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Last updated:

July 29, 2022


Unlimited Duration


This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration


This course examines wave equations for fluid and visco-elastic media, wave-theory formulations of acoustic source radiation and seismo-acoustic propagation in stratified ocean waveguides, and Wavenumber Integration and Normal Mode methods for propagation in plane-stratified media

Also covered are Seismo-Acoustic modeling of seabeds and ice covers, seismic interface and surface waves in a stratified seabed, Parabolic Equation and Coupled Mode approaches to propagation in range-dependent ocean waveguides, numerical modeling of target scattering and reverberation clutter in ocean waveguides, and ocean ambient noise modeling. Students develop propagation models using all the numerical approaches relevant to state-of-the-art acoustic research.

This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.853. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.068.

Course Curriculum

  • The Acoustic Wave Equation, Integral Transforms, The Helmholtz Equation Unlimited
  • Sources in Unbounded and Bounded Media, Green’s Functions, Green’s Theorem Unlimited
  • Reflection and Transmission, Integral Transform Solution, Source in Half-spaces Unlimited
  • Ideal Waveguides, The Pekeris Waveguide Unlimited
  • Wavenumber Integration: Layer Solutions and Interface Conditions Unlimited
  • Wavenumber Integration: Global Matrix Solution Unlimited
  • Wavenumber Integration: Propagator Matrix and Invariant Embedding Solution Unlimited
  • Wavenumber Integration: Numerical Evaluation of Wavenumber Integral, Aliasing and Wrap-around Unlimited
  • Wavenumber Integration: Numerical Methods Used in Wavenumber Integration Unlimited
  • Normal Modes: Mathematical Derivation, Model Expansion of the Green’s Function Unlimited
  • Normal Modes: Isovelocity Problem, Generalized Derivation Unlimited
  • Normal Modes: Munk Profile, Numerical Approaches Unlimited
  • Normal Modes: Numerical Approaches (contd.) Unlimited
  • Normal Modes: Numerical Procedures Unlimited
  • Normal Modes: Range-dependent Environment, Coupled Modes Unlimited
  • Normal Modes: 3-D Environment Unlimited
  • Parabolic Equation: Derivation of Parabolic Equations Unlimited
  • Parabolic Equation: Starting Fields (Make Up Class) Unlimited
  • Parabolic Equation: Energy Conservation Problem, Solutions by FDs FEs Unlimited
  • Doppler Shift in Waveguide Unlimited
  • Time Series Simulation, Signal and Noise Unlimited

About the instructor

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Massachusetts Institute of Technology