A fast three‐dimensional modeling technique and fundamentals of three‐dimensional frequency‐domain migration

The frequency‐domain approach to migration extends to three dimensions. Application of the ray‐tracing approach to simple seismic events, together with the principle of superposition for complex events, leads to the correct equation for frequency‐domain migration in a constant velocity medium and a further understanding of the basic migration procedure in three dimensions. In the frequency domain, three‐dimensional (3-D) migration may be reduced to a series of two‐dimensional (2-D) migrations. A 3-D seismic model can be generated economically for structures with combinations of radial and 2-D symmetry. Starting from a 2-D synthetic, a 3-D model can be constructed by rotation about the axis of symmetry. Any line across the model may then be synthesized from the basic 2-D data. Certain more complex 3-D models can also be developed using the superposition of simpler models. Synthetic examples are used to illustrate the fact that 2-D migration of 3-D seismic data will not generally result in a correct section.