Syllabus

Course Meeting Times

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

Description

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.

Requirements

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.

Grading

ACTIVITies	PERCENTAGEs
Homework	60
Term Project	40

Calendar

SES #	TOPICS	KEY DATES
Part I. Basics of Ocean Acoustics and Numerical Methods
Fundamentals
1	Why bother? Acoustic wave equation in 3D A look at the acoustic environment Simple solutions to wave equation
2	Potentials, Impedance, Intensity and other basic quantities Boundary conditions Plane wave reflection coefficient Rayleigh and Fresnel reflection formulae
3	Basics of Green functions Method of images in a waveguide Lloyd mirror effect	Problem set #1 assigned
Ray Theory
4	Basic assumptions Eikonal and transport equation derivations Solution of transport equation (ray tube) Solution of eikonal equation (ray codes/numerical solutions)
5	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
6	Sturm-Liouville problem Separation of variables solutions Hard bottom waveguide Intro to modal continuum Mode cycle distance, phase velocity, group velocity Pekeris waveguide
7	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
8	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
9	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
10	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
11	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
12	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
13	Brief review of physical oceanography and its acoustic effects Munk Award Lecture on “Acoustical oceanography and shallow water acoustics”
Acoustical Oceanography Instrumentation—Brief Overview
14	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
15	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
16	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

I have had the privilege of teaching graduate classes through the MIT/WHOI Joint Program in Oceanography and Oceanographic Engineering since 1984. (28 years?! Whoa!) And each year, our last class would be a lunch together (on the instructor, of course – I remember the tight budget I had as a grad student, and it’s still pretty much the same!) During these lunch’s, the conversation would generally be about the eagle’s eye view of the course, and how it fits into the larger world of science, technology, social needs and concerns, etc. This “bull session” overview of the world is a valuable one - often in grad school one gets overly focused on their research problem (with good reason), and ignores the bigger picture. In writing the lecture background notes, I tried to incorporate some of that overview material, and hope I have succeeded.

This year, Jessica Kloss of MIT OCW joined us for lunch, and her presence engendered a bit of discussion about online courses and remote learning. I personally believe that this is an important trend that is continually growing stronger, and this was one of my motivations to contribute to MIT OCW. (And if you don’t believe me, please dig out the November 19, 2012 New York Times article “College of the Future Could be Come One, Come All”; by Tamar Lewin on Massively Open Online Courses (MOOC’s).)

Another motivation I had to contribute to MIT OCW is that I’m an avid user. One of my hobbies is trying to keep a bit current in Physics, Mathematics, and Astronomy, and OCW has wonderful offerings here, which I am slowly grinding through. (OCW has not helped improve my World of Warcraft gaming skills, but I suppose that should be expected.)

As to my offering here, a few notes. First, this course covers a LOT of areas (purposely, this semester). Each of the areas of propagation theory, scattering, numerical modeling, and inversion has a complete one semester course (currently) taught about it at MIT, just in the context of ocean acoustics. And even for an abbreviated version of these, there is a lot of material covered in the notes. Second, I hope that my offering here can stand up reasonably to the other excellent courses on OCW. I know there may be some errors here and there, for which I apologize beforehand! (And if you spot some, please contact me, and I will be sure to have an up to date “errata” page posted somewhere accessible.) Third, I am an enthusiast about what I do, and science and engineering in general, and enjoy talking to other enthusiasts. I will be happy to reply and correspond to any comments, questions, and such from serious readers of this material.

Finally, let me give a big thanks to Jessica Kloss and Molly de Blanc of MIT OCW and Gretchen McManamin of WHOI who did the real legwork on this project, and made it possible. Also, my thanks to the MIT/WHOI Joint Program (a wonderful intersection of two great institutions) which gave me the opportunity to teach through the years. A big thanks to George Frisk, who pretty much got me started on teaching in the Joint Program. The Office of Naval Research also deserves a big thank you, as they were the sponsors of much of the work shown in this course. And finally, my profound thanks to all the students who have taken courses with me throughout the years – they have been a joy to interact with, and have taught me a lot!

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Acoustical Oceanography