The radiating near field of a circular normal transducer of arbitrary apodization on an elastic half-space

Abstract

A new fast method is developed for simulating the propagation of pulses radiated by a circular normal transducer of arbitrary apodization into an isotropic and homogeneous elastic half-space. First, the model proposed in Fradkin, Kiselev and Krylova for a time-harmonic uniform transducer [J. Acoust. Soc. Am. 104, 1178–1187 (1998)] is extended to the case of nonuniform load to obtain high-frequency asymptotics of the time-harmonic field. Then, the transient field is described by means of harmonic synthesis. The asymptotics elucidate the physics of the problem and give explicit dependence of the radiated waves on model parameters. The formulas are applicable in the radiating near field, that is the near field with the evanescent wave zone excluded. They involve in geometrical regions elementary and inside boundary layers, well-known special functions (Fresnel integral and Bessel functions). Unlike the uniform load case, the direct shear wave is present and the edge waves may be practically eliminated. The asymptotic code has been tested against an exact numerical solution when apodization is parabolic. It has proved to be hundreds of times faster but in many realistic cases the accuracy does not suffer much.