Born Inversion with a Stratified Reference Velocity.
COLORADO SCHOOL OF MINES GOLDEN CENTER FOR WAVE PHENOMENA
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Carter and Frazer 1984, and Bleistein and Gray 1984, presented inversion algorithms which included the effect of a stratified reference velocity, cz. Those papers did not address the question of obtaining accurate values of the reflection coefficient, this is the issue treated here. Thus, in the language of Bleistein, Cohen and Hagin 1984, the earlier algorithms provided structural inversions, the location of the subsurface layers, whereas the present algorithm also provides an accurate estimate off the reflectivity function, which depicts the reflectors and provides an estimate of the reflection strengths across the layers. Since we employ a perturbation assumption the Born Approximation , the constant reference speed inversion first described in Bleistein and Cohen 1979a and reviewed in BCH, is often not adequate at depth. Although recursive use of the algorithm is possible and although the results can be significantly enhanced by suitable pre- or post-processing e.g., see Hagin and Cohen 1984, extension of the perturbation method to a stratified reference profile is highly significant. It is far more likely that the actual velocity function can be well approximated by a stratified reference velocity than by a constant one, which in turn enhances the validity of the perturbation assumption and the inversion results.
- Theoretical Mathematics