It is widely known that the full-waveform inversion (FWI) gradient contains both tomography and migration components. One of the key points for the successful implementation of FWI is to first build a background velocity model by utilizing the tomography component and then recover the model interfaces using the migration component. Therefore, it is necessary to separate the two types of components in the FWI gradient. We propose a gradient-decomposition FWI (GFWI) method that provides a good initial velocity model for FWI using the tomography component. We first derive the FWI gradient based on the first-order stress-velocity acoustic wave equation and then decompose it into the tomography and migration components with a weighted Poynting vector separation method. Since the Poynting vectors can be directly obtained in the forward and backward wavefield extrapolation, the separation algorithm adds little additional computational effort. To better recover the low-wavenumber part of the model, only the tomography component is used for background velocity updates in the early iterations. Finally, we perform conventional FWI to obtain the final inversion result. Analyses on a sensitivity kernel test indicate that the proposed gradient decomposition algorithm is effective in separating the tomography and migration components. Numerical examples on a layered model with a high-velocity anomaly and the Marmousi model demonstrate that the new FWI method is robust and effective even for low-frequency missing data.

中文翻译：

---

基于梯度分解的全波形反演增强层析成像成分


众所周知，全波形反演（FWI）梯度包含层析成像和偏移分量。 FWI成功实现的关键点之一是首先利用层析成像组件建立背景速度模型，然后利用偏移组件恢复模型接口。因此，有必要将 FWI 梯度中的两类成分分开。我们提出了一种梯度分解 FWI (GFWI) 方法，该方法为使用断层扫描组件的 FWI 提供了良好的初始速度模型。我们首先基于一阶应力-速度声波方程推导FWI梯度，然后用加权坡印廷矢量分离方法将其分解为层析成像和偏移分量。由于坡印廷矢量可以在前向和后向波场外推中直接获得，因此分离算法几乎不增加额外的计算量。为了更好地恢复模型的低波数部分，在早期迭代中仅使用层析成像组件进行背景速度更新。最后，我们进行常规FWI以获得最终的反演结果。灵敏度核测试分析表明，所提出的梯度分解算法可以有效分离层析成像和偏移分量。具有高速异常的分层模型和 Marmousi 模型的数值示例表明，即使对于低频缺失数据，新的 FWI 方法也是稳健且有效的。