Generative adversarial network-enhanced directional seismic wavefield decomposition and its application in reverse time migration

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Reverse time migration (RTM) is an accurate method for imaging complex geologic structures without imposing any dip limitations. However, a large amount of high-amplitude low-frequency noise, which is mainly generated by the crosscorrelation of source and receiver wavefields propagating in the same directions, seriously contaminates the image quality. The causal imaging condition with separated up- and downgoing wavefields is an effective approach to reduce these low-frequency artifacts. Explicit up- and downgoing wavefield decomposition based on the Hilbert transform is computationally expensive due to additional wavefield extrapolation and storage for the imaginary parts. Directionally propagating wavefields have distinctive kinematic patterns such as traveltime and wavefront curvature, which provide us an opportunity to implement the wavefield decomposition using the statistical neural network method. Using extrapolated wavefields as the input and the decomposed up-, down-, left-, and rightgoing wavefields as the labeled data, we train a pair of generative adversarial networks to predict the directional wavefields. The training data sets are generated using seismic full-waveform modeling and explicit wavefield decomposition based on the Hilbert transform. Then, the decomposed directional wavefields are incorporated into a novel imaging condition that depends on the subsurface dip angles to compute the reflectivity perpendicular to the reflectors. Numerical experiments demonstrate that our method can produce accurate directional wavefield decomposition results and high-quality reflectivity images without low-wavenumber artifacts.