Topics in Current Physics B Topics in Current Physics Founded by Helmut K. V. Lotsch Volume 1 Beam-Foil Spectroscopy Editor: S. Bashkin Volume 2 Modern Three-Hadron Physics Editor: A. W. Thomas Volume 3 Dynamics of Solids and Liquids by Neutron ScaHering Editors: S. W. Lovesey and T. Springer Volume 4 Electron Spectroscopy for Surface Analysis Editor: H. Ibach Volume 5 Structure and Collisions of Ions and Atoms Editor: I. A. Sellin Volume 6 Neutron Diffraction Editor: H. Dachs Volume 7 Monte Carlo Methods in Statistical Physics Editor: K. Binder Volume 8 Ocean Acoustics Editor: J. DeSanto Volume 9 Inverse Source Problems in Optics Editor: H. P. Baltes Volume 10 Synchrotron Radiation Techniques and Applications Editor: C. Kunz Volume 11 Raman Spectroscopy of Gases and Liquids Editor: A. Weber Volume 12 Positrons in Solids Editor: P. Hautojarvi Volume 13 Computer Processing of Electron Microscope Images Editor: P. W. Hawkes Volume 14 Excitons Editor: K. Cho Volume 15 Physics of Superionic Conductors Editor: M. B. Salamon Ocean Acoustics Edited by J. A. DeSanto With Contributions by N. Bleistein J. K. Cohen R. L. Deavenport J. A. DeSanto F. R. DiNapoli J. P. Dugan R. P. Porter J. G. Zornig With 109 Figures Springer-Verlag Berlin Heidelberg New York 1979 Dr. John A. DeSanto Naval Resarch Laboratory, Washington, DC 20375, USA ISBN-13:978-3-642-81296-5 e-ISBN-13:978-3-642-81294-1 001: 10.1007/978-3-642-81294-1 Library of Congress Cataloging in Publication Data. Main entry under title: Ocean acoustics. (Topics in current physics; v. 8), Bibliography: p. Includes index. 1. Underwater acoustics. I. Bleistein, Norman. II. DeSanto, John A., 1941-. III. Series. QC242.2.023 551.4'601 78-25859 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, reuse of illustrations, broadcasting, reproduc- tion by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1979 Softcover reprint of the hardcover 1st edition 1979 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. 2153/3130-543210 Preface This Topics volume is devoted to a study of sound propagation in the ocean. The effect of the interior of the ocean on underwater sound is analogous to the effect of a lens on light. The oceanic lens is related, as in light propagation, to the index of refraction of the medium. The latter is giv~n by the ratio of the sound frequency to the speed of sound in water, typi ca lly about 1500 ms -1. It is the vari- ation of the sound speed due to changing temperature, density, salinity, and pres- sure in the complex ocean environment which creates the lens effect. Many oceanic processes such as currents, tides, eddies (circulating, translating regions of wa- ter), and internal waves (the wave-like structure of the oceanic density variabil- ity) contri bute in turn to the changes in sound speed'. The net effect of the ocean lens is to trap and guide sound waves in a channel created by the lens. The trapped sound can then propagate thousands of miles in this oceanic waveguide. In addition to the propagation in the interior of the ocean, sound can propagate into and back out of the ocean bottom as well as scatter from the ocean surface. Just as the sound produced by a loudspeaker in a room is affected by the walls of the room, so the ocean boundaries and the material properties below the ocean bottom are essential ingredients in the problem. Sever'al techniques are used to study underwater sound propagation. These include ex~eriments at sea, controlled simulation experiments in a water tank, and modeling the phenomenon using mathematical techniques and computer simulation. The experimen- tal methods use a sound source such as an explosive (at sea) or a mechanical device which radiates sound (like a loudspeaker) and a hydrophone receiver (like a micro- phone). The different paths which the sound waves take result in different modifica- tions of the initial signal. The received signals are recorded and processed using computers to yield the desired measurement. Mathematical methods model the physical situation, the resulting equations describing the model are solved using computers, and the results compared to the experimental data. All the above methods for the study of underwater sound propagation are discussed in the articles in this book. They are treated in such a way as to provide a rapid introduction to the field, as well as a thoroughly referenced review of the state- of-the-art experimental, theoretical, and computational methods in use. Washington, D.C. JOM A. DeSanto November 1978 Contents 1. Introduction. By J.A. DeSanto .......................................... .. 1.1 A Brief History ..................................................... 3 1.2 Outl ine of the Book................................................. 4 References ............................................................... 6 2. Theoretical Methods in Ocean Acoustics. By J.A. DeSanto (With 24 Figures) 7 2.1 Conservation Laws. Fluid and Acoustic Equations ...... ..... .......... 9 2.1.1 Conservation Laws and Fluid Equations .... .................... 9 2.1.2 A Parabolic Equation ......................................... 11 2.1.3 Perturbati on Method .......................................... 14 2.1.4 Combined Acoustic-Internal Wave Equations .................... 15 2.1.5 Sound Speed .................................................. 18 2.2 Propagation in Deterministic Media.................................. 19 2.2.1 One-Dimensional Problems ..................................... 19 a) The Pekeri s Wavegu ide ..................................... 20 b) Alternative Representations ...................... '" ...... 26 c) Solvable Profiles......................................... 28 d) Inverse Propaga t i on ....................................... 30 2.2.2 Two-Dimensional Problems..................................... 31 a) Ray-Theory ................................................ 32 b) Corrected Parabolic Approximation ......................... 33 c) Conforma 1 ~~appi ng ......................................... 36 2.2.3 Mu.lti-Dimensional Problems................................... 39 2.3 Wave Propagation in a Random Medium ................................. 40 2.3.1 The Hierarchy Problem........................................ 41 2.3.2 Coherent Waves ............................................... 44 2.3.3 Coherence Function and Related Work .......................... 47 2.3.4 Propagation of the Coherence Function in a Waveguide ......... 50 2.4 Scattering from Rough Surfaces ...................................... 54 2.4.1 The Rayleigh Hypothesis...................................... 55 2.4.2 Peri odi c Surfaces ............................................ 57 a) Rectangular Periodic Surfaces ............................. 57 b) The Sinusoidal Surface .................................... 62 VI II 2.4.3 Arbitrary Deterministic Surfaces ............................. 64 a) Green's Function Formalism ................................ 64 b) Di agrams .................................................. 66 2.4.4 Random Surfaces.............................................. 67 a) Gaussian Surfaces......................................... 67 b) Dyson Equation............................................ 69 c) Coherent Specular Intensity............................... 70 d) Remarks................................................... 73 References 73 3. NumericaZ ModeZs of Underwater Acoustic Propagation By F.R. DiNapoli and R.L. Deavenport (With 21 Figures) .................. 79 3.1 Range-Independent Models ............................................ 80 3.1.1 Depth-Dependent Green's Function (Impedance Formulation) ..... 82 a) Matrizant Method.......................................... 83 3.1.2 Direct Numerical Integration: Fast Field Program (FFP) ....... 90 3.1. 3 Normal ~1ode (and Branch Line Integral) Models ................ 92 a) Stickler (EJP Cuts). Bartberger (Pekeris Cuts) ............ 92 b) Stickler's Residue Contribution ........................... 95 c) Bartberger's Residue Contribution (Pekeris Cuts) .......... 97 d) Branch Cuts ~nd Branch Cut Integrals ...................... 98 e) Numerical Considerations .................................. 101 3.1.4 Depth Dependent Green's Function (Traveling-Wave Formulation) 103 3.1.5 Multipath Expansion Models ................................ '" 107 3.1.6 Connection Between Modes and Rays ............................. 117 3.1.7 Quantitative Model Assessment ................................ 121 3.1.8 Waveform Prediction Models ................................... 131 3.2 Range-Dependent Model s .............................................. 135 3.2.1 Split Step Algorithm for Parabolic Equation .................. 135 3.2.2 Parabolic Decomposition Method ............................... 137 3.2.3 Finite Differences ........................................... 138 3.2.4 Range-Dependent Normal Mode Theory ........................... 140 3.2.5 Range-Dependent Ray Theory Models ............................ 141 3.2.6 Finite Element ApfJroach ...................................... 142 a) The Finite Element Method ................................. 143 b) Merits/Shortcomings of the FEM ............................ 146 c) Transparent Boundary Simulation Techniques ................ 147 d) Solid Domain Boundaries ................................... 148 e) Fluid Domain Boundaries ................................... 149 f) Combined Solid-Fluid Domain Boundaries .................... 150 g) Fluid Finite Elements ..................................... 153 References 154 IX 4. PhysiaaZ ModeZing of Underwater Aaoustias By J.G. Zornig (With 17 Figures) ......................................... 159 4.1 Background Information ...........................•.....•....•....... 159 4.1.1 Definition and Purpose ....................................... 159 4.1.2 Relationship to Ocean Experimentation ........................ 160 4.1.3 Historical Overview .......................................... 160 4.2 Water Facilities .................................................... 162 4.2.1 Model Tanks .•...................•..•...•..................... 162 4.2.2 Lakes and Bays ............................................... 163 4.3 Targets .......•......•..•........................................... 164 4.3.1 Wind Driven Surfaces ................. , ....................... 164 4.3.2 Fi xed Surfaces ....................•.......................... 168 4.3.3 Volume Targets ............................................•.. 169 4.4 Instrumentation and Signal Processing ............................... 170 4.4.1 Sources. . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . • . . . • . . . . • . . .. 170 4.4.2 Data Acquisition .............•.........•..................... 173 4.4.3 Signal Processing ............................................ 174 4.5 Results of Physical Model Experimentation .......................•... 176 4.5.1 Scattered Intensity .......................................... 176 4.5.2 Coherence Studies .........................•.................. 178 4.5.3 Second-Order Coherence ....................................... 179 4.5.4 Frequency Spreadi ng .......................................... 181 4.6 Remarks ....••...•..•................................................ 184 References ....................................•.......................... 185 5. Oaeanography in Underwater Aaousties By J. P. Dugan (With 15 Fi gures) .......................................... 187 5.1 Properties of Seawater .............................................. 187 5.2 Ocean Variability ................................................... 191 5.2.1 Ocean Climatology ............................................ 192 5.2.2 Ocean Weather ................................•............... 196 5.2.3 Internal Waves ............................................... 207 5.2.4 Fi ne Structure ........•............................•......... 214 5.2.5 Near-Surface Structure .................................•..... 216 References 221 6. Inverse Methods for RefZeator Mapping and Sound Speed ProfiZing By N. Bleistein and J.K. Cohen (With 9 Figures) .•......•................. 225 6.1 The POFFIS Identi ty ......•...•.•••........................•.....•..• 225 6.1.1 Derivation of the POFFIS Identity ...........•.........•...•.• 226 6.1.2 The Limited Aperture Problem for the POFFIS Identity ......... 230 x 6.2 An Inverse Method for Determining Small Inhomogeneities in a Medium. 234 6.2.1 An Integral Equation for Three-Dimensional Velocity Variation ........................................... 235 6.2.2 Direct Inversion for Backscatter over a Medium with Two-Dimensional Velocity Variation ...................... 237 6.2.3 Direct Inversion for a Case with Separated Source and Recei ver .......................................... 240 6.2.4 Direct Inversion for a One-Dimensional Problem ............... 241 6.2.5 Direct Inversion in Free Space ............................... 241 References 242 7. Acoustic Probing of Space-Time Scales in the Ocean By R.P. Porter (With 23 Figures) ......................................... 243 7.1 Sound Probes of Ocean Currents ...................................... 245 7.1.1 SOFAR Floats for Lagrangian Current Measurements ............. 245 7.1.2 Current Measurements by Reciprocal Transmissions ............. 246 7.2 Acoustic Fluctuations as a Measure of Ocean Dynamics ................ 247 7.2.1 CW Transmissions and Tides ................................... 248 7.2.2 Short Pulse Transmissions Along Single Paths ................. 249 7.2.3 Spatial and Temporal Fluctuations of CW Transmissions ........ 250 7.2.4 Spectra of Phase and Amplitude Fluctuations .................. 252 7.3 Sound Speed Variations and Internal Gravity Waves ................... 260 7.3.1 Internal Gravity Wave Spectra ................................ 261 7.3.2 Fluctuations in the Index of Refraction ...................... 264 7.4 Acoustic Fluctuation Theories and Their Relationship to Ocean Dynami cs ................................................... 265 7.4.1 Acoustic Fluctuation Theories and Their Relationship to Ocean Dynami cs ........................................... 266 7.4.2 Effect of Large Scale Flows on Acoustic Amplitude and Phase .. 267 7.4.3 Effect of Internal Waves on Acoustic Amplitudes and Phases ... 269 7.4.4 Multipath Fluctuations for Stable Paths ...................... 272 7.4.5 Stability of Single Paths .................................... 274 7.5 Implications for Ocean Probing ...................................... 276 References 277 Subject Index ................................................................ 279