Convolutional-neural-network-based reflection-waveform inversion

14 Full-waveform inversion (FWI) is a non-linear optimization algorithm to estimate the 15 velocity model by fitting the observed seismic data. With a smooth starting velocity model, 16 FWI mainly inverts for the shallower background velocity model by fitting the observed di17 rect, diving and refracted data, and updates the interfaces by fitting the observed reflected 18 data. As the deeper background velocity model cannot be effectively updated by fitting the 19 reflected data in FWI, the deeper interfaces are less accurate than the shallower interfaces. 20 To update the deeper background velocity model, many reflection-waveform inversion (RWI) 21 algorithms were proposed to separate the tomographic and migration components from 22 the reflection-related gradient. We propose a convolutional-neural-network-based reflection23 waveform inversion (CNN-RWI) to repeatedly apply the iteratively-updated CNN to predict 24 the true velocity model from the smooth starting velocity model (the tomographic compo25 nents), and the high-resolution migration image (the migration components). The CNN 26 is iteratively updated based on the more representative training dataset, which is obtained 27 from the latest CNN-predicted velocity model by the proposed spatially-constrained divisive 28 hierarchical k-means parcellation method. The more representative training velocity models 29 are, the more accurate CNN-predicted velocity model. Synthetic examples using different 30 portions of the Marmousi2 P-wave velocity model show that CNN-RWI inverts for both 31 the shallower and deeper velocity model more accurately than the conjugate-gradient FWI 32 (CG-FWI) does. Both the CNN-RWI and the CG-FWI are sensitive to the accuracy of the 33 starting velocity model and the complexity of the unknown true velocity model. 34 Plain Language Summary 35 Full waveform inversion (FWI) is generally a combination of tomography and migra36 tion techniques. However, the conventional FWI cannot estimate the deeper background 37 velocity model accurately. By separating the tomographic and migration components, 38 reflection-waveform inversion (RWI) effectively utilizes the tomographic component to up39 date the deeper background velocity model. We propose a convolutional-neural-network40 based reflection-waveform inversion (CNN-RWI) to combine the smooth starting velocity 41 model (the tomographic component) and the corresponding migration image (the migration 42 component), to accurately predict both the background velocity and interfaces in the veloc43 ity model. The conventional CNN application predicts the velocity model, by following the 44 training dataset preparation, CNN training, and the CNN prediction, once only. In contrast, 45 the CNN-RWI contains an innovative outer loop to iteratively update the CNN to predict 46 the more accurate velocity model from the original starting velocity model and migration 47 image, by dynamically recreating the more representative training velocity models for the 48 CNN training. We also propose a novel spatially-constrained divisive hierarchical k-means 49 parcellation method to obtain the more representative velocity models by parcellating the 50 latest CNN-predicted velocity model into a model basis. 51