Summary

Wave-equation-based traveltime tomography has been extensively applied in both global tomography and seismic exploration. Typically, the traveltime Fréchet derivative is obtained using the first-order Born-approximation, which is only satisfied for weak velocity perturbations and small phase shifts (i.e. the weak-scattering assumption). Although the small phase-shift restriction can be handled with the Rytov approximation, the weak velocity-perturbation assumption is still a major limitation. The recently-developed generalized Rytov approximation (GRA) method can achieve an improved phase accuracy of the forward-scattered wavefield, in the presence of large-scale and strong velocity perturbations. In this paper, we combine GRA with the classical finite-frequency theory and propose a GRA-based traveltime sensitivity kernel (GRA-TSK), which overcomes the weak-scattering limitation of the conventional finite-frequency methods. Numerical examples demonstrate that the accumulated time-delay of forward-scattered waves caused by large-scale smooth perturbations can be correctly handled by the GRA-based traveltime sensitivity kernel, regardless of the magnitude of the velocity perturbations. Then, we apply the new sensitivity kernel to solve the traveltime inverse problem, and we propose a matrix-free Gauss-Newton method which has a faster convergence rate compared with the gradient-based method. Numerical tests show that, compared with the conventional adjoint traveltime tomography, the proposed GRA-based traveltime tomography can obtain a more accurate model with a faster convergence rate, making it more suited for recovering the large-intermediate scale of the velocity model, even for strong-perturbation and complex subsurface structures.

中文翻译：

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使用广义Rytov逼近的有限频率行进时间层析成像

概要

基于波方程的行进时间层析成像技术已广泛应用于全球层析成像和地震勘探中。通常，使用一阶Born逼近来获得行进时间Fréchet导数，这仅在弱速度扰动和小相移（即弱散射假设）下得到满足。尽管可以使用Rytov近似来处理较小的相移限制，但弱的速度摄动假设仍然是主要限制。在存在大范围和强速度扰动的情况下，最近开发的广义Rytov逼近（GRA）方法可以提高前向散射波场的相位精度。在本文中，我们将GRA与经典有限频率理论相结合，并提出了一个基于GRA的行进时间灵敏度核（GRA-TSK），克服了传统有限频率方法的弱散射限制。数值算例表明，基于GRA的传播时间灵敏度核可以正确处理大规模平滑扰动引起的前向散射波的累积时延，而与速度扰动的大小无关。然后，我们使用新的灵敏度核来解决行程时间逆问题，并提出了一种无矩阵的高斯-牛顿法，该方法与基于梯度的方法相比具有更快的收敛速度。数值测试表明，与传统的伴随旅行时间层析成像相比，基于GRA的旅行时间层析成像能够以更快的收敛速度获得更精确的模型，使其更适合于恢复速度模型的大中尺度。