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From Cagniard’s method for solving seismic pulse problems to the method of the differential transform. (English) Zbl 0483.73087


MSC:

74L05 Geophysical solid mechanics
74J99 Waves in solid mechanics
44A15 Special integral transforms (Legendre, Hilbert, etc.)
44A10 Laplace transform
74J10 Bulk waves in solid mechanics
86A15 Seismology (including tsunami modeling), earthquakes

Citations:

Zbl 0402.44001
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Full Text: DOI

References:

[1] Garvin, W. W., Exact transient solution of the buried line source problem, (Proc. Roy. Soc., London Ser. A., 203 (1956)), 528-541 · Zbl 0071.40101
[2] De Hoop, A. T., The surface line source problem in elastodynamics, Nederlands Elektronicaen Radiogenootschap, 35, 1-28 (1970)
[3] Alterman, Z. S.; Loeventhal, D., Algebraic expressions for the impulsive motion of an elastic half space, Israel J. Technol., 7, 495-504 (1969)
[4] Cagniard, L., Reflection and Refraction of Progressive Seismic Waves (1962), McGraw-Hill: McGraw-Hill New York, (Translated and revised by E. A. Flinn and C. H. Dix) · Zbl 0116.24001
[5] Dix, C. H., The method of Cagniard in seismic pulse problems, Geophys., 19, 722-738 (1954)
[6] De Hoop, A. T., A modification of Cagniard’s method for solving seismic pulse problems, Appl. Sci. Res. B, 8, 349-356 (1960) · Zbl 0100.44208
[7] Gakenheimer, D. C.; Miklowitz, J., Transient excitation of an elastic half-space by a point load travelling on the surface, J. Appl. Mech., 36, 505-515 (1969) · Zbl 0194.27702
[8] Ungar, A., A new operational calculus method, Int. J. Engng Sci., 18, 43-59 (1980) · Zbl 0441.73025
[9] A. Ungar, The differential transform: An integral-free integral transform. To be published.; A. Ungar, The differential transform: An integral-free integral transform. To be published. · Zbl 0249.44004
[10] Ewing, W. M.; Jardetsky, W. S.; Press, Frank, Elastic Waves in Layered Media (1957), McGraw-Hill: McGraw-Hill New York · Zbl 0083.23705
[11] Chapman, C. H., Lamb’s problem and comments on the paper “On leaking modes” by Usha Gupta, Pure Appl. Geophys., 94, 233-247 (1972)
[12] Robinson, N. I.; Ungar, A., Concentrated load on an elastically supported strip, ZAMM, 54, 441-442 (1974)
[13] Ungar, A., Wave generation in an elastic half space by a normal point load moving uniformly over the free surface, Int. J. Engng Sci., 14, 935-943 (1976) · Zbl 0337.73018
[14] Ungar, A.; Robinson, N. I., The application of the differential transform technique to point source problems of elasticity, Int. J. Engng Sci., 15, 157-170 (1977) · Zbl 0356.73020
[15] Ungar, A., An electromagnetic progresing wave representation for the field of a uniformly moving point charge, SIAM J. Appl. Math., 28, 411-418 (1975) · Zbl 0294.35064
[16] Ungar, A., The propagation of elastic waves from moving normal point loads in layered media, Pure Appl. Geophys., 114, 845-861 (1976)
[17] Ungar, A., The differential transform technique for solving problems of wave propagation, (Miklowitz, J.; Achenbach, J. D., Modern Problems in Elastic Wave Propagation (1978), John Wiley: John Wiley New York), 83-102
[18] Ungar, A., The use of a new operational method in solid mechanics, Solid Mechanics Archives, 4, 1-29 (1979) · Zbl 0422.73031
[19] A. Ungar, A note on Ranger’s line rotelet near a plabe. Int. J. Comp. Math. Applics.; A. Ungar, A note on Ranger’s line rotelet near a plabe. Int. J. Comp. Math. Applics. · Zbl 0484.44009
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