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Fast Least-Squares Reverse Time Migration Via Approximating the Hessian as the Sum of Kronecker Products
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 81st EAGE Conference and Exhibition 2019, Jun 2019, Volume 2019, p.1 - 5
Abstract
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.