Summary Full waveform inversion (FWI) updates the velocity model by minimizing the discrepancy between observed and simulated data. However, incomplete seismic acquisition can introduce errors that propagate through the adjoint operator, affecting the accuracy of the velocity gradient and reducing the convergence accuracy and speed. To mitigate the influence of acquisition-related noise on the gradient, we employ a convolutional neural network (CNN) to extend the velocity representation and refine the velocity model before forward simulation, thus reducing gradient noise and providing a more accurate velocity update direction. The same data misfit loss is used to update both the velocity and the network parameters, forming a self-supervised learning procedure. Here, the CNN acts as a dynamic velocity conditioner that is optimized to help fit the data. In this method, the velocity representation is extended (VRE) by combining a neural network with conventional grid-based velocities. Thus, we refer to this general approach as VRE-FWI. Synthetic and real data tests demonstrate that the proposed VRE-FWI achieves higher velocity inversion accuracy compared to traditional FWI, with only a marginal additional computational cost ∼1%.
Mu et al. (Sat,) studied this question.