Tomographic Inversion In Reflection Seismology

SUMMARY Recently there has been much interest in performing tomographic inversion on data acquired in seismic reflection configurations. Several approaches to dealing with the unknown geometry of reflectors have evolved, the most natural of which seems to be to parametrize them in a manner consistent with the velocity field discretization. the inversion may then be formulated to treat both sets of parameters equally, avoiding the possibility of in‐built bias. One appropriate formulation may be a least‐squares optimization with a priori and step‐length damping terms, which may be accomplished by a multiple‐parameter class subspace method. Unfortunately a standard, ‘naive’ application of such an optimization method appears to fall foul of trade‐offs between reflector depth and near‐reflector velocities. These are manifested in the poor reconstruction of the lower portion of test models from synthetic data. Considerations of determinacy, strategies for non‐linear problems and regularization inspired the idea of a multiple‐stage approach, in which successive stages admit progressively shorter scale lengths of variation in both velocity field and reflector. an algorithm implementing this approach demonstrates a significant improvement in the reconstruction of longer‐wavelength components of test models. However the tests also suggest that the shorter‐wavelength velocity‐depth trade‐offs at the reflector are unresolvable without further information.