Accelerating Marchenko Imaging by Self‐Supervised Prediction of Focusing Functions

• Published in: Journal of geophysical research. Machine learning and computation Vol. 2; no. 3
• Main Authors: Wang, N., Ravasi, M., Alkhalifah, T.
• Format: Journal Article
• Language: English
• Published: 01.09.2025
• DOI: 10.1029/2025JH000673
• ISSN: 2993-5210

Marchenko redatuming retrieves full‐wavefield Green's functions, which can be used to generate subsurface images free from artifacts caused by internal multiples. This is achieved by solving the Marchenko equations for focusing functions, which establish a link between Green's functions and the surface reflection response. However, the calculation of focusing functions is computationally intensive, especially for large‐scale imaging areas. To address this challenge, we propose a self‐supervised learning framework for estimating focusing functions. Specifically, a U‐Net network is trained on a small subset of precomputed focusing functions derived from the conventional iterative scheme. The network aims to learn the prediction of the final up‐going focusing function from its initial estimate. The predicted up‐going focusing function is subsequently used to calculate the down‐going focusing function, as well as Green's functions using the Marchenko physical relationships. This hybrid approach leverages data‐driven predictions and physical constraints to enhance computational efficiency and accuracy. The method is initially validated using synthetic data sets, demonstrating the consistency between the predicted focusing functions and those obtained via the iterative scheme. The corresponding subsurface images are also shown to be consistent, revealing the reliability of the proposed method. The proposed method is further applied to the Volve field data, yielding results that are comparable to those of the conventional iterative method; this verifies its robustness to field‐data scenarios. Both synthetic and field examples indicate a significant reduction in computational time, highlighting the potential of this approach in making the Marchenko method more practical for large‐scale seismic imaging tasks. Seismic imaging helps us detect and visualize what is underground using echoes of sound waves—similar to how an ultrasound works for the human body. One powerful technique for such imaging is the Marchenko method, which produces clearer images by removing unwanted noise caused by waves bouncing inside the Earth, like multiple echoes. However, the Marchenko method is computationally expensive, making it difficult to use for large‐scale applications. To address this challenge, we used machine learning, a type of artificial intelligence, to speed up the Marchenko process. Specifically, we trained a model called a U‐Net to learn how to perform part of the Marchenko method more efficiently. Instead of doing complex calculations each time, our approach learns from a small set of examples and quickly predicts the needed wave patterns to apply the Marchenko method. We tested our approach on both synthetic and field data sets. The results show that it produces images just as accurate as the traditional method, but up to 50 times faster. This makes advanced seismic imaging more practical for large‐scale projects in both research and industry. A self‐supervised learning framework is proposed to accelerate Marchenko imaging, achieving up to 50 times reduction in computational time The integration of physical constraints, improves the robustness and accuracy of the predicted focusing functions The framework relies only on data from the target imaging area, eliminating the need for external data sets and simplifying implementation