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A combination of Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) asymptotics and the Cagniard-DeHoop method is used to determine the space-time domain acoustic wave field in a continuously horizontally layered configuration. First, a Laplace transformation with real and positive transform parameter is applied with respect to the time coordinate, followed by a two-dimensional Fourier transformation with respect to the horizontal coordinates. Using the integral equations of the resulting transform domain problem, a recurrence scheme is derived for the coefficients of the WKBJ asymptotic expansions of the transform domain solutions. This scheme is well-suited for implementation in a symbolical manipulation program. The space-time domain is performed with the aid of the Cagniard-DeHoop method, which is particularly efficient in this case. If both the source and the receiver are located in one homogeneous half-space of the configuration, the Cagniard-DeHoop method allows for an almost completely analytical transformation back to the space-time domain. For various configurations numerical results are presented, which show that the method is valid for instants ranging up to several times the arrival time.
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