Introduction

3D acquisition geometry can have a tremendous impact on the quality of the final image. Detailed exploration objectives such as detection of fracture density and orientation from P-wave surface seismic data have pushed 3D seismic surveys to be carefully designed carefully. Many important and sometimes conflicting issues influence 3D survey design; we need to be concerned about adequate midpoint sampling, azimuth and offset distribution and high fold for best quality images. Conventional 3D seismic survey design software is based on CMP analysis of these bin attributes. However, with current recording geometries it is impossible to sample the five dimensional wavefield completely. Vermeer 1994 has proposed a criterion for the sampling of the prestack wavefield based on an extension of the 2-D cryteria for symmetric sampling. He presented sampling principles for two major classes of geometries: the patch geometries and line geometries. The spatial continuity of symmetric sampling would then be well preserved in the shot or receiver domain. Figure 1 shows an example of a Button-Patch geometry for a real 3D survey which we use in our simulations. It is characterized by a dense areal arrangement of receiver stations and sparse sampling of shots.

For 3D data, obstructions, cable feathering, environmental objectives, economic constraints, and many other factors cause seismic data to be sampled in sparse and irregular fashion. These irregularities are always observed in the form of variations in fold coverage, which can manifest itself as an acquisition foot-imprint on prestack data or even the stacked image. If not accounted for, irregular sampling can affect prestack data analyses and may introduce noise, cause amplitude distortions, and even structural distortions when 3D wave equation processes are applied to the data Beasley (1994); Black and Schleicher (1989); Gardner and Canning (1994). Many techniques with varying accuracy and effective cost have been proposed for processing irregularly sampled data; among them equalized DMO Beasley and Klotz (1992), geometrically calibrated DMO Ronen et al. (1995) and spatial dealiasing Ronen and Liner (1987).

Chemingui and Biondi 1996a have demonstrated that the effects of irregularly-sampled data on seismic amplitudes can be substantial and have proposed a method for processing wide-azimuth 3D surveys that can largely overcome these problems. The technique is based on applying the AMO transformation Biondi and Chemingui (1994) in order to organize the data into common-azimuth common-offset cubes and, therefore, to allow interpolation to a regular grid before imaging. In this paper, we propose a new development in our technique to compensate for the effects of irregular fold distributions. The method extends the multiplicity concept to wave equation processes and uses a normalization procedure to correct and equalize for the effects of irregular coverage.