Frequency-domain wave equation and its time-domain solutions in attenuating media

Journal of the Acoustical Society of America

Volumn 115, Issue 4, 2004, Pages 1431-1436

  Sushilov, Nikolai V ^a   Cobbold, Richard S C ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ATTENUATION; FOURIER TRANSFORMS; FREQUENCY DOMAIN ANALYSIS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; TIME DOMAIN ANALYSIS; WAVE EQUATIONS;

ALGEBRAIC EQUATIONS; SZABO EQUATION;

ACOUSTIC WAVES;

ACOUSTICS;

ARTICLE; FOURIER TRANSFORMATION; FREQUENCY ANALYZER; FREQUENCY DOMAIN WAVE EQUATION; LINEAR SYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICS; PRIORITY JOURNAL; TIME; TIME DOMAIN SOLUTION;

ACOUSTICS; ANIMALS; FOURIER ANALYSIS; HUMANS; SPACE-TIME CLUSTERING; ULTRASONOGRAPHY; VISCOSITY;

EID: 1842530332     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.1675817     Document Type: Article

References (20)

1. F. A. Duck, Physical properties of tissue. A Comprehensive Reference Book (Academic, London, 1990), Chap. 4, pp. 108-110.
2. T. L. Szabo, "Causal theories and data for acoustic attenuation obeying a frequency power law," J. Acoust. Soc. Am. 97, 14-24 (1995).
3. G. G. Stokes, "On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids," Trans. Cambridge Philos. Soc. 8, 287-319 (1845).
4. A. J. Nachman, J. F. Smith III, and R. C. Waag, "An equation for acoustic propagation in inhomogeneous media with relaxation losses," J. Acoust. Soc. Am. 88, 1584-1595 (1990).
5. A. P. Berkhoff, J. M. Thijssen, and R. J. F. Homan, "Simulation of ultrasonic imaging with linear arrays in causal absorptive media," Ultrasound Med. Biol. 22, 245-259 (1996).
6. T. L. Szabo, "Time domain wave equation for lossy media obeying a frequency power law," J. Acoust. Soc. Am. 96, 491-500 (1994).
7. K. R. Waters, M. S. Hughes, G. H. Brandenburger, and J. G. Miller, "On a time-domain representation of the Kramers-Kronig dispersion relations," J. Acoust. Soc. Am. 108, 2114-2119 (2000).
8. G. V. Norton and J. C. Novarini, "Including dispersion and attenuation directly in the time domain for wave propagation in isotropic media," J. Acoust. Soc. Am. 113, 3024-3031 (2003).
9. W. Chen and S. Holm, "Modified Szabo's wave equation models for lossy media obeying frequency power law," J. Acoust. Soc. Am. 114, 2570-2574 (2003).
10. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications (Gordon and Breach, New York, 1987).
11. W. Chen and S. Holm, "Fractional Laplacian, time-space models for linear and nonlinear media exhibiting arbitrary frequency power law dependency," J. Acoust. Soc. Am. 115, 1424-1430 (2004).
12. A. Ben-Menahem and S. J. Singh, Seismic Waves and Sources (Springer-Verlag, New York, 1981), pp. 893-897.
13. T. L. Szabo, "Causal theories and data for acoustic attenuation obeying a frequency power law," J. Acoust. Soc. Am. 97, 14-24 (1995).
14. K. R. Waters, M. S. Hughes, J. Mobley, G. H. Brandenburger, and J. G. Miller, "On the applicability of Kramers-Kronig relations for ultrasonic attenuation obeying a frequency power law," J. Acoust. Soc. Am. 108, 556-563 (2000).
15. W. I. Futterman, "Dispersive body waves," J. Geophys. Res. 67, 5279-5291 (1962).
16. K. R. Waters, M. S. Hughes, J. Mobley, and J. G. Miller, "Differential forms of the Kramers-Kronig relations," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 68-76 (2003).
17. N. V. Sushilov and R. S. C. Cobbold, "Wave propagation in media whose attenuation is proportional to frequency," Wave Motion 38, 207-219 (2003).
18. R. Donnelly and R. Zilokowski, "A method for constructing solutions of homogeneous partial differential equations: localized waves," Proc. R. Soc. London, Ser. A 437, 673-692 (1992).
19. I. S. Gradstein and I. M. Ryzhik, Tables of Integrals, Series and Products, 4th ed. (Academic, New York, 1965).
20. L. J. Ziomek, Fundamentals of Acoustic Field Theory and Space-Time Signal Processing (CRC Press, Boca Raton, 1995).