Least squares Marchenko imaging

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Multiple reflections significantly influence seismic migration because they can lead to spurious events in traditional methods, including reverse time migration and Kirchhoff migration. Marchenko imaging represents a transformative advancement in the field of seismic migration that relocates seismic data containing internal multiples to accurate subsurface locations. Through the continuous pursuit of methodological refinement, we developed an innovative approach: incorporation of the Marchenko method within a least-squares migration framework, named least-squares Marchenko imaging (LSMI), based on the steepest descent method to minimize the L1 norm of gradient images. In the LSMI, to solve the problem that the conventional Born approximation can only simulate primary waves, we used the Marchenko Green’s function and the Born approximation to construct a Marchenko demigration operator, which can successfully simulate synthetic seismic data containing internal multiples. However, Marchenko demigration based on the Born approximation requires a large amount of calculation, and multiple iterations increase the computation time. Therefore, we introduce a parallel-computing framework implemented in the frequency domain to improve the computational efficiency of the Marchenko demigration. We partition the frequency-domain-transformed Green’s function into discrete chunks and implement parallel computation. This parallel processing significantly accelerates the Marchenko demigration process. The effectiveness of the proposed method is validated by applying it to a layered model. The experimental results show that LSMI converges with the L1 norm. Moreover, the superiority of our method over conventional Marchenko imaging is evident from its notable enhancement related to artifact suppression, resolution improvement, and illumination compensation. To further validate the effectiveness of our proposed method, we conducted additional experiments on the Sigsbee2A model, demonstrating that our method is also effective for this complex model. This is a novel approach to seismic migration, particularly in areas with internal multiples.