动态网络最短路径射线追踪

最短路径射线追踪算法,用预先设置的网络节点的连线表示地震波传播路径,当网络节点稀疏时,获得的射线路径呈之字形,计算的走时比实际走时系统偏大. 本文在波前扩展和反向确定射线路径的过程中,在每个矩形单元内,通过对某边界上的已知走时节点的走时进行线性插值,并利用Fermat原理即时求出从该边界到达其他边界节点的最小走时及其子震源位置和射线路径,发展了相应的动态网络算法. 从而克服了最短路径射线追踪算法的缺陷,大大提高了最小走时和射线路径的计算精度.     

迭代优化的网络最短路径射线追踪方法研究

网络最短路径射线追踪算法,用预先设置的网格节点的连线表示地震波传播路径,当网格节点稀疏时,获得的射线路径呈Z字形,计算的走时比实际走时偏差大.本文在网络最短路径射线追踪算法的基础上,提出了迭代法与网络最短路径相结合的射线追踪算法,运用迭代法优化计算由网络最短路径算法得到的射线路径,并对迭代法进行修正,从而克服了最短路径射线追踪算法的缺陷,大大提高了最小走时和射线路径的计算精度.     

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.     

一种线性走时插值射线追踪改进算法

针对线性走时插值算法(LTI)不能正确追踪逆向传播射线的问题, 目前已提出多种改进算法, 如扩张收缩LTI算法、 循环计算LTI算法、 动态网络最短路径射线追踪算法等, 但这些算法的计算效率普遍偏低. 在分析各种改进LTI算法的优劣后, 本文提出了改进动态网络最短路径射线追踪算法. 该改进算法依据波的传播规律以及LTI算法的基本方程, 排除动态网络最短路径射线追踪算法中大量冗余节点计算, 并采用传统的二叉树堆排序算法对波前阵列节点进行管理. 数值算例表明, 本文提出的改进算法具有较高的计算效率, 其计算效率是动态网络最短路径射线追踪算法的4.5—30倍, 是原始LTI算法的2—6.5倍; 当动态网络最短路径射线追踪算法采用堆排序算法时, 改进算法的计算效率是其3.5—15倍.      

对旅行时进行抛物型插值的地震射线追踪方法

提出一种对旅行时进行抛物线插值的地震射线追踪方法（简称PTI方法）,它比基于旅行时线性插值方法（简称LTI方法）计算结果更准确.PTI和LTI方法都是基于2D网格单元模型,用于计算地震波的旅行时和射线路径.首先介绍了相关方法的一些基本概念.旅行时和射线路径都是在网格边界上进行计算的,因此,射线路径在同一恒速网格内是直线.其计算过程有两步.第一步,计算旅行时,第二步追踪射线路径.然后给出了LTI算法的基本公式.因为在炮点网格内可能存在折射波,文章也相应导出了其公式.最后详细推导了PTI 方法的公式.通过模型试算对比说明,用PTI方法较LTI算法更精确、更有效,PTI方法是一种很有发展前途的地震射线追踪算法.     

初至波层析成像正演模拟中多发多收模式计算方法研究

初至波层析成像正演模拟中的多发多收模式计算,常规正演模拟方法是将其简单地分解为多个单发多收模式的计算.对于发射点和接收点分别位于模型对边的情况,如井间地震层析成像,常规方法存在较多的无效计算,计算效率偏低.针对这一问题,本文基于互换原理及费马原理,提出了改进计算方法:利用少量发射点至各接收点的最小走时路径确定其他发射点至各接收点最短走时路径所在区域,减少了无效计算,提高了层析成像正演模拟的计算效率.数值算例表明:对于射线追踪算法为最短路径法的情况,改进方法的计算效率是常规正演模拟方法的2倍左右.     

水平层状VTI介质高效射线追踪计算方法

准确、快速计算水平层状VTI(vertical transverse isotropic)介质的走时和射线路径是实现VTI介质地震叠前时间偏移和微地震监测速度建模的基础.水平层状VTI介质射线追踪的常用算法包括打靶法和最短路径法.打靶法原理简单、实现容易,但在长偏移距时存在微小初射角度变化导致射线路径巨大扰动的问题;最短路径法原理直观,但需要沿射线群速度方向(群角)计算走时,计算特定群角对应的群速度值需要先搜索对应的相速度角度(相角),显著降低了计算效率.本文综合打靶法和最短路径法的优点,从震源同时出射一系列射线,以这些射线到达界面的交点构成稀疏的网格节点,自适应加密实现检波点周围网格节点间距高于精度要求,采用插值算法获得检波点的走时和动态网格方法获得不位于网格节点上的检波点的射线路径.本文方法严格计算已知相角对应的群角和群速度,未使用弱各向异性群速度近似公式,适用于任意强度各向异性VTI介质qP、qSV和qSH直达波和反射波射线追踪;以相角确定震源出射射线,不用遍历群角和群速度对应关系.同传统最短路径方法的数值实验对比表明本文方法具有高精度和高效性,非常适合于需要多次正演计算的地震叠...     

基于图形结构的三维射线追踪方法

在地震层析成像研究中,为了克服最小走时射线路径追踪方法存在的问题,对该方法计算过程中的关键步骤进行了改进．在节点走时的计算中引入Ｂｒｅｓｅｎｈａｍ画线算法;在最小走时节点查寻中,结合使用快速排序算法与插入排序算法,替代以往方法中多采用的堆排序算法;所采用的节点设置方式,可以引入速度界面,还可以实现反射波射线追踪．模型计算证明,改进的最小走时射线路径方法具有精度高,速度快的特点,所提出的三维空间反射波射线追踪算法简便易行。     

矩形网格三点Fermat射线追踪技术

矩形网格三点Fermat射线追踪法是基于矩形网格三点扰动法的一种提高计算速度的方法．取矩形网格三个点,在Fermat最小旅行时原则下求取扰动中间点的位置,而不象扰动法那样依次扰动．因此,计算速度比扰动法提高2倍多,同时不受扰动摄动量大小选择的困扰．该方法继承了矩形网格三点扰动法的优点,对任意离散的速度场,总能找到最短时间路径,避免了射线盲区和追踪路径并非时间最短路径问题．     

射线法模拟分析井间地震观测的波场特征

按照井间地震的观测系统,用改进的突变点加插值射线追踪方法,追踪每炮每道的射线路径,计算几种主要类型的波沿射线路径的波至时间和射线振幅,制作井间地震多炮多道水平分量和垂直分量的合成记录.并将合成记录选排为井间共炮点道集、共接收点道集、共偏移距道集和共中心深度点道集,系统地分析了不同道集内几种主要类型的地震波的传播特征.对野外观测的实际井间地震记录进行了模拟,从复杂的井间地震记录中,识别出井间地震实际观测到的不同类型的波场,为随后的井间地震资料处理和应用提供了依据.     

界面二次源波前扩展法全局最小走时射线追踪技术

以Moser方法为代表的最短路径射线追踪算法可以快速稳定地获得整个追踪区域的全局最小走时和路径,但它存在两个缺陷：一是射线大多由折线呈锯齿状相连,长度和位置偏离真实射线路径;二是在低变速区容易出现射线路径多值现象．本文提出的界面二次源波前扩展法全局最小走时射线追踪技术（以下简称界面源法）旨在解决上述两个问题．不同于Moser方法,界面源法只在物性分界面上设置子波源点,子波出射射线可以到达任何不穿越物性界面而直接到达的空间点和界面离散点,在均匀块体内或层内地震波以精确的射线路径传播．显然,界面源法的子波出射方向数远远大于传统方法,算法的追踪误差主要由界面离散引起的,因此,界面源法很好地解决了Moser法存在的问题,大大提高了追踪的精度．同时,由于界面源法的子波源点数远远小于Moser法,因而效率也很高．模型实算证实了该算法的高效性．     

A new 3-D ray tracing method based on LTI using successive partitioning of cell interfaces and traveltime gradients

We present a new method of three-dimensional (3-D) seismic ray tracing, based on an improvement to the linear traveltime interpolation (LTI) ray tracing algorithm. This new technique involves two separate steps. The first involves a forward calculation based on the LTI method and the dynamic successive partitioning scheme, which is applied to calculate traveltimes on cell boundaries and assumes a wavefront that expands from the source to all grid nodes in the computational domain. We locate several dynamic successive partition points on a cell's surface, the traveltimes of which can be calculated by linear interpolation between the vertices of the cell's boundary. The second is a backward step that uses Fermat's principle and the fact that the ray path is always perpendicular to the wavefront and follows the negative traveltime gradient. In this process, the first-arriving ray path can be traced from the receiver to the source along the negative traveltime gradient, which can be calculated by reconstructing the continuous traveltime field with cubic B-spline interpolation. This new 3-D ray tracing method is compared with the LTI method and the shortest path method (SPM) through a number of numerical experiments. These comparisons show obvious improvements to computed traveltimes and ray paths, both in precision and computational efficiency.     

ITERATIVE TOMOGRAPHIC METHODS TO LOCATE SEISMIC LOW-VELOCITY ANOMALIES: A MODEL STUDY1

The possibilities for reconstructing seismic velocity distributions containing low-velocity anomalies by iterative tomographic methods are examined studying numerical and analogue 2D model data. The geometrical conditions of the model series were designed to generalize the geometrical characteristics of a typical cross-hole tomographic field case. Models with high (30%) and low (8%) velocity contrasts were realized. Traveltimes of 2D ultrasonic P-waves, determined for a dense net of raypaths across each model, form the analogue data set. The numerical data consists of traveltimes calculated along straight raypaths. Additionally, a set of curved-ray traveltimes was calculated for a smoothed version of the high-contrast model. The Simultaneous Iterative Reconstruction Technique (SIRT) was chosen from the various tomographic inversion methods. The abilities of this standard procedure are studied using the low-contrast model data. The investigations concentrate on the resolving power concerning geometry and velocity, and on the effects caused by erroneous data due to noise or a finite time precision. The grid spacing and the source and receiver patterns are modified. Smoothing and slowness constraints were tested. The inversion of high-contrast analogue model data shows that curved raypaths have to be considered. Hence, a ray-tracing algorithm using velocity gradients was developed, based on the grid structure of the tomographic inversion. This algorithm is included in the SIRT-process and the improvements concerning anomaly localization, resolution and velocity reconstruction are demonstrated. Since curved-ray tomography is time-consuming compared with straight-ray SIRT, it is necessary to consider the effects of grid spacing, ray density, slowness constraints and the     

A hybrid approach to compute seismic travel times in three-dimensional tetrahedral meshes

We propose an optimized method to compute travel times for seismic inversion problems. It is a hybrid method combining several approaches to deal with travel time computation accuracy in unstructured meshes based on tetrahedral elementary cells. As in the linear travel time interpolation method, the proposed approach computes travel times using seismic ray paths. The method operates in two sequential steps: At a first stage, travel times are computed for all nodes of the mesh using a modified version of the shortest path method. The difference with the standard version is that additional secondary nodes (called tertiary nodes) are added temporarily around seismic sources in order to improve accuracy with a reasonable increase in computational cost. During the second step, the steepest travel time gradient method is used to trace back ray paths for each source–receiver pair. Travel times at each receiver are then recomputed using slowness values at the intersection points between the ray path and the traversed cells. A number of numerical tests with an array of different velocity models, mesh resolutions and mesh topologies have been carried out. These tests showed that an average relative error in the order of 0.1% can be achieved at a computational cost that is suitable for travel time inversion.     

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.     

SEISMIC RAY TRACING USING LINEAR TRAVELTIME INTERPOLATION1

A new ray-tracing method called linear traveltime interpolation (LTI) is proposed. This method computes traveltimes and raypaths in a 2D velocity structure more rapidly and accurately than other conventional methods. The LTI method is formulated for a 2D cell model, and calculations of traveltimes and raypaths are carried out only on cell boundaries. Therefore a raypath is considered to be always straight in a cell with uniform velocity. This approach is suitable to tomography analysis. The algorithm of LTI consists of two separate steps: step 1 calculates traveltimes on all cell boundaries; step 2 traces raypaths for all pairs of receivers and the shot. A traveltime at an arbitrary point on a cell boundary is assumed to be linearly interpolated between traveltimes at the adjacent discrete points at which we calculate traveltimes. Fermat's principle is used as the criterion for choosing the correct traveltimes and raypaths from several candidates routinely. The LTI method has been compared numerically with the shooting method and the finite-difference method (FDM) of the eikonal equation. The results show that the LTI method has great advantages of high speed and high accuracy in the calculation of both traveltimes and raypaths. The LTI method can be regarded as an advanced version of the conventional FDM of the eikonal equation because the formulae of FDM are independently derived from LTI. In the process of derivation, it is shown theoretically that LTI is more accurate than FDM. Moreover in the LTI method, we can avoid the numerical instability that occurs in Vidale's method where the velocity changes abruptly.     

Improving modelling and inversion in refraction seismics with a first-order Eikonal solver

A first-order Eikonal solver is applied to modelling and inversion in refraction seismics. The method calculates the traveltime of the fastest wave at any point of a regular grid, including head waves as used in refraction. The efficiency, robustness and flexibility of the method give a very powerful modelling tool to find both traveltimes and raypaths. Comparisons with finite-difference data show the validity of the results. Any arbitrarily complex model can be studied, including the exact topography of the surface, thus avoiding static corrections. Later arrivals are also obtained by applying high-slowness masks over the high-velocity zones. Such an efficient modelling tool may be used interactively to invert for the model, but a better method is to apply the refractor-imaging principle of Hagedoorn to obtain the refractors from the picked traveltime curves. The application of this principle has already been tried successfully by previous authors, but they used a less well-adapted Eikonal solver. Some of their traveltimes were not correct in the presence of strong velocity variations, and the refractor-imaging principle was restricted to receiver lines along a plane surface. With the first-order Eikonal solver chosen, any topography of the receiving surface can be considered and there is no restriction on the velocity contrast. Based on synthetic examples, the Hagedoorn principle appears to be robust even in the case of first arrivals associated with waves diving under the refractor. The velocities below the refractor can also be easily estimated, parallel to the imaging process. In this way, the model can be built up successively layer by layer, the refractor-imaging and velocity-mapping processes being performed for each identified refractor at a time. The inverted model could then be used in tomographic inversions because the calculated traveltimes are very close to the observed traveltimes and the raypaths are available.     

CDP mapping in tilted transversely isotropic (TTI) media. Part I: Method and effectiveness

Transverse isotropy with a tilted axis of symmetry (TTI) causes image distortion if isotropic models are assumed during data processing. A simple anisotropic migration approach needs long computational times and is sensitive to the signal-to-noise ratio. This paper presents an efficient, general approach to common-depth-point (CDP) mapping to image the subsurface in TTI media from qP-wave seismic data by adding anisotropic and dip parameters to the velocity model. The method consists of three steps: (i) calculating traveltimes and positions of the CDP points; (ii) determining CDP trajectories; (iii) CDP imaging. A crucial step is the rapid computation of traveltimes and raypaths in the TTI media, which is achieved by the Fermat method, specially adapted for anisotropic layered media. The algorithm can image the subsurface of a given model quickly and accurately, and is suitable for application to a bending reflector. The effectiveness of the method is demonstrated by comparing the raypaths, the traveltimes and the results of CDP mapping, when assuming isotropic media, transversely isotropic media with a vertical axis of symmetry (TIV), and TTI media.