Theoretical and numerical issues in the determination of reflector depths in seismic reflection tomography

Abstract

Seismic reflection tomography obtains an estimate of the subsurface slowness field and the location of strong reflectors by minimizing the difference between measured travel times from seismic reflection events and the corresponding travel times computed from a model of the subsurface. We present some theoretical results for the undiscretized problem regarding the possible ambiguity between slowness and depth. These results indicate that the depths of the reflectors are determined in theory except for edge effects, but a sufficiently large aperture at the reflector is necessary to resolve this ambiguity in practice. The slowness field, however, does have some undetermined features. These results have strong implications for how the tomography problem should be discretized and regularized to compute solutions which are accurate in the features of the model which are well determined from the travel time data. In particular, the slowness model should not be discretized much more coarsely than the reflectors as a way of regularizing the problem because that may force the computed reflector depths to try to match aspects of the travel time data which are caused by features in the slowness field.