The theory for skeletonized least-squares wave equation migration is presented. The key idea is to solve the wave equation only once to get the Green's functions. These Green's functions are skeletonized into a few samples and saved to disk. The skeletonized migration kernel is obtained through convolution of source-side and receiver-side Green's functions followed by a filtering plus thresholding scheme. Both storage and I/O costs are greatly reduced compared to saving the entire migration kernel, and the GDM image is computed by a dot product of the migration operator with the recorded shot gathers. The outstanding feature of skeletonized least-squares GDM is that in the least-squares mode, the migration kernel is reused and does not require new solutions to the wave equation. Hence, least-squares GDM might not be significantly more costly than standard RTM. If this procedure is combined with multisource technology, I believe that the cost of it is much less than that of conventional RTM. This method can also be used with one-way wave equation methods such as phase-shift migration and is applicable for rapid migration velocity analysis as well.
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