2.682 | Spring 2012 | Graduate

Acoustical Oceanography


Course Meeting Times

Lectures: 1 session / week, 3 hours / session (mandatory coffee break in the middle of class)


The Spring 2012 offering of “2.682: Acoustical Oceanography” was, for reasons of course scheduling and student needs, somewhat of an amalgam of three courses: 1) “Ocean and Seabed Acoustics”, based on the book of the same name by George Frisk, 2) “Computational Ocean Acoustics,” based on the book of that name and taught by MIT Professor Henrik Schmidt, and 3) “Acoustical Oceanography,” taught by WHOI Senior Scientist Jim Lynch.  The inclusion of the wave propagation theory and numerical modeling components made the course more general; but it also meant sacrificing some of the depth of the usual acoustical oceanography component. This “realization” of the course should provide a good graduate level introduction to all three areas treated, especially if the student works seriously at the homework and term projects.


MATLAB® is required for the homework and term projects.

Special Course Notes

  • Students will be sent class notes and problem sets as PDF files before class.
  • I will schedule talks with each student very early in the semester to determine both their background and research interests (and thus the term project). This project has actually been fun for students in my previous courses, and I hope it will continue to be in this course.
  • I would appreciate getting an e-mail note from you with a bit of preliminary information about your background and research interests, so our meeting is not a “cold start.” Also, would appreciate your phone number if you wish to give it out—that way I can contact you (as well as by e-mail) about any class schedule changes or other events. However, given how things are nowadays, I certainly won’t insist on that last piece of information.
  • I traditionally have a “post term” lunch with students, my treat.


Homework 60
Term Project 40


Part I. Basics of Ocean Acoustics and Numerical Methods

Why bother?

Acoustic wave equation in 3D

A look at the acoustic environment

Simple solutions to wave equation


Potentials, Impedance, Intensity and other basic quantities

Boundary conditions

Plane wave reflection coefficient

Rayleigh and Fresnel reflection formulae


Basics of Green functions

Method of images in a waveguide

Lloyd mirror effect

Problem set #1 assigned
Ray Theory

Basic assumptions

Eikonal and transport equation derivations

Solution of transport equation (ray tube)

Solution of eikonal equation (ray codes/numerical solutions)


Coherent and incoherent propagation loss

Fermat’s principle

Fresnel sones/Fresnel tubes

Gaussian beams

WKB ray theory and transition from rays to modes

Problem set #1 due

Problem set #2 assigned

Normal mode theory and wavenumber integration

Sturm-Liouville problem

Separation of variables solutions

Hard bottom waveguide

Intro to modal continuum

Mode cycle distance, phase velocity, group velocity

Pekeris waveguide


Continuum effects—EJP branch line integral

Hankel transform and wavenumber integration techniques

Range dependence and coupled mode theory

The adiabatic mode approximation

Some real-world examples of mode-coupling solutions

A simplified coupled equation system

Supplemental material on endpoint methods and normal modes

Problem set #2 due

Problem set #3 assigned


Ray-mode picture connection

Rays as interfering modes

Horizontal rays and vertical modes—a simple 3D acoustics approach

Modal propagation in a coastal wedge

The “horizontal Lloyd’s mirror”

Perturbation theory approach to attenuation, soundspeed changes, and group velocity


Normal mode numerical methods—general discussion

Finite difference mode solution

Shooting method solution

Root finder solution

“Stepwise coupled modes” solution to full range dependent waveguide

Wavenumber integration techniques—general discussion

Fast field approximation to Hankel transform

Truncation of integration intervals, discretization, aliasing

Problem set #3 due

Problem set #4 assigned

Parabolic Equation—PE

Derivation of simple PE

Numerical solution to PE—marching solution

Comparison of PE with normal mode solution

Wide angle PE and the Pade approximation

Implicit Finite Difference (IFD) solution to PE

A simple PE Code (needed for term project on numerical methods)

Assorted Topics of Interest

Ray/mode picture revisited—modes as interfering rays and how to distinguish ray vs. mode multipath arrivals

Filtration of modes and rays using vertical and horizontal arrays

Matched field processing

Time reversal mirror of the sound field

Problem set #4 due
Rough Surface Scattering in a Nutshell

Verbal description of surface, volume, and bottom scatterers in the ocean

Statistical characterization of rough surfaces

Method of small perturbations (MSP)

Average intensity in MSP

Attenuation of the coherent component

Helmholtz integral and scattering approximations to it

Modal scattering in a shallow water waveguide

Problem set #5 assigned
Part II. Acoustical Oceanography and Inverse Methods
Acoustical Oceanography

Brief review of physical oceanography and its acoustic effects

Munk Award Lecture on “Acoustical oceanography and shallow water acoustics”

Acoustical Oceanography Instrumentation—Brief Overview

Ocean acoustic tomography

RAFOS and SOFAR floats

Inverted Echo sounders

Pegasus profiler

Acoustic backscatter imaging of buoyant plumes

Acoustic Doppler Current Profilers (ADCPs)

Problem set #5 due
Inverse theory

Classes of inverse problems and some examples

Empirical Orthogonal Functions and objective analysis interpolation

Linear inversion basics—the Lanczos decomposition and generalized inverse

Resolution and variance

Tikhonov regularization, ill-posedness, condition number

Additional regularization constraints—bounds and Lagrange multipliers

An example of inversion—ocean seabed properties


Bayesian methods

Example of Bayesian inversion for seabed properties

Nonlinear methods—simulated annealing and genetic algorithms

Example of nonlinear inverse for seabed properties

Term project due

Course Info

As Taught In
Spring 2012
Learning Resource Types
Problem Sets
Lecture Notes