The time-lapse imaging problem is addressed using least-squares shot-profile migration. The procedure for designing forward (de-migration) and adjoint (migration) operators of shot-profile wave-equation migration algorithm is explained. The least-squares optimization of the problem is achieved using conjugate gradients. Two main approaches for least-squares shot-profile migration of time-lapse data namely, inversion of difference data and joint inversion, are discussed. Some practical considerations for performance of least-squares shot-profile migration are investigated using synthetic data examples. Also, a synthetic data examples is provided for examining the time-lapse shot-profile migration of difference data.
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