Full-waveform inversion (FWI) is among the most effective methods of velocity modelling in seismic exploration. However, because of the strong nonlinearity of the FWI, if the velocity in the target geobody is not sharply different from that in its surroundings, the total variation (TV) of the model will not be sufficiently sparse. To alleviate this issue, we propose a novel TV-regularised FWI method that can consider the sparsity of the high-order regularisation operator and consequently improve the stability of the inversion process and produce more focused model boundaries. We use a split-Bregman algorithm to solve the inversion optimisation problem while building the TV-regularised objective function. We show that stable model updates can be obtained by this algorithm, which proved to be effective and reliable in the numerical tests. These tests also show that the proposed method converges faster, can model the velocity domain better than conventional methods and can effectively identify layer boundaries with a weak velocity contrast. We conclude that the novel FWI method based on high-order TV regularisation is robust and accurate.

中文翻译：

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一种全波形反演的高阶全变正则化方法

全波形反演（FWI）是地震勘探中最有效的速度建模方法之一。然而，由于 FWI 的强非线性，如果目标地质体中的速度与其周围的速度没有显着差异，则模型的总变差 (TV) 将不够稀疏。为了缓解这个问题，我们提出了一种新颖的 TV 正则化 FWI 方法，该方法可以考虑高阶正则化算子的稀疏性，从而提高反演过程的稳定性并产生更集中的模型边界。我们使用 split-Bregman 算法来解决反演优化问题，同时构建 TV 正则化目标函数。我们表明，该算法可以获得稳定的模型更新，在数值测试中证明是有效和可靠的。这些测试还表明，所提出的方法收敛速度更快，可以比传统方法更好地模拟速度域，并且可以有效地识别速度对比较弱的层边界。我们得出结论，基于高阶 TV 正则化的新型 FWI 方法是稳健且准确的。