Stability and accuracy analysis of the space-frequency domain wavefield extrapolators

Kun Liu, Hugh D. Geiger, John C. Bancroft, Gary F. Margrave

Space-frequency domain wavefield extrapolators have attractive advantages compared to wavenumber-frequency domain extrapolators. The most attractive merit is that they can accurately handle strong lateral velocity variations without incurring a significant increase in computational cost. It is well-known that finite space-frequency domain extrapolators are designed as approximations to the exact phase-shift operator. These approximations manifest themselves as small instabilities and inaccuracies in the performance of the extrapolators. These effects are best examined in the wavenumber-frequency domain, where the extrapolator response can be compared to the exact response, and in the space-time domain, where angular aperture, wavelet stability, and artifacts can be evaluated and compared. In this paper, we compare the 19- and 39-point Hale, Nautiyal (Gaussian tapered), and Kirchhoff (Hanning tapered) extrapolators. We use a common set of standards to visualize the various extrapolators and quantitatively investigate their stability and accuracy. The dip responses of the extrapolators are compared using constant velocity 2-D impulse responses (zero-offset) and a constant velocity pre-stack depth migration of a single shot-record over a carefully designed set of dipping reflectors.