Full-waveform inversion (FWI) suffers from the local minima problem and requires a sufficiently accurate starting model to converge to the correct solution. Wave-equation traveltime inversion (WETI) is an effective tool to retrieve the long-wavelength components of the velocity model. We have developed a joint diving/direct and reflected wave WETI (JDRWETI) method to build P- and S-wave velocity macromodels. We estimate the traveltime shifts of seismic events (diving/direct waves and PP- and PS-reflections) through the dynamic warping scheme and construct a misfit function using the time shifts of diving/direct and reflected waves. We derive the adjoint wave equations and the gradients with respect to the background models based on the joint misfit function. We apply the kernel decomposition scheme to extract the kernel of the diving/direct wave and the tomography kernels of PP- and PS-reflections. For an explosive source, the kernels of the diving/direct wave and PP-reflections and the kernel of the PS-reflections are used to compute the P- and S-wave gradients of the background models, respectively. We implement JDRWETI by a two-stage inversion workflow: First, we invert the P- and S-wave velocity models using the P-wave gradients, and then we improve the S-wave velocity model using the S-wave gradients. Numerical tests on synthetic and field data sets reveal that the JDRWETI method successfully recovers the long-wavelength components of P- and S-wave velocity models, which can be used for an initial model for the subsequent elastic FWI. Moreover, the JDRWETI method prevails over the existing reflection WETI method and the cascaded diving/direct and reflected wave WETI method, especially when large velocity errors are present in the shallow part of the starting models. The JDRWETI method with the two-stage inversion workflow can give rise to reasonable inversion results even for the model with different P- and S-wave velocity structures.

中文翻译：

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用于建立纵横波速度宏模型的俯冲波/直接波和反射波的联合波方程走时反演

全波形反演 (FWI) 存在局部最小值问题，需要足够准确的起始模型才能收敛到正确的解。波方程走时反演 (WETI) 是检索速度模型长波长分量的有效工具。我们开发了联合潜水/直接和反射波 WETI (JDRWETI) 方法来构建 P 波和 S 波速度宏模型。我们通过动态扭曲方案估计地震事件（潜水/直接波和 PP 和 PS 反射）的旅行时偏移，并使用潜水/直接波和反射波的时移构建失配函数。我们基于联合失配函数推导出伴随波动方程和关于背景模型的梯度。我们应用核分解方案来提取俯冲波/直达波的核以及 PP 和 PS 反射的层析成像核。对于爆炸源，俯冲/直接波和 PP 反射的内核以及 PS 反射的内核分别用于计算背景模型的 P 波和 S 波梯度。我们通过两阶段反演工作流程实现 JDRWETI：首先，我们使用 P 波梯度反演 P 波和 S 波速度模型，然后我们使用 S 波梯度改进 S 波速度模型。对合成和现场数据集的数值测试表明，JDRWETI 方法成功地恢复了 P 波和 S 波速度模型的长波长分量，可用于后续弹性 FWI 的初始模型。而且，JDRWETI 方法优于现有的反射 WETI 方法和级联潜水/直接和反射波 WETI 方法，特别是当启动模型的浅层部分存在较大的速度误差时。即使对于具有不同纵横波速度结构的模型，采用两阶段反演工作流程的 JDRWETI 方法也能得到合理的反演结果。