Least squares migration (LSM) finds the reflectivity distribution that minimizes the regularized sum of the squared differences between the predicted and observed data. Many studies show that LSM can sometimes reduce migration artifacts due to ringy source wavelets, sparse source-receiver sampling, and weak illumination in the subsurface due to defocusing/geometric spreading of seismic waves. The most significant liability of LSM is that it costs about two rounds of migration or more, and the goal is to reduce this cost to be about that for standard migration. We now overview the current procedures of applying LSM to seismic data, point out their benefits and challenges, and suggest possible “Roads Ahead” for the improvement of LSM.


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