Two-point ray tracing in 3-D

Algorithm for determination of all two-point rays of a given elementary wave by means of the shooting method is presented. The algorithm is designed for general 3-D models composed of inhomogeneous geological blocks separated by curved interfaces. It is independent of the initial conditions for rays and of the initial-value ray tracer. The algorithm described has been coded in Fortran 77, using subroutine packages MODEL and CRT for model specification and for initial-value ray tracing.     

Common-ray tracing and dynamic ray tracing for S waves in a smooth elastic anisotropic medium

Anisotropic common S-wave rays are traced using the averaged Hamiltonian of both S-wave polarizations. They represent very practical reference rays for calculating S waves by means of the coupling ray theory. They eliminate problems with anisotropic-ray-theory ray tracing through some S-wave slowness-surface singularities and also considerably simplify the numerical algorithm of the coupling ray theory for S waves. The equations required for anisotropic-common-ray tracing for S waves in a smooth elastic anisotropic medium, and for corresponding dynamic ray tracing in Cartesian or ray-centred coordinates, are presented. The equations, for the most part generally known, are summarized in a form which represents a complete algorithm suitable for coding and numerical applications.     

弯曲射线追踪中Dijkstra算法的改进与实现

文章针对图论中寻找最短路径的Dijkstra算法内存占用量大,效率低的缺点,对该算法进行了改进,修改后的算法计算效率是原来的四倍,内存使用量和图中节点数呈线性关系.在此基础上,用新算法求出了激发点和接收点的最短走时路径,并由激发接收点的旅行时结合联合迭代法对理论模型和实际场地进行了反演.结果表明：和直射线追踪相比,弯曲射线路径能更好地反演出地质体内部的速度场分布.理论模型和实际探测结果证实改进后的算法是有效的.     

基于牛顿迭代法求解群速度的地震波射线追踪模拟

地下介质中普遍存在着各向异性,当前基于各向异性的地震波射线追踪多是在弱各向异性介质中进行且采用群速度近似表示方法,这些近似方法在强各项异性介质中会导致很大误差而无法真正模拟地震波的传播规律.根据地下普遍存在各向异性的事实和地震波基本传播规律,提出利用牛顿迭代法高效求解群速度,基于Paraview平台 自动化构建三维地质...     

Theory of anisotropic dynamic ray tracing in ray-centred coordinates

A 4×4-propagator matrix formalism is presented for anisotropic dynamic ray tracing, including the propagation across curved interfaces. The computations are organised in the same way as in ervený's well-known isotropic propagator matrix formalism. Attention is paid to cases where double eigenvalues of the Christoffel matrix result in unstable expressions in the dynamic ray tracing system, but where geometrical spreading is well-behaved.     

椭球坐标系下多震相地震射线追踪

地震射线追踪方法技术在地震学领域有着较为广泛的应用,然而大多数算法建立在直角坐标系或球坐标系下,实际地球并非完美的球体,而是两极略扁的椭球体,因此,球坐标系下计算结果与真实情况存在一定误差.传统的做法一般是在球坐标系下进行计算,而后进行椭球校正.本文提出了一种直接在椭球体模型中采用分区多步最短路径算法进行多震相地震射线追踪的方法技术,实现了椭球坐标系下多震相地震波射线路径追踪和走时计算.与解析解的对比表明：该算法具有较高的计算精度,适用于任意形状的椭球体,且不需要进行额外的走时校正.数值模拟结果表明,计算所得P波和PcP反射波的走时与AK135走时表的误差小于0.1 s.当震中距较大时,使用球对称模型和椭球体模型计算所得的走时差异显著,说明采用椭球坐标系的必要性.

     

一种最短路径射线追踪的快速算法

为提高最短路径射线追踪的精度,需要增加模型的剖分网格和离散节点,并增加子波传播方向,或者采用其他方法改善计算结果,这些处理会带来大量的额外计算.本文的快速算法改进了波前点的管理和子波传播的计算这两项耗时的工作,较大幅度地提高了传统算法的效率.在波前点的管理上,采用按时间步划分区间的方法,实现了波前点的桶排序管理,其效率高于传统方法中常用的堆排序算法. 在子波传播的计算上,利用斯奈尔定律,同时参考来自邻近节点的波的走时,来限定当前子波传播的有效区域,排除大量不需要计算的子波传播方向. 模型实算表明,本文快速算法的计算速度是传统方法的几倍至十多倍.     

A rapid and accurate two-point ray tracing method in horizontally layered velocity model

Introduction The determination of the ray path between a source and a receiver is fundamental to many seismic problems such as earthquake location, travel time inversion, computation of synthetic seismograms, depth migration, and seismic tomography. The calculation of travel times and their derivatives depend on the determination of ray paths, which is the most time-consuming work in seismic tomography. Therefore, a fast and accurate ray tracing method is particularly important. Many ray-traci…     

基于波前面三角形网格剖分的波前重建法三维射线追踪

在许多地震反演和偏移成像方法中,都要涉及到射线路径和旅行时的计算.本文将波前面三角形网格剖分和三维波前重建法射线追踪技术结合使用,实现了射线路径和旅行时的准确快速计算.三维波前重建法射线追踪过程中可以保证稳定合理的射线密度,克服了常规射线追踪方法存在阴影区的问题.波前面三角形网格剖分在描述和拆分波前面时更加准确有效,而且不需太多的网格数目,从而提高了射线追踪的精度和效率.该方法在三维复杂构造成像方面有独特的优势,目前在实际的Kirchhoff 偏移中的已经有相关应用.     

A note on dynamic ray tracing in ray-centered coordinates in anisotropic inhomogeneous media

Dynamic ray tracing plays an important role in paraxial ray methods. In this paper, dynamic ray tracing systems for inhomogeneous anisotropic media, consisting of four linear ordinary differential equations of the first order along the reference ray, are studied. The main attention is devoted to systems expressed in a particularly simple choice of ray-centered coordinates, here referred to as the standard ray-centered coordinates, and in wavefront orthonormal coordinates. These two systems, known from the literature, were derived independently and were given in different forms. In this paper it is proved that both systems are fully equivalent. Consequently, the dynamic ray tracing system, consisting of four equations in wavefront orthonormal coordinates, can also be used if we work in ray-centered coordinates, and vice versa. vcerveny@seis.karlov.mff.cuni.cz     

复杂地质层面的网格化模型及两点射线追踪方法

本文针对三维复杂介质的两点射线追踪的适用性和有效性,提出了网格模型和层状模型相结合的建模方式,文中利用规则网格化的层状模型对复杂地质单元进行数值描述,一方面避免了用纯粹复杂地质网格体描述时需要的大量内存,另一方面结合运用规则化的层状模型,必有利于提高计算效率,在计算单元自动生成的射线追踪方法基础上,本文结合波前法提出一种快速、有效的两点射线追踪方法,利用反射波波前在地表形成的射线方位角和倾角坐标体系,能快速、准确地收敛到所有从源点到接收点的射线路径,亦可有效地解决射线路径的多值解难题,从而可适用于复杂地质模型的特点.     

Modeling,ray tracing,and block nonlinear travel-time inversion in 3D

We describe an integrated forward and inverse three-dimensional modeling system that can deal with complex geological structures. The system has been designed to handle large-scale problems by using a distributed approach. It uses seismic ray tracing for forward simulation, time-to-depth mapping, and nonlinear travel-time inversion.A novel decomposition method is our tool to attack large-scale problems in a parallel approach. The system is fully implemented and we demonstrate its performance with synthetic examples.This research was partially supported by the National Science Foundation under SBIR Grant III-9300992.     

南海潜在海啸传播过程的数值模拟：初始海啸衰减的影响

准确预估南海海啸风险是有效防灾减灾的前提.前人一般把弹性半无限空间背景下解算出来的海底位错直接等同于初始海啸分布,继而开展海啸传播过程研究.由于断层破裂并非瞬时完成,破裂过程会导致初始海啸波高小于海底位错量,即初始海啸衰减.本文基于高精度地形和高密度网格,求解非线性浅水方程,分别针对马尼拉断裂带的南段、中段和北段,构建南海海啸传播数值模型,试图定量考察初始海啸衰减作用对南海海啸的影响.模拟结果表明一定幅度的初始波高衰减将导致几乎相同幅度的海啸波高衰减,相应的偏差可以忽略.在保守的初始海啸衰减幅度（10%）下,模拟结果显示我国东南沿海、越南东部沿海和巴拉望岛为海啸危险区.另外,模型显示科里奥利力导致的波高变化幅度小于5 cm且其分布样式符合预期,这进一步佐证了数值模型的可靠性,也表明在实际南海海啸模拟中可以忽略科里奥利力进而提高计算效率.结合前人的沉积学认识和本文的数值模拟结果,本文认为南澳岛、西沙东岛和越南绥和周边曾同时遭受海啸侵袭,产生海啸的断裂带最有可能是马尼拉断裂带南段.后续有必要加强南澳岛、西沙东岛和越南东部的沉积学研究,识别更早的海啸事件,以期有力约束南海下次海啸事件的发生年份.

     

海啸传播模型与数值模拟研究进展

海啸在浅水大陆架的传播问题由于其非线性作用和浅水效应而变得十分复杂,然而目前成熟的海啸传播理论及数值模拟结果在这方面与实际并不一致.本文比较分析了可用来模拟大陆架海啸传播的浅水波模型和数值方法,并提出对我国东海陆架边缘可能发生的近海海啸需要开展数值试验研究.     

三维场地波动传播的快速射线追踪法

本文基于Snell定律和Fermat原理对三维任意界面情况下的两点间射线追踪问题进行了研究，从同一条射线满足相同的射线参数出发，推得一个适用于任意界面情况下计算反（折）射点的一阶近似公式。结合迭代技术，给出了三维场地条件下射线追踪迭代算法的计算格式，并进行了三维场地射线追踪模拟计算。计算表明：计算速度相当快，且其计算精度可以根据需要满足要求。     

利用射线追踪方法研究化学物质释放对高频加热的聚焦效应

电离层化学物质释放能导致释放区域电子密度的损耗,从而产生明显的电离层空洞现象.高频电波通过电离层空洞时,由于电子密度不同,对电波产生折射效果进而形成聚焦效应.本文利用射线追踪方法,评估高频电波通过空洞形成聚焦加热的效果.结果表明,释放水分子与SF6都能对电离层产生明显的空洞,空洞半径约为25~50 km,电子密度的损耗率10%以上,在释放点附近有时能达到90%.不同摩尔数的化学物质释放能带来不同的效果.在300 km高度释放100 mol的水分子并且高频电波频率为15 MHz时聚焦效果最好.聚焦后电波能量吸收可增加10 dB左右,增幅达两倍左右.加热后的温度可以提升约20%.     

一种改进的线性走时插值射线追踪算法

线性走时插值法（LTI）在走时的计算中,由于射线方向考虑不全,计算得到的节点走时不一定最小,导致追踪的射线路径无法满足最小走时.针对这一问题,本文提出了一种改进的射线追踪算法,通过采用多方向的循环计算,得到所有计算节点的最小走时,使追踪到的射线路径能真正满足最小走时,以确保射线追踪的精度.模拟实验结果表明,在介质速度变化剧烈的结构中,该算法与传统的LTI算法相比,有效地提高了射线追踪的精度.     

Automatic detection,location and quantification of earthquakes: Application to tsunami warning

We describe a fully automated seismic event detection and location system, providing for real-time estimates of the epicentral parameters of both local and distant earthquakes. The system uses 12 telemetered short-period stations, with a regional aperture of 350 km, as well as two 3-component broad-band stations. Detection and location of teleseismic events is achieved independently and concurrently on the short-period and long-period channels. The long-period data is then used to obtain an estimate of the seismic momentM ₀ of the earthquake through the mantle magnitudeM _m, as introduced byOkal andTalandier (1989). In turn, this estimate ofM ₀ is used to infer the expected tsunami amplitude at Papeete, within 15 minutes of the recording of Rayleigh waves. The performance of the method is discussed in terms of the accuracy of the epicentral parameters and seismic moment obtained in real time, as compared to the values later published by the reporting agencies. Our estimates are usually within 3 degrees of the reported epicenter, and the standard deviation on the seismic moment only 0.19 unit of magnitude for a population of 154 teleseismic events.     

Nonlinear ray perturbation theory with its applications to ray tracing and inversion in anisotropic media

A comprehensive approach, based on the general nonlinear ray perturbation theory (Druzhinin, 1991), is proposed for both a fast and accurate uniform asymptotic solution of forward and inverse kinematic problems in anisotropic media. It has been developed to modify the standard ray linearization procedures when they become inconsistent, by providing a predictable truncation error of ray perturbation series. The theoretical background consists in a set of recurrent expressions for the perturbations of all orders for calculating approximately the body wave phase and group velocities, polarization, travel times, ray trajectories, paraxial rays and also the slowness vectors or reflected/transmitted waves in terms of elastic tensor perturbations. We assume that any elastic medium can be used as an unperturbed medium. A total 2-D numerical testing of these expressions has been established within the transverse isotropy to verify the accuracy and convergence of perturbation series when the elastic constants are perturbed. Seismological applications to determine crack-induced anisotropy parameters on VSP travel times for the different wave types in homogeneous and horizontally layered, transversally isotropic and orthorhombic structures are also presented. A number of numerical tests shows that this method is in general stable with respect to the choice of the reference model and the errors in the input data. A proof of uniqueness is provided by an interactive analysis of the sensitivity functions, which are also used for choosing optimum source/receiver locations. Finally, software has been developed for a desktop computer and applied to interpreting specific real VSP observations as well as explaining the results of physical modelling for a 3-D crack model with the estimation of crack parameters.     

基于E-FAST法分析海啸波高对潜在海啸源参数的敏感性

以马尼拉海沟的北断层发生M_W8.0地震在南海引发海啸为假想的模拟情景, 利用E-FAST法定量分析了COMCOT海啸数值模型输出(最大海啸波高)对震级, 震源深度, 震中位置和断层走向、 倾角、 滑动角等震源参数的敏感性, 以及各震源参数间的交互效应对最大海啸波高的影响. 结果表明, 观测点B₁( 20.1°N, 119.4°E)、 B₂(18.4°N, 118.1°E)和B₃(13.5°N, 117.6°E)的最大海啸波高都对震级十分敏感, 对震中位置、 断层走向和倾角较为敏感. 敏感的震源参数在影响上述3个观测点的最大海啸波高时, 与其它震源参数产生了较强的交互效应. 但是对于不同的观测点, 各震源参数的重要度排序则存在一定的差异. 该分析结果有助于更好地认识海啸波高与潜在海啸源参数之间的关系.