INTRODUCTION

Sparsity of spatial sampling results in aliased seismic data, and aliased integral operators in data space. Generally the operator is treated with some variety of bandpass which antialiases the operator and largely prevents the generation of spurious events. For example, the triangle filtering applied to Kirchhoff migration in BEI Claerbout (1995) is really a dip-dependent bandpass on the migration hyperbola. In a typical prestack 3D geometry, source and receiver spacings are likely to vary significantly in the inline and crossline directions (button and patch geometry seems an exception, see Chemingui 1996). It is problematic to bandpass a 3D prestack datuming operator in the case that sampling varies significantly. Varying operator bandwidth means that reflectors with equal dip will be preferentially preserved according to strike. Energy moving across crossline offsets will frequently be bandpassed to irrelevance.

One is free to choose some particular principle time dip at which an operator is not antialiased. In general this is chosen to be zero dip, because the operator will then respect positive and negative dips in the data equally. Where one can make an assumption to limit the data's dip range, the operator can be tuned to preserve higher temporal frequencies than is possible antialiasing relative to zero dip. Performing prestack 3D datuming with antialiasing tuned to respect limited dips along the poorly sampled axes can help make up for the sparse sampling. This can not be done safely in shot and receiver coordinates, where any nontrivial geologic structure is likely to create conflicting dips in the recorded data. Prestack seismic data contains only non-negative dips in midpoint and offset coordinates, so the operator is less likely to lose energy. However, the operator becomes more expensive.

In this paper I demonstrate the principle on synthetic 3D data in shot and receiver coordinates, by assuming (nearly) flat reflectors. I then discuss the incomplete extension of this idea to midpoint and offset coordinates, where the flat reflector assumption is unnecessary.