The Wavefield Radiated Into an Elastic Half-Space by a Transducer of Large Aperture

The wavefield radiated into an elastic half-space by an ultrasonic transducer, as well as the radiation admittance of the transducer coupled to the half-space, are studied. Two models for the transducer are used. In one an axisymmetric, Gaussian distribution of normal traction is imposed upon the surface, while in the other a uniform distribution of normal traction is imposed upon a circular region of the surface, leaving the remainder free of traction. To calculate the wavefield, each wave emitted by the transducer is expressed as a plane wave multiplied by an asymptotic power series in inverse powers of the aperture’s (scaled) radius. This reduces the wave equations satisfied by the compressional and shear potentials to their parabolic approximations. The approximations to the radiated waves are accurate at a depth where the wavefield remains well collimated.