Deep learning-based closed-loop surface-related multiple elimination

Abstract Surface-related multiple elimination (SRME) is a widely adopted method in suppressing surface-related multiples. However, when primaries and multiples interfere, the adaptive subtraction process in SRME often results in the loss of primary energy. To address this limitation, the closed-loop SRME (CLSRME) method is developed by using the advantages of waveform inversion, enabling more accurate multiple suppression without relying on the adaptive subtraction. Nevertheless, the inversion process incurs significant computational costs, hindering its practical application. To resolve both the primary energy loss in SRME and the high computational cost of CLSRME, a deep learning-based CLSRME (DL -CLSRME) method is proposed in this paper. This method takes advantage of the high computational efficiency and robust nonlinear mapping capacity of deep learning, enabling accurate and cost-effective internal multiple suppression. Based on the theories of SRME and CLSRME, we first derived the relationship between the predicted multiples using SRME and the accurate multiples estimated by CLSRME, thereby establishing the mapping between the two theoretically. Then, a U-net model is trained to learn the mapping from predicted multiples to actual multiples. Once trained, the model enables efficient and accurate multiple estimation, which is then subtracted from the seismic records to achieve effective multiple suppression. Numerical experiments and field data applications demonstrate that the proposed DL -CLSRME achieves a favourable balance between accuracy and efficiency compared with the conventional methods, highlighting its potential for practical seismic data processing.