . . . . . . . . . . . . . . . . 651
A.2.5 Plancherel’s theorem . . . . . . . . . . . . . . . . . . . . . . . . 652
A.3 Stationary phase method for evaluation of integrals . . . . . . . . 652
A.3.1 Stationary phase approximation . . . . . . . . . . . . . . . . 652
A.3.2 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653
A.4 Solution to quadratic, cubic, and quartic equations . . . . . . . . . 655
A.4.1 Quadratic equation . . . . . . . . . . . . . . . . . . . . . . . . 655
A.4.2 Cubic equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 655
A.4.3 Quartic and higher order equations . . . . . . . . . . . . . . 656
A.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656
B Units and nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659
B.1 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659
B.1.1 SI units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659
B.1.2 Non-SI units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659
B.1.3 Logarithmic units . . . . . . . . . . . . . . . . . . . . . . . . . 659
B.2 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665
B.2.1 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665
B.2.3 Names of ﬁsh and marine mammals . . . . . . . . . . . . . 666
B.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671
C Fish and their swimbladders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673
C.1 Tables of ﬁsh and bladder types . . . . . . . . . . . . . . . . . . . . . 673
C.2 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
Contents xi

Preface
The science of sonar performance modeling is traditionally separated into a ‘‘wet end’’
comprising the disciplines of acoustics and oceanography and a ‘‘dry end’’ of signal
processing and detection theory. This book is my attempt to bring both aspects
together to serve as a modern reference for today’s sonar performance modeler,
whether for research, design, or analysis, as Urick’s Principles of Underwater Sound
did for sonar engineers of his day. The similarity in the title is no accident.
During the process I made some valuable discoveries that I now share with the
reader. The radar literature provides a deep mine of resources, with applicable results
from the theories of wave propagation, signal processing, and (an especially rich vein,
largely unexploited in the sonar literature) statistical detection. From oceanography
we learn that each of the world’s oceans has its own unique physical, chemical, and
biological signature, with sometimes profound consequences for sonar.
Marine mammals have evolved a sonar of their own, the remarkable properties of
which we are only beginning to unravel, as reported in the increasingly sophisticated
bioacoustics literature. Governments and industry around the world have begun to
take seriously the environmental consequences of man’s use, whether deliberate or
incidental, of sound in the sea. I have done my best to provide a representative
snapshot of this rapidly developing field.
Some readers will treat this book as a repository of facts, figures, and formulas,
while others will seek in it explanations and clarity. It has been my intention to satisfy
the needs of both types of reader by including mathematical derivations and worked
examples, supplemented with measurements or estimates of relevant input param-
eters. Of all readers I request the patience to overlook the flaws that undoubtedly
remain, despite my best attempts to weed them out.
Michael A. Ainslie
TNO, The Hague, The Netherlands, March 2010

Foreword
Underwater acoustics is largely a branch of physics, perhaps merging with geophysics
and oceanography, but as soon as one attempts to assess a sonar’s performance under
realistic conditions, a host of other engineering factors come into play. Is the desired
target signal louder than all the other natural noise from wind, waves, ship engines,
strumming cables? Is it louder than sound scattered from other distant objects? How
do the standard signal-processing techniques such as beamforming, spectral analysis,
and statistical analysis influence the probability of achieving a target detection and the
probability of a false alarm?
The author, Dr. Mike Ainslie, is a physicist with a considerable academic
publication record and many years’ hands-on experience in sonar assessment for
the U.K.’s MOD and for TNO in The Netherlands. Through a firm foundation in
physics, always taking great care over the physical units, Principles of Sonar Per-
formance Modeling introduces rigor and clarity into the traditional sonar equation
while still answering the fundamental engineering questions. As well as dealing with
the more pure disciplines of sound generation, propagation, and reverberation, it
tackles sound sources, targets, signal processing, and detection theory for man-made
and biological sonar.
Underlying all this is a desire ‘‘to see the wood for the trees’’. For instance, it is
often the case with propagation that, despite all the complexities of refraction,
reflection, diffraction, scattering, and so on, some simple mechanism dominates,
and sometimes one can express the entire transmission loss, ambient noise level,
or reverberation level by a simple formula. This insight, or even revelation, is an
important bonus and check if one is to have faith in numerical assessment of
complicated search scenarios. It can also become a useful shortcut when a particular
scenario is to be investigated under many different acoustic, or processing, conditions.
Examples of such insights will be found throughout.
The cornerstone is the derivation of the sonar equations—too often presented as
indisputable fact—from simple physical principles. The derivation is presented

initially in terms of ratios of simple physical quantities, and converted to decibels only
at the end. Such an approach provides both clarity and a systematic rationale for
determining how to evaluate each sonar equation term, and occasionally throws up
unexpected new corrections.
The book will provide a useful reference for acousticians, engineers, physicists,
mathematicians, sonar designers, and naval sonar operators whether working in
research labs, the defense industry, or universities.
Chris Harrison
NATO Undersea Research Centre (NURC), Italy, March 2010
xvi Foreword

Acknowledgments
The eight years it has taken me to write this book were spent working at TNO in
The Hague. It has been a pleasure and a privilege to do so. The Sonar Department,
despite two changes of name and two changes of leadership in that time, has provided
constant support and understanding for the necessary extra-curricular activities.
I wish to thank all at TNO—too many to mention all by name—who helped to make
it possible.
I thank D. A. Abraham, P. Blondel, D. M. F. Chapman, P. H. Dahl,
C. A. F. de Jong, P. A. M. de Theije, D. D. Ellis, R. M. Hamson, C. H. Harrison,
J. A. Harrison, R. A. Hazelwood, D. V. Holliday, T. G. Leighton, A. J. Robins,
S. P. Robinson, C. A. M. van Moll, K. L. Williams, M. Zampolli, and two anonymous
referees, all of whom reviewed at least one complete chapter and helped to improve the
quality of the final product. Any remaining errors that find their way into print are
entirely mine and not of the reviewers.
Through his written publications, David Weston is an eternal inspiration—I have
lost count of the number of times his name is cited. I also benefited from discussions
with Chris Harrison, Chris Morfey, Christ de Jong, Dale Ellis, Frans-Peter Lam,
Mario Zampolli, Peter Dahl, and Tim Leighton.
Data or artwork were made available to me by Pascal de Theije (Figure 7.6),
Peter Dahl (Figure 8.3), Alvin Robins (Figure 8.5), Vincent van Leijen (Figure 8.13),
Peter van Holstein (Figure 8.14), Henry Dol (Figures 9.24 and 9.25), Mathieu Colin
(all figures in Chapter 9 making use of either BELLHOP or SCOOTER),
Robbert van Vossen (Figures 9.28 and 9.29), Wim Verboom (miscellaneous seal
and porpoise audiograms), Garth Mix (thumbnail images of marine mammals),
and Paul Wensveen (Figure 11.20).
The computer model INSIGHT (version 1.4.2) was used, with permission of
CORDA Ltd., to illustrate many of the sonar performance calculations. Also used
were the acoustic propagation models SCOOTER and BELLHOP from the Ocean
Acoustics Library (http://oalib.hlsresearch.com). Other valuable Internet resources

include FishBase (www.ﬁshbase.org), the Ocean Biogeographic Information System
(www.iobis.org), Mathworld (http://mathworld.wolfram.com) and Wikipedia (www.
wikipedia.org).
Phillipe Blondel and Clive Horwood were always available when needed for
advice. Neil Shuttlewood is responsible for a professional end-product.
Last but not least, none of this would have been possible without the
unquestioning love and support from my wife Pilar and patience of my daughter
Anna, whose teenage years are forever tinted with shades of sonar performance.
Michael A. Ainslie
TNO, The Hague, The Netherlands, March 2010
xviii Acknowledgments

Figures
1.1 Sketch of Beudant’s experiment of ca. 1816 . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Sketch of the Colladon–Sturm experiment of 1826 . . . . . . . . . . . . . . . . . . . 9
1.3 Inventor Reginald Fessenden and physicist Jean Daniel Colladon . . . . . . . . 9
1.4 Physicists Paul Langevin and Robert William Boyle . . . . . . . . . . . . . . . . . . 11
1.5 French statesman and mathematician Paul Painleve´ . . . . . . . . . . . . . . . . . . 13
1.6 Installation of early U.S. passive-ranging sonar with two towed eels . . . . . . 15
1.7 Sound absorption vs. frequency in seawater . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Attenuation coefficient and audibility vs. frequency in seawater . . . . . . . . . . 30
2.2 Radiation from a point source of power W in free space . . . . . . . . . . . . . . 33
2.3 Radiation from a point source in the presence of a reflecting boundary . . . . 35
2.4 Radiation from a sheet source element of width r. . . . . . . . . . . . . . . . . . . 38
2.5 Beam patterns for L= ¼ 5 and steering angles 0, 45 deg. . . . . . . . . . . . . . . 46
2.6 Probability density functions of noise and signal-plus-noise observables . . . 50
3.1 Principles of passive detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2 Spectral density level of the radiated power at the source and intensity at the
receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3 Spectral density level of the transmitter source factor and mean square pressure
at the receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.4 Coherent propagation loss vs. range and target depth. . . . . . . . . . . . . . . . . 66
3.5 Spectral density level of background noise. . . . . . . . . . . . . . . . . . . . . . . . . 67
3.6 Spectral density level of signal and noise . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.7 ROC curves for a Rayleigh-distributed signal in Rayleigh noise. . . . . . . . . . 72
3.8 Propagation loss and figure of merit vs. target range . . . . . . . . . . . . . . . . . 76
3.9 Signal level vs. target range, and in-beam noise level . . . . . . . . . . . . . . . . . 77
3.10 Linear signal excess and twice detection probability vs. range for NB passive
sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.11 Signal excess vs. target range and depth . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.12 Spectral density level of the transmitter source factor and mean square pressure
at the receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.13 Propagation loss vs. frequency and target range . . . . . . . . . . . . . . . . . . . . . 83

3.14 Spectral density level of signal and noise . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.15 ROC curves for a BB signal in Rayleigh noise . . . . . . . . . . . . . . . . . . . . . . 86
3.16 Propagation loss and figure of merit vs. range . . . . . . . . . . . . . . . . . . . . . . 91
3.17 Signal spectrum level vs. range, and in-beam noise spectrum level . . . . . . . . 92
3.18 Linear signal excess and twice detection probability vs. range for BB passive
sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.19 Propagation loss vs. range and depth for the BB passive worked example . . 94
3.20 Principles of active detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.21 Propagation loss and figure of merit vs. target range at fixed array depth and vs.
array depth for fixed range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
3.22 Signal level and in-beam noise level vs. target range at fixed array depth and vs.
3.23 Linear signal excess and twice detection probability for coherent CW active
sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
3.24 Signal excess vs. target range and array depth . . . . . . . . . . . . . . . . . . . . . . 111
3.25 Signal and (in-beam) background levels vs. target range at fixed array depth and
vs. array depth for fixed range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.26 Total background, background components, and in-beam background level vs.
target range at fixed array depth and vs. array depth for fixed range . . . . . . 119
3.27 Propagation loss and figure of merit vs. target range at fixed array depth and vs.
3.28 Linear signal excess and twice detection probability for incoherent CW active
sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.1 Global bathymetry map derived from satellite measurements of the gravity field 127
4.2 Annual average temperature map at depth 3 km. . . . . . . . . . . . . . . . . . . . . 129
4.3 Geographical variations in surface temperature for northern winter and
northern summer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.4 Temperature profiles for locations in the northwest Pacific Ocean and northeast
Atlantic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.5 Bathymetry map for the northwest Pacific Ocean . . . . . . . . . . . . . . . . . . . . 132
4.6 Bathymetry map for the north Atlantic Ocean . . . . . . . . . . . . . . . . . . . . . . 132
4.7 Annual average salinity map at depth 3 km . . . . . . . . . . . . . . . . . . . . . . . . 133
4.8 Temperature salinity diagram for the World Ocean . . . . . . . . . . . . . . . . . . 134
4.9 Seasonal variations in surface salinity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.10 Salinity profiles for locations in the northwest Pacific Ocean and northeast
Atlantic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
4.11 Density profiles for locations in the northwest Pacific Ocean and northeast
Atlantic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.12 Global acidity (K) contours at sea surface and at depth 1 km . . . . . . . . . . . 140
4.13 Arctic acidity (K) contours at the sea surface and at depth 1 km . . . . . . . . . 142
4.14 Acidity (K) profiles for major oceans . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
4.15 Sound speed profiles for locations in the northwest Pacific Ocean and northeast
Atlantic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
4.16 Seawater attenuation coefficient vs. frequency . . . . . . . . . . . . . . . . . . . . . . 149
4.17 Fractional sensitivity of seawater attenuation to temperature, salinity, acidity,
and depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.18 Geographical distribution of herring and Norway pout in the North Sea . . . 160
4.19 Wind speed scaling factors to convert from a 20 m reference height to the
standard reference height of 10 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
xx Figures

4.20 Near-surface bubble population density spectra . . . . . . . . . . . . . . . . . . . . . 170
4.21 Compressional and shear speed vs. density of rocks . . . . . . . . . . . . . . . . . . 181
4.22 Compressional and shear speeds vs. density for all rocks and for basalts . . . 183
5.1 Illustration of compressional and shear wave propagation. . . . . . . . . . . . . . 195
5.2 Fluid sediment layer between two uniform half-spaces . . . . . . . . . . . . . . . . 202
5.3 Form function j f ðkaÞj vs. ka for a rigid sphere, a tungsten carbide sphere, and
spheres made of various metals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
5.4 Resonance frequency vs. bubble radius for air bubbles in water. . . . . . . . . . 238
5.5 Resonant bubble radius vs. frequency for air bubbles in water. . . . . . . . . . . 241
6.1 Sinc beam patterns for steering angles 0, 30, 60, and 90 deg . . . . . . . . . . . . 254
6.2 Beam patterns for continuous line array: cosine and Hann shading . . . . . . . 258
6.3 Beam patterns for continuous line array: raised cosine shading . . . . . . . . . . 260
6.4 Hamming family shading patterns and beam patterns. . . . . . . . . . . . . . . . . 262
6.5 Beam pattern of unshaded circular array. . . . . . . . . . . . . . . . . . . . . . . . . . 265
6.6 Directivity index for an unsteered continuous line array vs. normalized array
length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
6.7 Directivity index vs. steering angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
6.8 Shading factor vs. steering angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
6.9 Power spectrum for a Gaussian LFM pulse . . . . . . . . . . . . . . . . . . . . . . . . 288
6.10 Power spectrum for a rectangular LFM pulse . . . . . . . . . . . . . . . . . . . . . . 289
6.11 Generic ambiguity surface for Gaussian CW pulse . . . . . . . . . . . . . . . . . . . 302
6.12 Ambiguity surfaces for Gaussian CW pulses of duration 0.5 s and 2.0 s . . . . 303
6.13 Generic ambiguity surfaces for Gaussian LFM pulse . . . . . . . . . . . . . . . . . 305
7.1 ROC curves for non-fluctuating amplitude signal in Rayleigh noise . . . . . . . 315
7.2 Rayleigh, one-dominant-plus-Rayleigh, Dirac, and Rice probability distribu-
tion functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
7.3 ROC curves for Rayleigh-fading signal in Rayleigh noise . . . . . . . . . . . . . . 319
7.4 ROC curves for Rician fading signal in Rayleigh noise. . . . . . . . . . . . . . . . 321
7.5 Rice probability density functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
7.6 ROC curves for 1D þ R signal in Rayleigh noise . . . . . . . . . . . . . . . . . . . . 324
7.7 Graph of xðMÞ vs. M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
7.8 ROC curves (Albersheim approximation) for a non-fluctuating amplitude
signal: variation of detection threshold with M for fixed pfa . . . . . . . . . . . . 332
7.9 ROC curves (Albersheim approximation) for a non-fluctuating amplitude
signal: variation of detection threshold with pfa for fixed M . . . . . . . . . . . . 333
7.10 ROC curves for a non-fluctuating amplitude signal: incoherent addition with
M ¼ 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
7.11 ROC curves for a non-fluctuating amplitude signal: incoherent addition with
M ¼ 1 to M ¼ 300 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
7.12 ROC curves for a broadband signal: limit of large M. . . . . . . . . . . . . . . . . 338
7.13 Supplementary ROC curves for a broadband non-fluctuating signal. . . . . . . 339
7.14 ROC curves for a Rayleigh fading signal: incoherent addition with M ¼ 30 . 341
7.15 ROC curves for a 1D þ R signal: incoherent addition with M ¼ 30 . . . . . . . 343
7.16 Fusion gain vs. pfa for OR operation (fixed pd) . . . . . . . . . . . . . . . . . . . . . 352
7.17 Fusion gain vs. F for OR operation (fixed D) . . . . . . . . . . . . . . . . . . . . . . 353
7.18 ROC curves for a non-fluctuating signal: effect of AND and OR fusion. . . . 354
7.19 ROC curves for a 1D þ R signal: effect of AND and OR fusion . . . . . . . . . 355
7.20 ROC curves for a Rayleigh-fading signal: effect of AND and OR fusion . . . 356
8.1 Variation of surface reflection loss with wind speed (1–4 kHz) . . . . . . . . . . . 366
Figures xxi

8.2 Surface reflection loss in nepers calculated vs. angle and frequency . . . . . . . 368
8.3 Surface reflection loss vs. wind speed (30 kHz) . . . . . . . . . . . . . . . . . . . . . . 369
8.4 Seabed reflection loss vs. grazing angle for uniform unconsolidated sediments 376
8.5 Seabed reflection loss vs. angle and frequency–sediment thickness product for a
layered unconsolidated sediment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
8.6 Seabed reflection loss vs. angle for rocks . . . . . . . . . . . . . . . . . . . . . . . . . . 385
sand sediment overlying a granite basement and clay over basalt. . . . . . . . . 387
sand sediment of thickness 10 m overlying a granite basement and a clay
sediment of thickness 300 m over basalt. . . . . . . . . . . . . . . . . . . . . . . . . . . 390
8.9 Seabed backscattering strength for a medium sand sediment and frequency
1–30 kHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
8.10 Comparison between predicted and measured seabed backscattering strength
for a fine sand sediment and frequency 35 kHz. . . . . . . . . . . . . . . . . . . . . . 394
8.11 Seabed backscattering strength for a coarse clay sediment. . . . . . . . . . . . . . 395
8.12 Comparison between predicted and measured seabed backscattering strength
for a medium silt sediment and frequency 20 kHz. . . . . . . . . . . . . . . . . . . . 396
8.13 Typical ambient noise spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416
8.14 Typical values of sound pressure level and peak pressure level. . . . . . . . . . . 418
8.15 Measured equivalent source spectral density levels: commercial and industrial
shipping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
8.16 Estimated third-octave monopole source level: cargo ship Overseas Harriette 423
8.17 Areic dipole source spectrum: wind noise . . . . . . . . . . . . . . . . . . . . . . . . . 426
8.18 Areic dipole source spectrum: rain noise . . . . . . . . . . . . . . . . . . . . . . . . . . 428
8.19 Measured waveform and frequency spectrum of a single shrimp snap . . . . . 430
9.1 Geometry for bottom reflections in deep water . . . . . . . . . . . . . . . . . . . . . 441
9.2 Propagation loss vs. range for reflecting seabed at f ¼ 250 Hz . . . . . . . . . . . 442
9.3 Bottom-refracted ray paths travel through the sediment and form a caustic in
the reflected field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
9.4 Propagation loss vs. range for a reflecting and refracting seabed at f ¼ 250 Hz 446
9.5 Propagation loss vs. range for a reflecting and refracting seabed: sensitivity to
sediment properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
9.6 Reflection loss vs. angle for sand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
9.7 Propagation loss vs. range, and reflection loss vs. angle for sand and mud in
shallow water at frequency 250 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
9.8 Sound speed profile in the northwest Pacific . . . . . . . . . . . . . . . . . . . . . . . 460
9.9 Propagation loss vs. range for northwest Pacific summer and winter at
f ¼ 1500 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463
9.10 Propagation loss vs. range and depth for northwest Pacific winter profile: effect
of upward refraction in surface duct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465
9.11 Depth factor vs. receiver depth in surface duct. . . . . . . . . . . . . . . . . . . . . . 469
9.12 Ray trace illustrating formation of caustics and cusps in surface duct up to a
range of 40 km, for a source depth of 30 m, and for the same case as Figure 9.10 470
9.13 Propagation loss vs. frequency and range for a surface duct . . . . . . . . . . . . 473
9.14 Ray trace illustrating the formation of convergence zones at the sea surface 475
9.15 Propagation loss vs. range and depth: effect of downward refraction on Lloyd
mirror interference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
xxii Figures

9.16 Propagation loss vs. range for shallow water with a mud bottom for two
different sound speed profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
9.17 Approximation to D= for fixed min . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
9.18 Predicted deep ocean noise spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
9.19 Sensitivity of deep-water ambient noise spectra to rain rate. . . . . . . . . . . . . 486
9.20 Sensitivity of deep-water noise spectra to wind speed . . . . . . . . . . . . . . . . . 487
9.21 Predicted ambient noise spectral density level vs. frequency and depth . . . . . 488
9.22 Effect of the seabed on the ambient noise spectrum in isovelocity water . . . . 489
9.23 Effect of the sound speed profile on the ambient noise spectrum for a clay seabed 490
9.24 Dredger noise map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
9.25 Bathymetry used for Figure 9.24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
9.26 Reverberation for problem RMW11 and frequency 3.5 kHz . . . . . . . . . . . . 499
9.27 Reverberation depth factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
9.28 Reverberation for problem RMW12 and frequency 3.5 kHz . . . . . . . . . . . . 504
9.29 Reverberation for problem RMW12 and frequency 3.5 kHz (close-up) . . . . . 505
9.30 Ray trace illustrating formation of caustics and cusps in a bottom duct, and
propagation loss vs. range and depth at f ¼ 3.5 kHz. . . . . . . . . . . . . . . . . . 506
9.31 SRR depth factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
10.1 Maximum multibeam echo sounder and sidescan sonar source levels vs.
transmitter frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
10.2 Unweighted and Gaussian-weighted cosine pulses from Table 10.16 . . . . . . 530
10.3 Exponentially damped sine and decaying exponential pulses from Table 10.17 532
10.4 Mean square pressure vs. energy fraction. . . . . . . . . . . . . . . . . . . . . . . . . . 535
10.5 Comparison of echolocation pulses made by the harbor porpoise and killer
whale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548
10.6 Underwater audiograms for harbor porpoise . . . . . . . . . . . . . . . . . . . . . . . 551
10.7 Underwater audiograms for killer whale . . . . . . . . . . . . . . . . . . . . . . . . . . 552
10.8 Underwater audiograms for harbor seal . . . . . . . . . . . . . . . . . . . . . . . . . . 554
10.9 Underwater audiograms for human divers . . . . . . . . . . . . . . . . . . . . . . . . . 556
10.10 Underwater sound level weighting curves for three groups of cetaceans plus
pinnipeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561
11.1 Directivity index DI ¼ 10 log10 GD for an unsteered continuous line array vs.
normalized array length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581
11.2 ROC curves for 1D þ R amplitude signal in Rayleigh noise . . . . . . . . . . . . 582
11.3 Propagation loss vs. range for NWP winter case . . . . . . . . . . . . . . . . . . . . 584
11.4 In-beam signal and noise levels vs. range for NWP winter and Chapter 3 NBp
worked example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
11.5 Input parameters for northwest Pacific (NWP) problem . . . . . . . . . . . . . . . 588
11.6 Signal excess vs. range and depth for NWP winter . . . . . . . . . . . . . . . . . . . 589
11.7 Signal excess vs. range and depth for NWP winter: close-up of first convergence
zone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590
11.8 Albersheim’s approximation for the detection threshold . . . . . . . . . . . . . . . 598
11.9 Propagation loss vs. range and depth for SWS and for the Chapter 3 BBp
worked example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600
11.10 Signal and noise spectra for SWS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601
11.11 In-beam signal and noise levels vs. range for SWS and BBp . . . . . . . . . . . . 602
11.12 Signal excess vs. range and depth for SWS . . . . . . . . . . . . . . . . . . . . . . . . 603
11.13 Input parameters for shallow-water sand (SWS). . . . . . . . . . . . . . . . . . . . . 604
11.14 In-beam signal and noise spectra for SWS . . . . . . . . . . . . . . . . . . . . . . . . . 605
Figures xxiii

11.15 Signal excess vs. range and rainfall rate for SWS . . . . . . . . . . . . . . . . . . . . 606
11.16 Geometry for worked example involving killer whale hunting salmon . . . . . 614
11.17 Example measurements of orca pulse shapes and power spectra . . . . . . . . . 615
11.18 Variation in orca source level with distance from target . . . . . . . . . . . . . . . 617
11.19 Propagation loss vs. distance and broadband correction . . . . . . . . . . . . . . . 618
11.20 Orca audiogram and individual hearing threshold measurements . . . . . . . . . 620
11.21 Echo level and noise level vs. distance between orca and salmon: wind speed
2 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621
11.22 Echo level and noise level vs. distance between orca and salmon: wind speed 2 to
10 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624
11.23 Background level vs. distance between orca and salmon: wind speed 10 m/s . 628
11.24 Array gain vs. distance between orca and salmon: wind speed 10 m/s . . . . . . 629
11.25 Signal and background levels vs. distance between orca and salmon: wind speed
10 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
A.1 The complementary error function erfcðxÞ and three approximations . . . . . . 638
A.2 The gamma function and four approximations. . . . . . . . . . . . . . . . . . . . . . 643
A.3 The modiﬁed Bessel function and Levanon’s approximation . . . . . . . . . . . . 647
xxiv Figures

Tables
2.1 Detection truth table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1 Sonar equation calculation for NB passive example . . . . . . . . . . . . . . . . . . 76
3.2 Sonar equation calculation for BB passive example . . . . . . . . . . . . . . . . . . 90
3.3 Sonar equation calculation for CW active sonar example with Doppler filter 107
3.4 Sonar equation calculation for CW active sonar example with incoherent
energy detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.1 Average salinity and potential temperature by major ocean basin . . . . . . . . 133
4.2 Seawater parameters used for evaluation of attenuation curves plotted in Figure
4.16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.3 Mass, length, and aspect ratio of selected sea mammals . . . . . . . . . . . . . . . 154
4.4 Volume and surface area of ellipsoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.5 Acoustical properties of fish flesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.6 Acoustical properties of whale tissue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
4.7 Acoustical properties of euphausiids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.8 Values of zooplankton density and sound speed ratios . . . . . . . . . . . . . . . . 157
4.9 North Sea fish population estimates by species. . . . . . . . . . . . . . . . . . . . . . 158
4.10 WMO Beaufort wind force scale and estimated wind speed. . . . . . . . . . . . . 162
4.11 Comparison of wind speed estimates for Beaufort force 1–11 based on WMO
code 1100 and CMM-IV with those of da Silva . . . . . . . . . . . . . . . . . . . . . 165
4.12 Definition of sea state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
4.13 Beaufort wind force: relationship between wind speed and wave height . . . . 168
4.14 Sea state: relationship between wave height and wind speed . . . . . . . . . . . . 168
4.15 Sediment type vs. grain diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
4.16 Definition of sediment grain sizes and qualitative descriptions . . . . . . . . . . . 174
4.17 Default HF geoacoustic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
4.18 Default MF geoacoustic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
4.19 Names of sedimentary rocks resulting from the lithification of different
sediment types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
4.20 Geoacoustic parameters for sedimentary and igneous rocks. . . . . . . . . . . . . 183

5.1 Compressional speed, shear speed, and density used to calculate the form
factors for the four metals shown in Figure 5.3 . . . . . . . . . . . . . . . . . . . . . 212
5.2 Backscattering cross-sections of large rigid objects . . . . . . . . . . . . . . . . . . . 213
5.3 Backscattering cross-sections of large fluid objects . . . . . . . . . . . . . . . . . . . 215
5.4 Water and solid grain sediment parameter values needed for Buckingham’s
grain-shearing model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
5.5 Values of physical constants used for the evaluation of the bubble resonance
characteristics in Figures 5.4 and 5.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
6.1 Summary of properties for various taper functions. . . . . . . . . . . . . . . . . . . 264
6.2 Summary of beam properties for selected shading . . . . . . . . . . . . . . . . . . . 265
6.3 Summary of frequency domain properties of simple pulse envelopes . . . . . . 284
6.4 Summary of time domain properties of simple pulse shapes (envelope). . . . . 285
6.5 Summary of time domain properties of simple pulse shapes (phase). . . . . . . 285
6.6 Summary of amplitude envelopes required to synthesize simple power spectra 291
6.7 Autocorrelation functions for CW and LFM pulses . . . . . . . . . . . . . . . . . . 296
6.8 Derivation of matched filter gain for pulse duration and sample interval . . . 306
6.9 Effect of multipath on matched filter gain . . . . . . . . . . . . . . . . . . . . . . . . . 308
7.1 Comparison table: moments of probability distribution functions . . . . . . . . 320
7.2 DT þ 5 log10 M vs. M and pfa for three different pd values . . . . . . . . . . . . . 334
7.3 Application of the detection theory results of Section 7.1 to active sonar CW
and FM pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
7.4 Equations for the detection probability for different signal amplitude distribu-
tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
7.5 Application of detection theory results to NB and BB passive sonar . . . . . . 346
7.6 Detection threshold for various statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 347
7.7 Detection threshold for a 1D þ R amplitude distribution . . . . . . . . . . . . . . 348
7.8 ROC relationships and fusion gain for AND and OR operations for fixed SNR 353
8.1 Sediment properties at top and bottom of the transition layer . . . . . . . . . . . 381
8.2 p and s critical angles for representative rock parameters . . . . . . . . . . . . . . 385
8.3 Parameters for uniform fluid sediment and rock half-space . . . . . . . . . . . . . 388
8.4 Defining parameters for a layered solid medium. . . . . . . . . . . . . . . . . . . . . 389
8.5 Measurements of the Lambert parameter . . . . . . . . . . . . . . . . . . . . . . . . . 397
8.6 Target strength measurements for bladdered fish . . . . . . . . . . . . . . . . . . . . 401
8.7 Target strength measurements for whales . . . . . . . . . . . . . . . . . . . . . . . . . 403
8.8 Target strength measurements for euphausiids and bladder-less fish . . . . . . . 404
8.9 Target strength measurements for jellyfish . . . . . . . . . . . . . . . . . . . . . . . . . 407
8.10 Target strength measurements for siphonophores . . . . . . . . . . . . . . . . . . . . 407
8.11 Second World War measurements of the target strength of man-made objects 408
8.12 Predicted average night-time contribution to VBS, CS, and attenuation due to
pelagic fish in the North Sea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410
8.13 Default advice for VBS for sparse, intermediate, and dense marine life . . . . 411
8.14 Wake strength measurements for various WW2 surface ships . . . . . . . . . . . 414
8.15 Wake strength for various WW2 submarines . . . . . . . . . . . . . . . . . . . . . . . 414
8.16 Third-octave source levels of various commercial and industrial vessels . . . . 421
9.1 Characteristic properties from Chapter 4 of medium sand and mud. . . . . . . 454
9.2 Sound speed profiles for the northwest Pacific location. . . . . . . . . . . . . . . . 461
9.3 Nomenclature used for shipping densities . . . . . . . . . . . . . . . . . . . . . . . . . 484
9.4 Seabed parameters for problems RMW11 and RMW12 . . . . . . . . . . . . . . . 500
xxvi Tables

9.5 Caustic ranges and corresponding two-way travel arrival times for a source at
depth 30 m and receiver at depth 50 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . 507
10.1 Source level of single-beam echo sounders . . . . . . . . . . . . . . . . . . . . . . . . . 516
10.2 Source level of sidescan sonar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
10.3 Source level of multibeam echo sounders. . . . . . . . . . . . . . . . . . . . . . . . . . 518
10.4 Source level of depth profilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520
10.5 Source level of fisheries search sonar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520
10.6 Source level of hull-mounted search sonar . . . . . . . . . . . . . . . . . . . . . . . . . 521
10.7 Source level of helicopter dipping sonar . . . . . . . . . . . . . . . . . . . . . . . . . . 521
10.8 Source level of active towed array sonar . . . . . . . . . . . . . . . . . . . . . . . . . . 522
10.9 Source level of miscellaneous search sonar (including coastguard and risk
mitigation sonar). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522
10.10 Source level of low-amplitude acoustic deterrents . . . . . . . . . . . . . . . . . . . . 524
10.11 Source level of high-amplitude acoustic deterrents . . . . . . . . . . . . . . . . . . . 525
10.12 Source level of acoustic communications systems . . . . . . . . . . . . . . . . . . . . 526
10.13 Source level of selected acoustic transponders and alerts . . . . . . . . . . . . . . . 527
10.14 Source level of acoustic cameras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
10.15 Source level of miscellaneous oceanographic sonar . . . . . . . . . . . . . . . . . . . 528
10.16 Relationships between different source level definitions for two symmetrical
wave forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529
10.17 Relationships between different source level definitions for two asymmetrical
wave forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531
10.18 Relative MSP, averaged over time window during which local average exceeds
specified threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533
10.19 Relative MSP, averaged over time window during which pulse energy
accumulates to specified proportion of total. . . . . . . . . . . . . . . . . . . . . . . . 534
10.20 Dipole source level of air guns and air gun arrays . . . . . . . . . . . . . . . . . . . 536
10.21 Zero-to-peak source level of generator–injector air guns . . . . . . . . . . . . . . . 537
10.22 Zero-to-peak source level of seismic survey sources other than air guns . . . . 538
10.23 Summary of peak pressure and pulse energy for three types of explosive . . . 540
10.24 Specific pulse energy and apparent specific SLE for pentolite. . . . . . . . . . . . 541
10.25 Echolocation pulse parameters for selected animals . . . . . . . . . . . . . . . . . . 543
10.26 Maximum peak-to-peak source levels of high-frequency marine mammal clicks 546
10.27 Peak equivalent RMS and peak-to-peak source levels of low-frequency marine
mammal pulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548
10.28 Hearing thresholds and sensitive frequency bands of selected cetaceans . . . . 553
10.29 MSP and EPWI hearing thresholds in air and water for four pinnipeds plus
human subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555
10.30 Hearing thresholds in water for 10 species of fish. . . . . . . . . . . . . . . . . . . . 557
10.31 Parameters of bandpass filter used in M-weighting . . . . . . . . . . . . . . . . . . . 560
10.32 Genera represented by the functional hearing groups . . . . . . . . . . . . . . . . . 561
10.33 Proposed thresholds of M-weighted sound exposure level for permanent and
temporary auditory threshold shift in cetaceans and pinnipeds . . . . . . . . . . 562
10.34 Proposed thresholds of peak pressure for permanent and temporary auditory
threshold shift in cetaceans and pinnipeds . . . . . . . . . . . . . . . . . . . . . . . . . 563
10.35 Outline of the severity scale from Southall et al. (2007). . . . . . . . . . . . . . . . 564
10.36 Spread of sound pressure level values resulting in the specified behavioral
responses in cetaceans and pinnipeds for nonpulses. . . . . . . . . . . . . . . . . . . 564
Tables xxvii

10.37 Spread of sound pressure level values resulting in the specified behavioral
responses in cetaceans and pinnipeds for multiple pulses . . . . . . . . . . . . . . . 565
11.1 List of applications of man-made active and passive underwater acoustic
sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575
11.2 Error in DT incurred by assuming 1D þ R statistics . . . . . . . . . . . . . . . . . . 582
11.3 Sonar equation calculation for NWP winter . . . . . . . . . . . . . . . . . . . . . . . 587
11.4 Filter gain vs. bandwidth in octaves for a white signal and colored noise . . . 596
11.5 Sonar equation calculation for shallow-water sand . . . . . . . . . . . . . . . . . . . 604
11.6 Active sonar example, limited by hearing threshold . . . . . . . . . . . . . . . . . . 620
11.7 Active sonar example, limited by wind noise . . . . . . . . . . . . . . . . . . . . . . . 624
A.1 Integrals of integer powers of the sine cardinal function . . . . . . . . . . . . . . . 636
A.2 Selected values of the gamma function GðxÞ for 0 x 1 . . . . . . . . . . . . . 640
A.3 Examples of Fourier transform pairs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650
B.1 SI prefixes for indices equal to an integer multiple of 3. . . . . . . . . . . . . . . . 660
B.2 SI prefixes for indices equal to an integer between þ3 and À3. . . . . . . . . . . 661
B.3 Frequently encountered non-SI units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662
B.4 List of abbreviations and acronyms, and their meanings . . . . . . . . . . . . . . . 667
C.1 Bladder presence and type key used in Tables C.3, C.4, and C.7 . . . . . . . . . 674
C.2 Reference key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674
C.3 Bladder type by order for ray-finned fishes (Actinopterygii) . . . . . . . . . . . . 675
C.4 Bladder type by family. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676
C.5 ‘‘Catchability’’ key (Yang groups) used in Table C.7 . . . . . . . . . . . . . . . . . 677
C.6 Length key used in Table C.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677
C.7 Fish and their bladders, sorted by scientific name. . . . . . . . . . . . . . . . . . . . 678
xxviii Tables

1
Introduction
Wee represent Small Sounds as Great and Deepe; Likewise
Great Sounds, Extenuate and Sharpe; Wee make diverse
Tremblings and Warblings of Sounds, which in their Originall
are Entire. Wee represent and imitate all Articulate Sounds and
Letters, and the Voices and Notes of Beasts and Birds. Wee have
certaine Helps, which sett to the Eare doe further the Hearing
greatly. Wee have also diverse Strange and Artificiall Eccho’s,
Reflecting the Voice many times, and as it were Tossing it; And
some that give back the Voice Lowder then it came, some
Shriller, and Some Deeper; Yea some rendring the Voice,
Differing in the Letters or Articulate Sound, from that they
receyve. Wee have also meanes to convey Sounds in Trunks and
Pipes in strange Lines, and Distances.
Francis Bacon (1624)
1.1 WHAT IS SONAR?
Sonar can be thought of as a kind of underwater radar, using sound instead of radio
waves to interrogate its surroundings. But what is special about sound in the sea?
Radio waves travel unhindered in air, whereas sound energy is absorbed relatively
quickly. In water, the opposite is the case: low absorption and the presence of natural
oceanic waveguides combine to permit propagation of sound over thousands of
kilometers, whereas the sea is opaque to most of the electromagnetic spectrum.
The word sonar is an acronym for sound navigation and ranging. The primary
purpose of sonar is the detection or characterization (estimation of position, velocity,
and identity) of submerged, floating, or buried objects. Electronic systems capable of

underwater detection and localization were developed in the 20th century, motivated
initially by the sinking of RMS Titanic in 1912 and the First World War (WW1), and
spurred on later by the Second World War (WW2) and the Cold War. Nevertheless,
by comparison with marine fauna, man remains a novice user of underwater sound.
Deprived of light in their natural habitat, dolphins have evolved a sophisticated form
of sonar over millions of years, without which they would be almost blind. They
transmit bursts of ultrasound, and sense the world around them by interpreting the
echoes. Many fish and other aquatic animals are also capable of both producing and
hearing sounds.
1.2 PURPOSE, SCOPE, AND INTENDED READERSHIP
This book is aimed at anyone, novice and experienced practitioner alike, with an
interest in estimating the performance of sonar, or understanding the conditions for
which a particular existing or hypothetical system is likely to make a successful
detection. This includes sonar analysts and designers, whether for oceanographic
research, navigation, or search sonar. It also includes those studying the use of sound
by marine mammals and the impact of exposure of these animals to sound. Regard-
less of application, the objective of sonar performance modeling is usually to support
a decision-making process. In the case of man-made sonar, the decision is likely to
involve the optimization of some aspect of the design, procurement, or use of sonar.
(What frequency or bandwidth is appropriate? How many sonars are needed to
complete the task in the time available?) For bio-sonar there is increasing interest
in the assessment (and mitigation) of the risk of damage to marine life due to
anthropogenic sources of underwater sound. (What level of sound might disrupt a
dolphin’s ability to locate and capture its prey? How can the risk of hearing damage
be prevented or minimized?)
The nature of the sought object, known as the sonar target, depends on the
application. Examples include man-made objects of military interest (a mine or
submarine), shipwrecks (as a navigation hazard or archeological artifact), and fish
(the target of interest to a whale or fisherman).
In general, sonar can be grouped into two main categories. These are active sonar
and passive sonar, which are distinguished by the presence and absence, respectively,
of a sound transmitter as a component of the sonar system.
. An active sonar system comprises a transmitter and a receiver and works on the
principle of echolocation. If a signal (in this case an echo from the target) is
detected, the position of the target can be estimated from the time delay and
direction of the echo. The echolocation principle is also used by radar, and by the
biological sonar of bats and dolphins.
. A passive sonar includes a receiver but no transmitter. The signal to be detected is
then the sound emitted by the target.
Examples of man-made sonar include
4 Introduction [Ch. 1

. Echo sounder: perhaps the most common of all man-made sonars, an echo
sounder is a device for measuring water depth by timing the delay of an echo
from the seabed. The strength and character of the echo can also provide an
indication of bottom type.
. Fisheries sonar: sonar equipment used by the fisheries industry exploits the same
principle as the echo sounder, except that the purpose is to detect fish instead of
the sea floor.
. Military sonar: modern navies deploy a wide variety of sonar systems, designed to
detect and track potential military threats such as surface ships, submarines,
mines, or torpedoes. The diverse nature of these threats and of the platforms
on which the sonar systems are mounted means that military sonars are them-
selves diverse, with each specialized system dedicated to a particular task.
. Oceanographic sensor: scientific work aimed at understanding and surveying the
sea (acoustical oceanography) makes extensive use of a variety of different kinds
of sonar, many of which are variants of the echo sounder.
. Shadow sensor: in exceptional cases, the sonar ‘‘signal’’, instead of being the
sound emitted or scattered by the target, might actually be some perturbation
to the expected background. For example, the shadow of an object lying on the
seabed might be detectable when the object itself is not.
Many readers will be familiar with Urick’s classic Principles of Underwater Sound for
Engineers,1
which provided its readers with the tools they needed to carry out sonar
design and assessment studies. These tools come in the form of a set of equations
relating the predicted signal-to-noise ratio to known parameters such as the radiated
power of the sonar transmitter, or the size and shape of the target. This set of
equations is known as the ‘‘sonar equations’’. The same basic requirement remains
today, but the modeling methods have increased in sophistication during the 25 years
that have elapsed since Urick’s third and final edition, with a bewildering array of
computer models to choose from (Etter, 2003). The present objective is to meet the
needs of the modern user or developer of such models by documenting established
methods and relevant research results, using internally consistent definitions and
notation throughout. The discipline of sonar performance modeling is perceived
sometimes as a black art. The purpose of this book is, above all, to demystify this
art by explaining the jargon and deriving the sonar equations from physical princi-
ples.
The book’s scope includes underwater sound, the properties of the sea relevant
to the generation and propagation of sound, and the processing that occurs after
an acoustic signal has been converted to an electrical one2
and then digitized.
The estimation of sonar performance is taken as far as the detection (and false
alarm) probability, but no further than that. While the scope excludes localization,
1.2 Purpose, scope, and intended readership 5]Sec. 1.2
1
See Urick (1967) and two later editions (Urick, 1975, 1983).
2
Conversion between electrical and acoustical energy (known as transduction), whether on
transmission or reception, is excluded from the scope. The interested reader is referred to Hunt
(1954) and Stansfield (1991).

classification, and tracking tasks, such as the estimation of position and velocity of a
sonar target, a satisfactory detection capability is a prerequisite for any of these.
1.3 STRUCTURE
Sonar performance modeling is a multidisciplinary science, requiring knowledge of
subjects as diverse as mathematics, physics, electrical engineering, chemistry, geology,
and biology.3
It is convenient to group the material into four foundation categories
(or ‘‘pillars’’), on which the science of sonar performance modeling is built: sonar
oceanography, underwater acoustics, sonar signal processing and statistical detection
theory. The book has three main parts, described below.
1.3.1 Part I: Foundations (Chapters 1–3)
Part I comprises this Introduction and two further chapters, also of an introductory
nature. The purpose of Chapter 2 is to describe the essential concepts required for a
basic understanding of the sonar equations, which are derived in Chapter 3. Four
generic types of sonar are introduced, with a simple worked example provided for
each. The material in Chapters 2 and 3 is intended as a primer, to illustrate the
principles, and generally preferring simplicity to realism. Advanced readers might
prefer to skip the introductory part and start reading from Chapter 4, consulting
Chapter 3 only for definitions.
1.3.2 Part II: The four pillars (Chapters 4–7)
Each of the four chapters in Part II is devoted to one of the four pillars. The one on
oceanography (Chapter 4) describes the sea as a medium for sound propagation.
Relevant properties of the oceans’ contents and boundaries are considered, such
as the geoacoustical properties of sediments and rocks, sea surface waveheight
spectra, near-surface bubble density, and the acoustical properties of marine life.
The chapter on acoustics (Chapter 5) provides a theoretical foundation for
understanding the behavior of sound in the sea, including reflection and scattering
from its contents and boundaries. Cumulative propagation effects associated with
multiple boundary reflections are the subject of Chapter 9.
An acoustic signal arriving at a sonar receiver is converted to an electrical signal
by a device known as a ‘‘transducer’’. This electrical signal is subjected to a series of
operations designed to determine the presence or otherwise of a sonar target. These
operations are known collectively as signal processing, which is the subject of Chapter
6. The purpose of signal processing can be thought of as either to enhance the signal
from the target or to reduce the background noise. These two points of view are
3
The reader is assumed to have completed a degree-level course in a numerate discipline such
as physics, applied mathematics, or engineering.

entirely equivalent, as in the end what matters is the ratio of signal power to noise
power.
Finally, to be of practical use, the output of the signal processing must be
interpreted by a decision-maker. The chance that a sonar operator correctly (or
incorrectly) deduces that a target is present is known as the probability of detection
(or false alarm). The quantitative study of detection and false alarm probabilities is
known as statistical detection theory, and this is the subject of Chapter 7.
1.3.3 Part III: Towards applications (Chapters 8–11)
The purpose of the final chapters is to show how to apply the principles from Parts I
and II to more realistic situations. Chapter 8 provides quantitative information about
the sources, reflectors, and scatterers of underwater sounds, while Chapter 9 describes
sound propagation in the sea and its impact on both the signal and background.
Chapter 10 describes the characteristics of both man-made and biological sonar,
including the sensitivity of marine animals to underwater sound.
Chapter 11 brings together information from all the preceding chapters and
applies it to a set of problems partly based on the worked examples of Chapter 3,
introducing more advanced concepts and definitions where necessary. It closes with a
speculative account of possible future development of sonar performance modeling in
the 21st century.
1.3.4 Appendices
In addition to the 11 chapters, there are three appendices. Two of these provide
information needed for the correct interpretation of the main text, describing special
functions and mathematical operations (Appendix A), and units and nomenclature
(Appendix B). Finally, Appendix C can be thought of as an extension to Chapter 4. It
contains information about fish and their swim bladders that will be of use to a reader
interested in the interaction of sound with fish or fish shoals.
1.4 A BRIEF HISTORY OF SONAR
The remainder of this Introduction is devoted to a historical account of the devel-
opment of sonar. It is the author’s tribute to the work of Constantin Chilowski,4
Daniel Colladon, Pierre and Jacques Curie, Maurice Ewing, Reginald Fessenden,
Harvey Hayes, Paul Langevin, H. Lichte, Leonard Liebermann, J. Marcum, Stephen
Rice, and Albert Beaumont Wood. It owes its existence in no small part to the
detailed accounts of Hunt (1954), Wood (1965), and Hackmann (1984).
The history focuses on developments in France, Britain, and the U.S.A., as these
are the places where the main early advances took place, especially during WW1.
Developments in Germany and the U.S.S.R. are mentioned only briefly, partly due to
1.4 A brief history of sonar 7]Sec. 1.4
4
Zhurkovich (2008) transcribes this name as ‘‘K.V. Shilovsky’’.

the difficulty in finding reliable sources for them (in the case of Russian and Soviet
acoustics, corrected recently by the publication of the History of Russian Underwater
Acoustics, edited by Godin and Palmer, 2008).
1.4.1 Conception and birth of sonar (–1918)
1.4.1.1 Discovery and ingenuity
The concept of echo ranging, by which the distance to an object is determined by
measuring the time delay to an echo from that object, originates from at least as far
back as the 17th century. More recent origins of sonar can be traced to two seemingly
unrelated scientific developments in the 19th century, the first being the measurement
of the speed of sound in seawater, ca. 1816, by Franç ois Beudant, in the French
Mediterranean. Beudant used a crude but effective method (illustrated in Figure 1.1),
involving an underwater bell and a swimmer waving a flag. A more precise determina-
tion, with improved light–sound synchronization (Figure 1.2), was made in 1826 by
Colladon (Figure 1.3) and Sturm, in Lake Geneva.5
Both measurements are described
by Colladon and Sturm (1827), and in both cases the values obtained (1,500 m/s and
Figure 1.1. Sketch of Beudant’s experiment of ca. 1816 (reprinted fom Girard, 1877).
5
Their purpose was not to measure the speed of sound for its own sake, but to determine the
bulk modulus of water, which can be calculated from the sound speed if its density is known.

Figure 1.2. Sketch of the Colladon–Sturm experiment of 1826 (reprinted fom Girard, 1877).
Figure 1.3. Inventor Reginald Fessenden (left) and physicist Jean Daniel Colladon (right). The
image of Fessenden is reprinted from http://www.ieee.ca/millennium/radio/radio_unsung.html,
last accessed October 22, 2009, RadioScientist.#

1,435 m/s) are consistent with modern expectation for the respective measurement
conditions.
The second important development is the discovery of piezoelectricity by Pierre
and Jacques Curie in 1880. Experiments with certain special dielectric crystals
(especially quartz and Rochelle salt) revealed that these materials respond to an
applied pressure by developing a small potential difference. The converse effect,
whereby an applied electric field distorts the shape of the crystal, was predicted
shortly afterwards by Gabriel Lippmann and confirmed by the Curie brothers in
1881.
In the late 1890s and early 1900s, some lightships were fitted with underwater
bells, which were rung to alert approaching vessels of danger in conditions of poor
visibility. In good visibility these sounds provided an indication of distance as well, by
estimating the time delay between light and sound signals, as when estimating the
distance from an electrical storm by counting seconds to the thunder following a bolt
of lightning. These early underwater signaling systems would eventually mature into
what we now call sonar.
1.4.1.2 The Titanic and the Fessenden oscillator
The tragic collision and subsequent sinking of RMS Titanic on the night of April 14/
15, 1912 resulted in a flurry of activity and ideas directed at providing advance
warning of nearby icebergs. Lewis Richardson filed patents first for an airborne
echolocation system in April 1912 and a month later for an underwater one. Reginald
Fessenden (Figure 1.3) patented an electromagnetic transducer in 1913 and demon-
strated its use by detecting the presence of an iceberg on April 27, 1914 at a distance
of ‘‘nearly two miles’’ (i.e., approximately 3–4 km). This device became known as the
Fessenden oscillator (Waller, 1989).
1.4.1.3 WW1: a sense of urgency
It took an even greater tragedy, the loss of life inflicted by U-boats during WW1, to
provide the focus of intellect and resources that would lead to the development of a
working underwater detection system. French and British efforts began in 1915, with
Paul Langevin (Figure 1.4) working in Paris with Russian engineer Constantin
Chilowski, while A. B. Wood worked with Harold Gerrard in Manchester. The focus
of the French research was on echolocation (‘‘active sonar’’ in modern terminology),
while the British team concentrated initially on listening devices known as hydro-
phones (‘‘passive sonar’’).
At the outset of WW1, Lord Rutherford had assembled an extraordinary group
of physicists at his laboratory at the University of Manchester, including the house-
hold names Bohr, Geiger, and Chadwick. In his autobiographical account, A. B.
Wood recalls (Wood, 1965): ‘‘It would be difficult to find anywhere such a galaxy of
scientific talent, either before or since, working together in the same physics labora-
tory at the same time.’’ Of particular relevance here are the arrivals of Wood himself
in 1915 and of the Canadian physicist Robert Boyle (Figure 1.4) the following year.
The Board of Invention and Research (BIR) was established in 1915, with

facilities at Hawkcraig (in Fifeshire, Scotland), and expanded in 1917 to a team of
more than 80 scientists and technicians working at Parkeston Quay (Harwich,
England) under the leadership of Professor W. H. Bragg. Amongst them were Boyle
and Wood from Rutherford’s group, responsible, respectively, for research investi-
gating echolocation and passive listening.
Boyle made promising initial progress with the Fessenden oscillator, such that by
late 1917 a submarine detection had been reported at a distance of 1,000 yd (910 m)
(Hackmann, 1984, p. 75).6
Nevertheless, this line of work was abandoned because the
frequency of Fessenden’s transmitter (1 kHz) was too low to obtain the necessary
resolution in bearing for its intended purpose of locating submarines. A high-
frequency transducer was needed to achieve this.
In France, Langevin had begun to experiment with quartz early in 1917 after
obtaining a small supply from a Paris optician. Quartz is a piezoelectric material
suitable for the radiation of high-frequency sound,7
but the unampliﬁed received
Figure 1.4. Physicists Paul Langevin (left) and Robert William Boyle (right). The image of
Langevin is reprinted from Anon. (wp, a) and that of Boyle from http://www.100years.ualberta.
ca, last accessed October 26, 2009.
6
The yard (symbol yd) is a unit of length deﬁned as 0.9144 meters (see Appendix B).
7
Use here of the term ‘‘sound’’ is not restricted to the audible frequency range, but refers also
to ‘‘ultrasound’’, which means that the frequency is above the upper limit of normal human
hearing (i.e., 20 kHz). In general, it can also refer to sounds below 20 Hz, known as
‘‘infrasound’’. Langevin’s early experiments with quartz (April 1917) were at a frequency of
150 kHz. The frequency was later lowered to 40 kHz in order to reduce absorption.

signals were found to be very weak. Fortunately, a suitable valve amplifier, designed
by Le´ on Brillouin and G. A. Beauvais,8
was made available to Langevin soon after,
enabling him to build a system by November 1917 that ‘‘gave a signalling distance of
up to six kilometres’’ (Hackmann, 1984, p. 81).
The real breakthrough came when the French and British teams started sharing
their findings after a series of high-level meetings held in Washington, D.C. between
May and July 1917. Boyle visited Langevin shortly afterwards, when he would have
learnt of the French advances. On his return to England, Boyle started working on
quartz transducers, and the French amplifier was made available to the British team
at Parkeston Quay. The reliance on quartz was such that, until a suitable supply was
identified from Bordeaux, Boyle threatened to ‘‘raid the crystal exhibits in several
geological museums’’.
Meanwhile, Langevin continued with his own work in Toulon, and by February
1918 had obtained echoes from a submarine using the high-frequency (40 kHz) quartz
transducers. Boyle followed suit a month later with a submarine echo from a distance
of 500 yd (about 460 m). The Armistice of November 1918 led to the cancellation of
plans to fit both British and French navy ships in early 1919, but asdics (as the
technology of high-frequency echolocation was then called) was born.9
The term
sonar was coined during WW2.
The origin of the term asdics as an acronym for Anti-Submarine Division -ics,
where the ‘‘ics’’ meant ‘‘activities pertaining to’’ in the same way as in ‘‘physics’’, is
recounted by Wood (1965). The alternative explanation (for the term asdic, without
the second ‘‘s’’) as an acronym for ‘‘Allied Submarine Detection Investigation
Committee’’ appears to be a myth created by the British Admiralty in 1939 in
response to a question by Oxford University Press (Hackmann, 1984, p. xxv). During
the initial development of the sensor at Parkeston Quay, secrecy was such that even
the material quartz was referred to by its codename ‘‘asdivite’’.
On the subject of semantics, it is worth mentioning the change in meaning of the
word ‘‘supersonic’’ after the end of WW2. Between the two world wars, this term was
used in the U.S.A. to mean ‘‘pertaining to sound whose frequency is too high to be
heard by the human ear’’, synonymous with the European term ‘‘ultrasonic’’ (Klein,
1968). Today the European term has been adopted worldwide, presumably as a
consequence of the modern use of ‘‘supersonic’’ to describe ‘‘faster than sound’’
flight.
The first working active sonar was built in November 1918 by Boyle, a Canadian
scientist working in England. Reading an account of the early history of echo rang-
ing, however, one cannot help being struck by a series of key contributions made by
8
This work was assisted by a wireless expert, Paul Pichon. Having deserted from the French
army he found himself importing some American valve amplifiers to his adoptive Germany
early in WW1. Realizing the military value of these, he took them instead to France where he—
though immediately arrested—handed over his equipment to the French authorities. These
early valves provided the basis for the Beauvais–Brillouin design (Hackmann, 1984, pp. 80–81).
9
Boyle’s quartz system was fitted to a trawler on November 16, 1918, five days after the end of
WW1.

French scientists, including:
— the earliest known description of the echo-ranging concept, by Mersenne (1636);
— the measurement of the speed of sound in seawater, by Beudant (ca. 1816);
— the discovery of piezoelectricity, by the Curie brothers and Lippmann (1880–
1881);
— the development of the valve amplifier, by Beauvais and Brillouin (ca. 1916);
— pioneering research on the use of quartz transducers, including the first ever
detection of an echo from a submarine, by Langevin10
(1917–1918).
To this impressive list one can add the work of a remarkable statesman named Paul
Painleve´ (Figure 1.5). In January 1915, Chilowski had written a letter urging the
French government to develop an underwater echolocation device as a defense
against U-boats. Recognizing its importance and urgency, Painleve´ forwarded
this letter to Langevin without delay, thus facilitating the early Langevin–Chilowski
collaboration. Painleve´ also saw the value
in Anglo-French co-operation, requesting a
scientific exchange agreement between France
and Britain in December 1915. Despite delays
caused by opposition from the Admiralty, the
agreement, without which the co-operation
between Langevin and Boyle might not have
flourished, was eventually approved by the
British Government in October 1916 (Hack-
mann, 1984, p. 39).
1.4.1.4 Origins of passive sonar
By comparison with active sonar, invented in
a race against time between Chilowski’s 1915
letter and the first successful French and Brit-
ish tests in 1917, the arrival of passive sonar
was a gradual affair that lasted centuries. Its
15th-century conception in Leonardo da Vin-
ci’s device able to detect ships ‘‘at a great
distance’’ was followed by a 400-year gesta-
tion, including the 18th-century observations
of Benjamin Franklin (see Section 1.4.3.3),
and culminating in the listening equipment
fitted to shipping vessels at the end of the
Figure 1.5. French statesman and
mathematician Paul Painleve´ —rep-
rinted from Anon. (wp, b). Painleve´
was Minister for Public Instruction
and Inventions during the period
1915–1917, and later served two brief
periods as Prime Minister in 1917 and
1925.
10
Langevin is one of five sonar scientists after whom the Pioneers of Underwater Acoustics
Medal, awarded to this day by the Acoustical Society of America, is named. The others are
H. J. W. Fay, R. A. Fessenden, H. C. Hayes, and G. W. Pierce. In 1959, Hayes became the first
ever recipient of this medal, which was also awarded to Wood (in 1961) and to Urick (1988).

19th century to notify them of the presence of nearby lightships: in 1889, the U.S.
Lighthouse Board described an invention of L. I. Blake comprising an underwater
bell and microphone receiver, and a similar system—patented in 1899 (Hersey,
1977)—was developed a few years later by Elisha Gray and A. J. Mundy (Lasky,
1977).11
In common with the echolocation devices of Langevin and Boyle, it was
WW1 that provided the final impetus for the birth of passive sonar. An important
difference, though, is that underwater listening equipment was put to practical use
well before the end of the war. Portable omnidirectional hydrophones were available
as early as 1915, and directional ones followed in 1917. Towed hydrophones were
operational before the end of WW1, and in 1918 a prototype passive-ranging system
was fitted to an American destroyer.
British listening devices used during WW1, based on early American work, were
developed at BIR by Wood and Gerrard (occasionally assisted by Rutherford) at
Parkeston Quay and by Captain C. P. Ryan at Hawkcraig. To reduce noise, direc-
tional hydrophones could be towed behind the ship in a streamlined capsule known
as a ‘‘fish’’, developed by G. H. Nash.
Ryan constructed a network of up to 18 underwater listening stations positioned
strategically in British coastal waters. These listening stations, each comprising a field
of hydrophones, were manned with shore-based operators, who listened for distinc-
tive U-boat sounds and reported their position to the nearest anti-submarine flotilla.
Some minefields were also equipped with special listening devices (magneto-
phones), with which it was possible to determine the precise moment at which a
U-boat was passing overhead. The mines could then be detonated remotely from a
shore-based monitoring facility. According to Hackmann (2000), such minefields
were responsible for the destruction of four U-boats towards the end of WW1, the
first taking place on August 29, 1918.
Early in WW1, Rutherford had proposed the use of an array of multiple hydro-
phones, in theory able to both amplify the signal and provide bearing information.
The Royal Navy considered the proposed device too unwieldy and the idea was
dropped in Britain, but American scientists pursued it and by the end of the war
had developed the most sophisticated listening devices of that time (Hayes, 1920).
This American research took place at the Naval Experimental Station in New
London, under the direction of Harvey Hayes.
The property of sound waves that Rutherford wished to exploit is that they retain
their phase coherence over distances of at least several wavelengths. The first Amer-
ican device to use this property was the ‘‘M-B tube’’, comprising two groups of eight
hydrophones each. The (acoustic) signals from each group were combined coherently
by a sequence of equal-length delay lines before being presented (binaurally, one
coherently summed group in each ear) to a human listener. The construction was such
that coherent reinforcement took place from only one direction at a time, so in order
to scan over different bearings it was necessary to rotate this device in the water. The
inconvenience of the M-B tube—it needed to be lowered into the sea each time it was
11
Gray coined the term ‘‘hydrophone’’ to describe their underwater microphone, while Mundy
went on to co-found the Submarine Signal Company (now part of Raytheon) in 1901.

used—was overcome by the introduction of variable-length delay lines, which per-
mitted the operator to select the direction of listening without any form of mechanical
rotation. This meant that the entire device, known as the ‘‘M-V tube’’, could be fixed
to a ship’s hull, and used with the ship in motion. The M-V tube had two groups of six
hydrophones (later, two groups of ten), the signals from which were presented
binaurally in the same way as for the M-B tube.
The capability to use the M-V tube in motion was a huge advantage, but it came
at a price—the din from a ship underway. To counter the noise problem the ‘‘U-3
tube’’ (nicknamed the ‘‘eel’’), was invented. The eel comprised two groups of six
hydrophones towed behind the ship, thus benefiting from lower noise levels. The
U-3’s streamlined housing gave it the appearance of a snake or eel—hence its
nickname. The key advance that made this possible was the use of electrical instead
of acoustical delay lines, making the equipment less bulky. An experimental device
comprising two towed eels and two ship-mounted M-V tubes was fitted to an
American destroyer in April 1918 (Figure 1.6). The combined system was capable
of passive ranging by triangulation of the two different bearings (Hayes, 1920). The
first working sonar capable of localization in range and bearing was neither a French
nor a British invention, but an American one.
1.4.2 Sonar in its infancy (1918–1939)
1.4.2.1 Fathometers and fish finders
In peacetime, the thoughts of sonar engineers turned away from U-boats and back
initially to maritime safety, and later to fishing. The principle of acoustic echo ranging
was applied to measuring water depth, and Fessenden’s oscillator turned out to be
Figure 1.6. Installation of early U.S. passive-ranging sonar with two towed eels of length 40 ft
(12 m), and 12 ft (4 m) apart, and two hull-mounted M-V tubes of the same length. The eel was
towed about 300–500 ft (100–150 m) behind the ship (reprinted with permission from Lasky,
1977, copyright 1977 American Institute of Physics).

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