Abstract
A new method of calculation of theoretical seismograms is proposed, which is based on space-time Gaussian beams. The method permits one to overcome the difficulties of calculation of the wave field near caustics and does not contain any calculations of Fourier transforms. Numerical experiments confirm the efficiency of the method for the calculation of theoretical seismograms.
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Literature cited
V. M. Babich and T. F. Pankratova, “On discontinuities of the Green's function of the mixed problem for the wave equation,” in: Problems of Mathematical Physics [in Russian], Vol. VI (1973), pp. 9–27.
M. M. Popov, “A new method for the calculation of wave fields in the high-frequency approximation,” in: Mathematical Questions in Wave Propagation Theory, 11, J. Sov. Math.,20, No. 1 (1982).
A. P. Kachalov and M. M. Popov, “Application of the method of summation of Gaussian beams to the calculation of high-frequency wave fields,” Dokl. Akad. Nauk SSSR,258, No. 5, 1097–1100 (1981).
V. E. Grikurov and M. M. Popov, “Summation of Gaussian beams in a surface waveguide,” Wave Motion,5, 225–233 (1983).
A. P. Katchalov and M. M. Popov, “Application of the Gaussian beam method to elasticity theory,” Geophus. J. R. Astron. Soc.,81, 205–214 (1985).
R. Madariaga, “Gaussian beam synthetic seismograms in a vertically varying medium,” Geophys. J. R. Astron. Soc.,79, 589–612 (1984).
C. Cerveny, “Gaussian beam synthetic seismograms,” J. Geophys.,58, 44–72 (1985).
M. M. Popov, “Summation of space-time Gaussian beams in nonstationary problems,” Preprint of the Leningrad Branch of the Mathematical Institute of the Academy of Sciences of the USSR, P-6-85, Leningrad (1986).
V. M. Babich and V. V. Ulin, “The complex space-time ray method and ‘quasiphotons,’” in: Mathematical Questions of Wave Propagation Theory, 12, J. Sov. Math.,24, No. 3 (1984).
A. P. Kachalov, “Application of ‘quasiphotons’ to the problem of wave fields in an elastic medium,” in: Mathematical Questions of Wave Propagation Theory, 15, J. Sov. Math.,38, No. 1 (1987).
A. S. Alekseev, V. M. Babich, and B. Ya. Gel'chinskii, “The ray method of calculation of the intensity of wave fronts,” in: Questions of the Dynamical Theory of the Propagation of Seismic Waves [in Russian], Leningrad State Univ. (1961), pp. 3–24.
Yu. L. Gazaryan, “On the propagation of sound in inhomogeneous media,” in: Questions of the Dynamical Theory of Propagation of Seismic Waves [in Russian], Leningrad State Univ. (1961), pp. 90–114.
M. M. Popov, “The method of summation of Gaussian beams in the isotropic theory of elasticity,” Izv. Akad. Nauk SSSR, Fiz. Zemli, No. 9, 39–50 (1983).
V. M. Babich, “On the space-time ray method in the theory of elastic waves,” Izv. Akad. Nauk SSSR, Fiz. Zemli, No. 2, 3–13 (1979).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 73–97, 1986.
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Kachalov, A.P., Popov, M.M. Application of the method of summation of Gaussian beams to the calculation of theoretical seismograms. J Math Sci 50, 1727–1742 (1990). https://doi.org/10.1007/BF01097103
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DOI: https://doi.org/10.1007/BF01097103