Apparent layering in common‐midpoint stacked images of two‐dimensionally heterogeneous targets

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Abstract
Model studies with finite‐difference synthetic data demonstrate a fundamental spatial bias in the appearance of common‐midpoint (CMP) stacked images. The CMP stack of data recorded over a target having 2-D random variations in velocity shows numerous short reflection segments; similar reflection patterns in field data are often interpreted in terms of 1-D fine‐scale layering. The stacked image appears layered because of enhanced lateral continuity attributable to the well‐known dip filter of the stacking process. The stack filter can be characterized using the formulation of Bolondi et al. (1982). Lateral correlation in the target and its seismic image is quantified with a measure based on the spectral coefficient of coherence. Broadband primary reflectivity (defined as the vertical‐incidence, primaries‐only reflection coefficients of the 2-D target) is often taken as an ideal seismic image. The primary reflectivity section of a 2-D random target, however, shows greater apparent lateral correlation than is present in the random structure. This apparent increase in lateral continuity is attributable to the fact that reflectivity measured from the surface depends on the vertical derivative of velocity but depends on horizontal changes in velocity directly. The dip‐filtering effects of stacking cannot be reversed by poststack migration; the synthetic data demonstrate the necessity of migration before stack or equivalent processing (such as dip moveout correction). A field data example illustrates the effects of CMP stack filtering using lateral coherence functions measured on stacked and unstacked sections.

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