We present an approach called multiple migration fitting (MMF) designed to automatically determine 2-D background velocities from prestack seismic data. In this approach, we maximize a scalar similarity index (SI) for a collection of migrated sections obtained by various illuminations of the same earth. Numerical investigation shows that this index is a rather smooth, nonoscillatory function of velocity that tends to be a maximum for good velocity profiles, and hence is amenable to maximization by local gradient techniques. This maximization will be practically feasible, as we prove that the exact gradient of SI can be computed at an additional cost of only twice that required for the computation of the collection of migrated sections, independently of the number of velocity unknowns. Application to synthetic data shows that MMF leads to enhanced background velocities and stacked migrated sections.
Frequency domain migration is founded upon the wave equation, and so includes diffractions and other effects. This paper seeks to motivate and illuminate frequency domain migration using straightforward geometric techniques and simple frequency domain observations.
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.
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