High-frequency asymptotic description of head waves and boundary layers surrounding the critical rays in an elastic half-space

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Abstract
The high-frequency asymptotic description of head waves as well as the field inside boundary layers surrounding the critical rays are obtained for two cases: (a) a point source, and (b) a circular transducer, both acting normally on an isotropic and homogeneous elastic half-space. The edge head waves underneath a circular transducer are described by the asymptotics of a higher order compared to those of direct compressional, edge compressional, and shear waves, but are still discernible in the radiating near zone and thus might be useful in nondestructive evaluation of industrial materials. The asymptotic formulas produced involve in geometrical zones elementary functions and inside boundary layers well-known special functions. Therefore, they allow us to elucidate the physics of the problem and can be used in writing computer codes which simulate the radiating near field of a circular transducer orders of magnitude faster than full numerical schemes. The formulas have been tested against exact integral solutions evaluated numerically.

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