Determination of the influence zone for surface wave paths
Determination of the influence zone for surface wave paths
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DOI：
10.1046/j.1365-246x.2002.01659.x
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发表时间：
2002-05
影响因子：
2.8
通讯作者：
K. Yoshizawa;B. Kennett
中科院分区：
文献类型：
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作者：
K. Yoshizawa;B. Kennett
摘要通过研究感兴趣的频率范围的菲涅尔区，提供了对面波传播路径周围的影响区域的近似描述。表面波在其上具有相干相位的表面波路径的影响区被确定为第一菲涅尔区宽度的大约三分之一。一种被称为菲涅耳面波射线追踪(FRT)的技术已经被用来估计每个频率的射线路径周围的这一区域。FRT技术是通过结合两种标准射线跟踪方法，即运动射线跟踪(KRT)和动态射线跟踪(DRT)而发展起来的。要在横向非均匀结构中获得准确的菲涅耳面积，需要求解大量的KRT方程。相比之下，FRT方法只需要几次光线跟踪计算。在第一步中，通过求解KRT系统来计算所需频率处的相速度分布，从而计算面波的轨迹。在下一步中，通过求解两次DRT系统来计算KRT路径周围区域中的射线的行为；一次是从源到接收器，另一次是从接收器到源沿相同的轨迹。最后，结合这些光线追踪系统的解，利用近轴光线理论，可以估计出中心光线周围的菲涅耳面积。利用FRT，可以在横向不均匀结构中围绕中心射线路径构建稳定相位场。然后，利用关于扰动波场的简单假设，从驻相函数估计光线路径周围的影响区域。利用FRT技术可以有效地计算横向非均匀结构中影响带的估计，并允许扩展现有的面波分析方法，这些方法通常基于几何射线理论和大圆传播的近似。这种方法可以处理有限宽度的射线，以及最近的断层成像模型所揭示的由中等横向非均质性引起的传播偏离大圆的情况。这种有限宽度的射线应该是增强基于射线的表面波层析成像的主要益处。
SUMMARY An approximate description of the zone of influence around the propagation path for a surface wave is provided by investigating the Fresnel zones for the frequency range of interest. The influence zone about surface wave paths, over which surface waves are coherent in phase, is identified as approximately one-third of the width of the first Fresnel zone. A technique called Fresnel-area ray tracing (FRT) for surface waves has been used to estimate this region around the ray path for each frequency. The FRT technique is developed by combining two standard ray tracing methods, i.e. kinematic ray tracing (KRT) and dynamic ray tracing (DRT). To obtain the exact Fresnel area in a laterally heterogeneous structure would require the solution of a large number of KRT equations. In contrast, the FRT approach requires just a few ray tracing calculations. In the first step, the trajectory of the surface wave is computed by solving the KRT system for the phase-velocity distribution at the required frequency. In the next step, the behaviour of rays in the zone surrounding the KRT path is calculated by solving the DRT system twice; once from the source to the receiver and once more from the receiver to the source along the same trajectory. Finally, combining the solutions of these ray tracing systems using paraxial ray theory, the Fresnel area around a central ray can be estimated. Using FRT, stationary-phase fields can be constructed around a central ray path in a laterally heterogeneous structure. The influence zone around the ray path is then estimated from the stationary-phase function with simple assumptions concerning the perturbed wavefield. The estimate of the influence zone can be efficiently calculated in laterally heterogeneous structure by using the FRT technique, and allows an extension of current methods of surface wave analysis, which have commonly been based on geometrical ray theory and on the approximation of great-circle propagation. This approach allows the treatment of finite-width rays as well as deviations in propagation from the great circle induced by moderate lateral heterogeneity as revealed by recent tomography models. Such finite-width rays should be of major benefit in enhancing ray-based surface wave tomography.