Closed-loop internal multiple elimination

Internal multiple suppression is a crucial and challenging task in seismic data processing, aiming to mitigate the impact of internal multiples on imaging and seismic interpretation. A major difficulty arises because internal multiples often overlap with primaries, particularly in complex geological settings, making their accurate suppression difficult. Conventional internal multiple elimination (IME) methods rely on adaptive subtraction, which may cause primary energy loss in regions where primaries and internal multiples overlap. To address this issue, this paper derives internal multiple suppression formulas based on the well-known feedback model from a novel perspective. On this basis, we propose a Closed-Loop Internal Multiple Elimination (CL-IME) method. By formulating a new objective function, the proposed CL-IME method accurately estimates and suppresses internal multiples through inversion, thereby avoiding the primary energy loss associated with adaptive subtraction. Numerical experiments demonstrate that CL-IME achieves significantly higher accuracy than conventional IME in suppressing internal multiples, particularly in regions where primaries and multiples strongly overlap, thereby providing a more reliable approach for seismic data processing in complex structural settings.