标题： 一种用于计算吸收介质中衰减算子$t^*$的新颖快速扫描方法 显示英文标题

标题： A novel fast sweeping method for computing the attenuation operator $t^*$ in absorbing media

摘要： $t^*$表示总路径衰减，表征传播地震波的振幅衰减。 在地震衰减层析成像中通常需要计算衰减算子$t^*$。 传统的$t^*$计算方法需要显式确定射线路径。 然而，在处理大数据集时，射线追踪可能会非常耗时，并且常规的射线追踪技术甚至可能在轻度非均质介质中失效。 在这项研究中，我们提出了一种改进的快速扫描方法（MFSM），用于求解$t^*$的控制方程而不显式计算射线路径。 该方法包括两个主要步骤。 首先，通过使用快速扫描方法数值求解Eikonal方程来计算走时场。 其次，基于从走时梯度导出的上风方案对$t^*$梯度的离散化，利用MFSM求解$t^*$的控制方程。 通过与解析解的比较以及在简单和复杂模型下网格细化后的$t^*$误差检验，严格验证了MFSM的有效性。 评估了包括收敛性、迭代次数和计算时间在内的关键性能指标。 针对笛卡尔坐标系和球坐标系开发了两种版本的MFSM。 我们展示了所开发的MFSM在计算北岛$t^*$中的实际适用性，并讨论了该方法在估算地震反应谱方面的效率。 显示英文摘要

摘要： $t^*$ represents the total path attenuation and characterizes the amplitude decay of a propagating seismic wave. Calculating the attenuation operator $t^*$ is typically required in seismic attenuation tomography. Traditional methods for calculating $t^*$ require determining the ray path explicitly. However, ray tracing can be computationally intensive when processing large datasets, and conventional ray tracing techniques may fail even in mildly heterogeneous media. In this study, we propose a modified fast sweeping method (MFSM) to solve the governing equation for $t^*$ without explicitly calculating the ray path. The approach consists of two main steps. First, the traveltime field is calculated by numerically solving the eikonal equation using the fast sweeping method. Second, $t^*$ is computed by solving its governing equation with the MFSM, based on the discretization of the gradient of $t^*$ using an upwinding scheme derived from the traveltime gradient. The MFSM is rigorously validated through comparisons with analytical solutions and by examining $t^*$ errors under grid refinement in both simple and complex models. Key performance metrics, including convergence, number of iterations, and computation time, are evaluated. Two versions of the MFSM are developed for both Cartesian and spherical coordinate systems. We demonstrate the practical applicability of the developed MFSM in calculating $t^*$ in North Island, and discuss the method's efficiency in estimating earthquake response spectra.