In controlled-source seismology, the standard full waveform inversion (FWI) can't reliably recover the macrovelocity structure in the deep part, if the surface seismic data lack of ultra-long offsets and very low frequencies. Reformulating the FWI for pre-critical reflections based on model scale separation leads to reflection waveform inversion (RWI), which aims to improve the reconstruction of low-to-intermediate model wavenumbers. However, the state-of-art RWI approaches rely on the gradient-type optimization, resulting in slow convergence and inaccurate recovery of the deep macrovelocities. Therefore, we present a Hessian-based second-order optimization in the context of RWI. Based on the reflection Fréchet derivative with respect to the background model, the approximate Hessian and the point spread functions (PSFs) on toy models with two and three layers are constructed to gain physical insights about parameter coupling and spatial resolution at the scale of low-to-intermediate wavenumbers for finite-offset and band-limited data. The high-velocity anomaly and checkerboard experiments demonstrate the benefit of incorporating the inverse approximate Hessian effect on the functional gradient. Accordingly, for large-scale applications, we propose a matrix-free Gauss-Newton RWI approach, in which the Hessian-vector product is formulated with the second-order adjoint-state method and an optimal updating direction is estimated in the nested inner loop to accelerate the convergence. A synthetic example and an application to the real data from East China Sea demonstrate that the proposed method can improve velocity model building and seismic imaging, especially for the deep targets.

中文翻译：

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使用伴随状态法进行二阶优化的反射全波形反演

在控源地震学中，如果地面地震数据缺乏超长偏移距和极低频率，标准全波形反演（FWI）不能可靠地恢复深部的宏观速度结构。基于模型尺度分离重新制定前临界反射的 FWI 导致反射波形反演 (RWI)，其目的是改善中低模型波数的重建。然而，最先进的 RWI 方法依赖于梯度类型的优化，导致深度宏速度收敛缓慢和恢复不准确。因此，我们在 RWI 的背景下提出了基于 Hessian 的二阶优化。基于相对于背景模型的反射 Fréchet 导数，构建了两层和三层玩具模型上的近似 Hessian 函数和点扩散函数 (PSF)，以获得有关有限偏移和带限数据的中低波数尺度上的参数耦合和空间分辨率的物理见解. 高速异常和棋盘实验证明了将逆近似 Hessian 效应合并到函数梯度上的​​好处。因此，对于大规模应用，我们提出了一种无矩阵的 Gauss-Newton RWI 方法，其中 Hessian 向量乘积用二阶伴随状态方法制定，并在嵌套内循环中估计最佳更新方向以加速收敛。