Uniform asymptotic representation of a field of reflected and head waves
1969 ◽
Vol 313
(1515)
◽
pp. 477-490
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Keyword(s):
A uniform asymptotic expansion for integrals of the type ʃ +∞ -∞ u ½ F ( u ) exp {i kψ ( u )}d u has been obtained in terms of generalized Airy functions, which are the solutions of the equation V"( z )+ z 2 V ( z ) = 0. This result is applied to the construction of a uniform asymptotic representation of a solution of the wave equation in the case of reflexion of a spherical wave from a plane boundary in a region including a critical ray. This asymptotic series may be divided into two series corresponding to reflected and head waves respectively, which are transformed into the ray series for these waves far from the critical ray and reduced to the expressions given by Brekhovskikh (1960) in the vicinity of the critical ray.
1971 ◽
Vol 69
(3)
◽
pp. 227-245
1986 ◽
Vol 102
(3-4)
◽
pp. 253-257
◽
1979 ◽
Vol 16
(7)
◽
pp. 1388-1401
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Keyword(s):
2003 ◽
Vol 01
(02)
◽
pp. 213-241
◽
2012 ◽
Vol 44
(2)
◽
pp. 391-407
◽
1980 ◽
Vol 85
(3-4)
◽
pp. 299-305
◽
1990 ◽
Vol 430
(1880)
◽
pp. 653-668
◽