3-D Frequency-Domain Acoustic Wavefield Simulations Based on Deep Transfer Learning Preconditioned BiCGSTAB Solvers

The problem of low efficiency in solving the linear system is one of the main topics for 3-D frequency-domain modeling. Except for a relatively large problem scale, it is also attributed to the denser, indefinite, and severely ill-posed impedance matrix in high-frequency situations. To address these issues, the deep neural network (DNN) is trained to construct effective preconditioners incorporated with the Krylov subspace method (typically, BiCGSTAB) for solving the linear system. Compared with traditional approaches, the deep learning-based preconditioned method can overcome adverse properties of the impedance matrix to sufficiently enhance the convergence and achieve the acceleration effects. Furthermore, to improve the efficiency enough, the transfer learning is employed to suppress the training cost as much as possible for solving a set of linear systems with multiple frequencies and multiple sources. To examine the effectiveness of this deep transfer learning method, we conduct numerical experiments of frequency-domain acoustic wavefield simulation in several typical 3-D media models and compare with other classical solvers. Then, the obtained frequency-domain wavefields during a certain frequency range are used to synthesize the time-domain wavefields, which presents multifrequency and multisource problem case. Various results illustrate the correctness and superiority of the proposed method in 3-D wavefield simulation.