A method of computing synthetic seismograms by means of the three-parametric summation of Gaussian packets over space is proposed. The expansion of the wavefield specified in terms of a complex-valued amplitude and a phase function into Gaussian packets is very similar to the expansion into Gaussian beams, with the additional summation over points along the rays. The initial conditions for the wavefield, for which the initial directions of the rays are time-independent (e.g. the point source), are assumed. The summation is performed in the frequency domain. The synthetic seismograms are then evaluated by the fast Fourier transform for any source time function. The method should not require a substantial increase of the computational time with respect to the ray and Gaussian beam methods.
Seismic waves, summation of Gaussian packets, space-time Gaussian beams, high-frequency asymptotics, paraxial approximation.
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