Seismic reflection tomography

Abstract

Velocity analysis in current conventional seismic processing is beginning to appear inadequate for dealing with the increasingly complex geological structures of interest today. Tomographic imaging using individual arrival traveltimes from a given reflector may offer the prospect of reconstructing in detail an accurate velocity field above that reflector, and, by extension, the velocity field in a layered medium. Bearing in mind the likely scale of this inverse problem we formulated it as a least-squares optimisation and derived a descents-type algorithm; synthetic tests in which the reflector was assumed to be known demonstrated its potential for recovering lateral variations in particular. However the more realistic problem in which the reflector is unknown and presumed to have structure on a scale similar to the velocity field, necessitating its inclusion in the inversion, is less tractable. As one might intuitively have expected, there are reflector depth trade-offs with near-reflector slownesses resulting in indeterminacy with severe implications for the usefulness of the reconstruction and which cannot be simply resolved. The robustness of excessively overdetermined problems suggests a multi-stage inversion in which the scale of model parameterisation is successively reduced until e.g. no further gain in resolution is achieved. Synthetic tests here suggest that while such schemes may yield significant improvements, they are dependent on the actual early-stage (large-scale) parameterisations used. Fortunately it turns out that we can use multi-stage, decreasing scale-length smoothing to achieve similar effects without such dependence.