Abstract
In the paper a new method of computing wave fields in the high-frequency approximation is proposed. The method is based on the summation of Gaussian pencils at the point of observation; each pencil is connected with a ray passing in some neighborhood of this point. The idea of describing the high-frequency asymptotics of the wave field as an integral over Gaussian pencils was first proposed in the work of V. M. Babich and T. F. Pankratova of 1973 and was used in mathematical investigations of discontinuities of the Green function of a mixed problem for the wave equation.
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Literature cited
V. M. Babich, “The ray method of computing the intensity of wave fronts,” Dokl. Akad. Nauk SSSR,110, No. 3, 355–357 (1956).
V.M. Babich and A. S. Alekseev, “On the ray method of computing the intensity of wave fronts,” Izv. Akad. Nauk SSSR, Ser. Geofiz., No. 1, 17–31 (1958).
V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Problems of the Diffraction of Short Waves [in Russian], Moscow (1972).
V. Červeny, I. A. Molotkov, and I. Pšenčik, The Ray Method in Seismology, Praha, Univerzita Karlova (1977).
V. P. Maslov, Perturbation Theory and Asymptotics Methods [in Russian], Moscow (1965).
V. M. Babich and T. F. Pankratova, “On discontinuities of the Green function of the mixed problem for the wave equation with a variable coefficient,” in: Probl. Mat. Fiz., Leningrad (1973), pp. 9–27.
T. F. Pankratova, “On the proper oscillations in an annular resonator,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,15, 122–141 (1969).
N. Ya. Kirpichnikova, “On the construction of solutions of the equations of the theory of elasticity which are concentrated near rays for an inhomogeneous, isotropic space,” Tr. Mosk. Inst. Akad. Nauk,115, 103–133 (1971).
M. M. Popov, “On a method of computing the geometric divergence in an inhomogeneous medium containing a boundary of separation,” Dokl. Akad. Nauk SSSR,237, No. 5, 1059–1062 (1977).
M. M. Popov and I. Psencik, “Ray amplitudes in inhomogeneous media with curved interfaces,” Geofysikalni Sb. XXIV (1976), Praha (1978), pp. 111–129.
M. M. Popov, I. Pšenčik, and V. Červeny, “Uniform ray asymptotics for seismic wave fields in laterally inhomogeneous media,” EGS Meeting, Budapest (1980).
M. M. Popov and I. Psencik, “Computation of ray amplitudes in inhomogeneous media with curved interfaces,” Stud. Geoph. Geod.,22, 248–258 (1978).
M. V. Fedoryuk, The Method of Descent [in Russian], Moscow (1977).
M. M. Popov and L. G. Tyurikov, “On two approaches to the computation of the geometric divergence in an inhomogeneous, isotropic medium,” in: Vopr. Dinam. Teor. Raspr. Seism. Voln, Vol. 20 (1980), pp. 61–68.
V. I. Smirnov, A Course of Higher Mathematics, Vol. 3, Part 1, Pergamon (1964).
V. M. Babich and N. Ya. Kirpichnikova, The Method of the Boundary Layer in Diffraction Problems [in Russian], Leningrad (1974).
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Translated from Zapiski Nauchnykh Seminarov Leningr ads kogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 104, pp. 195–216, 1981.
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Popov, M.M. A new method of computing wave fields in the high-frequency approximation. J Math Sci 20, 1869–1882 (1982). https://doi.org/10.1007/BF01119372
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DOI: https://doi.org/10.1007/BF01119372