2.5-D TRUE-AMPLITUDE MIGRATION AND DEMIGRATION

Kirchhoff-type migration and demigration for three dimensions are exce edingly expensive processes in laterally inhomogeneous media due to th e intense numerics required. For simpler types of media, however, the formulas to be implemented simplify considerably. For 3-D in-plane wav e propagation in 2-D media, i.e., the 2.5-D situation, 2-D ray tracing is sufficient for full 3-D true-amplitude migration or demigration. I n 1-D media, both imaging operations require the solution of certain i ntegrals of a semi-analytic character which can be implemented in an e ven cheaper way. For some specific velocity distributions (such as con stant velocity, constant velocity gradient, constant gradient of quadr atic slowness and constant gradient of logarithmic velocity) fully ana lytic expressions can be derived. If the velocity distribution in the true earth model can be reasonably well represented by one of the cons idered situations, a very fast approximate true-amplitude Kirchhoff-ty pe migration can be performed. Moreover, simple models in which the al gorithms perform fast and accurately can be of great value for (a) val idating the algorithms so as to ensure correct results in the desired realistic situations and (b) gaining insight on how to interpret the r esults.