Multiple elimination is a crucial step in seismic data processing. Surface-related multiple elimination algorithms are well-developed, while most currently used internal multiple elimination algorithms generally require manual selection of the layers that generate internal multiples. The Marchenko theory offers a fully data-driven approach to eliminate internal multiples, necessitating solely a background velocity model or the original data. This method involves conducting correlation and convolution calculations on the input seismic data in order to acquire the primary, thereby accomplishing the internal multiple elimination, which obviates the necessity of manually selecting underground reflection layers, and its calculation process is entirely driven by the seismic data. However, like other data-driven methods, the Marchenko method mandates a full wave-field as an input. Unfortunately, actual seismic data frequently fail to satisfy this prerequisite, missing traces can greatly compromise the result of internal multiple elimination. The focal transform is introduced to address this issue in this paper. This transform utilizes the background velocity to construct a focal operator. It can map missing seismic data to the noisy region in the focal domain, and by removing the noise, seismic data reconstruction can be achieved. Therefore, we can combine the focal transform with MME to eliminate multiples while achieving seismic data reconstruction simultaneously. The experiment from the SMAART model demonstrates its validity and practicability.

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