Summary

The theory for least-squares phase-encoded GDM is presented. The key idea is to solve the wave equation only once to get the receiver-side Green's function and the source-side Green's function. The multisource migration kernel is obtained through convolution of the receiver-side Green's function and the source-side Green's function followed by phase-encoding. Both storage and I/O costs of migration kernel are greatly reduced due to phase-encoding, and the multisource GDM image is computed by a dot product of the multisource migration kernel with the phase-encoded shot gathers. The outstanding feature of least-squares phase-encoded GDM is that the multisource migration kernel is reused at each iteration and does not require new solutions to the wave equation. Hence, least-squares phase-encoded GDM might not be significantly more costly than standard RTM.

However, there are some limitations with GDM compared to RTM. Even with a phase-encoding scheme, the size of the multisource migration kernel is still a function of number of receivers, number of time samples and the computational model size. In the 2D case, it takes hundreds of gigabytes of storage, and loading all of the migration kernels at each iteration is time consuming. For 3D, the storage cost of the migration kernel will be many times more than the 2D case. Therefore this method is not ready for use with 3D surveys except in a target oriented mode. Future work will be focused on further compression of the multisource migration kernel and multisource cross-talk noise elimination.

=2