SONAR (SOund NAvigation Ranging) has been in use for decades to detect submerged objects, but researchers are finding how to extract new information from its echoes. With the help of multiphysics modeling software, a group of researchers at the NATO Undersea Research Centre in La Spezia, Italy, are studying how lowfrequency echoes can determine what an object is made of.

SONAR uses sound waves traveling through water to detect and identify objects. The technique is similar to the more widely known RADAR (RAdio Detection And Ranging), which is based on electromagnetic waves instead of acoustic waves. RADAR is not used underwater because radio waves cannot reach very far in that medium due to absorption. During WWII, SONAR was used primarily to detect submarines; today these techniques are used to look for undersea objects such as shipwrecks and for measuring fish abundances and distributions. Similar acoustic techniques are being applied to wide-ranging applications such as ultrasonic NDT (nondestructive testing), acoustic-transducer design, medical acoustics, and geoacoustics.

SONAR traditionally has used frequencies for which the wavelengths are far smaller than the size of the objects being studied. This makes it possible to discriminate the shape of objects rather well, and leads to advanced applications such as underwater acoustic cameras. However, it is difficult to identify the material of an object using high-frequency signals. Thus researchers are turning their attention to low-frequency schemes (see Figure 1).

Figure 1: SONAR Frequency Response of a scuba tank (modeled as an empty cylindrical shell) computed with a model implemented in COMSOL Multiphysics. TS (target strength) is a logarithmic measure of the echo at a large distance from the target.

Researchers have found out that the low-frequency echoes also can contain information that describes other properties of a submerged object, such as the physics of its materials. This is because solids, unlike liquids, support not only longitudinal vibrations, but also transverse, or shear, vibrations, and thus can propagate sound in a number of modes. Particularly useful is the Lamb wave, a complex wave that travels through the entire thickness of a material layer. Propagation of these waves depends on the material's density as well as its elastic and material properties; they are also influenced by the selected frequency and material thickness.

A physical model of the waves' propagation would have to consider that there is more than one relevant wavelength: besides the sound wave that bounces off the structure, there are also the solidborne waves in the structure. It is also known that the longitudinal wave travels along the interface between the elastic solid and the water more quickly than the shear waves and the Lamb waves. In fact, the Lamb waves can be up to two orders of magnitude shorter than the wavelength of the sound in water. And yet, the Lamb wave effects in the bounced sound waves contain a great deal of information. For example, one can understand the physical properties of an elastic shell by examining the Lamb wave's resonance effects.

An advanced SONAR receiver must therefore deal with a complex signal made up of multiple waves that, taken together, determine the echo's resonant structure. Making matters more complex is the fact that there are no analytical models that describe such activity, so it is necessary to unscramble the signal by knowing the underlying physics. In short, one needs to know what to look for in such a signal. Only with a mathematical model can a researcher predict the form and structure of the low-frequency waveform emitting from a submerged object.

The NATO Undersea Research Centre team built such a model using COMSOL Multiphysics. This multiphysics model describes the frequencydomain elastic-displacement wave equation for a submerged object and couples it to an acoustic-wave equation that describes the waves in the fluid domain. Because the Lamb waves are so short, a finite-element model of the object must have many more degrees of freedom than one might expect. According to the researchers, the slow, or short, waves present a challenge in the modeling process, and getting a mesh and convergence is difficult.

Figure 2: Using the Azimuthal Fourier Modal Decomposition, it is possible to take a 3D model (left) and work with it as a 2D axisymmetric model (right).
Figure 3: The use of Berenger PML BoundaryConditions eliminates the need to model thesurrounding water, and simulates infiniteboundaries.

For their initial model, that of a cylinder with two end caps representing a scuba tank, the team treated the 3D geometry as an axisymmetric 2D problem (see Figures 2 and 3). They then solved a added these solutions together through an azimuthal Fourier series to reconstruct the 3D field. Although the target must be axisymmetric, the incident SONAR signal need not be so. The Sommerfeld radiation condition is approximated numerically by Bérenger PMLs (Perfectly Matched Layers), which the researchers easily implemented into the multiphysics software. The PML layers absorb outgoing waves, making it possible to simulate efficiently a target immersed in an infinite fluid domain using a finite-sized mesh (see Figure 3).

The scheme also employs COMSOL Script for solver scripting as well as for hands-on postprocessing with the Fourier decomposition of the Helmholtz- Kirchhoff far-field integral (see Figure 4). The modeling method significantly reduced problem size, and the team was able to model echoes from objects in the mid-frequency regime.

Figure 4: The Frequency Domain Response can be post-processed with the inverse Fourier transform to convert the result into a time-domain echo, whichis what would be measured physically at a receiver. The time-domain echo can in turn be transformed into a time-frequency spectrogram by applying a short time-window Fourier transform. The time-frequency spectrogram exhibits various “ringing” features, which are closely related to the material propertiesand the geometry of the scuba tank.

The team's studies don't fall into conventional areas, so there are no specialized tools for this type of project. With the multiphysics software, the team was able to tailor virtually everything to its particular needs. For instance, the team used weak-form modeling heavily for the azimuthal Fourier decomposition of the structural-acoustics equations.

This work was done by Dr. Mario Zampolli, Dr. Alessandra Tesei, Dr. Gaetano Canepa, and Dr. Finn Jensen of the NATO Undersea Research Centre, using software from COMSOL, Inc. For more information, visit

NASA Tech Briefs Magazine

This article first appeared in the September, 2006 issue of NASA Tech Briefs Magazine.

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