| Migration is a crucial step in seismic data processing. Improving the computational efficiency of migration is very important because of the high cost associated to migrate seismic data. In this thesis, we discuss application of time-frequency analysis techniques to the problem of seismic data migration and propose two new methods which enable us to perform fast migration by using a few elements of the compressed data space.; In particular, we examine two different problems. First, we present an algorithm to migrate seismic data which have been filtered using wavelet transform. The wavelet transform is used to isolate the energy that need to be migrated. This fast migration algorithm is suitable for time migration. Our second approach entails the application of the matching pursuit algorithm to migrate post and prestack data. This algorithm is suitable for depth migration. In this case, the seismic energy that contributes to the migrate image is first located by means of a matching pursuit algorithm. The latter permits us to migrate only a few strong arrivals per trace instead of migrating the complete data volume. The approach speeds up the conventional matching pursuit depth migration by using searching and sorting methods to invert the associated travel time tables. |
