The natural relation between prestack time migration and residual statics analysis
Xinxiang Li, John C. Bancroft
In terms the purpose of data processing, conventional residual statics analysis methods are essentially trying to correct randomly distributed traveltime errors on seismic traces for the best possible stacked section. On the other hand, in terms of residual statics analysis, CMP stacking is the essential process for conventional methods to provide reference traces with less traveltime errors.
Prestack migration also contains a stacking process after proper time correction. The scattered energy on different traces from a scatter point will be aligned in time. The migration stacking process sums these time-corrected traces and produces the time imaging of the scatter point.
From migrated traces, an inverse migration process can be applied to produce multi-offset reference data volume. The stacking processes in both migration and its inverse (de-migration) involve much more traces than NMO plus CMP stacking, and statistically attenuate traveltime errors more efficiently. Unfortunately, prestack migration (especially depth migration) is more velocity sensitive than NMO plus CMP stacking process.
Equivalent offset migration (EOM) introduces an intermediate step for prestack time migration, which is a constant time mapping from source-receiver offset to migration equivalent offset. This equivalent offset mapping, also as a stacking process, reduces the traveltime error effects. An inverse mapping from equivalent offset back to source-receiver offset can be applied to form a set of reference traces. Comparing to the full prestack migration and its inverse (de-migration), the main advantages of the forward and inverse equivalent offset mappings are:
(1) No time shift is involved in the process, which avoids time direction distortion, such as NMO stretch.
(2) It is velocity insensitive, and practically no velocity information is needed.
(3) It is computationally more efficient.
Plausible results have been obtained from the application of residual statics analysis based on the reference model data created by equivalent offset mapping.