Improving the Born approximation for the scattering of ultrasound in elastic solids

It has recently been demonstrated that the Born approximation for predicting the scattering response of flaws can be improved through the use of simple modifications called the "doubly distorted Born approximation". In this paper the doubly distorted Born approximation itself is modified with phase and amplitude corrections that further improve the Born scattering results for isotropic elastic media. The reliability of this new modification of the Born approximation has been evaluated by comparison with the exact solution for spherical inclusions obtained with the method of separation of variables. Unlike the ordinary Born approximation which works well only for very weak scattering inclusions, our modification of the doubly distorted Born approximation gives improved scattering results for both weak and strong scattering inclusions.