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11.10 DIP MOVEOUT                              529

           dimension (the side-sweeps) are completely   The first part of Eq. (11.3) is the NMO term,
           removed, resulting in a significantly improved  while the second part is known as the DMO
           illumination with sharp fault planes, and the  term. According to Eq. (11.3), we can first apply
           reflections have better trace-by-trace consistency.  an NMO correction using the velocity of the
                                                        upperlying medium, and then a DMO correc-
                                                        tion is applied. Although NMO is valid in the
                    11.10 DIP MOVEOUT
                                                        CDP domain, the DMO term must be defined
                                                        in the common offset domain, which allows us
              Poststack migrations generally do not yield
                                                        to discriminate the dipping events.
           correct results since stack sections are not per-
                                                           Consecutive applications of NMO and DMO
           fectly equivalent to zero-offset sections, due to
                                                        processes remove the offset and provide a more
           the conflicting dip issues and in the case of lateral
                                                        accurate NMO correction for all available dips in
           velocity variations, which leads to use of costly
                                                        the data. The poststack migration followed by
           prestack algorithms. Prestack partial migration,
                                                        the NMO and DMO processing sequence will
           or the DMO approach, provides a better stack
                                                        provide almost identical results with a prestack
           section that is almost identical to the zero-offset
                                                        migration (Fig. 11.39) and with a considerably
           section, so that one can apply a more economical
                                                        low cost, since the processing flow given in
           poststack migration to the DMO output to obtain
                                                        Fig. 11.39 is much more computationally effec-
           an image very similar to that from prestack
                                                        tive as compared to conventional prestack time
           migration. The issue to be solved with the
                                                        migration. Furthermore, in contrast to NMO cor-
           DMO process is conflicting dips, which originate
                                                        rection, which is rather sensitive to velocity
           from the dip dependent stacking velocities.  errors, constant velocity DMO is almost inde-
           NMO correction becomes a dip filter in areas  pendent from the velocities picked during the
           of structurally dipping reflectors (Liner, 1999),  velocity analysis (Liner, 1999).
           and the processor picks the velocities in favor  For the zero-offset case of identical source-
           of only one dipping event (Fig. 11.33).      receiver pairs on the earth’s surface, the reflector
              Recalling the Levin equation, given by Eq.  may be found at any depth and may have any
           (10.7)
                                                        inclination in the subsurface. For instance, if
                                    2
                                        2
                                   x cos ϕ              the recorded zero-offset time is 1.0 s and the
                        2
                              2
                       t xðÞ ¼ t 0ðÞ +           (11.2)
                                     V 2                propagation velocity is 1000 m/s, we only have
           where ϕ is the inclination of the reflector, V is the  the information that the total distance traveled
           velocity of the upperlying medium, and x is the  will be 1000 m for all of the source-receiver pairs.
           source-receiver offset. Considering the equality  Based on this information, one can conclude that
                     2
              2
           sin ϕ +cos ϕ ¼ 1, we can divide Eq. (11.2) into  there may be several possibilities to determine
           two parts to get                             the correct location of the reflector, since it
                                                        may be located at any position on an ellipse
                                    2
                                        2
                               x 2  x sin ϕ
                         2
                   2
                  t xðÞ ¼ t 0ðÞ +                (11.3)  1000 m away from all available source-receiver
                               V 2   V 2                pairs. The NMO term gives only the possibility
                         |fflfflfflfflfflffl{zfflfflfflfflfflffl} |fflfflfflffl{zfflfflfflffl}
                           NMO       DMO                of the horizontal reflector case just below the
           FIG. 11.39  Dip moveout (DMO) flow followed by a poststack migration can be used instead of costly prestack
           migration flow.
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