UNDERWATER ACOUSTICS. Monograph Series in

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1 Monograph Series in UNDERWATER ACOUSTICS Sponsored by Office of Naval Research Editorial Board: Jeffrey A. Simmen, Ph.D., Chair Homer P. Bucker, Ph.D. Ira Dyer, Ph.D. Finn B. Jensen, Ph.D. Ellen S. Livingston, Ph.D. For further volumes:

2 Monograph Series in UNDERWATER ACOUSTICS In 2001 the Office of Naval Research began a program to publish a selected monograph series in the field of underwater acoustics. The series publishes in-depth reviews and analysis on the state of understanding of the physics of sound in selected areas of research. The monograph series covers the most important topics in underwater sound in an in-depth, critical, scholarly, and comprehensive fashion. It is intended to provide researchers with an understanding of the physics of underwater sound, based on both theory and experiment. The discussion of important unanswered questions is encouraged. Topics of particular importance in the field are low-frequency sound in the deep ocean, shallow-water acoustics, and ambient noise. Sponsored by: Office of Naval Research One Liberty Center 875 North Randolph Street, Suite 1425 Arlington, VA onrpao@onr.navy.mil Series Editors: Jeffrey A. Simmen, Ph.D. Applied Physics Laboratory University of Washington 1013 NE 40th Street Seattle, WA simmen@apl.washington.edu Ira Dyer, Ph.D. Weber Shaughness Professor of Ocean Engineering, Emeritus Massachusetts Institute of Technology Cambridge, MA Homer P. Bucker, Ph.D. Space and Naval Warfare Systems Center, retired 808 Moana Drive San Diego, CA bucker@nosc.mil Finn B. Jensen, Ph.D. Emeritus Scientist NATO Undersea Research Centre La Spezia, Italy jensen@nurc.nato.int Ellen S. Livingston, Ph.D. Associate Director Ocean and Undersea Science U.S. Office of Naval Research Global 86 Blenheim Crescent West Ruislip, Middlesex HA4 7HB United Kingdom ellen.livingston@onrg.navy.mil

3 Boris Katsnelson l James Lynch Valery Petnikov Fundamentals of Shallow Water Acoustics

4 Boris Katsnelson Voronezh State University Universitetskaya Square 1 Voronezh , Russia katz@phys.vsu.ru Valery Petnikov A.M. Prokhorov General Physics Institute Russian Academy of Sciences Moscow , Russia petniko@kapella.gpi.ru James Lynch Woods Hole Oceanographic Institution Woods Hole 02543, MA, USA jlynch@whoi.edu ISBN e-isbn DOI / Springer New York Dordrecht Heidelberg London Library of Congress Control Number: # Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (

5 Series Preface The efficacy of sound to penetrate the seas made acoustic systems in the past century the leading tools for sensing objects in and measuring properties of the seas. For over 60 years, the US Office of Naval Research (ONR) has been a major sponsor of undersea research and development at universities, national laboratories, and industrial organizations. Appropriately ONR is the sponsor of this monograph series. The intent of the series is to summarize recent accomplishments in, and to outline perspectives for, underwater acoustics in specific fields of research. The general field has escalated in importance and spread broadly with richness and depth of understanding. It has also, quite naturally, become more specialized. The goal of this series is to present monographs that critically review both past and recent accomplishments in order to address the shortcomings in present understanding. In this way, these works will bridge the gaps in understanding among the specialists and favorably color the direction of new research and development. Each monograph is intended to be a stand-alone advanced contribution to the field. We trust that the reader will also find that each is a critical introduction to related specialized topics of interest as well. ONR has sponsored the series through grants to the authors. Authors are selected by ONR based on the quality and relevance of each proposal and the author s experience in the field. The editorial board, selected by ONR, has, at times, provided independent views to ONR in this process. Its sole official role, however, is to judge the manuscripts before publication and to assist each author at his request through the process with suggestions and broad encouragement. Jeffrey A. Simmen, Ph.D. Homer P. Bucker, Ph.D. Ira Dyer, Ph.D. Finn B. Jensen, Ph.D. Ellen S. Livingston, Ph.D. v

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7 Preface and Acknowledgments Shallow water acoustics is a very active area of underwater acoustics research, as the continental shelves and slopes have great economic, social, and military importance to humans, and all these areas interact with ocean sound. However, books dedicated to this specific topic are in short supply, and indeed the book Shallow Water Acoustics published over two decades ago in Russian by the two Russian authors of this present book was the first volume specifically dedicated to this branch of underwater acoustics. The authors then had this book translated into English, and it represented the state of the art up to about However, a huge amount of research has been done in this area in the last 15 years, and so we thought that it would be a good thing for the three of us to collaborate on a book that would update the coverage of the field, as well as point out more strongly where we thought the future might lie. As the Office of Naval Research (ONR) was publishing a book series on underwater sound, and was amenable to the idea, we signed on with them and produced this book, guided by a technical Editorial Board that reviewed and critiqued our work. It may seem strange to some that a book on underwater sound was written jointly by an American and two Russians, but in fact it is a rather natural development given the history of the last 50 years. During the Cold War era, both the USA and Russia developed considerable expertise in underwater sound, and had large communities working in the area. And though (obviously) any transfer of classified work was and is strictly prohibited by both countries, the transfer of basic research knowledge was and still is fairly open. Indeed, American researchers studied the works of the famous Russian acoustician Leonid Brekovskikh, while Russian researchers were just as familiar with the textbooks by Bob Urick and Clarence Clay. When the Cold War subsided in around 1990, actual meetings of Russian and American investigators became common, and indeed that is when the three authors of this book first met, at a port call of the Russian research vessel Akademik Sergey Vavilov in Boston, MA. What struck us all was just how much we had in common scientifically we spoke one common language well, even if the Russians English was poor and the American s Russian nonexistent. We were excited about the basic vii

8 viii Preface and Acknowledgments acoustics science, and as the international doors had opened sufficiently, we started to collaborate. In the post-cold War era, Russian support for experimental ocean acoustics dropped precipitously, and seagoing efforts became few and far between. However, a strong community with a good understanding of experiments and a sterling knowledge of theory existed, and started to look outwards for collaboration and funding. US funding also dropped some, but ONR still maintained a vibrant ocean acoustics program, including a strong experimental and technological component. Given the data coming out of the US program, and the analysis capabilities of the Russian researchers, a natural partnership was possible, and indeed came to fruition in many cases, not just for this book. This bit of technological symbiosis has been good for all concerned, and we fervently hope it will continue. Regarding the book itself, we have written a book that is intended for graduate students, postdocs, and more advanced researchers, that is also a cross between a research monograph and a textbook. As there are few textbooks in this area (see the above remarks), we thought that covering the elements of the field, but at an advanced level, would be useful On the other hand, we also wanted to provide a monograph that showed the state of the art in research, and also tried to point the way for future efforts. This made the book a bit of a balancing act, and we hope that it has succeeded. We also have couched much of the physics of this book in terms of the modal picture, which we think is the most natural one for shallow water. That is not to say that we have avoided ray theory or WKB, but that our emphasis has been on lower frequency modal work. We also note that some of the physics can be explained in the ray picture as well as the mode, and indeed one of our Editorial Board members, Dr. Ira Dyer, is a strong advocate of looking at things that way. Our feeling is that, once you have understood the physics in one picture or the other, you can understand it both ways the picture translation is not so hard. One might also notice a bias in the experimental data discussed to the Barents Sea and the East Coast of the USA. This is because these are the places that were most frequented experimentally by the authors and their home Institutions (Voronezh State University, the General Physics Institute and the Woods Hole Oceanographic Institution). We are most familiar with the data from these areas, and so naturally used them first for examples. Next, you will note in reading this book that it speaks with both a Russian and an American (New Jersey) accent, depending on the section. We have tried hard to make things grammatically correct, and clear as well, but the linguistic lilt of the various sections we left intact. As all of us are fans of the great physicist Richard Feynman, we think that speaking in your own voice is no crime, and has a noble precedent. Feynman would have contended, as we do, it is what you say about the science, and not the regional accent that counts. As with any larger piece of work, many people were involved and contributed to its completion. From the Russian side, the authors would like to acknowledge Fyodor V. Bunkin, Yuri A. Kravtsov, and the many other colleagues from the A.M. Phokhorov General Physics Institute and the Voronezh State University

9 Preface and Acknowledgments ix whose work in the execution of large-scale experiments on the shelf of the Barents Sea and the interpretation of the results was invaluable. From the American side, the author also warmly acknowledges the numerous colleagues with whom he has gone to sea, analyzed data, and argued over what it all means at meetings, workshops, seminars, and other venues. Regarding funding, all the authors give their heartfelt thanks to the US Office of Naval Research and the Robert W. Morse Senior Scientist Chair at WHOI, both of which paid for the majority of this work. From the Editorial side, the efforts of the Editorial Review Board (Drs. Ralph Goodman (deceased), Ira Dyer, Jeffrey Simmen, and Finn Jensen have been enormously helpful. The enthusiasm and project management of Dr. Ellen Livingston is also warmly appreciated. Also, our great thanks to Ms. Sheila Hurst for her editorial work and skills, and Ms. Gretchen McManamin for her administrative assistance. Finally, our thanks to our wives and families, who put up with our often erratic and travel heavy oceanographer lifestyles, which are prerequisites to writing such a book. The only really hard thing about being an oceanographer is being away from such wonderful families for long periods of time. Voronezh, Russia Moscow, Russia Woods Hole, MA, USA Boris Katsnelson Valery Petnikov James Lynch

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11 Contents 1 What Is Shallow Water Acoustics? Deep Versus Shallow Past and Present of Shallow Water Acoustics The Future of Shallow Water Acoustics Some Old Favorite Research Areas Revisited and Updated Coastal Oceanography, Geology, and Biology The Coast as Acoustic Waveguide Properties of Sea Water: Vertical Stratification and Its Seasonal Variability Horizontal Stratification and Its Variability: Fronts and Eddies, Surface Ducts, and Storm Surges Dynamics of the Ocean Surface: Surface Waves Dynamical Processes Inside the Ocean: Tides and Internal Waves Experimental Studies of Coastal Internal Waves Coastal Geology and Geophysics Acoustics of Sediments Bottom Roughness Solid and Multicomponent Layered Bottom Models Acoustics of Biological Objects in a Coastal Area Foundations of the Theory of Propagation of Sound Field of a Point Source in a Layered Waveguide with Absorbing Boundaries The Pekeris Model Perturbation Theory and WKB Methods xi

12 xii Contents 3.4 Ray Description of the Sound Field and Ray-Mode Connections Ray Theory Rays as Interfering Modes Modes as Interfering Rays Distinguishing Between Ray and Mode Arrivals Mode Coupling in a Shallow Water Waveguide with Small Inhomogeneities Mode Coupling in Shallow Water with Smooth Inhomogeneities Horizontal Refraction in Shallow Water (The 3D Problem) Parabolic Equation Examples Illustrating the Characteristics of Waveguide Propagation A General Transmission Loss Example, Including a Simplified Theory of Shallow Water Attenuation Simplified Description of Solid, Multicomponent, Poro-Elastic, and Layered Bottom Models Optimum Frequency Interference Structure and Interference Invariant of the Sound Field Waveguide Dispersion of Sound Signals in Shallow Water Averaged Description of the Sound Field in a Waveguide Channel with Constant Sound Speed and Variable Depth Irregular Near-Bottom Sound Channel Sound Field in Shallow Water with Random Inhomogeneities Structure and Models of Different Kinds of Random Inhomogeneities Description of a Random Sound Field by Coherent and Incoherent Parts Equations for Mode Interactions Equations for Intensity The Diffusion Equation and Averaged Decay Laws Some Examples Waveguide of Constant Depth Irregular Waveguide Dependence of the Intensity on Depth

13 Contents xiii 5.7 Sound Field Fluctuations in the Presence of Background Internal Waves Models and Statistics of Intensity Fluctuations Intensity Fluctuations: Stochastic Modeling Experimental Measurements and the Statistics of Intensity Fluctuations Broadband Fluctuations Low-Frequency Bottom Reverberation in Shallow Water Introduction: Sound Backscattering by the Sea Bottom Mode Theory of Bottom Reverberation in a Regular Waveguide Numerical Simulation of Low-Frequency Bottom Reverberation Long-Range Reverberation Studies Using Extended Arrays Long-Range Reverberation in a Randomly Inhomogeneous Waveguide The Inverse Problem General Considerations: The Linear Inverse Problem Bottom Versus Water Column Influences on the dq l and Inverse The Generalized Inverse Solution, Its Error, and an Example from the Corpus Christi GEMINI Experiment Examples of Nonlinear Bottom Property Inversion Using Various Data Types Horizontal Interference Structure and Bottom Parameters Estimation Using the Vertical Interference Pattern for Bottom Parameter Estimation Broadband Experiments and the Frequency Dependence of the Bottom Parameters Bottom Geoacoustic Inversions Using Ambient Noise Sources Inversion for Bottom Properties from Ship Self-Noise Inversion for Bottom Properties from Random Ship of Opportunity Noise Inversion for Bottom Properties from Random Surface Noise

14 xiv Contents 8 Signal Processing Fundamentals of Data Processing Techniques Matched Field Processing in Shallow Water Conventional MFP, Bartlett Beamformer Two (Analytic) Examples of the Parameter Ambiguity Function Maximum Likelihood Beamformer Variable Coefficient Likelihood Beamformer Comparison of Processors for Simple Examples Spatial Coherence of the Sound Field in Shallow Water and Array Signal Gain Mode Filtration Time-Reversal Mirror of the Sound Field in Shallow Water Acoustic Uncertainty Noise Field in Shallow Water Introduction. Model of a Noise Source: General Equations Relationship Between the Continuous and the Discrete Components of the Field of Surface Noise Sources in a Waveguide Effect of the Frequency Dependence of the Bottom Absorption Coefficient on the Noise Spectrum Vertical Directivity of the Sound Field and the Effect of Random Inhomogeneities Effect of the Sound Speed Profile on the Vertical Distribution of the Noise Field Intensity Equipment for Shallow Water Acoustics and Experimental Considerations The Frequency Band Used for Large-Scale Acoustic Monitoring Low-Frequency Sources of Sound Receiving Acoustic Arrays and the Design of Large-Scale Acoustic Monitoring Experiments on the Shelf The Future Introduction Physical Oceanography Bottom Acoustic Properties New Directions in Theory and Modeling of the Sound Propagation D Problems Interference Invariant Dislocations of the Wave Field

15 Contents xv 11.5 Physical Phenomena, Concerned with Stochastic Effects Inverse Problems Water Layer Bottom Layer Signal Processing New and Prospective Developments in Oceanographic and Acoustical Equipment and Survey Methods AUV, Gliders, Etc. and the Construction of Detailed Oceanographic Models Appendix A Waves and Signals Appendix B Modal Decomposition of the Sound Field from a Point Source (Green Function) Appendix C Mode Coupling Equations Appendix D Empirical Orthogonal Functions Appendix E Scattering at Localized Inhomogeneities in the Waveguide. Approximate Description Appendix F Reflection of a Plane Wave from Half-Space Main Provisional Notation References Abbreviations Index