Surface-Related Multiple Suppression Based on Field-Parameter-Guided Semi-Supervised Learning for Marine Data

Surface-related multiple suppression is a critical step in seismic data processing, while traditional adaptive matching subtraction methods often distort primaries, resulting in either the leakage of primaries or the residue of surface-related multiples. To address these challenges, we propose a field-parameter-guided semi-supervised learning (FPSSL) method to more effectively eliminate surface-related multiples. Field parameters refer to the time–space coordinate information derived from the seismic acquisition system, including offsets, trace spaces, and sampling intervals. These parameters reveal the relative positional relationships of seismic data in the time–space domain. The FPSSL framework comprises a supervised network module (SNM) and an unsupervised network module (USNM). The input and output data of the SNM are a small sample of full wavefield data and the weights of a polynomial function, respectively. A linear weighted sum method is employed to represent the SNM outputs (weights), the full wavefield data, and field parameters as a polynomial function of the primaries, which is matched with adaptive subtraction label data. The trained SNM generates preliminary estimates of the primaries and multiples with improved lateral continuity from full wavefield data, both of which are used as inputs to the USNM. The USNM is essentially an optimization operator that refines the underlying nonlinear mapping relationship between primaries and full wavefield data using the local wavefield feature loss function, thereby obtaining more accurate prediction results with respect to primaries. Examples from synthetic data and real marine data demonstrate that the FPSSL method surpasses the traditional L1-norm adaptive subtraction method in suppressing multiples, significantly reducing the leakage of primaries and the residuals of surface-related multiples in the estimated demultiple results. The effectiveness and efficiency of our proposed method are verified through two sets of synthetic data and one marine data example.