LAUSR

Surface-related multiples are generally removed as noise. To suppress surface-related multiples, we propose an unsupervised deep neural network approach based on ensemble learning (UDNNEL). The unsupervised deep neural network (UDNN) has excellent nonlinear mapping ability, which maps the predicted surface-related multiples to true surface-related multiples, thus completing the separation and estimation of multiples and primaries. UDNN consists of three deep neural networks (DNNs), one input data, six outputs, and six pseudo-labels (PLs). In practical use, input data are the predicted surface-related multiples, PLs consist of full-wavefield data and 0 matrices, and outputs are the desired results of estimated true surface-related multiples and differences between these desired results. Input data, one DNN, and corresponding output data are combined into a single base learner. Each base learner corrects amplitudes and phases of the predicted surface-related multiples and maps predicted multiples to true surface-related multiples under the minimization of the total loss function. The principle ensures that our UDNNEL method does not need true primaries or true multiples as training data and solves the problem of missing training datasets. Ensemble learning combines the advantages of three base learners and integrates the nonlinear optimization capabilities of three DNNs to achieve better multiple suppression effectiveness than a single base learner. Therefore, UDNNEL is better than UDNN based on a single base learner (UDNNSBL). Two synthetic data examples verify that our proposed method has a good surface-related multiple suppression effectiveness. Another field data example demonstrates that our proposed method can efficiently suppress multiples under complex conditions.