Full-waveform inversion (FWI) is a highly nonlinear and ill-posed inverse problem, which needs proper regularization to produce reliable results. Recently, sparsity and overcompleteness have been successfully applied to seismic data processing. In this study, we propose a novel adaptive sparsity-promoting regularization for FWI which combines the L-BFGS algorithm with an adaptive overcomplete dictionary learning method. The dictionary is learned from many small imaging patches taken from the optimal velocity model that is obtained by previous L-BFGS iterations. Our dictionary learning method tries to exploit the 2D geometric structure of the training patches in a more direct way and is simple to implement. We test our proposed method on a smoothed Marmousi model, a BG Compass model, and a SEG/EAGE salt model. Since total variation (TV) regularization plays an important role in FWI, the inversion results using the TV regularization method are also presented for comparison purposes. From these experiments, we conclude that the proposed method can achieve better performance than the FWI with the TV regularization method.

中文翻译：

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基于自适应过完备字典学习的全波形反演的稀疏促进正则化

全波形反演 (FWI) 是一个高度非线性和不适定的反演问题，需要适当的正则化才能产生可​​靠的结果。最近，稀疏性和过完备性已成功应用于地震数据处理。在这项研究中，我们为 FWI 提出了一种新的自适应稀疏促进正则化，它将 L-BFGS 算法与自适应过完备字典学习方法相结合。该字典是从从先前 L-BFGS 迭代获得的最佳速度模型中获取的许多小成像块中学习的。我们的字典学习方法试图以更直接的方式利用训练补丁的二维几何结构，并且易于实现。我们在平滑的 Marmousi 模型、BG Compass 模型和 SEG/EAGE 盐模型上测试我们提出的方法。由于总变差 (TV) 正则化在 FWI 中起着重要作用，因此还提供了使用 TV 正则化方法的反演结果以供比较。从这些实验中，我们得出结论，所提出的方法可以比使用 TV 正则化方法的 FWI 获得更好的性能。