Physics-Informed Self-Supervised Learning With Phase Resemblance Constraint for Internal Multiple Attenuation

Internal multiple attenuation is a kind of significant coherent noise for imaging and comprehending subsurface structures from primaries in exploration seismic data. Traditional prediction-subtraction strategy heavily relies on predicting the traveltimes and matching the amplitudes for internal multiples, which poses a risk of primary distortions. Neural network methods face challenges about missing primary labels, limited applications on prestack field data, and high demand for prior information and manual intervention. To alleviate these problems, this article develops a physics-informed self-supervised neural network (SSN) to attenuate internal multiples by reducing requirements for prior information and employing the phase resemblance (PR) as the physics loss to adaptively prevent primary distortions. First, the initial internal multiples (IIMs) predicted by the virtual event (VE) method are taken as inputs for SSN to provide prior information, where no authentic primaries are required for training labels. Then, a U-shaped SSN equipped with attention mechanisms and a pyramid dilated convolution (PDC) unit is constructed to map IIMs to the estimated true internal multiples (EIMs) under a physics-informed hybrid loss. We introduce the PR constraint as the physics loss by cross-coherence of traces and kurtosis calculation to adaptively prevent primary distortions and constrain the network training. The result without internal multiples is finally obtained by subtracting EIMs from the recorded data. Synthetic and field data examples demonstrate the superior performance of our method in internal multiple suppression and primary retention ability compared with traditional workflow and the purely data-driven neural network.