Accelerating Marchenko Imaging by Self-Supervised Prediction of Focusing Functions

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 pre-computed 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 a synthetic dataset, 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.