A fast method for simulating the propagation of pulses radiated by a rectangular normal transducer into an elastic half-space

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Abstract
A new fast method for simulating the propagation of pulses radiated by a rectangular normal ultrasonic transducer which is directly coupled to an isotropic and homogeneous elastic half-space is proposed. First, the so-called two-tier approach introduced in Fradkin et al. [“The radiating near-field asymptotics of a time-harmonic circular normal ultrasonic transducer in an elastic half-space,” J. Acoust. Soc. Am. 104, 1178–1187 (1998)] and the uniform stationary phase method are used to obtain both nonuniform and uniform high-frequency asymptotics of the time-harmonic field. Then, the transient field is described by means of harmonic synthesis. The nonuniform asymptotics elucidate the physics and all the asymptotics 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. The asymptotics involve in geometrical regions elementary and inside boundary layers, well-known special functions (Fresnel integral and generalized Fresnel integral). The code based on the uniform asymptotics has been tested in all regions against an exact numerical solution. It is at least 104 times faster but in many realistic cases the accuracy does not suffer. The trains of pulses generated by rectangular and circular transducers are compared.

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