Surface-related multiple attenuation based on self-supervised deep neural network with local wavefield characteristics

Multiple suppression is a very important step in seismic data processing. To suppress surface-related multiples, we propose a self-supervised deep neural network method based on a local wavefield characteristic loss function (SDNN-LWCLF). The first and second input data and the output data of the self-supervised deep neural network (SDNN) are the predicted surface-related multiples, the full-wavefield data, and the estimated true surface-related multiples, respectively. The role of the SDNN is to replace the convolutional filter part of adaptive subtraction. Although there are differences in amplitudes and phases between the predicted and true surface-related multiples, the predicted surface-related multiples correspond kinematically to the true surface-related multiples and can be mapped to the estimated true surface-related multiples by the SDNN. The SDNN-LWCLF uses a local wavefield characteristic (LWC) loss function with physical properties to constrain the nonlinear optimization process. The LWC loss function is composed of the mean-absolute-error (MAE) and local normalized cross-correlation (LNCC) loss functions. LNCC can measure the local similarity between the estimated multiples and the estimated primaries. By minimizing the LWC loss function, the MAE loss function corrects amplitudes and phases of the predicted surface-related multiples to their true values, and the LNCC loss function automatically checks and reduces the leaked multiples and residual primaries in the estimated true surface-related multiples. Our proposed SDNN-LWCLF method does not need label data, such as true primaries and true surface-related multiples, which are usually unavailable in real-world applications. Therefore, the SDNN-LWCLF solves the problem of missing training data. Synthetic and field data examples demonstrate that our proposed method can well suppress the surface-related multiples, and its suppression effect is better than both the traditional L1-norm adaptive subtraction method and the SDNN method only based on the MAE loss function (SDNN-MAELF).