Underwater Acoustics 201


This two-day course explains how to translate our physical understanding of sound in the sea into mathematical formulas solvable by computers. It provides a comprehensive treatment of all types of underwater acoustic models including environmental, propagation, noise, reverberation and sonar performance models. Specific examples of each type of model are discussed to illustrate model formulations, assumptions and algorithm efficiency. Guidelines for selecting and using available propagation, noise and reverberation models are highlighted. Demonstrations illustrate the proper execution and interpretation of PC-based sonar models.

Each student will receive a copy of Underwater Acoustic Modeling and Simulation (4th edition) by Paul C. Etter, in addition to a complete set of lecture notes.

What you will learn:

  • Principles of underwater sound and the sonar equation.
  • How to solve sonar equations and simulate sonar performance.
  • What models are available to support sonar engineering and oceanographic research.
  • How to select the most appropriate models based on user requirements.
  • Models available at APL.

Course Outline:

  1. Introduction. Nature of acoustical measurements and prediction. Modern developments in physical and mathematical modeling. Diagnostic versus prognostic applications. Latest developments in inverse-acoustic sensing of the oceans.
  2. Acoustical Oceanography. Distribution of physical and chemical properties in the oceans. Sound-speed calculation, measurement and distribution. Surface and bottom boundary conditions. Effects of circulation patterns, fronts, eddies and fine-scale features on acoustics. Biological effects.
  3. Propagation. Basic concepts, boundary interactions, attenuation and absorption. Ducting phenomena including surface ducts, sound channels, convergence zones, shallow-water ducts and Arctic half-channels. Theoretical basis for propagation modeling. Frequency-domain wave equation formulations including ray theory, normal mode, multipath expansion, fast field (wavenumber integration) and parabolic approximation techniques. Energy-flux models. Prediction uncertainties in complex environments. Model summary tables. Data support requirements. Specific examples.
  4. Noise. Noise sources and spectra. Depth dependence and directionality. Slope-conversion effects. Theoretical basis for noise modeling. Ambient noise and beam-noise statistics models. Pathological features arising from inappropriate assumptions. Model summary tables. Data support requirements. Specific examples.
  5. Reverberation. Volume and boundary scattering. Shallow-water and under-ice reverberation features. Theoretical basis for reverberation modeling. Cell scattering and point scattering techniques. Bistatic reverberation formulations and operational restrictions. Model summary tables. Data support requirements. Specific examples.
  6. Sonar Performance Models. Sonar equations. Monostatic and bistatic geometries. Model operating systems. Model summary tables. Data support requirements. Sources of oceanographic and acoustic data. Specific examples.
  7. Simulation. Review of simulation theory including advanced methodologies and infrastructure tools.
  8. Demonstrations. Guided demonstrations illustrate proper execution and interpretation of PC-based monostatic and bistatic sonar models.


This course is not on the current schedule of open enrollment courses. If you are interested in attending this or another course as open enrollment, please contact us at (410)956-8805 or at ati@aticourses.com and indicate the course name and number of students who wish to participate. ATI typically schedules courses with a lead time of 3-5 months. Group courses can be presented at your facility. For on-site pricing, request an on-site quote. You may also call us at (410)956-8805 or email us at ati@aticourses.com.


  • Paul C. Etter has worked in the fields of ocean-atmosphere physics and environmental acoustics for the past forty years supporting federal and state agencies, academia and private industry. He received his BS degree in Physics and his MS degree in Oceanography at Texas A&M University. Mr. Etter served on active duty in the U.S. Navy as an Anti-Submarine Warfare (ASW) Officer aboard frigates. He is the author or co-author of more than 200 technical reports, professional papers and books addressing environmental measurement technology, underwater acoustics and physical oceanography. Mr. Etter is the author of the textbook Underwater Acoustic Modeling and Simulation.

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