Wave-equation Common Image Gathers and their Combination with Nonlinear Ray-based Tomography

It has been reported that if the migration velocity is erroneous, then different migrations lead to different RMO in common image gathers. However, it is widely assumed that the travel-time along the ‘migration ray’ is the same as the actual travel-time for the corresponding source and receiver positions. Travel-times are kinematic invariants for Kirchhoff migration, but not generally for WE migration. In the current paper we show that (i) RMO from dual domain WE CS migration is the same as that for double-square-root migration, (ii) for both migrations, RMO of offset slowness gathers satisfies the condition of preserving the plane-wave travel-times (PWTT), (iii) for CS migration, offset-slowness gathers obtained by plane-wave decomposition from source and receiver sides are the same as those calculated by the Radon transform of extended images, and finally, (iv) PWTT are used when combining RMO from CS WE migration with non-linear ray-based tomography. The described tomography does not involve any linearization and does not require closeness of the initial model to the true one. We illustrate the approach with a synthetic 3D example, where we obtain accurate inversion results after a single iteration of migration, RMO analysis, reconstruction of PWTT, and tomography.