基于空间—波数域联合深度学习的数值频散压制

有限差分法是地震勘探领域常用的波场数值模拟方法，当空间网格间距大或使用低阶差分算子时会产生严重数值频散现象，影响模拟精度。为此提出一种基于联合学习深度卷积神经网络的数值频散压制方法，该方法使用卷积神经网络自适应提取波场特征进行频散校正。首先，利用波场数据在空间域和波数域的稀疏特征构建残差学习卷积神经网络，提取波场的主要特征；其次，基于L₁范数对网络模型进行稀疏优化，降低模型的复杂度，增加网络的泛化能力；最后，构造联合目标优化函数，使网络在空间—波数域联合约束的语义下学习频散压制的非线性逼近能力。将所提方法应用到不同模型正演的波场数据，结果表明：该方法可有效保护地震信号、压制频散；将网络与迁移学习结合，用于新模型的正演数据，可取得较好效果。与同类算法相比，该方法可以提高粗网格的计算精度、降低计算成本，所得波场快照具有较高的信噪比。

Numerical dispersion suppression based on joint deep learning in the space and wave number domains

The finite-difference scheme is commonly applied in seismic prospecting for numerical simulation of wavefields. The simulation accuracy, however, is affected by the serious numerical dispersion caused by spatial coarse grids or low-order operators of difference. In this paper, a numerical dispersion suppression method based on the joint learning of deep convolutional neural networks (CNNs) is proposed, which uses CNNs to adaptively extract wavefield features for dispersion correction. Firstly, the sparse features of the wavefield data in the space and wavenumber domains are used to build a CNN based on residual learning for the extraction of the main features of the wavefield data. Secondly, the L₁ norm is used for the sparse optimization of the network model, which can reduce the complexity of the model and enhance the generalization ability of the network. Finally, a joint objective optimization function is constructed to enable the network to learn the non-linear approximation capability of dispersion suppression under the semantics of the joint space-wavenumber domain constraints. The proposed method is applied to wavefield data from different forward models, and the results reveal that the method can effectively protect seismic signals and suppress dispersion; the combination of the network with migration learning is applied to the data from the new forward model, and good results can be achieved. Compared with similar algorithms, the proposed method boasts higher computational accuracy of coarse grids, lower computational costs, and a higher signal-to-noise ratio (SNR) of the obtained wavefield snapshot.