Conventional methods

Even in areas with poor illumination, there is generally some signal present, it is just weak and obscured by noise. Conventional methods for trying to improve imaging in poorly illuminated areas often try to improve the signal-to-noise ratio. One of the simplest ways to do this is to apply some type of weighting (scaling) to the image after migration. One common example of this attempted improvement is automatic gain control (AGC). There are other better ways to a apply weighting such as the illumination-dependent operator described by (). Unfortunately, these weighting methods can easily increase the level of noise as well as the signal level.

Other methods to improve imaging in poorly illuminated areas often manipulate the migration algorithm itself. For example, it is well known that long-time industry standard prestack Kirchhoff migration will not perform well in areas like those beneath salt edges. Kirchhoff migration tries to add up all of the energy in the recorded data that can be connected to a point in the subsurface with ``rays'' that trace a path through the subsurface from the seismic source to the receivers. Results from such migration algorithms contain poorly illuminated areas that are full of artifacts, many of which are caused by multipathing (). These artifacts can be reduced by using a Kirchhoff algorithm that creates an image in reflection angle space (). However, even this Kirchhoff algorithm will produce a result with shadow zones beneath the salt edges. One reason for this occurrence is that Kirchhoff methods impose an implicit high frequency assumption on the wave equation. They use ray-based theories of wave propagation in the subsurface, which break down around large velocity contrasts like those at salt boundaries.

Fortunately, we now have the computational power to use migration algorithms that are based on the wave equation without making a high frequency assumption. An example of this type of algorithm is downward-continuation migration. Downward continuation (source-receiver) migration uses the Double Square Root equation to push the wavefield recorded at the surface back into the subsurface, which ``moves'' the seismic energy to its proper depth. Since this algorithm uses the whole recorded wavefield rather than making a high frequency assumption, it has less severe illumination problems in areas of large velocity contrasts. This can be further improved by reducing multipathing artifacts with a downward-continuation migration algorithm that creates an image in reflection angle space ().

These are just a few of the possible methods to improve imaging in poorly illuminated areas. The examples described here are sufficient background for the work that will be presented in this thesis.