Stable explicit depth extrapolation of seismic wavefields.

摘要

Stable explicit filters for depth extrapolation of seismic wavefields may be derived through a modification of the conventional Taylor series method. The modified Taylor series method described here yields extrapolators with maximally-flat amplitude spectra in their passband, while ensuring that no spectral components in the wavefield are amplified by any factor greater than one. The price for stability is increased phase error. For low normalized frequencies, implicit extrapolators are more accurate than the 39-coefficient stable explicit extrapolator described here. However, the small spatial sampling intervals required to obtain high phase accuracy in implicit extrapolation imply that this accuracy is rarely achieved in practice. Over the wide range of normalized frequencies likely to be encountered in practice, stable explicit extrapolators outperform implicit ones. The method presented here for deriving stable explicit extrapolators is in no formal sense optimal. It is only guaranteed to yield stable extrapolators. In my limited experience with alternative methods for designing stable extrapolators, the method presented here produced the least phase error while ensuring stability. Nevertheless, a simple method for designing optimal (in some sense) stable explicit extrapolators would be preferred over the method presented here. 7 refs., 15 figs.