Adaptive Feedback Convolutional‐Neural‐Network‐Based High‐Resolution Reflection‐Waveform Inversion

Abstract Full‐waveform inversion (FWI) applies non‐linear optimization to estimate the velocity model by fitting the observed seismic data. With a smooth starting velocity model, FWI mainly inverts for the shallower background velocity model by fitting the observed direct, diving and refracted data, and updates the interfaces by fitting the observed reflected data. As the deeper parts of background velocity model cannot be effectively updated by fitting the reflected data in FWI, the deeper interfaces are less accurate than the shallower interfaces. To update the deeper background velocity model, many reflection‐waveform inversion (RWI) algorithms were proposed to separate the tomographic and migration components from the reflection‐related gradient. We propose a convolutional‐neural‐network‐based reflection‐waveform inversion (CNN‐RWI) to repeatedly apply the iteratively updated convolutional neural network (CNN) to predict the true velocity model from the smooth starting velocity model (the tomographic components), and the high‐resolution migration image (the migration components). The CNN is iteratively updated by the more representative training data set, which is obtained from the latest CNN‐predicted velocity model by the proposed spatially constrained divisive hierarchical k‐means parcellation method. The more representative the training velocity models are, the more accurate the CNN‐predicted velocity model becomes. Synthetic examples using different portions of the Marmousi2 P‐wave velocity model show that CNN‐RWI inverts for both the shallower and deeper parts of velocity models more accurately than the conjugate‐gradient FWI (CG‐FWI). Both the CNN‐RWI and the CG‐FWI are sensitive to the accuracy of the starting velocity model and the complexity of the unknown true velocity model.