The inversion results obtained by regularizing the inversion process with one-dimensional filters are significantly better than the results of simple migration. We plan to apply soon this method to the real data set shown in this paper.
The inversion results obtained by regularizing the inversion process with two-dimensional filters are lower frequency and more artificial looking than we want them to be. We have found that we can increase the frequency content by increasing the rate of depth sampling. However, doubling the sample rate increases the computational cost. We would prefer to find a solution that can solve both the frequency and the appearance problems.
We are hoping to use this method to fill in areas of poor illumination. This means that it can be used on a specific target. This can be partially done by downward continuing the data to a depth just above the region of interest, then following the described inversion scheme just over the target area. Additionally, we want to find a way to apply the smoothing on just one reflector or at least in a small area. This would leave the frequency content and appearance of the rest of the image near that of the migrated image.