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.

11/11/1997