Seismic depth migration using the Gabor imaging theories
Seismic depth migrations are used to image the earth with more plausible details; they become important tools to obtain 'true' pictures of the subsurface and attract more and more attention. This thesis is dedicated to developing a wave-equation depth migration method, called Gabor depth migration, where the Gabor transform is employed.
The Gabor depth migration method is developed to image structures with strong lateral velocity variations. The wavefield is localized by narrow and uniform partitions such that the most rapidly varying velocity can be accommodated to get accurate images. However, such narrow and uniform partitions introduce inefficient depth migrations, which is not always necessary. Instead, wide and optimized partitions should be utilized according to lateral velocity variations given accuracy criteria.
Adaptive partitioning algorithms are developed to consolidate narrow, small partitions where lateral variations are considered as minor given accuracy criteria. Such a consolidation process usually results in fewer and wider partitions, leading to fewer Fourier transforms in the wavefield extrapolation. Therefore, computational cost is minimized under given accuracy thresholds. Three adaptive partitioning algorithms described in this thesis help to achieve efficient Gabor depth migrations at the cost of losing some imaging accuracy. The Gabor depth migration method can achieve accurate images by increasing accuracy thresholds. An optimized imaging process can be obtained by using trade-off between efficiency and accuracy in the migration method.
The Gabor depth migration method is made more efficient using the spatial resampling without losing imaging accuracy. The depth migration method reduces computational cost by down-sampling wavefields at low frequencies, giving a faster imaging process. Depth images from the Marmousi data verify the improvement of migration speed without obvious loss of imaging quality.
In addition, the Gabor depth migration method is modified to work with topographic seismic data. Tests on a synthetic 2D topographic seismic data set show accurate images.
The Gabor depth migration method can be extended straightforward from 2D to 3D. The adaptive partitioning algorithm using lateral position errors is easy to extend to higher dimensions, which simplifies the implementation of the adaptive Gabor depth migration in 3D.