Most current full-waveform inversion (FWI) algorithms minimize the data residuals to estimate a velocity model based on the assumption that the updated model is the sum of a background model and an estimated model perturbation. We have performed reparameterization of the initial velocity model, by the weights in a convolutional neural network (CNN), to automatically capture the salient features in the initial model, as a priori information. The prior information in CNN weights is iteratively updated as regularization to constrain the CNN-domain inversion to refine the features captured in CNN pretraining by reducing the data misfit. Synthetic examples using a 1D increasing velocity function v(z) and a 2D smoothed version of the correct Marmousi2 model as initial models indicate that the performance of the CNN-domain FWI depends on the existence and accuracy of the prior information in the initial velocity model (i.e., whether features whose positions, shapes, and values are present in the correct model are approximately included in the initial model). Forty different sets of randomly initialized CNN weights are used to parameterize and test CNN-domain FWI, using a 2D smoothed Sigsbee model as the initial velocity model. All 40 sets invert for the Sigsbee salt body more accurately (with a smaller standard deviation of the final rms model errors), by CNN-domain FWI, than FWI does. Features that are not represented within the CNN hidden layers in the initial velocity model, and so cannot be recovered by CNN-domain FWI, can be recovered using the final CNN-domain FWI velocity model as the starting model in a subsequent conventional FWI.

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is a powerful algorithm to perform a least squares non-linear data-fitting optimization to estimate a high-resolution velocity model. The conventional FWI gradient, obtained by zero-lag cross-correlating both the source and residual wavefields, can be divided into three components (Alkhalifah, 2014;Wu & Alkhalifah, 2015;Xu et al., 2012;Yao et al., 2020): (a) the low-wavenumber components obtained from the direct, refracted, and diving waves, (b) the low-wavenumber (tomographic) components associated with reflections and (c) the high-wavenumber (migration) components associated with reflections. Because of the shallower penetration depth of the direct, refracted, and diving waves (relative to the reflected waves) and also because of the overlapping of their wavepaths in both the source and residual