AMPLITUDE-VERSUS-OFFSET MEASUREMENT ERRORS IN A FINELY LAYERED MEDIUM

Recently Spratt (1987) showed how amplitude-versus-offset analysis (AVO) can be sensitive to small residual velocity errors. However, even when the velocity is determined perfectly, serious AVO distortions remain due to normal-moveout stretch, differential tuning as a function of offset, spherical divergence, and source and receiver directivity patterns. I have found that all of these errors can be expanded in a Taylor series about the zero-offset event time, assuming it is much larger than the wavelet width. The first term of this series represents the residual velocity error term found by Spratt, while the second term encompasses the remaining effects mentioned. In practice, either term can be larger than the underlying amplitude variations being estimated. For example, Ricker wavelet stretch leads to a peak AVO error which is 61 percent of the peak zero-offset reflectivity, even though the velocity field is uniform and correct. This result is independent of the wavelet frequency, and the range of incidence angles used in the analysis. Positive gradients in moveout velocity amplify this error, while narrowband filtering of the data prior to AVO analysis greatly widens its temporal extent. Aligning a particular event with static shifts instead of normal-moveout correction can eliminate stretch, but not differential tuning error, in a finely layered target zone whose wavelets overlap.