A generalized Rytov approximation for accurate calculation of phase variation in strong perturbation media
A generalized Rytov approximation for accurate calculation of phase variation in strong perturbation media
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用于精确计算强扰动介质中相位变化的广义 Rytov 近似
DOI：
10.1093/gji/ggz338
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发表时间：
2019
影响因子：
2.8
通讯作者：
Wang Huazhong
中科院分区：
文献类型：
--
作者：
Feng Bo;Wu Ru Shan;Wang Huazhong
在前向散射长距离传播的情况下，由于速度扰动引起的相位变化的累积，将违反玻恩近似的有效性。相比之下，相变累积可以通过 Rytov 近似来处理，该近似已广泛用于仅涉及前向散射或小角度散射的长距离传播。然而，Rytov近似中的弱散射假设（即小速度扰动）限制了其应用范围。为了解决这个问题，我们使用 Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) 近似分析 Rytov 变换的积分核，并证明积分核是速度扰动和散射角的函数。通过应用小散射角近似，我们表明相位变化与慢度扰动具有线性关系，无论扰动的幅度有多大。因此，新的积分方程被称为广义 Rytov 近似（GRA），因为它克服了 Rytov 近似的弱散射假设。为了展示 Rytov 近似的局限性和所提出的 GRA 方法的优点，我们首先设计一个两层模型，并使用平面波入射分析计算小散射角假设引入的误差。我们表明，GRA 预测的相位（行程时间）变化总是比 Rytov 近似更准确。特别是，无论速度扰动的大小如何，GRA 都能为法向入射平面波产生精确的相位变化。使用高斯异常模型的数值例子表明，散射角对 GRA 的精度具有至关重要的影响。如果小散射角假设成立，即使速度扰动非常强，GRA 也可以产生精确的相位近似。相反，当散射角足够大时，一阶Rytov近似和GRA都无法得到令人满意的结果。所提出的GRA方法有潜力用于大规模强扰动介质的走时建模和反演。
In the case of long-range propagation of forward scattering, due to the accumulation of phase changes caused by the velocity perturbations, the validity of the Born approximation will be violated. In contrast, the phase-change accumulation can be handled by the Rytov approximation, which has been widely used for long-distance propagation with only forward scattering or small-angle scattering involved. However, the weak scattering assumption (i.e. small velocity perturbation) in the Rytov approximation limits its scope of application. To address this problem, we analyse the integral kernel of the Rytov transform using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation and we demonstrate that the integral kernel is a function of velocity perturbation and scattering angle. By applying a small scattering angle approximation, we show that the phase variation has a linear relationship with the slowness perturbation, no matter how strong the magnitude of perturbation is. Therefore, the new integral equation is then referred to as the generalized Rytov approximation (GRA) because it overcomes the weak scattering assumption of the Rytov approximation. To show the limitations of the Rytov approximation and the advantages of the proposed GRA method, first we design a two-layer model and we analytically calculate the errors introduced by the small scattering angle assumption using plane wave incidence. We show that the phase (traveltime) variations predicted by the GRA are always more accurate than the Rytov approximation. Particularly, the GRA produces accurate phase variations for the normal incident plane wave regardless of the magnitude of velocity perturbation. Numerical examples using Gaussian anomaly models demonstrate that the scattering angle has a crucial impact on the accuracy of the GRA. If the small scattering angle assumption holds, the GRA can produce an accurate phase approximation even if the velocity perturbation is very strong. On the contrary, both the first-order Rytov approximation and the GRA fail to get satisfying results when the scattering angle is large enough. The proposed GRA method has the potential to be used for traveltime modelling and inversion for large-scale strong perturbation media.