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Unsupervised Local Primary‐and‐Multiple Orthogonalization Learning for Seismic Multiple Leakage Estimation.

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Bibliographic Details
Title:	Unsupervised Local Primary‐and‐Multiple Orthogonalization Learning for Seismic Multiple Leakage Estimation.
Authors:	Zhang, Dong¹ (AUTHOR) dongzhang1991@gmail.com, Rui, Zhenhua² (AUTHOR)
Source:	Geophysical Prospecting. Mar2026, Vol. 74 Issue 3, p1-11. 11p.
Subject Terms:	Orthogonalization, Machine learning, Adaptive filters, Imaging systems in seismology, *Attenuation of seismic waves
Abstract:	Seismic multiple attenuation remains a critical challenge in marine processing, particularly when separating primaries from multiples with complex wavefronts or interfering patterns. Conventional adaptive subtraction methods, which rely on linear matching filters to estimate multiples, often suffer from primary damage or multiple leakage. While deep learning offers powerful non‐linear mapping capabilities, standard supervised approaches are impractical for field data due to the lack of ground truth labels. To address this, we propose an unsupervised local primary‐and‐multiple orthogonalization learning (ULPMOL) framework specifically designed for high‐fidelity seismic multiple leakage estimation. This method redefines the neural network as a non‐linear matching filter that predicts the complex multiple leakage term directly from a reference multiple model. We eliminate the need for labelled training data by integrating a local orthogonality loss that enforces the decorrelation of primaries and multiples within local windows. To further address the severe pattern overlap problem where primary energy is erroneously extracted, we introduce an optional secondary unsupervised learning network that reshapes the extracted leakage, filtering out the coherent primary energy and isolating the multiple leakage. We validate the framework on a complex synthetic lens model and two field datasets from the North Sea, targeting both surface‐related multiples in the Nelson field and internal multiples in the Norwegian field depth images. The results demonstrate that the ULPMOL framework achieves results comparable to or slightly better than the state‐of‐the‐art deterministic local primary‐and‐multiple orthogonalization (LPMO) algorithm. In regions where primaries and multiples do not overlap, ULPMOL is capable of extracting residual multiples with high accuracy and resolution. In overlapping areas, it can estimate the residual multiples to a reasonable extent. Furthermore, the ULPMOL framework eliminates the computational burden of iterative shaping regularization within LPMO, offering a robust and efficient solution for adaptive multiple estimation. [ABSTRACT FROM AUTHOR]
Database:	Energy & Power Source

Description
Abstract:	Seismic multiple attenuation remains a critical challenge in marine processing, particularly when separating primaries from multiples with complex wavefronts or interfering patterns. Conventional adaptive subtraction methods, which rely on linear matching filters to estimate multiples, often suffer from primary damage or multiple leakage. While deep learning offers powerful non‐linear mapping capabilities, standard supervised approaches are impractical for field data due to the lack of ground truth labels. To address this, we propose an unsupervised local primary‐and‐multiple orthogonalization learning (ULPMOL) framework specifically designed for high‐fidelity seismic multiple leakage estimation. This method redefines the neural network as a non‐linear matching filter that predicts the complex multiple leakage term directly from a reference multiple model. We eliminate the need for labelled training data by integrating a local orthogonality loss that enforces the decorrelation of primaries and multiples within local windows. To further address the severe pattern overlap problem where primary energy is erroneously extracted, we introduce an optional secondary unsupervised learning network that reshapes the extracted leakage, filtering out the coherent primary energy and isolating the multiple leakage. We validate the framework on a complex synthetic lens model and two field datasets from the North Sea, targeting both surface‐related multiples in the Nelson field and internal multiples in the Norwegian field depth images. The results demonstrate that the ULPMOL framework achieves results comparable to or slightly better than the state‐of‐the‐art deterministic local primary‐and‐multiple orthogonalization (LPMO) algorithm. In regions where primaries and multiples do not overlap, ULPMOL is capable of extracting residual multiples with high accuracy and resolution. In overlapping areas, it can estimate the residual multiples to a reasonable extent. Furthermore, the ULPMOL framework eliminates the computational burden of iterative shaping regularization within LPMO, offering a robust and efficient solution for adaptive multiple estimation. [ABSTRACT FROM AUTHOR]
ISSN:	00168025
DOI:	10.1111/1365-2478.70164