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May 1988

Volume 83, Issue S1, pp. S1-S122

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back to top Session CC. Underwater Acoustics IV: Object Scattering
Contributed Papers
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Pulse scattering from an object submerged in the ocean (A)

Michael D. Collins and Michael F. Werby

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S59-S59 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The low grazing angle asymptotic limit, which is used to derive the parabolic equation, is used to derive an efficient computational method for propagation and scattering of acoustic pulses in the ocean. In order to avoid the time‐consuming frequency decomposition, all calculations involving the acoustic field are done in the time domain. The time domain equivalent of the parabolic equation [B. E. McDonald and W. A. Kuperman, J. Acoust. Soc. Am. 81, 1406–1417 (1987)] is used for propagation of the incident field up to the scatterer and for propagation of the scattered field away from the scatterer. Waterman's extended boundary condition, which is a frequency domain method, is used to construct a time domain integral operator that transforms incident waveforms into scattered waveforms and depends only on the geometry and composition of the scatterer. Like the parabolic equation method, this method offers an attractive combination of accuracy and efficiency. [Work supported by ONR and NORDA.]
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Principal curvatures of general wavefronts and of reflecting or refracting surfaces (A)

Cleon E. Dean, W. Patrick Arnott, and P. L. Marston

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S59-S59 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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A nonparametric derivation of the exact form of the two principal curvatures κ1,2 of general wavefronts and reflecting or refracting surfaces was made for Cartesian and polar coordinates. The standard expression for the Gaussian curvature κ1κ2 was recovered in the Cartesian case. For the polar case let
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,
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, and C  =  1 +Wr2 + (1/r2) Wθ2, where z = W(r,θ) is the polar equation of the surface and Wr = ∂W/∂r, Wrr = ∂2W/∂r2, and so forth; the analysis gives κ1,2  =  [B ± (B2 − 4HC)1/2]/(2C3/2). The Gaussian curvature is κ1κ2 = H/C2; κ1 and κ2reduce to previous results [D. G. Burkhard and D. L. Shealy, Appl. Opt. 20, 897–909 (1981)] in the special case z = W(r). These results should be useful for generalized ray tracing and for locating caustics in catastrophe acoustics and scattering calculations. [Work supported by ONR.]
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Harmonic angular perturbation of a toroidal wavefront: A simple unfolding of an axial caustic (A)

W. Patrick Arnott and Philip L. Marston

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S59-S59 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Axial caustics can be observed in backward and forward scattering from highly symmetric surfaces such as spheres. A wavefront that is locally toroidal, propagates to produce an axial caustic. The unfolding of the axial caustic generated by a harmonic perturbation of the wavefront shape in the aximuthal direction will be considered. The perturbed wavefront shape W is given by W(s,ψ)  =  [(s − b)2/2α] + Λ cos (2α), in polar coordinates (s,α), where α and β specify the characteristic radii of the unperturbed torus and Λ is a measure of the perturbation. The caustic associated with W consists of four connected transverse cusps in a distorted diamond shape known as an asteroid. The caustic shape has been identified for observation points from the near zone to the far zone. Locations on W that contribute rays near a cusp point, have been identified analytically. Observations of the asteroid caustic have been made by scattering light from freely rising oblate gas bubbles in water. The bubbles are oblate since they are larger than those considered in our previous study of backscattering [W. P. Arnott and P. L. Marston, 1. Opt. Soc. Am. A (in press)]. The far zone scattering exhibits an asteroid caustic decorated by a diffraction pattern. The calculated caustic agrees favorably with observations. This calculation should also be useful in acoustic reflection and scattering problems. [Work supported by ONR.]
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Comparison of asymptotic and exact results for scattering from rigid spheroids (A)

Michael F. Werby and Michael D. Collins

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S59-S59 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Results generated with the Kirchhoff approximation, which is effective for backscattering, and the diffraction integral method, which is effective for forward scattering, will be compared with the exact solution obtained with Waterman's extended boundary condition method. Calculations will be presented for kL/2 ranging from 5 to 300 and for aspect ratios ranging from 1 to 15. An additional asymptotic approximation, the method of stationary phase, is used for higher frequencies. For higher aspect ratio targets, one would expect the accuracy of high‐frequency methods to be difficult to predict and to depend not only on kL/2 but also on bistatic configurations due to the large variation of Gaussian curvature on these targets. Hence, the focus of the presentation will be to illustrate how accuracy depends upon kL/2, angle of incidence, and angle of observation for high aspect ratio targets. [Work supported by ONR and NORDA.]
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The effect of an object in a waveguide on the field produced by a point source (A)

Guy V. Norton and M. F. Werby

J. Acoust. Soc. Am. Volume 83, Issue S1, pp. S60-S60 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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When the acoustic wave produced by a point source in a shallow water waveguide ensonifies an object, the object acts as a secondary source and in turn generates a guided wave. The effect that the object has on the initial incident field is estimated. In particular, comparisons are made with transmission loss versus range for the point source by itself and with transmission loss versus range for the object as ensonified by the point source. To obtain the scattered field from the object, the scattered field is first generated in the vicinity of the object using a transition matrix that relates the incident field to the scattered field in a waveguide. The transition matrix is obtained from the extended boundary condition (EBC) method. This solution is coupled with the waveguide solution [G. V. Norton and M. F. Werby, “Some Numerical Approaches to Describe Acoustical Scattering from Objects in a Waveguide,” in Proc. Sixth Int. Conf. Math. Modeling, St. Louis, MO, 4‐7 Aug. 1987]. This method satisfies all appropriate boundary conditions and yields a continuous solution throughout the waveguide. The object used is a rigid spheroid of aspect ratio 5:1. The frequencies are 100 and 450 Hz. The source, receiver, and object depths are different combinations of 50, 75, and 200 m, and two waveguide water depths at 150 and 400 m are considered. The nature of the effect on the initial incident field due to the object and as influenced by the relative placement of the source and receiver relative to it is demonstrated. [Work supported by NORDA.]
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