The performance of the two popular migration methods, the Kirchhoff integral and the reverse-time migrations, are evaluated through applications to imaging complex structures using prestack shot records. The migration results from the Marmousi model data demonstrate that the reverse-time migration is more accurate in imaging the steeply dipping faults. Its better accuracy is based on the use of the correct velocity model, and is paid off by its huge amount of computations. In the application to the Alberta Foothills data where a good estimate of the velocity model is available; however, both the Kirchhoff and the reverse-time migration methods produce almost identical results. This implies that in the real world of exploration seismology it will be relatively difficult to identify which method performs better as we will never know the exact answer of the subsurface.
Reliable seismic depth migrations require an accurate input velocity model. Inaccurate velocity estimates will distort point diffractors into smiles or frowns on a depth section. For both poststack and prestack migrated sections, high velocities cause deep smiles while low velocities cause shallow frowns on migrated gathers. However, for prestack images in the offset domain, high velocities cause deep frowns while low velocities cause shallow smiles. If the velocity is correct, there will be no variation in the depth migration as a function of offset and no smiles or frowns in the offset domain. We explain migration responses both mathematically and graphically and thereby provide the basis for depth migration velocity analysis.
Reverse‐time migration applies finite‐difference wave equation solutions by using unaliased time‐reversed recorded traces as seismic sources. Recorded data can be sparsely or irregularly sampled relative to a finely spaced finite‐difference mesh because of the nature of seismic acquisition. Fortunately, reliable interpolation of missing traces is implicitly included in the reverse‐time wave equation computations. This implicit interpolation is essentially based on the ability of the wavefield to “heal itself” during propagation. Both synthetic and real data examples demonstrate that reverse‐time migration can often be performed effectively without the need for explicit interpolation of missing traces.
We produce depth images for an Alberta Foothills line by iteratively using a number of migration and velocity analysis techniques. In imaging steeply dipping layers of a foothills data set, it is apparent that thrust belt geology can violate the conventional assumptions of elevation datum corrections and common midpoint (CMP) stacking. To circumvent these problems, we use migration from topography in which we perform prestack depth migration on the data using correct source and receiver elevations. Migration from topography produces enhanced images of steep shallow reflectors when compared to conventional processing. In addition to migration from topography, we couple prestack depth migration with the continuous adjustment of velocity depth models. A number of criteria are used in doing this. These criteria require that our velocity estimates produce a focused image and that migrated depths in common image gathers be independent of source‐receiver offset. Velocity models are estimated by a series of iterative and interpretive steps involving prestack migration velocity analysis and structural interpretation. Overlays of velocity models on depth migrations should generally show consistency between velocity boundaries and reflection depths. Our preferred seismic depth section has been produced by using prestack reverse‐time depth migration coupled with careful geological interpretation.
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