A first potential resolution to the paradox is that the wavefront healing removes any effects of a slowness perturbation. This alone is a somewhat unsatisfactory explanation since it does not explain why traveltimes are sensitive to slowness perturbations just off the geometric ray-path.

A second potential resolution is that the hollowness of the banana is simply an artifact of modeling procedure. This is partially true. Both Born and Rytov are single scattering approximations, and a single scatterer located on the geometric ray-path may only contribute energy in-phase with the direct arrival. In contrast, if there are two scatterers on the geometric ray-path traveltimes may be affected. However, just because the paradox may appear to be an artifact of the modeling procedure does not mean it is not a real phenomenom. In the weak scattering limit, traveltimes will indeed be insensitive to a slowness perturbation situated on the geometric ray-path.

4/27/2000