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Computational Ocean acoustics.pdf
0-front-matter[1].pdf
Computational Ocean Acoustics
Series Preface
Preface to the Second Edition
Preface to the First Edition
Contents
1-Fundamentals of Ocean Acoustics.pdf
Chapter 1 Fundamentals of Ocean Acoustics
1.1 Introduction
1.2 The Ocean-Acoustic Environment
1.3 Some Acoustic Preliminaries
1.3.1 Sources and Receivers
1.3.2 Energy, Power and Intensity
1.3.2.1 Energy
1.3.2.2 Power and Intensity
1.3.2.3 Complex Notation and Intensity
1.3.3 Relevant Units
1.3.3.1 Intensity and Decibels
1.3.3.2 Spectrum Level
1.3.4 Transmission Loss
1.4 Sound Propagation in the Ocean
1.4.1 Characteristic Propagation Paths
1.4.2 Deep Water
1.4.2.1 Nearfield Lloyd-Mirror Pattern
1.4.2.2 Convergence-Zone Propagation
1.4.2.3 Deep-Sound-Channel Propagation
1.4.2.4 Surface-Duct Propagation
1.4.2.5 Arctic Propagation
1.4.3 Shallow Water
1.4.4 Range-Dependent Environments
1.4.4.1 An Ocean Front
1.4.4.2 A Seamount
1.5 Volume Attenuation
1.5.1 Attenuation of Plane Waves
1.5.2 Attenuation in Seawater
1.6 Bottom Loss
1.6.1 Fluid--Fluid Interface
1.6.2 Fluid--Solid Interface
1.6.3 Layered Fluid Halfspace
1.6.3.1 Quarter-Wavelength Layer
1.6.3.2 Half-Wavelength Layer
1.6.4 Arbitrary Layering
1.7 Boundary and Volume Scattering
1.7.1 Surface Scattering
1.7.2 Bottom Scattering
1.7.3 Volume Scattering
1.8 Ambient Noise
1.9 Sound Propagation Models
Problems
References
2-Wave Propagation Theory.pdf
Chapter 2 Wave Propagation Theory
2.1 The Wave Equation
2.1.1 The Nonlinear Wave Equation
2.1.2 The Linear Wave Equation
2.1.2.1 Wave Equation for Pressure
2.1.2.2 Wave Equation for Particle Velocity
2.1.2.3 Wave Equation for Velocity Potential
2.1.2.4 Wave Equation for Displacement Potential
2.1.2.5 Source Representation
2.1.2.6 Solution of the Wave Equation
2.2 The Helmholtz Equation
2.3 Homogeneous Media
2.3.1 Coordinate Systems
2.3.2 Source in Unbounded Medium
2.3.3 Source in Bounded Medium
2.3.4 Point Source in Fluid Halfspace
2.3.5 Transmission Loss
2.4 Layered Media and Waveguides
2.4.1 Integral Transform Techniques
2.4.1.1 Plane Propagation Problems
2.4.1.2 Axisymmetric Propagation Problems
2.4.2 Source in Fluid Halfspace
2.4.3 Reflection and Transmission
2.4.3.1 Hard Bottom
2.4.3.2 Soft Bottom
2.4.3.3 The Point Source Field
2.4.4 Ideal Fluid Waveguide
2.4.4.1 Image Method
2.4.4.2 Integral Transform Solution
2.4.4.3 Normal Modes
2.4.4.4 Modal Dispersion
2.4.4.5 The Waveguide Field
2.4.4.6 Relationship Between Image and Modal Solutions
2.4.5 The Pekeris Waveguide
2.4.5.1 Normal Modes
2.4.5.2 Modal Dispersion
2.4.5.3 The Waveguide Field
2.4.5.4 Reciprocity
2.4.5.5 Attenuation
2.4.5.6 General Waveguide Image Solution
2.4.6 Waveguide Invariants
2.4.6.1 Frequency--Range Waveguide Invariant
2.4.6.2 Generalized Waveguide Invariant
2.5 Deep-Ocean Waveguides
2.5.1 Exact Solutions
2.5.2 WKB Solutions
Appendix 1: Principle of Reciprocity
Problems
References
3-Ray Methods.pdf
Chapter 3 Ray Methods
3.1 Introduction
3.2 Ray Bending
3.3 Mathematical Derivation
3.3.1 Solving the Eikonal Equation
3.3.2 Solving the Transport Equation
3.3.3 Ray Amplitudes and Jacobians
3.3.4 Initial Conditions
3.3.5 Intensity Calculations
3.3.5.1 Dynamic Ray Tracing
3.3.5.2 Coherent Transmission Loss
3.3.5.3 Incoherent Transmission Loss
3.3.5.4 Semicoherent Transmission Loss
3.3.5.5 Geometric Beams
3.4 Ray Anomalies
3.4.1 Caustics and Shadow Zones
3.4.2 Region of Validity of the Ray Solution
3.5 Gaussian Beams
3.5.1 Gaussian Beams in Free Space
3.5.2 Gaussian Beam Tracing
3.6 Additional Mathematical Properties
3.6.1 Alternate Forms of the Ray Equations
3.6.1.1 -Form
3.6.1.2 z(r) and r(z) Forms
3.6.2 Treatment of Attenuation
3.6.3 Interfaces and Boundaries
3.6.4 Weak Interfaces and Ocean Sound-Speed Discontinuities
3.6.5 Fermat's Principle
3.6.6 Simplifications for Stratified Media
3.6.7 Snell's Law
3.6.8 Reciprocity
3.7 Numerical Solution
3.7.1 Direct Integration
3.7.1.1 Tracing the Rays
3.7.1.2 Boundary Reflections
3.7.1.3 Intensity Calculations
3.7.2 Cell Methods: n2 Linear
3.7.3 Cell Methods: c Linear
3.7.4 False Caustics and Profile Interpolation
3.7.5 Finding Eigenrays
3.7.5.1 Interpolation
3.7.5.2 Iteration
3.7.5.3 The Bending Method
3.7.5.4 The Continuation Method
3.8 Extensions and Related Techniques
3.8.1 The WKB Method
3.8.2 Ray Theory via the WKB Approximation
3.8.3 The Ray Invariant and the Waveguide Invariant
3.8.3.1 Example 1: Ideal Waveguide
3.8.3.2 Example 2: n2-Linear Refracting Waveguide
3.8.4 Hamiltonian Formulation of Ray Acoustics
3.8.5 Three-Dimensional Ray Tracing
Appendix 1: Recipe for Simple Ray Code
Appendix 2: A Useful Property of the Jacobian
Problems
References
4-Wavenumber Integration Techniques.pdf
Chapter 4 Wavenumber Integration Techniques
4.1 Introduction
4.2 Mathematical Derivation
4.2.1 Integral Transform Solution
4.2.2 Homogeneous Fluid Layers
4.2.3 n2-Linear Fluid Layers
4.2.4 Homogeneous Elastic Layers
4.2.5 Boundary Conditions
4.2.6 Attenuation
4.3 Numerical Solution of the Depth Equation
4.3.1 Direct Global Matrix Approach
4.3.1.1 Numerical Stability
4.3.1.2 Advantages and Disadvantages
4.3.2 Propagator Matrix Approach
4.3.2.1 Numerical Stability
4.3.2.2 Advantages and Disadvantages
4.3.3 Invariant Embedding Approach
4.3.3.1 Numerical Stability
4.3.3.2 Advantages and Disadvantages
4.4 Reflection Coefficients
4.5 Wavenumber Integration
4.5.1 Fast Field Approximation
4.5.2 Truncation of Integration Interval
4.5.3 Wavenumber Discretization: Aliasing
4.5.4 FFP: Fast Field Program
4.5.5 Complex Contour Integration
4.5.6 Fast Hankel Transforms
4.5.7 Trapezoidal Rule Integration
4.5.8 Filon Integration
4.5.9 Adaptive Integration
4.6 Frequency Integration
4.7 Range-Dependent Propagation
4.8 3-D Wavenumber Integration
4.9 Scattering and Reverberation in a Stratified Ocean
4.9.1 Target Scattering
4.9.2 Rough Interface Reverberation
4.9.2.1 Wavenumber Representation
4.9.2.2 Finite Roughness Patch
4.9.3 Scattering from Volume Inhomogeneities
4.9.3.1 Monostatic Backscatter
4.10 Numerical Examples
4.10.1 Waveguide with an Elastic Bottom
4.10.2 The Bucker Waveguide
4.10.3 Beam Reflection and Transmission
4.10.4 Arctic Propagation
4.10.5 Seabed Target Scattering and Reverberation
4.10.5.1 Reverberant Field
4.10.5.2 Target Scattering
4.10.6 Reverberation from Seabed Volume Inhomogeneities
4.10.6.1 Fast Sediment Layer with Volume Inhomogeneities
4.10.6.2 Upward Refracting Sediment Layer
Appendix 1: Recipe for Simple WI/FFP Code
Appendix 2: Roughness Perturbation Operators
Problems
References
5-Normal Modes.pdf
Chapter 5 Normal Modes
5.1 Introduction
5.2 Mathematical Derivation
5.2.1 Point Source in Cylindrical Geometry
5.2.2 Line Source in Plane Geometry
5.3 Modal Expansion of the Green's Function
5.4 The Isovelocity Problem
5.5 A Generalized Derivation
5.6 A Deep Water Problem: The Munk Profile
5.7 Numerical Approaches
5.7.1 Finite-Difference Methods
5.7.1.1 Sturm's Method
5.7.1.2 Inverse Iteration
5.7.1.3 Richardson Extrapolation
5.7.1.4 Treatment of Interfaces
5.7.1.5 Mode Normalization
5.7.2 Layer Methods
5.7.3 Shooting Methods
5.7.4 Root Finders
5.7.4.1 Bisection
5.7.4.2 Deflation
5.7.4.3 Brute-Force Search
5.7.4.4 Analytic Estimates
5.7.4.5 Continuation Methods
5.7.4.6 Approaches Unique to the Complex Plane
5.7.5 Choice of Numerical Algorithm
5.8 Prüfer Transformations and Mode Counting
5.8.1 Top Halfspaces
5.8.2 Bottom Halfspaces
5.9 Modal Perturbation Theory
5.9.1 Modal Propagation Loss
5.9.2 Modal Group Velocity
5.10 Elastic Media
5.10.1 Governing Equations
5.10.2 Numerical Discretization
5.10.3 Shooting Methods and Compound Matrices
5.10.4 Boundary and Interface Conditions
5.10.4.1 Perfectly Free Boundary (Dirichlet BC)
5.10.4.2 Perfectly Rigid Boundary (Neumann BC)
5.10.4.3 Acoustic Halfspace Conditions (Robin BC)
5.10.4.4 Elastic Halfspace Conditions
5.10.5 Numerical Example
5.11 Normal Modes for Range-Dependent Environments
5.11.1 Coupled Modes
5.11.2 One-Way Coupled Modes
5.11.3 The Adiabatic Approximation
5.11.4 Example: A Warm-Core Eddy
5.12 Scattering from Objects in a Waveguide
5.12.1 Scattering Geometry
5.12.2 The Plane-Wave Scattering Function
5.12.3 Scattering from Spherical Objects in a Waveguide
5.12.4 Scattering from Non-Spherical Objects
5.13 Normal Modes for 3-D Varying Environments
5.13.1 Horizontal Refraction Equations
5.13.2 Global Propagation
5.13.3 3-D Mode Coupling Around Seamounts
5.13.3.1 Mathematical Formulation
5.13.3.2 Spectral Coupled-Mode Solution
5.13.3.3 Azimuthally Scattered Mode Amplitudes
5.14 Waveguide Invariant and Dispersion for Realistic Environments
5.14.1 The Waveguide Invariant Is Variable!
5.14.2 Range-Dependent Group Speed and Adiabatic Mode Theory
5.14.3 Waveguide Invariant for Range-Dependent Environments
Appendix 1: Recipe for Simple Mode Code
Appendix 2: Evaluation of the Normalization Term
Problems
References
6-Parabolic Equations.pdf
Chapter 6 Parabolic Equations
6.1 Introduction
6.2 Derivation of Parabolic Equations
6.2.1 Standard PE Derivation
6.2.2 Generalized PE Derivation
6.2.3 Expansion of the Square-Root Operator
6.2.4 Phase Errors and Angular Limitations
6.3 The Elastic PE
6.4 Starting Fields
6.4.1 Numerical Starters
6.4.1.1 Modal Starter
6.4.1.2 PE Self Starter
6.4.2 Analytical Starters
6.4.2.1 Gaussian Source
6.4.2.2 Greene's Source
6.4.2.3 Thomson's Source
6.4.2.4 Generalized Gaussian Source
6.4.3 Spectral Properties of Sources
6.5 Solutions by FFTs
6.5.1 The Split-Step Fourier Algorithm
6.5.2 Error Analysis
6.5.3 Numerical Implementation
6.5.4 Variable Density
6.5.5 Attenuation
6.6 Solutions by FDs and FEs
6.6.1 Field Equations on Horizontal Interfaces
6.6.2 IFD Formulation
6.6.3 Error Analysis
6.6.4 Numerical Implementation
6.7 The Problem of Energy Conservation in PEs
6.8 Three-Dimensional PEs
6.8.1 Expansion of the Square-Root Operator
6.9 Numerical Examples
6.9.1 Beam Propagation
6.9.1.1 Beam Splitting
6.9.1.2 Beam Reflection and Transmission
6.9.1.3 Beam Focusing
6.9.2 Propagation in a 2-D Wedge
6.9.3 Propagation Over a Seamount
6.9.4 Propagation Over a Sloping Elastic Bottom
6.9.5 Propagation in a 3-D Wedge
Appendix 1: Recipe for Simple PE Code
Problems
References
7-Finite Differences and Finite Elements.pdf
Chapter 7 Finite Differences and Finite Elements
7.1 Introduction
7.2 Differential Equations
7.3 Finite-Difference Methods
7.3.1 Introduction
7.3.2 Difference Approximations
7.3.3 Convergence and Stability
7.3.4 The Wave Equation
7.3.4.1 Finite-Difference Scheme
7.3.4.2 Source Representation
7.3.4.3 Boundary and Radiation Conditions
7.4 Finite-Element Methods
7.4.1 Introduction
7.4.2 Mathematical Derivation
7.4.2.1 Weighted Residuals
7.4.2.2 Variational Principle
7.4.2.3 The FEM Equations
7.4.2.4 Trial Functions
7.4.2.5 Partial Discretization
7.4.3 The Acoustic Wave Equation
7.4.3.1 Galerkin Approaches
7.4.3.2 Finite Elements
7.4.3.3 Finite Elements in Two and Three Dimensions
7.4.3.4 Boundary and Radiation Conditions
7.4.4 The Elastic Wave Equation
7.4.5 Coupled Fluid--Elastic Domains
7.4.6 Steady-State Solutions
7.4.7 Perfectly Matched Layers
7.4.8 Time Recurrence
7.5 Boundary-Element Methods
7.5.1 Introduction
7.5.2 The Boundary-Integral Equation
7.5.3 Boundary-Element Equations
7.5.3.1 Trial and Weight Functions
7.5.4 Coupled Domains
7.5.4.1 Interior Boundary-Element Solution
7.5.4.2 Interior Finite-Element Solution
7.5.5 Virtual Source Concept
7.5.5.1 Green's Functions
7.5.5.2 Numerical Implementation Issues
7.6 Numerical Examples
7.6.1 Scattering by Arctic Ice Features
7.6.1.1 Finite-Difference Solution
7.6.1.2 Boundary-Element Solution
7.6.2 Scattering from Objects Near Interfaces
7.6.2.1 Filled Spherical Shell on the Seabed
7.6.2.2 Buried, Filled Spherical Shell
7.6.2.3 Half-Buried, Filled Spherical Shell
Appendix 1: Variational Formulation for Fluid--Elastic Interaction
Appendix 2: Farfield Computations
Problems
References
8-Broadband Modeling.pdf
Chapter 8 Broadband Modeling
8.1 Introduction
8.2 Fourier Synthesis of Frequency-Domain Solutions
8.2.1 Evaluation by FFT
8.2.1.1 Frequency Windowing
8.2.1.2 Fast Fourier Transforms
8.2.1.3 Time Windowing and Sampling
8.2.2 Complex Frequency Integration
8.3 Time-Domain Solutions
8.3.1 Ray Methods
8.3.2 Spectral Integral Techniques
8.3.3 Parabolic Equations
8.4 Doppler Shift in a Waveguide
8.4.1 Wavenumber Integral Representation
8.4.2 Normal Mode Representation
8.4.3 Doppler Shift for Active Sonar
8.5 Numerical Examples
8.5.1 The Head-Wave Problem
8.5.2 Mode Dispersion in a Waveguide
8.5.3 3-D Wedge Propagation
8.5.4 Seismic Interface Waves
8.5.5 Deep-Water Propagation
8.5.6 Surface-Duct Propagation with Leakage
8.5.7 Acoustic Emission from Ice Fractures
Problems
References
9-Ambient Noise.pdf
Chapter 9 Ambient Noise
9.1 Introduction
9.2 Surface Noise in a Stratified Ocean
9.2.1 Mathematical Derivation
9.2.2 Spatial Distribution of Noise Sources
9.2.3 Wavenumber Integral Representation
9.2.4 Normal Mode Representation
9.2.5 Noise in a Homogeneous Halfspace
9.2.6 Noise in Stratified Media
9.2.6.1 Fluid Waveguide
9.2.6.2 Elastic Waveguide
9.3 Extracting Time-Domain Green's Functions from Noise Correlation Functions
9.3.1 The Time-Domain Green's Function
9.3.2 Emergence of Coherent Wavefronts from Noise
9.3.3 Data Examples of Extracting Wavefronts from Noise
9.4 Surface Noise in a Three-Dimensional Ocean
9.4.1 Noise Modeling by Adiabatic Modes
9.4.2 Simulated Noise Fields in 3-D Environments
9.4.2.1 ``Image'' of Noise Levels
9.4.2.2 Noise Directionality
9.4.3 Noise Modeling by PE
9.4.4 Downslope and Deep-Ocean-Basin Noise Field
Appendix 1: Evaluation of the Cross-Spectral Density
Problems
References
10-signal in noise.pdf
Chapter 10 Signals in Noise
10.1 Introduction
10.2 The Energetics of Signals in Noise
10.2.1 Array Gain
10.2.2 Sonar Equation
10.2.2.1 Detection Threshold and ROC Curves
10.2.2.2 Passive Sonar Equation
10.2.2.3 Active Sonar Equation
10.3 Plane-Wave Beamforming
10.3.1 Linear Beamforming
10.3.2 Adaptive Beamforming
10.3.2.1 Estimating the Cross-Spectral Density Matrix
10.3.2.2 Minimum Variance Distortionless Processor
10.3.2.3 Eigenvector Beamformers
10.3.3 Multiple-Constraints Beamforming
10.3.4 White-Noise Constraint Processor
10.3.4.1 Derivation of the White-Noise Constraint Processor
10.4 Time-Domain Processing
10.4.1 Isovelocity Time-Delay Beamforming
10.4.2 Non-Isovelocity Time-Delay Beamforming: The Turning Point Filter
10.4.3 Example: Passive Fathometer
10.5 Performance Prediction: Modeling, Beamforming and the Sonar Equation
10.6 Matched-Field Processing
10.7 Simulating Matched-Field Processing
10.7.1 Depth--Range Matched Field Processing
10.7.1.1 Shallow-Water Simulation
10.7.1.2 Deep-Water Arctic Simulation
10.7.2 Three-Dimensional Matched Field Processing
10.7.2.1 2-D Ambiguity Surface for 3-D Problem
10.7.2.2 3-D Ambiguity Function
10.7.2.3 Broadband Matched-Field Processing
10.8 Vector-Sensor Beamforming
10.9 Synthetic Signals and Sensor Stimulation
10.9.1 Stochastic Signal and Noise Model
10.9.2 Snapshot Synthesis
10.9.3 Signal Variability
10.9.4 Noise Realizations
10.10 Phase Conjugation and Time Reversal
10.10.1 Theory and Simulation for Phase Conjugation/TRM in the Ocean
10.10.1.1 Harmonic Point Source
10.10.1.2 Pulse Excitation
10.10.1.3 Properties of the Focal Region: Modes and Images
10.10.1.4 Non-Reciprocal Time Reversal and Passive Time Reversal
10.10.1.5 Variable Range Focusing
10.10.1.6 Adaptive Phase Conjugation
10.10.1.7 Sourceless Time Reversal
10.11 Summary
Problems
References
11-back-matter.PDF
About the Authors
Name Index
Subject Index
Modern Acoustics and Signal Processing
Editor-in-Chief
WILLIAM M. HARTMANN
Michigan State University, East Lansing, Michigan
Editorial Board
YOICHI ANDO, Kobe University, Kobe, Japan
WHITLOW W. L. AU, Hawaii Institute of Marine Biology, Kane’ohe, Hawaii
ARTHUR B. BAGGEROER, Massachusetts Institute of Technology, Cambridge,
Massachusetts
NEVILLE H. FLETCHER, Australian National University, Canberra, Australia
CHRISTOPHER R. FULLER, Virginia Polytechnic Institute and State University,
Blacksburg, Virginia
WILLIAM A. KUPERMAN, University of California San Diego, La Jolla, California
JOANNE L. MILLER, Northeastern University, Boston, Massachusetts
MANFRED R. SCHROEDER, University of G¨ottingen, G¨ottingen, Germany
ALEXANDRA I. TOLSTOY, A. Tolstoy Sciences, McLean, Virginia
For further volumes:
http://www.springer.com/series/3754
Finn B. Jensen William A. Kuperman
Michael B. Porter Henrik Schmidt
Computational Ocean
Acoustics
Second Edition
ABC
Finn B. Jensen
NATO Undersea Research Centre
Viale San Bartolomeo 400
La Spezia, 19126, Italy
Jensen@nurc.nato.int
William A. Kuperman
Marine Physical Lab., Mail Code 0205
Scripps Institution of Oceanography
Gilman Dr. 9500
La Jolla, CA 92093-0238, USA
wkuperman@ucsd.edu
Michael B. Porter
Heat, Light, and Sound Research, Inc.
3366 North Torrey Pines Court, Suite 310
La Jolla, CA 92037, USA
Henrik Schmidt
Massachusetts Institute of Technology (MIT)
Massachusetts Avenue 77
Cambridge, MA 02139, USA
ISBN 978-1-4419-8677-1
DOI 10.1007/978-1-4419-8678-8
Springer New York Dordrecht Heidelberg London
e-ISBN 978-1-4419-8678-8
Library of Congress Control Number: 2011927154
c Springer Science+Business Media, LLC 2011
All rights reserved. This work may not be translated or copied in whole or in part without the written
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Series Preface
“...Soun is noght but air y-broke”
– Geoffrey Chauser
end of the 14th century
Traditionally, acoustics has formed one of the fundamental branches of physics. In
the twentieth century, the field has broadened considerably and become increas-
ingly interdisciplinary. At the present time, specialists in modern acoustics can be
encountered not only in Physics Departments, but also in Electrical and Mechanical
Engineering Departments, as well as in Departments of Mathematics, Oceanogra-
phy, and even Psychology. They work in areas spanning from musical instruments
to architecture to problems related to speech perception. Today, six hundred years
after Chauser made his brilliant remark, we recognize that sound and acoustics is
a discipline extremely broad in scope, literally covering waves and vibrations in all
media at all frequencies and at all intensities.
The series of scientific literature, entitled Modern Acoustics and Signal Process-
ing (MASP), covers all areas of today’s acoustics as an interdisciplinary field. It
offers scientific monographs, graduate level textbooks, and reference materials in
such areas as architectural acoustics, structural sound and vibration, musical acous-
tics, noise, bioacoustics, physiological and psychological acoustics, speech, ocean
acoustics; underwater sound; and acoustical signal processing.
Acoustics is primarily a matter of communication. Whether it be speech or mu-
sic, listening spaces or hearing, signaling in sonar or in ultrasonography, we seek
to maximize our ability to convey information, and at the same time, to minimize
the effects of noise. Signaling has itself given birth to the field of signal process-
ing, the analysis of all received acoustic information or, indeed, all information in
any electronic form. With the extreme importance of acoustics for both modern sci-
ence and industry in mind, AIP Press is initiating this series as a new and promising
publishing venture. We hope that this venture will be beneficial to the entire interna-
tional acoustical community, as represented by the Acoustical Society of America, a
founding member of the American Institute of Physics, and other related societies
and professional interest groups.
v
vi
Series Preface
It is our hope that scientists and graduate students will find the books in this
series useful in their research, teaching, and studies.
James Russell Lowell once wrote: “In creating, the only hard thing’s to begin.”
This is such a beginning.
Robert T. Beyer
Series Editor-in-Chief
Preface to the Second Edition
This is the second edition of our book Computational Ocean Acoustics, revised
and supplemented, including much new material reflecting the progress in compu-
tational acoustics and related signal processing issues over the past 17 years. New
material appears throughout the book, but we should like to draw attention to the
following topics: the basic theory of waveguide invariants in Chap. 2, with a gen-
eralization of the concept to realistic, range-dependent waveguides in Chap. 5. The
presentation of ray methods in Chap. 3 has been significantly modified to provide a
more intuitive development of the fundamental ray concepts. Some intricate issues
(aliasing, etc.) related to discrete wavenumber integration in Chap. 4 have been ex-
plained in detail, including several illustrative examples. Also, the extension of the
wavenumber-integration technique to 3-D scattering and reverberation scenarios in
horizontally-stratified waveguides has been included in Chap. 4, together with sev-
eral illustrative numerical examples. Within the framework of normal-mode theory
(Chap. 5), there is new material on mode identification, as well as on normal modes
in elastic media. In addition, a section on scattering from objects in a waveguide
has been added, together with a 3-D example of mode coupling around seamounts.
Chap. 6 has been updated with recent developments in parabolic-equation modeling,
notably improvements in dealing with elastic media, and 4-D code implementations
for pulse propagation in general 3-D environments. In Chap. 7, we have added a
description of the virtual-source concept (VSC) for target scattering, and also ex-
panded on the finite-element (FE) section to address the use of this technique for
target scattering in ocean waveguides. Several numerical examples illustrate current
capabilities in FE=VSC modeling. Chapter 8 contains new material on Doppler shift
in a waveguide, based both on wavenumber-integration and normal-mode theory.
Chapter 9 has a new section dedicated to the extraction of time-domain Green’s
functions from noise correlation functions. Finally, recent developments in sig-
nal processing for sonar applications have been added to Chap. 10, specifically on
time-domain processing, vector-sensor beamforming, synthetic signal and sensor
stimulation, and phase conjugation and time reversal. Finally, extensive use of color
illustrations throughout has improved the appearance of this book significantly.
The authors wish to thank the many colleagues who provided material for
the book or reviewed parts of the manuscript. These include Michael Ainslie,
Michael Collins, Kevin Cockrell, Lee Culver, Gerald D’Spain, Stephanie Fried,
vii
viii
Preface to the Second Edition
Peter Gerstoft, Oleg Godin, Paul Hursky, Kevin LePage, Wenyu Luo, Ed McDonald,
Peter Nielsen, Philippe Roux, Hee-Chun Song, Fr´ed´eric Sturm, and Shane Walker.
Special thanks go to Mario Zampolli for helping out with the section on finite-
element applications. Three of the authors’ research reported here has been sup-
ported by the U.S. Office of Naval Research, Ocean Acoustics Program, while one
author (FBJ) has been supported for 35 years by the NATO Undersea Research
Centre. This support is gratefully acknowledged.
Since this book represents a major milestone in the authors’ research careers,
we wish to acknowledge the unwavering support from our wives, Patrizia, Gaby,
Laurel, and Satu, to whom this new edition is dedicated.
Finn B. Jensen
William A. Kuperman
Michael B. Porter
Henrik Schmidt
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