Stability and Accuracy Analysis of Space-frequency Wavefield Extrapolators for Depth Migration

Kun Liu

Stability and accuracy are major concerns when designing recursive wavefield extrapolators implemented in the space-frequency domain. In this thesis, a common set of tools has been developed and utilized to conduct a comprehensive stability and accuracy analysis of selected space-frequency extrapolators. The analysis shows that the Hale extrapolator is superior over a limited-aperture Rayleigh extrapolator spatially tapered by either a Hanning or a Gaussian window. A key merit of the Hale extrapolator is that it preserves as much of the phase and amplitude of the propagating wavefield as possible, yet attenuates propagating waves where the extrapolator has significant phase error.

A new adaptive tapering scheme is proposed and compared with conventional tapering methods using both simple and complex models. The results show that adaptive tapering can be applied in the first extrapolation step to improve the image at shallow depth from a common-source migration.