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。     

Errors due to the anisotropic-common-ray approximation of the coupling ray theory

The common-ray approximation eliminates problems with ray tracing through S-wave singularities and also considerably simplifies the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies. It is thus of principal importance for numerical applications to estimate the errors due to the common-ray approximation applied. The anisotropic-common-ray approximation of the coupling ray theory is more accurate than the isotropic-common-ray approximation. We derive the equations for estimating the travel-time errors due to the anisotropic-common-ray (and also isotropic-common-ray) approximation of the coupling ray theory. The errors of the common-ray approximations are calculated along the anisotropic common rays in smooth velocity models without interfaces. The derivation is based on the general equations for the second-order perturbations of travel time.     

TI介质局部角度域射线追踪与叠前深度偏移成像

研究与实践表明,对于长偏移距、宽方位地震数据,忽略各向异性会明显降低成像质量,影响储层预测与描述的精度.针对典型的横向各向同性(TI)介质,本文面向深度域构造成像与偏移速度分析的需要,研究基于射线理论的局部角度域叠前深度偏移成像方法.它除了像传统Kirchhoff叠前深度偏移那样输出成像剖面和炮检距域的共成像点道集,还遵循地震波在成像点处的局部方向特征、基于扩展的脉冲响应叠加原理获得入射角度域和照明角度域的成像结果.为了方便快捷地实现TI介质射线走时与局部角度信息的计算,文中讨论和对比了两种改进的射线追踪方法:一种采用从经典各向异性介质射线方程演变而来的由相速度表征的简便形式;另一种采用由对称轴垂直的TI(即VTI)介质声学近似qP波波动方程推导出来的射线方程.文中通过坐标旋转将其扩展到了对称轴倾斜的TI(即TTI)介质.国际上通用的理论模型合成数据偏移试验表明,本文方法既适用于复杂构造成像,又可为TI介质深度域偏移速度分析与模型建立提供高效的偏移引擎.     

横向各向同性介质中地震波走时模拟

横向各向同性介质是地球内部广泛分布的一种各向异性介质.针对这种介质，我们对各向同性介质的最小走时树走时模拟方法进行了推广，推广后的方法可适用于非均匀、对称轴任意倾斜的横向各向同性介质模型.为保证计算效率，最小走时树的构建采用了一种子波传播区域随地震波传播动态变化的改进算法.对于弱各向异性介质，我们使用了一种新的地震波群速度近似表示方法，该方法基于用射线角近似表示相角的思想，对3种地震波（qP, qSV和qSH）均有较好的精度.应用本文地震波走时模拟方法对均匀介质、横向非均匀介质模型进行了计算，并将后者结果与弹性波方程有限元方法的模拟结果进行了对比，结果表明两者符合得很好.本文方法可用于横向各向同性介质的深度偏移及地震层析成像的深入研究.     

起伏地表条件下各向异性地震波最短路径射线追踪

在地震波正反演研究中,考虑起伏地表和地震各向异性具有非常重要的理论意义和实际应用价值.本文在前人研究的基础上,将最短路径追踪算法引入到起伏地表各向异性介质模型的地震波走时计算中.模型剖分时,整体模型划分成正方形单元,起伏边界附近以不规则网格逼近,进而采用非规则节点布置实现非规则网格处的最短路径计算.追踪计算中采用Sena群速度近似公式,得到各向异性地震波的走时,实现了复杂地表情况下各向异性介质模型中地震波的射线追踪.理论模型计算结果显示,本文方法能够可靠地应用于复杂各向异性介质模型,具有较高的计算精度.     

TI介质局部角度域高斯束叠前深度偏移成像

各向异性射线理论基础上的局部角度域叠前深度偏移方法能够为深度域构造成像与基于角道集的层析反演提供有力支撑,但是对于复杂地质构造而言,高斯度叠前深度偏移在不失高效、灵活等特点的情况下,具有明显的精度优势.为此,本文研究局部角度域理论框架下的高斯束叠前深度偏移方法.为提高算法效率与实用性,文中讨论了一种从经典弹性参数表征的各向异性介质运动学和动力学射线方程演变而来的由相速度表征的简便形式,并提出了一种比较经济的各向异性高斯束近似合成方案.结合地震波局部角度域成像原理,讨论一种适合高斯束偏移的角度参数计算方法.国际上通用的理论模型合成数据试验表明：相比局部角度域Kirchhoff叠前深度偏移成像方法,本文方法具有更高的成像精度与抗噪能力,既适用于复杂构造成像,也可为TI介质深度域偏移速度分析与模型建立提供高效的偏移引擎.     

基于初至波走时层析成像的Tikhonov正则化与梯度优化算法

初至波走时层析成像是利用地震初至波走时和其传播的射线路径来反演地下介质速度的技术.该问题本质上是一个不适定问题,需要使用正则化方法并辅之以适当的最优化技巧.本文从数值优化的角度介绍了初至波走时层析成像的反演原理,建立了Tikhonov正则化层析成像反演模型并提出求解极小化问题的加权修正步长的梯度下降算法.该方法可以从速度模型的可行域中迭代找到一个最优解.数值试验表明,该方法是可行和有应用前景的.     

Development and Applications of Double-difference Seismic Tomography

Double-difference (DD) tomography is a generalization of DD location; it simultaneously solves for the three-dimensional velocity structure and seismic event locations. DD tomography uses a combination of absolute and more accurate differential arrival times and hierarchically determines the velocity structure from larger scale to smaller scale. This method is able to produce more accurate event locations and velocity structure near the source region than standard tomography, which uses only absolute arrival times. We conduct a stability and uncertainty analysis of DD tomography based on a synthetic data set. Currently three versions of the DD tomography algorithms exist: tomoDD, tomoFDD and tomoADD. TomoDD assumes a flat earth model and uses a pseudo-bending ray-tracing algorithm to find rays between events and stations while tomoFDD uses a finite-difference travel-time algorithm and the curvature of the Earth is considered. Both codes are based on a regularly distributed inversion grid, with the former for a local scale and the latter for a regional scale. In contrast, tomoADD adapts the inversion mesh to match with the data distribution based on tetrahedral and Voronoi diagrams. We discuss examples of applying DD tomography to characterize fault zone structure, image high-resolution structure of subduction zones, and determine the velocity structure of volcanoes.     

三维TTI介质高效射线追踪方法

TTI介质是石油地震勘探领域最常用的各向异性介质,快速计算TTI介质射线路径和走时信息有重要的研究意义.TTI介质传统运动学射线追踪方法一般基于任意弹性介质射线方程,利用Bond变换或者四阶张量变换来处理复杂的21个弹性参数,因而非常耗时.实际野外对称轴统一的TTI介质模型,一般可以看成VTI介质模型旋转一定角度获得.为此,本文推导了三维VTI介质射线追踪方程,提出先在本构坐标系中进行VTI介质射线追踪,再通过坐标旋转将射线路径旋转至观测坐标系中,获得TTI介质射线路径.数值模型计算表明该方法高效和精确,较传统方法效率提高了近4倍.在强各向异性等特殊情况下,体波波前面都与理论群速度面一致.     

基于射线追踪技术计算地震定位中震源轨迹的改进方法

使用震源轨迹确定震源位置不仅稳健而且直观,但当介质复杂时震源轨迹难以给出解析解.基于最小走时树射线追踪技术计算震源轨迹的方法(以轨迹所在的残差场中残差最小的点(初始点)至残差较小的点(震源轨迹代表点)的射线路径表示震源轨迹)适用于复杂速度模型,但尚不能正确计算由多段组成的震源轨迹,同时兼顾计算轨迹的完整性和精细性较为困难,计算参数设置烦琐不适于大批量数据的自动处理.针对该方法存在的问题,本文对其进行了改进:(1)采用一种"削皮"算法选取震源轨迹所经过的模型单元的节点作为轨迹代表点;(2)将残差较小的区域作为震源轨迹计算区域(该区域依轨迹分布自适应地划分为若干个连通区域),从未计算的轨迹代表点中选取残差最小者作为射线路径初始点,利用最小走时树算法依次计算所有连通区域内的震源轨迹;(3)通过去掉较短的不再分叉的射线路径使震源轨迹更为精细.虚拟和真实事件的算例表明,改进方法有效克服了原方法的不足,可便捷地计算复杂速度模型中事件的震源轨迹,计算的轨迹精细且较完整.     

三角网波行面扩展最小走时射线追踪全局算法

To address the problem of subdividing inflexible rectangular grid models and their poor definition of velocity interfaces, we propose a complex structure triangular net for a minimum traveltime ray tracing global algorithm. Our procedure is: (1) Subdivide a triangle grid based on the Delaunay triangular subdivision criterion and the relationships of the points, lines, and the surfaces in the subdividing area. (2) Define the topology relationships and related concepts of triangular unit ray tracing. (3) The source point and wave arrival points at any time compose the propagating plane wave and the minimum traveltime and secondary source positions are calculated during the plane wave propagation. We adopt the hyperbolic approximation global algorithm for secondary source retrieving. (4) By minimum traveltime ray tracing, collect the path from receiver to source points with the neighborhood point’s traveltime and the direction of the secondary source. Numerical simulation examples are given to test the algorithm. The results show that the triangular net ray tracing method demonstrates model subdivision flexibility, precise velocity discontinuity interfaces, and accurate computations.     

Errors Due to the Common Ray Approximations of the Coupling Ray Theory

The common ray approximation considerably simplifies the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies. It is thus of principal importance for numerical applications to estimate the errors due to the common ray approximation.We derive the equations for estimating the travel-time errors due to the isotropic and anisotropic common ray approximations of the coupling ray theory. These equations represent the main result of the paper. The derivation is based on the general equations for the second-order perturbations of travel time. The accuracy of the anisotropic common ray approximation can be studied along the isotropic common rays, without tracing the anisotropic common rays.The derived equations are numerically tested in three 1-D models of differing degree of anisotropy. The first-order and second-order perturbation expansions of travel time from the isotropic common rays to anisotropic-ray-theory rays are compared with the anisotropic-ray-theory travel times. The errors due to the isotropic common ray approximation and due to the anisotropic common ray approximation are estimated. In the numerical example, the errors of the anisotropic common ray approximation are considerably smaller than the errors of the isotropic common ray approximation.The effect of the isotropic common ray approximation on the coupling-ray-theory synthetic seismograms is demonstrated graphically. For comparison, the effects of the quasi-isotropic projection of the Green tensor, of the quasi-isotropic approximation of the Christoffel matrix, and of the quasi-isotropic perturbation of travel times on the coupling-ray-theory synthetic seismograms are also shown. The projection of the travel-time errors on the relative errors of the time-harmonic Green tensor is briefly presented.     

各向异性弹性波有限元叠前逆时偏移

利用有限元法和最小走时射线追踪的界面点法，实现了各向异性弹性波的叠前逆时偏移.理论模型资料的偏移结果清晰准确，证实了该系统的可靠性.通过对各向异性模型资料的各向同性偏移处理，发现常规偏移剖面存在较大误差，地质体的垂向深度和横向位置与实际模型有偏离.     

Ray tracing and geodesic deviation of the SH and SV reference rays in a heterogeneous generally anisotropic medium which is approximately uniaxial

The coupling ray theory is usually applied to anisotropic common reference rays, but it is more accurate if it is applied to reference rays which are closer to the actual wave paths. If we know that a medium is close to uniaxial (transversely isotropic), it may be advantageous to trace reference rays which resemble the SH–wave and SV–wave rays. This paper is devoted to defining and tracing these SH and SV reference rays of elastic S waves in a heterogeneous generally anisotropic medium which is approximately uniaxial (approximately transversely isotropic), and to the corresponding equations of geodesic deviation (dynamic ray tracing). All presented equations are simultaneously applicable to ordinary and extraordinary reference rays of electromagnetic waves in a generally bianisotropic medium which is approximately uniaxially anisotropic. The improvement of the coupling–ray–theory seismograms calculated along the proposed SH and SV reference rays, compared to the coupling–ray–theory seismograms calculated along the anisotropic common reference rays, has already been numerically demonstrated by the authors in four approximately uniaxial velocity models.     

One-Dimensional qP-Wave Velocity Model of the Upper Crust for the West Bohemia/Vogtland Earthquake Swarm Region

The western part of the Bohemian Massif (West Bohemia/Vogtland region) is characteristic in the relatively frequent recurrence of intraplate earthquake swarms and in other manifestations of past-to-recent geodynamic activity. In this study we derived 1D anisotropic qP-wave model of the upper crust in the seismogenic West Bohemia/Vogtland region by means of joint inversion of two independent data sets - travel times from controlled shots and arrival times from local earthquakes extracted from the WEBNET seismograms. We derived also simple 1-D P-wave and S-wave isotropic models. Reasons for deriving these models were: (a) only simplified crustal velocity models, homogeneous half-space or 1D isotropic layered models of this region, have been derived up to now and (b) a significant effective anisotropy of the upper crust in the region which was indicated recently by S-wave splitting. Both our anisotropic qP-wave and isotropic P-and S-wave velocity models are constrained by four layers with the constant velocity gradient. Weak anisotropy for P-waves is assumed. The isotropic model is represented by 9 parameters and the anisotropic one is represented by 24 parameters. A new robust and effective optimization algorithm - isometric algorithm - was used for the joint inversion. A two-step inversion algorithm was used. During the first step the isotropic P- and S-wave velocity model was derived. In the second step, it was used as a background model and the parameters of anisotropy were sought. Our 1D models are adequate for the upper crust in the West Bohemia/Vogtland swarm region up to a depth of 15 km. The qP-wave velocity model shows 5% anisotropy, the minimum velocity in the horizontal direction corresponds to an azimuth of 170°. The isotropic model indicates the V_P/V_S ratio variation with depth. The difference between the hypocentre locations based on the derived isotropic and anisotropic models was found to be several hundreds of meters.     

三维非均匀地质模型中的逐段迭代射线追踪

地震射线追踪是地震定位、层析成像、偏移等领域的重要正演环节.随着这些领域研究的深入,针对传统的网格结构和层状结构在描述复杂地质模型遇到的很大困难,我们采用大小不等、形状各异的地质块组成的集合体来描述三维复杂地质模型,并用三角形面片来描述地质块之间的物性间断面,理论上可以描述任意复杂的地质模型.为适应任意非均匀速度分布的地质模型,基于费马原理,本文发展了与之相适应的逐段迭代射线追踪方法.该方法属于弯曲法范畴,对路径点采用一阶显式增量修正,相对于传统的迭代法,高效省时.数值试验表明,联合逐段迭代法和伪弯曲法的射线追踪扰动修正方案在三维复杂非均匀块状模型中有适用性和高效性.     

VTI介质角度域转换波高斯束偏移成像方法研究

转换波偏移可以利用纵横波波场信息,得到高分辨率的成像结果,从而为油藏描述提供高质量的地震资料.目前的研究主要是利用纵波波场信息进行偏移成像,然而,传统的纵波方法在复杂探区成像时具有一定的局限性.为此,本文在各向异性介质声波射线追踪算法的基础上,推导出各向异性介质转换波射线追踪方程,发展了一种转换波射线追踪算法;并将研究的追踪算法应用到偏移成像中,提出了一种各向异性VTI介质角度域转换波高斯束偏移成像方法.通过各向异性VTI介质断块模型和复杂构造模型试算,说明了本文方法的正确性和有效性.模型试算的结果表明,在考虑地下各向异性时,本文研究的方法具有更好的成像效果,提取的角道集结果可以为偏移速度分析提供依据.     

基于偏微分方程的定向插值在偏移成像中的应用

对于射线类偏移成像来说,求解射线追踪系统中所涉及的属性值不在网格节点上的插值计算问题是一个非常重要的环节,它影响到求解走时、路径和振幅信息的计算效率和精度,进而影响到整个偏移成像的质量和效率.本研究根据速度模型的空间梯度特点,考虑被插值点处速度的梯度在横向和纵向的分布特征,构建基于速度梯度空间变化的偏微分方程算法,将近几年发展起来的基于偏微分方程的定向插值算法引入到射线类偏移成像当中,实现射线追踪当中涉及的属性值不在网格节点上的插值计算.由于偏微分方程法本身固有的特性(局部特征不变性、解的唯一性和线性叠加性),因此,该算法可以实现不破坏原始速度模型空间梯度结构的非网格节点属性的插值计算.通过在常用的速度模型上的插值计算对比、不同速度模型上射线路径对比分析以及复杂介质模型上最后的偏移成像结果分析可以得出,应用基于速度梯度构建的偏微分方程插值算法在进行插值计算的过程当中可以实现不破坏原始速度模型空间速度梯度结构的属性计算,同时应用该算法可以最终提高射线类偏移成像的质量.     

地震立体层析成像的实现方法及效果分析

立体层析成像是一种新的地震反射波层析成像方法,能为叠前深度偏移提供较为精确的宏观速度模型。本文研究了立体层析成像的实现方法,包括斜率与走时数据的拾取、离散速度模型构建和初始化、射线参数的确定、斜率和走时及射线计算以及反演问题解法等,建立立体层析成像的算法流程。并通过对Marmousi模型试验,对立体层析成像运行所需的主要参数,如初始速度模型、拾取数据量、离散网格尺寸、速度平滑权重等进行测试和分析,总结这些不同参数对立体层析反演结果的影响规律,用以指导生产实践。