The decomposition of the wave field into optimized Gaussian packets represents a crucial step of the Gaussian packet prestack depth migration algorithm. The shape of optimized Gaussian packets, in the plane perpendicular to the central ray of the packet, depends not only on the frequency, but also on the coordinate of the intersection of the central ray of a Gaussian packet with the profile, on its arrival time, and on the component of the slowness vector along the profile. We express the amplitude of a Gaussian packet in the form of an integral transform similar to the forward coherent-state transform. Our method is suitable for a smooth distribution of the parameter determining the shape of a packet in the plane perpendicular to its central ray.
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