Some remarks on scattering theory and its application to seismic tomography

The purpose of the authors is to present a comparison of the merits and demerits of three different approximations in acoustic scattering theory, viz. the (first) Born approximation, the eikonal, and the Rytov approximation. For the most part, we limit our attention to far-field scattering in a spherically symmetric potential, and we are mainly interested in the case where the product of the wave number and the radius of the scattering potential is well in excess of unity.