\justifying Full-waveform inversion (FWI) is a non-linear optimization algorithm 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 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 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 based on the more representative training dataset, which is obtained from the latest CNN-predicted velocity model by the proposed spatially-constrained divisive hierarchical k-means parcellation method. The more representative training velocity models are, the more accurate CNN-predicted velocity model. Synthetic examples using different portions of the Marmousi2 P-wave velocity model show that CNN-RWI inverts for both the shallower and deeper velocity model more accurately than the conjugate-gradient FWI (CG-FWI) does. 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.

Accurate Q (quality factor) structures can provide important constraints for characterizing subsurface hydrocarbon/water resources in exploration geophysics and interpreting tectonic evolution of the Earth in earthquake seismology. The attenuation effects on seismic amplitudes and phases can be included in forward and inverse modeling by invoking a generalized standard linear solid rheology. Compared to traditional ray-based methods, full-waveform adjoint tomography, which is based on numerical solutions of the visco-elastodynamic wave equation, has the potential to provide more accurate Q models. However, applications of adjoint Q tomography are impeded by the computational complexity of Q sensitivity kernels, and by strong velocity-Q trade-offs. In this study, following the adjoint-state method, we show that the Q (P and S wave quality factors QP and QS) sensitivity kernels can be constructed efficiently with adjoint memory strain variables. A novel central-frequency difference misfit function is designed to reduce the trade-off artifacts for adjoint Q tomography. Compared to traditional waveform-difference misfit function, this misfit function is less sensitive to velocity variations, and thus is expected to produce fewer trade-off uncertainties. The multiparameter Hessian-vector products are calculated to quantify the resolving abilities of different misfit functions. Comparative synthetic examples are given to verify the advantages of this new misfit function for adjoint QP and QS tomography. We end with a 3D viscoelastic inversion example designed to simulate a distributed acoustic sensing/vertical seismic profile survey for monitoring of CO2 sequestration.