Least-squares migration has been shown to improve image quality compared to the conventional migration method and it is one of the hot spot of present research. Phase encoding technique can effectively improve the computation efficiency. But, conventional LSRTM not takes into account the random nature of the gradients. In this abstract, we extend the stochastic optimization approach to LSRTM, and find that the new methods perform better than the conventional LSRTM. Besides, an isotropic acoustic LSRTM is a potential technique of seismic imaging, but the imaging result is not accurate when dealing with model in TTI media. Therefore, we extended the isotropic acoustic LSRTM is to anisotropic acoustic LSRTM in TTI media.


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