Wave equation reflection traveltime inversion (RTI) takes advantage of the convexity of traveltime objective function to robustly build the background velocity structure for seismic migration and waveform inversion. However, the current wave-equation-based RTI suffers from slow convergence and low resolution because the widely used gradient-based optimization can not account for the blurring effects caused by the finite observation. To accelerate the convergence and improve the accuracy, we propose a Gauss–Newton RTI (GN-RTI) method by incorporating the Hessian information. We derive the reflection traveltime Fréchet derivative and Hessian matrix based on the Born scattering theory. The explicitly constructed Hessian matrix and point spread functions show that the parameter coupling effects of different spatial locations in RTI vary significantly in the model space. Based on the understandings of these coupling effects, a matrix-free approach is applied to solve the Gauss–Newton equation of RTI using the conjugate-gradient method in a nested inner loop. Synthetic and real data examples show that the proposed GN-RTI method can effectively retrieve the background velocity structures for seismic imaging and subsequent waveform inversion.

中文翻译：

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通过神经网络进行 SFN 增益预测，以增强 LDM 系统中的第 2 层覆盖范围


波动方程反射走时反演（RTI）利用走时目标函数的凸性，稳健地构建地震偏移和波形反演的背景速度结构。然而，当前基于波动方程的RTI存在收敛速度慢和分辨率低的问题，因为广泛使用的基于梯度的优化无法解释有限观测引起的模糊效应。为了加速收敛并提高精度，我们提出了一种结合 Hessian 信息的高斯牛顿 RTI (GN-RTI) 方法。基于玻恩散射理论推导了反射走时Fréchet导数和Hessian矩阵。显式构造的Hessian矩阵和点扩散函数表明，RTI中不同空间位置的参数耦合效应在模型空间中存在显着差异。基于对这些耦合效应的理解，采用无矩阵方法在嵌套内循环中使用共轭梯度法求解 RTI 的高斯-牛顿方程。合成和真实数据实例表明，所提出的GN-RTI方法可以有效地反演背景速度结构，用于地震成像和后续波形反演。