2.5-D true-amplitude migration and demigration

Kirchhoff-type migration and demigration for three dimensions are exceedingly expensive processes in laterally inhomogeneous media due to the intense numerics required. For simpler types of media, however, the formulas to be implemented simplify considerably. For 3-D in-plane wave 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. In 1-D media, both imaging operations require the solution of certain integrals of a semi-analytic character which can be implemented in an even cheaper way. For some specific velocity distributions (such as constant velocity, constant velocity gradient, constant gradient of quadratic slowness and constant gradient of logarithmic velocity) fully analytic expressions can be derived. If the velocity distribution in the true earth model can be reasonably well represented by one of the considered situations, a very fast approximate true-amplitude Kirchhoff-type migration can be performed. Moreover, simple models in which the algorithms perform fast and accurately can be of great value for (a) validating the algorithms so as to ensure correct results in the desired realistic situations and (b) gaining insight on how to interpret the results.