When an explosive point source is buried less than one wavelength from the free surface in a perfectly elastic, homogeneous, isotropic half-space, a very strong non-geometric arrival, tentatively denoted as S* by Hron and Mikhailenko (1981), exists in the reflected shear wave field. It has all basic characteristics of an ordinary shear body wave (linear polarization, transverse particle motion, and shear wave velocity) and, as such, it can be also reflected or transmitted upon incidence at an interface according to the rules governing ordinary body waves. Because of its very strong amplitude which at most epicentral distances exceeds even the amplitude of a direct P wave, the S* arrival is undoubtedly responsible for a large part of the shear wave energy content seen in the seismic records in oil exploration, which deals almost exclusively with shallow explosive sources. In our paper, we develop a high-frequency approximation to the S* arrival applying a saddle-point method to the integral representing a shear wave reflected from the free surface due to the incidence of a spherical longitudinal wave radiated by the shallow point source. Numerical results presented in the paper show that our high-frequency approximation preserves all basic features of the S* arrival, thereby making it suitable for easy incorporation into any synthetic seismogram computation based on the ray approach.

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