An attractive feature of finite-difference modeling in the frequency domain is the low recomputation cost to simulate seismic waves for many sources through the same velocity model. However, it is time consuming if many frequencies are involved for solving the linear wave equations, particularly, for large 3D velocity models. We propose accelerating the modeling by applying deep learning. Because similarity appears among the wavefields in near frequencies, we can extract similar features and reconstruct the unknown wavefields by deep learning. We compute fewer frequency-domain wavefields with a large frequency interval by conventional modeling methods, such as finite-difference methods, and then interpolate more frequency-domain wavefields with a small frequency interval by applying deep learning. Numerical examples demonstrate that the U-Net, which is trained by the data on 10 2D simple-layered models, can be used to interpolate the data on SEG Advanced Modeling models and also can be used to interpolate the data on the 3D layered model and 3D overthrust model. A series of tests on perturbation models prove that the U-Net performance is still good when the root-mean-square value of the velocity model perturbation relative to the initial model is up to 15%. Compared with traditional modeling methods, the computational time of interpolating by applying deep learning is negligible, especially for 3D models. After the network is trained, the acceleration strategy helps to reduce the runtime by approximately 50% for a modeling problem because the U-Net can be used to interpolate 50% of the data that would otherwise need to be modeled. Although training the model will take some time, good generalization of the U-Net, especially for 3D problems, enhances its benefits on the application for frequency-domain forward modeling.

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