Scattering by Flaws in a Slab or a Half-Space

It is the main function of quantitative NDE to detect and to evaluate defects. Some of the most dangerous defects are cracks, especially cracks on or near surfaces. These cracks can be found by scattering ultrasonic waves from them (either bulk waves or surface waves), but up to now there is no theory (at least in the most interesting low-to-intermediate frequency region) which has been implemented to compute scattering from surface or near-surface cracks in 3d. The purpose of the present report is to explain, via a simple scalar example, the principles of a general boundary-integral-representation method which has been used1 to calculate scattering of waves of all polarizations by a 2d surface or subsurface crack. The method is developed for bulk defects and cracks in a slab as well as in a half-space, and is straightforwardly applicable to 3-dimensional problems as well as to 2d ones