Modeling space-time domain acoustic wave fields in media with attenuation: The symbolic manipulation approach

Journal of the Acoustical Society of America

Volumn 97, Issue 2, 1995, Pages 831-843

  Verweij, Martin D ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

GREEN'S FUNCTION; LOSSY EQUIVALENT FLUIDS; SOUND ATTENUATION; SOUND WAVES;

ACOUSTICS; ARTICLE; PRIORITY JOURNAL; SOUND TRANSMISSION; SPACE; TIME; WAVEFORM;

EID: 0028976380     PISSN: 00014966     EISSN: NA     Source Type: Journal    
DOI: 10.1121/1.412128     Document Type: Article

References (29)

1. H. Kolsky, Stress Waves in Solids (Clarendon, Oxford, 1953).
2. M. N. Toksoz and D. H. Johnston, “Attenuation mechanisms, “ in Seismic Wave Attenuation, edited by M. N. Toksoz and D. H. Johnston (Society of Exploration Geophysicists, Tulsa, 1981).
3. J. E. White, Underground Sound (Elsevier Science, New York, 1983).
4. A. Ben-Menahem and S. J. Singh, Seismic Waves and Sources (Springer-Verlag, New York, 1981).
5. D. H. Johnston and. Toksoz, “Definitions and terminology, “ in Seismic Wave Attenuation, edited by M. N. Toksoz and D. H. Johnston (Society of Exploration Geophysicists, Tulsa, 1981).
6. K. Aki and P. G. Richards, Quantitative Seismology: Theory and Methods (Freeman, San Francisco, 1980), Vol. I.
7. E. L. Hamilton, “Compressional-wave attenuation in marine sediments, “ Geophysics 37, 620-646 (1972).
8. W. I. Futterman, “Dispersive body waves, “ J. Geophys. Res. 67, 5257-5291 (1962).
9. R. S. Jacobson, “An investigation into the fundamental relationships between attenuation, phase dispersion, and frequency using seismic refraction profiles over sedimentary structures, “ Geophysics 52, 72-87 (1987).
10. D. R. Bland, The Theory of Linear Viscoelasticity (Pergamon, Oxford, 1960).
11. E. Strick, “Applications of linear viscoelasticity to seismic wave propagation, “ in Wave Propagation in viscoelastic Media, edited by F. Mainardi (Pitman, London, 1982).
12. L. Boltzmann, “Zur Theorie der elastischen Nachwirkung, “ Sitzber. Kaiserl. Akad. Wiss. Wien, Math.-Naturw. Kl. 70, Sect. II, 275-306 (1874).
13. L. Boltzmann, “Zur Theorie der elastischen Nachwirkung, “ Ann. Phys. Chem. (Poggendorf), Erganzungsband 7, 624-654 (1876).
14. D. Graffi, “Mathematical models and waves in linear viscoelasticity, “ in Wave Propagation in Viscoelastic Media, edited by F. Mainardi (Pitman, London, 1982).
15. C. C. Chao and J. D. Achenbach, “A simple viscoelastic analogy for stress waves, “ in Stress Waves in Anelastic Solids, edited by H. Kolsky and W. Prager (Springer-Verlag, Berlin, 1964).
16. A. T. de Hoop, “Similarity in wave propagation under a global relaxation law, “ in Second International Conference on Mathematical and Numerical Aspects of Wave Propagation, edited by R. Kleinman, T. Angell, D. Col-ton, F. Santosa, and I. Stackgold (Society for Industrial and Applied Mathematics, Philadelphia, 1993).
17. A. T. de Hoop, “Acoustic radiation from an impulsive point source in a continuously layered fluid-An analysis based on the Cagniard method, “ J. Acoust. Soc. Am. 88, 2376-2388 (1990).
18. M. D. Verweij and A. T. de Hoop, “Determination of seismic wavefields in arbitrarily continuously layered media using the modified Cagniard method, “ Geophys. J. Int. 108, 731-754 (1990).
19. M. D. Verweij, Transient Acoustic Waves in Continuously Layered Media (Delft U.P., Delft, The Netherlands, 1992).
20. Mathematica is a registered trademark of Wolfram Research Inc.
21. J. R. Carson, Electric Circuit Theory and the Operational Calculus (McGraw-Hill, New York, 1926).
22. D. V. Widder, The Laplace Transform (Princeton U.P., Princeton, 1946).
23. L. Cagniard, Reflection et Refraction des Ondes Seismiques Progressives (Gauthier-Villars, Paris, 1939) [in French; translated and revised version: E. A. Flinn and C. H. Dix, Reflection and Refraction of Progressive Seismic Waves (McGraw-Hill, New York, 1962)].
24. S. Wolfram, Mathematica-A System for Doing Mathematics by Computer (Addison-Wesley, New York, 1991).
25. A. T. de Hoop, “A modification of Cagniard's method for solving seismic pulse problems, “ Appl. Sci. Res. B8, 349-356 (1960).
26. de Hoop, “Theoretical determination of the surface motion of a uniform elastic halfspace produced by a dilatational, impulsive, point source, “ in Proceedings Colloque International du C.N.R.S. (Marseille, 1961), No. 111, pp. 21-31.
27. M. D. Verweij, “Transient acoustic wave modeling: Higher-order Wentzel-Kramers-Brillouin-Jeffreys asymptotics and symbolic manipulation, “ J. Acoust. Soc. Am. 92, 2223-2238 (1992).
28. J. van der Hijden, Propagation of Transient Elastic Waves in Stratified Anisotropic Media (North-Holland, Amsterdam, 1987).
29. E. Strick, “A predicted pedestal effect for pulse propagation in constant-Q solids, “ Geophysics 35, 386-403 (1970).