Generalized two‐pass three‐dimensional migration for imaging steep dips in vertically inhomogeneous media

Conventional two‐pass 3-D time migration is exactly equivalent to full 3-D time migration in a homogeneous medium. For vertically inhomogeneous media representing typical earth velocities, however, conventional two‐pass 3-D migration fails to correctly image dips beyond about 45 degrees. This failure is the result of an inherent velocity error incurred during the first pass of a two‐pass 3-D migration. For a vertically inhomogeneous medium, the theory of residual migration can be combined with the results for homogeneous media to derive a series of successive two‐pass migration stages which are equivalent to a full 3-D migration. Each stage of this generalized two‐pass 3-D migration is implemented using an appropriate constant migration velocity. In practice, the required number of two‐pass stages can be reduced to a computationally manageable few; and the I/O can be reduced by one‐third to one‐half of that required using a straightforward application of repeated two‐pass migrations. This procedure allows existing 2-D migration programs to be upgraded to steep‐dip 3-D migration programs by use of a simple I/O structure. Any of the basic 2-D migration algorithms can be used, but we have employed a 50-degree finite‐difference algorithm. In addition, generalized two‐pass 3-D migration overcomes the dip limitations of the underlying 2-D finite‐difference migration algorithm for the same reasons that cascaded 2-D migration extends the dip range of 2-D migration algorithms. Synthetic data examples clearly show the success of this method in imaging steep dips in vertically inhomogeneous media.