Several important applications of the paraxial ray approximation (PRA) to numerical modelling of high-frequency seismic body wavefields are discussed. The PRA can be used to evaluate the displacement vector not only directly on the ray, as in the standard ray method, but also approximately in the vicinity of this ray. The PRA also offers simple ways of approximate evaluation of paraxial rays, situated in the vicinity of the central ray, and of two-point ray tracing. A very important application of the PRA consists in a simple, fast and effective computation of body-wave synthetic seismograms in general, 3-D, laterally inhomogeneous, layered structures. Examples of synthetic seismograms for 3-D structures, computed using the PRA, are presented.
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