Structural interpretation - 3-D Seismic Interpretation - page 100

estimating the velocity v would result in a 4% error in this shift, or about 31 m. This is
not likely to cause problems. However, for a reflector dipping at 25 ◦ at a time of 4 s, the
shift would be 2535 m and a 4% error in this would be 101 m, enough to cause serious
concern when planning a well. In such a case, careful investigation of the migration
velocity is needed to establish its likely accuracy.
Complications arise as soon as the overburden shows significant velocity variation,
particularly if there are rapid velocity changes laterally. The effect of ray-bending in
the overburden then has to be taken into account. Time migration algorithms assume
hyperbolic moveout, and account for lateral velocity variation by varying the shape of
the hyperbola with map location; this is satisfactory only if the velocity structure does
not vary laterally across a CMP gather. The technically correct approach in the case of
rapid lateral variation is pre-stack depth migration. This is, however, time-consuming
and expensive, because of the effort needed to build a correct 3-D velocity model; if
the model is incorrect, the migrated image may be worse than that from a simple time
migration. Various methods have therefore been suggested to apply corrections for
lateral shift to time-migrated data. One method is the use of image rays. The basic idea
(Hubral, 1977 ) of the image ray is that it starts vertically downwards from a point at
the surface, and propagates through the subsurface refracting at all velocity boundaries
until the travel time is used up. The corrected horizons are positioned at the end point
of the image rays. However, image rays will correct for ray-bending only in the case
where the target horizon has zero time-dip; in other cases the lateral displacement
derived by this method will be incorrect, because the overburden sampled by the image
ray is different from that seen by the actual physical rays reflected from the dipping
surface (Calvert, 2002) .
References
Al-Chalabi, M. (1979). Velocity determination from seismic reflection data. In: Developments in
Geophysical Exploration methods - I (ed. A. A. Fitch), pp. 1-68. Applied Science Publishers,
Barking.
(1994). Seismic velocities - a critique. First Break , 12 , 589-96.
Anstey, N. A. & O'Doherty, R. F. (2002). Cycles, layers and reflections. The Leading Edge , 21 ,44-51.
Armstrong, P. N. Chmela, W. & Leaney, W. S. (1995). AVO calibration using borehole data. First
Break , 13 , 319-28.
Armstrong, T., McAteer, J. & Connolly, P. (2001). Removal of overburden velocity anomaly effects
for depth conversion. Geophysical Prospecting , 49 ,79-99.
Backus, G. E. (1962). Long-wave elastic anisotropy produced by horizontal layering. J. Geophys.
Res. , 67 , 4427-40.
Bahorich, M. & Farmer, S. (1995). 3-D seismic discontinuity for faults and stratigraphic features: the
coherence cube. The Leading Edge , 14 , 1053-8.
Calvert, R. (2002). Image rays and the old myth about correcting time migrated positioning. First
Break , 20 , 715-16.