Page 31 - \Winter 2015

The Physics Underlying an
Acoustic Scattering Signature
Consider an arbitrary object in free space that is insonified by a monochromatic (single frequency) sound wave (Figure 2). Real objects are made of solid materials (metals, plastics, bones, flesh, etc.) which change shape or volume “elastically” when any stress is applied (albeit by microscopic amounts when small acoustic pressures are applied). The incident sound wave is an oscillatory pressure disturbance in the wa- ter. As it strikes the object, the oscillating pressure on the sur- face of the object induces elastic (solid) waves to propagate throughout all parts of the structure. The vibrating object will, in turn, exert an oscillating pressure on the surround- ing water, which produces pressure waves in the water that propagate away from the object, so-called scattered waves (also called echoes). The scattered waves will propagate out in all directions, with different intensity in different direc- tions. As the incident sound wave changes direction relative to the object (the angle θ in Figure 2) or changes frequency, the vibrations in the object will change, which, in turn, will change the scattered waves.
Figure 2. An object submerged in a fluid is insonified by a plane wave (red arrow), causing the object to vibrate (interior elastic waves, represented by blue arrows), which re-radiates scattered waves (black arrows) back into the fluid in all directions.
When an object (also called “target”) is insonified by a plane
wave (wave fronts are planar, rather than curved, as occurs
when the sound source is far from the object), the intensity
Figure 3. (a) Insonifying a steel cylindrical closed shell. (b) The result- ing acoustic scattering signature template.
where f is frequency, θ is the aspect angle of the incident
sound wave (defined for each different problem, but is usu-
ally the azimuthal angle, which is a horizontal angle about
the vertical to the ocean bottom), p(r) is the pressure of the
scattered wave, | | indicates magnitude (since p is a complex-
valued function), r is a position vector from the object to the
“observer” (where the TS is being measured), r is its mag-
nitude, and ro and po are a reference distance and pressure
that normalize and make dimensionless the argument of the
logarithm. In 3-dimensional space, p(r) α 1/r far away from
the object, in the so-called far field; hence the numerator, r|
le Equations
An acoustic scattering signature is the target strength of an object, Equation (1), that has been insonified over a broad band of frequencies and, for each frequency, over a broad range of aspect angles. The resulting values of TS are plot- ted as a template (terminology from radar) of TS vs. f and θ, with TS displayed as a color. This is illustrated below for a steel cylindrical closed shell, with a color bar on the right to quantify the TS values (Figure 3).
One can see that there is a great deal of information about the object in such a template. For example, the geometry of object and incident sound wave in part (a) of Figure 3 is clearly symmetric about the incident directions that are par- allel to the axis of the cylinder (endfire, θ = 0o) and perpen- dicular to the axis (broadside, θ = 90o), and this is manifest-
ed in corresponding symmetries in the template in part (b).
of the scattered pressure wave back in the same direction that the sound wave came from is expressed by the monos- tatic (source and observer in same direction) far-field target strength, TS:
(1)
(1)
p(r)|, converges to a limiting value as r →∞. The symbol Lim r→∞
means evaluate the scattered pressure far enough away to obtain the limiting value. The units of TS are decibels (dB).
⎛ r p(r) ⎞ TS(f,θ)=Lim20Log10⎜⎜ rp ⎟⎟
r→∞ ⎝00⎠
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