Accurate multiple removal remains an important step in seismic data processing sequences. Most multiple removal methods, such as surface-related multiple elimination (SRME), consist of a multiple prediction step and an adaptive subtraction step. Due to imperfect circumstances (e.g., coarse data sampling) or built-in assumptions (e.g., 2D method versus 3D data), multiple leakage is commonly observed in the results. More aggressive adaptive multiple subtraction can reduce the leakage problem, for example, by using small local windows and a long filter length, but at the risk of severely damaging the primaries due to overfitting. In contrast, conservative adaptive subtraction with large or global windows and a short filter length can preserve most primary energy while tending to have more multiple leakage because of underfitting. Assuming that the primaries and multiples do not correlate locally in the time-space domain, our solution to this problem is to extract the leaked multiples from the initially estimated primaries using local primary-and-multiple orthogonalization (LPMO) rather than restoring the damaged primaries. Our framework consists of two steps: an initial primary estimation step and a multiple leakage extraction step. The initial step corresponds to conservative SRME (or an equivalent method) that produces the initially estimated primary and multiple models. The second step is based on LPMO to retrieve the leaked multiples from the estimated primaries via a time- and space-varying weight function that is estimated from the local correlation of predicted multiples and residual multiples in the estimated primaries with the help of shaping regularization. In this way, we can obtain a better primary model that has much less leaked multiple energy and less primary damage at the same time. We find good performance of our framework via two synthetic data examples and one field data example.

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