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474                      10. NORMAL MOVEOUT CORRECTION AND STACKING

           data is collected as shot gathers in shot and  improved proportional to √N because in-phase
           receiver coordinates (Fig. 10.14A), and then  primary reflection amplitudes strengthen each
           transformed into shot and receiver midpoint  other after stacking. Random noise components,
           coordinates by CDP sorting (Fig. 10.14B), and  however, are trace-by-trace inconsistent and are
           the offset distance is removed by NMO correc-  out-of-phase in the NMO corrected CDPs. After
           tion to reduce all the traces into zero-offset  summing up the traces during stacking, random
           arrival times (Fig. 10.14C). Finally, the traces in  noise is drastically suppressed, leading to an
           the CDPs are summed up to produce a stacked  improved S/N ratio. Fig. 10.16 shows an exam-
           trace (Fig. 10.14D).                         ple to emphasize the effect of stacking on the
              Stacking yields an interpretable seismic sec-  random noise suppression. An NMO corrected
           tion for 2D surveys, and a seismic cube for 3D  synthetic CDP gather consisting of 120 traces
           surveys. While a 2D stack section provides a ver-  with two reflections of zero phase wavelets con-
           tical section along the survey line only     taminated by a 50% random noise is shown in
           (Fig. 10.15A), a seismic cube allows us to extract  Fig. 10.16A. Fig. 10.16B illustrates stacked traces
           several, even irregular, 2D lines in any direction  obtained using an increased number of traces
           throughout the cube (Fig. 10.15B). In addition, a  involved in stacking: 4, 12, 24, 36, 48, 60, 72,
           horizontal slice of amplitudes at a given time  96, and 120 traces, respectively. As the number
           sample, known as a time slice, can be extracted  of traces in stacking increases, the amount of
           from the cube, which exposes the 3D extension  random noise in the stacked trace is significantly
           of the target structure.                     reduced.
              Stacking has two considerable effects on the  Offset distance between source and receivers
           data: First, providing an accurate velocity anal-  is removed by NMO correction, and the traces in
           ysis for primary reflections, multiples are still  an NMO corrected CDP as well as within the
           hyperbolic and out-of-phase while primaries  stack section are thought to be a zero offset.
           are flattened and in-phase on the CDPs after  Due to several practical reasons, a stack section
           NMO correction, which results in a considerable  is not fully equivalent to a zero-offset section,
           suppression of the multiples after stacking  but is an approximation. Poststack migration
           (Section 7.1). Second, if the number of traces  algorithms assume that the incoming data is
           involved in stacking is N, then the S/N ratio is  zero offset. Normally, acquisition with CDP






















           FIG. 10.15  (A) An example stack section from a 2D survey, and (B) a seismic cube from a 3D survey.
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