Modeling Ultrasonic Pulse-Echo Signals from a Flat-Bottom Hole in Immersion Testing Using a Multi-Gaussian Beam

This paper proposes an ultrasonic measurement model that can predict the pulse-echo signals from a flat-bottom hole in an isotropic, homogeneous solid specimen immersed in water in a computationally efficient manner. To develop such a model, a measurement model approach is adopted based on two important assumptions: the paraxial approximation for the transducer beam and the small flaw assumption for the flat-bottom hole. The modular model that results from these two assumptions contains three terms: a diffraction correction term, a far-field scattering amplitude term and a system efficiency factor term. The diffraction correction is defined based on a multi-Gaussian beam model which allows the rapid evaluation of the wave field incident on the hole. The far-field scattering amplitude of the flat-bottom hole is obtained using the Kirchhoff approximation together with the small flaw assumption. The system efficiency factor is determined by deconvolution of an experimental front surface reflection signal by a reference reflector model. Here, the contribution of each of these three terms to the overall measurement model are described in detail and the accuracy of the proposed model is verified by the comparison of the model-based predictions to experiments.