Full Wavefield Reconstruction and Full Waveform Inversion

Two-way reverse time extrapolation of the recorded seismic data is the essential step in seismic reverse time migration (RTM). Various RTM algorithms have been developed to produce accurate image locations rather than correct amplitude information because of inadequate compensation of attenuation, dispersion, and transmission losses. Thus, there is a need to evaluate the requirements, and determined the theoretical feasibility, of true amplitude recovery of recorded seismic data. We apply analytic Zoeppritz equations and numerical elastodynamic finite differencing to evaluate the validity and requirements for true amplitude recovery of incident plane and spherical waves, respectively. An application of true amplitude recovery to remove downgoing reflections produced at interfaces at depths shallower than a horizontal well, in reconstructed incident wavefields, is demonstrated. The migration performance also relies on the accuracy of the velocity model, which determines both the kinematics (image locations) and amplitude information. Conventional full waveform inversion (FWI) is a least-squares optimization method to update a seismic velocity model by iteratively fitting the calculated data to the observed data. We propose three FWI algorithms to update a seismic velocity model in different ways: parametric convolutional neural-network-domain FWI (CNN-domain FWI), source-domain FWI, and CNN-boosted FWI. Parametric CNN-domain FWI implements CNN within full waveform inversion to automatically capture the salient features (e.g., salt bodies) in a given initial training velocity model, and then concentrate the velocity inversion on the captured features in the velocity model. Source-domain FWI updates velocity model by minimizing source-domain misfit function, which contains the least-squares virtual source artifacts. Virtual source artifacts are created by replacing the propagating source wavefield by the forward-time observed data at the receiver positions, as a data-residual constraint. Similar to conventional FWI, source domain FWI can be implemented in either the frequency or the time domain, which is unlike previous source-domain solutions, which have to be implemented only in the time domain, to solve the normal equations. CNN-boosted FWI applies CNN as a weak learner, at each iteration, to approximate the model residuals, by minimizing the data residuals. In addition to finding the optimal step length, just as gradient-descent FWI does, CNN-boosted FWI fixes this optimal step length and optimizes the CNN, which is originally trained to approximate the negative gradients at each iteration, to update the velocity model. CNN-boosted FWI inverts for the velocity model with lower model and data errors than the gradient-descent FWI does.