Least-squares reverse time migration (LS-RTM) for complex fields imaging becomes an increasingly popular imaging method. It also enjoys some other advantages. For example, it is capable of attenuating migration artifacts, compensating the image amplitude which is distorted by geometrical spreading and unbalanced illumination, improving resolution via compressing the seismic source wavelet and it can also handle incomplete and noisy data. However, the massive

computational overhead of LS-RTM poses a big challenge for modern super-computers and its computation time can easily exceed hundreds of hours. To overcome the shortcomings

mentioned above, we propose a fast alternative method for LS-RTM. The new approach is formulated in the model (image) domain. The Hessian matrix is approximated via

the superposition of Kronecker products which honour the block-band character of the Hessian matrix. We name the Kronecker product-based new imaging method as

KLSRTM. Our numerical tests show the computation time is reduced significantly and the result of the proposed method is comparable to the output of conventional LS-RTM. Also,

approximating the Hessian matrix by a superposition of Kronecker products permits for efficient exploration of tradeoff parameters for regularized LS-RTM as the computation cost for solving the KLSRTM is trivial after Kronecker factors are estimated.


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