Full waveform inversion (FWI) is an extremely important velocity-model-building method. However, it involves a large amount of calculation, which hindsers its practical application. The multi-source technology can reduce the number of forward modeling shots during the inversion process, thereby improving the efficiency. However, it introduces cross-noise problems. In this paper, we propose a sparse constrained encoding multi-source FWI method based on K-SVD dictionary learning. The phase encoding technology is introduced to reduce crosstalk noise, whereas the K-SVD dictionary learning method is used to obtain the basis of the transformation according to the characteristics of the inversion results. The multi-scale inversion method is adopted to further enhance the stability of FWI. Finally, the synthetic subsag model and the Marmousi model are set to test the effectiveness of the newly proposed method. Analysis of the results suggest the following: (1) The new method can effectively reduce the computational complexity of FWI while ensuring inversion accuracy and stability; (2) The proposed method can be combined with the time-domain multi-scale FWI strategy flexibly to further avoid the local minimum and to improve the stability of inversion, which is of significant importance for the inversion of the complex model.

中文翻译：

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基于K-SVD字典学习的稀疏约束编码多源全波形反演方法

全波形反演（FWI）是一种非常重要的速度模型建立方法。但是，它涉及大量的计算，这阻碍了其实际应用。多源技术可以减少反演过程中前向建模镜头的数量，从而提高效率。但是，它引入了交叉噪声问题。本文提出了一种基于K-SVD字典学习的稀疏约束编码多源FWI方法。引入了相位编码技术以减少串扰噪声，而根据反演结果的特征，使用K-SVD字典学习方法来获得变换的基础。采用多尺度反演方法进一步提高了FWI的稳定性。最后，设置了合成的下陷模型和Marmousi模型来检验新方法的有效性。对结果的分析表明：（1）在保证反演精度和稳定性的同时，可以有效降低FWI的计算复杂度。（2）所提出的方法可以与时域多尺度FWI策略灵活地结合，以进一步避免局部极小值，提高反演的稳定性，这对于复杂模型的反演具有重要意义。