High-Frequency Elastodynamic Boundary Integral Equation Inversion Using Asymptotic Phase Information

Abstract

Ultrasonic transmission and scattering in the high frequency regime are important problems in ultrasonic NDE, relating to both scattering from large flaws, and the transmission behavior of an ultrasonic beam in a complex geometry component. Ultrasonic modeling efforts are often confronted with problems for which asymptotic methods such as geometrical diffraction theory (GTD) prove inadequate due to insufficiently high frequency or lack of an appropriate canonical solution, but which are too high in frequency (too large in ka) for conventional numerical methods such as boundary element methods (BEM). The inefficiency of BEM at high frequency arises from the need to represent a rapidly oscillating wavefield, resulting in a fine BEM mesh. It is observed in this paper that if the phase characteristics of the wavefield are known a priori, the spatial frequency bandwidth of the unknowns to be determined via numerical methods can be significantly reduced, resulting in a significant reduction in the number of basis functions (boundary elements) required for solution. It is fortunate that GTD generally yields good asymptotic phase information with few complications: it is in the determination of field amplitudes where GTD most often runs into difficulties, such as with singularities in the transport equations (caustics), and the determination of diffraction coefficients. A solution method described here which transforms the boundary integral equation (BIE) using an ansatz similar to that of GTD, in which the field phase is prescribed a priori via GTD analysis, and field amplitudes are determined via a BEM-type numerical scheme. An example of application to critical angle beam transmission at a curved fluid-solid interface is presented.