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Some practical considerations

The following is a brief discussion of the parameters that need to be taken into consideration in order to optimize the results of migration.

1. Migration aperture width
Theoretically, a diffraction hyperbola extends to infinite time and distance. However in practice only a truncated hyperbolic summation path is considered. The choice of aperture is usually made by considering the maximum dipping events and the size of diffractions present on the input data.

2. Velocity errors
The use of a low migration velocity results in an incomplete collapse of diffractions, and dipping events are only partially repositioned to their true location. Converseley, if the velocity used is too high, diffraction hyperbolas are overmigrated and on sections these are manifested as inverted hyperbolas, or ``smiles''. High velocity also results in excessive lateral shifts of dipping events, and higher dips than the actual dips of the subsurface reflectors.

3. Spatial aliasing
Spatial aliasing on migration of field data is minimized by the right choice of CMP trace interval. Another way of minimizing the aliasing effect is by doing trace interpolation before migration.

4. Ambient noise
Considering the summation of random noise along a hyperbolic curve, the final summation is independent of the curvature of the summation trajectory, since random noise amplitude is uniform over the region of the hyperbola. Therefore after migration the noise background is actually reduced by the spherical spreading factor. In a medium where velocity increases with increasing time, the velocity factor in the amplitude scaling factor results in a greater reduction of noise towards the bottom of the section, where the velocities are higher. However background noise becomes more coherent in regions of high velocities. At high velocities the summation hyperbola is very nearly flat. Summation along the curve emphasizes the lower wave numbers, so that the data appears smeared and lateral resolution becomes limited. Therefore noise coherency due to migration is more severe in the bottom section. Another possible adverse effect on a migrated section is shown as ``smiles''. These are due to sparsely distributed bursts of amplitude in the input section.

5. Length of profile
If the section to be migrated is too short, this will result in insufficient space for dipping events to move during migration. Another adverse effect is that the effective aperture near the boundaries of the section will be smaller than the aperture width used to migrate the rest of the data. The smearing effect due to this condition contaminates a large percentage of the final migrated section, since the latter is too short. Migration algorithms assume that the data outside the side boundaries of the input stacked section is of zero amplitude or zero gradient. If traces of zero amplitude are appended to the edges of the section, dipping events can move freely into the zero-amplitude region during migration.

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Stanford Exploration Project