Rayleigh scattering from nonspherical particles

Journal of the Acoustical Society of America

Volumn 99, Issue 4 I, 1996, Pages 1901-1912

  Palmer, D R ^a  

^a ATLANTIC OCEANOGRAPHIC AND METEOROLOGICAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; ANALYTICAL ERROR; ARTICLE; CLOUD; DENSITY; DISPERSION; ECHOLOCATION; ENTROPY; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; SEA; SOUND INTENSITY; THEORY;

EID: 0029994622     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.415373     Document Type: Article

References (31)

1. For a review, see D. R. Palmer, "Acoustical imaging of naturally occurring plumes," in Acoustical Imaging, Volume 21, edited by J. Jones (Plenum, New York, 1995).
2. P. A. Rona, D. R. Palmer, C. Jones, D. A. Chayes, M. Czarnecki, E. W. Carey, and J. C. Guerrero, "Acoustic images of hydrothermal plumes: East Pacific Rise, 21°N, 109°W," Geophys. Res. Lett. 18, 2233-2236 (1991).
3. P. A. Rona and D. R. Palmer, "Imaging plumes beneath the sea," J. Acoust. Soc Am. 93, 569-570 (1993).
4. RISE Project Group, "East Pacific Rise: Hot springs and geophysical experiments," Science 207, 1421-1433 (1980).
5. D. R. Palmer, P. A. Rona, and M. J. Mottl, "Acoustic imaging of high-temperature hydrothermal plumes at seafloor spreading centers," J. Acoust. Soc. Am. 80, 888-898 (1986).
6. J. A. Reagan and B. M. Herman, "Light scattering by irregularly shaped particles versus spheres: What are some of the problems presented in remote sensing of atmospheric aerosols?" in Light Scattering by Irregularly Shaped Particles, edited by D. W. Schuerman (Plenum, New York, 1980).
7. D. A. Darling and T. B. A. Senior, "Low-frequency expansions for scattering by separable and nonseparable bodies," J. Acoust. Soc. Am. 37, 228-234 (1965).
8. For an early contribution see T. B. A. Senior and D. J. Ahlgren, "Rayleigh scattering," IEEE Trans. Antennas and Propag. 21, 134 (1973).
9. M. H. Orr and F. R. Hess. "Remote acoustic monitoring of natural suspensate distributions, active suspensate resuspension, and slope/shelf water intrusion," J. Geophys. Res. 83, 4062-4068 (1978).
10. A. E. Hay, "On the remote acoustic detection of suspended sediment at long wavelengths," J. Geophys. Res. 88, 7525-7542 (1983).
11. J. Sheng and A. E. Hay, "An examination of the spherical scatterer approximation in aqueous suspensions of sand," J. Acoust. Soc. Am. 83, 598-610 (1988).
12. Multiple scattering effects can probably be incorporated into our formalism using the phenomenoiogical approach developed for studies of laser imaging of particulate plumes in the atmosphere. See, for example, W. L. Eberhard, G. T. McNice, and S. W. Traxel, "Lidar sensing of plume dispersion: Analysis methods and product quality for light-scattering tracer particles," J. Atmos. Oceanic Technol. 4, 674-689 (1987).
13. J. J. Faran, "Sound scattering by solid cylinders and spheres," J. Acoust. Soc. Am. 23, 405-418 (1951).
14. J. Van Bladel, "Low-frequency scattering by hard and soft bodies," J. Acoust. Soc. Am. 44, 1069-1073 (1968).
15. T. B. A. Senior, "Low-frequency scattering," J. Acoust. Soc. Am. 53, 742-747 (1973).
16. For electromagnetic scattering, the more general problem has been considered by A. F. Stevenson, "Solution of electromagnetic scattering problems as power series in the ratio (dimension of scatterer)/wavelength." J. Appl. Phys. 24, 1134-1142 (1953).
17. A reviewer has pointed out that much of the material in the first part of Sect. II and in Appendix A is, indeed, available; see, for example, R. E. Kleinman and T. B. A. Senior, in Low and High Frequency Asymptotics, edited by V. K. Varadan and V. V. Varadan (Elsevier Science, Amsterdam, 1986), Chap. 1. The justification for including this material reduces to the desirability of making the paper self-contained and of exposing the readership to the type of mathematics used, as well as the importance of establishing notation.
18. A. D. Pierce, Acoustics: An Introduction to Its Physical Principles and Applications (McGraw-Hill, New York, 1981).
19. For a somewhat related discussion, see L. Tsang, "Scattering of electromagnetic waves from a half space of nonspherical particles," Radio Sci. 19, 1450-1460 (1984).
20. See, for example, L. E. Payne, "Isoperimetric inequalities and their applications," SIAM Rev. 9, 453-488 (1967), and G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Ann. of Math. Studies, No. 27 (Princeton U.P., Princeton, 1951).
21. See, for example, L. E. Payne, "Isoperimetric inequalities and their applications," SIAM Rev. 9, 453-488 (1967), and G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Ann. of Math. Studies, No. 27 (Princeton U.P., Princeton, 1951).
22. J. B. Keller, R. E. Kleinman, and T. B. A. Senior, "Dipole moments in Rayleigh scattering," J. Inst. Math. Appl. 9, 14-22 (1972).
23. R. E. Kleinman and T. B. A. Senior, "Rayleigh scattering cross sections," Radio Sci. 7, 937-942 (1972).
24. See, for example, The Maximum Entropy Formalism, edited by R. D. Levine and M. Tribus (MIT, Cambridge, MA, 1979).
25. M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957); A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, NJ, 1960).
26. M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957); A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton U.P., Princeton, NJ, 1960).
27. There are situations where this assumption is not valid. For example, the age of the particle cloud may be such that the heavier particles have had an opportunity to settle to a greater extent than the lighter ones.
28. P. M. Morse and K. V. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968).
29. C. S. Clay and H. Medwin, Acoustical Oceanography: Principles and Applications (Wiley, New York, 1977).
30. δ>1 can be developed.
31. This result does not have any bearing on the utility of multifrequency acoustic systems for estimating size distributions and concentrations. In the Rayleigh region, where the frequency dependence of the backscattered intensity consists solely of a multiplicative factor of the frequency to the fourth power, the most that a multifrequency system can provide beyond a single-frequency one is confirmation that scattering is indeed in the Rayleigh region, a check of the calibration and a reduction in ambient noise with appropriate processing.