Anti-Aliasing and Amplitude Preserving 2D and 3D DMO — some Practical Considerations

Abstract

A practical definition of DMO (Dip Move-Out) is that it is a mapping to zero offset. In order to avoid the arbitrary attenuation of dipping events in this mapping process, Amplitude-Preserving or True-Amplitude DMO is needed. Such a DMO algorithm will be an invaluable tool in the study of AVO (Amplitude-Versus-Offset) effects. A method is described whereby both anti-aliasing and Amplitude-Preserving DMO can be implemented using the integral approach (also known as Kirchhoff DMO, Summation DMO, and (x-t) or space-time DMO). Anti-aliasing is accomplished by using band-limited sincfunction interpolators based upon local dip of the impulse response of the DMO operator. This enables the appropriate amplitude weighting along the DM0 impulse response to be applied. That gives rise to the so-called True-Amplitude and Amplitude-Preserving DMO algorithms. The F-K domain offers a useful platform for the comparison and implementation of various weighting factors for the DMO impulse response. F-K analyses of impulse responses can be used to illustrate the effects of anti-aliasing and amplitude properties of integral DMO. In 2D, where in general there is regular sampling in the common offset plane, the anti-aliasing and Amplitude-Preserving DMO algorithm improves the image quality in the mapping of pre-stack data to zero offset. In the 3D case the DMO ellipse is exactly the same as the 2D DMO ellipse, apart from the fact that for 3D DMO we must rotate the ellipse to lie in the direction given by the source-receiver axis with respect to the processing grid. This grid is usually organised in terms of 3D binline and 3D CMP (Common Mid-Point). In marine data, streamer feathering has the effect of spreading midpoints (3D CMPs), for a given sail line, over several 3D binlines. The result of this is to vary the distribution of source-receiver azimuths (feather angles) within a given bin. This leads to irregular sampling in the common offset-azimuth plane where 3D DMO is performed. Whilst Kirchhoff methods have the flexibility of dealing with irregularly sampled data, the desirability of regular sampling in this common offset-azimuth plane in order to preserve amplitudes is illustrated. Methods for data regularisation in offset and azimuth are not discussed here. Instead we question the need for 3D DMO in certain marine applications. A simple criterion for determining the condition under which cable feathering becomes a significant factor in determining the need for 3D DMO is presented in tabular form and its implications are discussed.