Physics-Guided Deep Learning for Adaptive Surface-Related Multiple Subtraction

Abstract

Surface-related multiple elimination is a fundamental step in seismic data processing, typically relying on a two-stage procedure: multiple prediction followed by adaptive subtraction. While the prediction step is physically robust, the adaptive subtraction stage often struggles to resolve complex non-stationary discrepancies and overlapping primary-multiple events using conventional energy minimization criteria. In this paper, we propose a physics-guided deep learning (PGDL) framework to address these limitations by treating adaptive subtraction as a non-linear, physics-constrained mapping task. We utilize a U-Net architecture with a specialized dual-channel input: the original recorded full wavefield and the globally estimated multiples derived from the wave equation–based multi-dimensional convolution. By explicitly incorporating the multiple models, we inject robust kinematic constraints (i.e., physics) into the network, allowing the learning process to focus on the non-linear residual mapping required to correct amplitude and phase errors rather than learning wave propagation from scratch. We validate the proposed framework through three comprehensive scenarios: (1) synthetic-to-synthetic generalization, (2) field-to-field application using pseudo-labels and (3) a cross-data-distribution test training on synthetic data and applying it to field data. Our results demonstrate that the PGDL framework effectively suppresses surface-related multiples while preserving weak primary energy that is often damaged by traditional methods. Furthermore, we show that a transfer learning strategy using minimal field data effectively bridges the data distribution gap between synthetic training sets and real-world field acquisition, offering a scalable and computationally efficient way for industrial deployment.