The singularity expansion method as applied to the elastodynamic scattering problem

A basic problem in non-destructive testing of materials is the classification of defects with respect to size and geometry. Utilizing elastrodynamic scattering, ultrasonic test methods reduce this problem either to the application of reconstruction algorithms or to the parametrization of experimental data in terms of quantities being related to the physical scattering mechanisms. The so-called Singularity Expansion Method (SEM), originally developed for broadband electromagnetic scattering by arbitrarily shaped targets proves essentially useful to predict and understand impulsive scattering of ultrasound; in addition, even though not yet fully solved in practice, it seems possible to parametrize experimentally obtained time records in a sense which is physically intuitive.

SEM starts either with the eigenfunction expansion in the complex Laplace domain for canonical objects such as a sphere or spheroids, or with a corresponding integral equation formulation for more arbitrarily shaped defects. The essential point is then an expansion in terms of the singularities of the scattered field in the Laplace domain similar to the expansion of transfer functions in linear system theory. It turns out that the location of these singularities is characteristic for the geometry of the scattering body; therefore, it might be a useful tool to parametrize size and shape of the defects.

Several theoretically derived singularity patterns are presented for various body shapes and material compositions, which yield a thorough and physically intuitive interpretation in terms of distinct creeping wave modes. They are compared with first experimental results for a spherical void in a steel test specimen.