Deep learning preconditioned methods based on generative adversarial networks for frequency-domain reverse time migration

Abstract To overcome the difficulty in efficiently solving the ill-posed linear systems with multi-source terms in frequency-domain reverse time migration, a kind of preconditioned iterative method combined with deep learning is proposed in this paper. To be specific, the generative adversarial networks are used to construct efficient preconditioners accelerating the convergence of classical Krylov subspace methods for wavefield extrapolation during the migration process. By employing the powerful feature extraction capabilities of this network architecture, the constructed preconditioned methods can get rid of the adverse mathematical properties of the impedance matrix. Compared to single convolutional neural networks, the generative adversarial network architecture adaptively optimizes the generative training process by introducing a discriminator, which can form an adversarial training mechanism. This mechanism enables the generator to effectively capture the structural dependency and the distribution features in sample data, thereby facilitating the construction of efficient preconditioners by neural networks. To evaluate the effectiveness of the proposed method, migration experiments are conducted by using several representative media models and some classical solvers are considered for comparison. The obtained numerical results illustrate that this method can effectively improve the efficiency of frequency domain reverse time migration while ensuring the accuracy of the solution. Using Sigsbee2B model as an example, generative adversarial network-based preconditioned iterative solver reduces the total computational time by approximately 42.33%, 40.74%, and 23.97% compared with the original iterative method, incomplete-factorization preconditioner, and the single-network preconditioner, respectively.