界面和速度反射联合成像──理论与方法

依据波逆行原理重新推导了由地震波反射走时资料反演界面深度的关系式──走时对界面偏导数关系，它不仅适用于反射波，也适用于透射波．还给出了任意多个复杂界面情况下走时对界面偏导数关系的离散形式．另外，正交算子投影法被推广用来解决速度与界面的同时成像问题．数值模拟的结果表明，本文的方法是有效的．     

速度分布和界面位置的联合反演

提出了横向非均匀介质中由地震波走时资料同时反演介质速度分布和界面位置的方法．计算中，由于变步长技术和线性内插技术(包括理论走时和偏导矩阵的线性内插)的应用，大大提高了运算速度．与国内目前流行的同类程序相比，运算速度快5倍以上．而且，在界面位置的反演中，除反射波外，还考虑了透射波走时对于界面位置的偏导数，从而充分利用了各类透射波资料中所含界面位置的信息，加快了收敛速度．数字模拟实验和实测资料的处理结果表明了该方法和程序的有效性及实用性．      

射线近似中弯曲界面的Fréchet导数

本文讨论了射线和射束理论地震图对速度模型和弯曲界面变化的敏感性.Nowack和Lutter(1989)以前的成果给出走时和射线振幅相对于光滑变化的速度变化导数,在实施构造的线性化最大似然反演时这些导数是需要的.在射线近似中,局部应用Snell定律、校正波前曲率以及使用局部平面波反射/透射系数来体现光滑界面,利用费马原理可沿着原始射线轨迹直接计算走时的偏导数.对于反射/透射射线的振幅扰动,必须考虑扰动后的两点射线轨迹的射线偏移.本文遵循的方法是利用没有额外射线追踪的扰动理论近似计算扰动后的两点射线,然后沿着这条近似的两点射线直接计算扰动的射线振幅,包括修正过的反射/透射系数和几何扩展.进行了若干次数值实验,利用走时和振幅反演速度和界面形状来检验所得出的偏导数算子、走时和振幅反演结果,还与对大尺度性质不太敏感而对不均匀曲率较敏感的振幅作了比较.     

近震资料确定三维地震速度结构的一种方法

我们研究了由近震得到的地震走时资料估计地震波速度三维结构的反演方法。这种方法由同时确定速度界面的二维深度分布、三维速度分布、台站校正和震源来表征。速度界面的深度分布和慢度扰动的分布以纬度、经度和深度的幂级数来拟合。这种三维地震结构的表示不仅有助于减少未知参数的个数,也有助于解析地求取界面深度、速度和走时关于未知参数偏导数的值。连接震源和台站之间的射线轨迹,是在具有确切界面深度分布的简化的速度分布条件下由称为试射法的射线追踪方法确定的。数值试验证明,我们的反演方法可成功地估计三维速度结构。     

三维复杂地壳结构非线性走时反演

中国大陆中西部乃至全球造山带普遍具有复杂地壳结构.随着矿产资源勘探和深部探测研究的深入,探测造山带及盆山耦合区下方地壳精细结构正逐渐成为当前面临的巨大挑战.人工源深地震测深方法正越来越清晰地揭示出不同构造域地壳速度结构的基本特征,然而传统的层状结构模型参数化方法难以准确描述复杂地质模型,通常情况下多忽略速度结构的精细间断面且采用层边界平滑处理,难以满足地壳精细结构成像的发展要求.针对上述困难,本文采用最近发展的块状结构建模方案构建三维复杂地壳模型,基于逐段迭代射线追踪正演走时计算方法,推导了走时对三角形界面深度以及网格速度的偏导数,开展了非线性共轭梯度走时反演方法研究.发展了利用直达波和反射波等多震相走时数据对界面深度和网格速度的多参数联合反演方法,并引人不同种类震相数据的权系数和不同类型参数偏导数归一化的方法.数值算例表明,基于块状结构的非线性共轭梯度走时反演方法适用于复杂地壳结构模型,在利用人工源走时数据反演复杂地壳精细结构领域具有良好的应用前景.     

三维多层介质重力-地震同步联合反演

联合反演是地球物理勘探的重要解释手段,能够提高模型参数的反演精度.本文在归纳和分析重力与地震资料联合反演的研究和应用现状的基础上,利用三维多层介质模型的地震走时和重力正演公式,推导了地震走时和重力异常对界面深度的雅可比矩阵,实现了三维重力-地震同步联合反演界面成像.最后进行了数值理论模型模拟和实例计算,结果表明地震走时和重力同步联合反演很好的重建了三维多层介质界面.     

利用地震回折波资料反演界面位置与速度分布

论述了利用地震回折波资料反演界面位置与速度分布的方法，推导了地震波走时对于界面位置偏导数的计算公式。数值模拟和实测资料的计算结果表明了该方法的有效性和编制的计算程序的实用性。该方法最突出的特点是充分地利用了透射波资料中所含的界面位置的信息。界面位置的分辨率与界面两边的速度反差有关，速度差别越大，则分辨率越高。     

任意介质中的动态规划法地震波三维走时计算

任意介质中的地震波三维走时计算是复杂介质情况下Kirchhoff积分法三维叠前深度偏移及走时层析成像的核心.走时算法的效率及精度决定了成像方法的应用范围及效果,对复杂地质构造区域的地震波成像时需要有稳健的走时计算方法.本文把Schneider等提出的用动态规划法计算二维任意复杂介质中走时的方法推广到三维.此方法的核心是构造从源点到当前计算点的平均慢度,基于Fermat原理,用球面波近似导出走时计算所用的公式,并用动态规划法搜索到达当前计算点的初至走时.它适用于任意复杂的介质情况,对速度差异没有限制,计算过程中考虑到各个可能的方向到达当前计算点的初至波.首波及回转波的初至走时也能正确地计算出来.各种理论速度模型上的走时计算及胜利油田某探区的三维叠前深度偏移的成功实践验证了方法的正确性.     

利用地震回以资料反演界面位置与速度分布

论述了利用地震回折波资料以界面位置与速度分布的方法，推导了地震波走时对于界面位置偏导数的计算公式。数值模拟和实测资料的计算结果表明了该方法的有效性和编制的计算程序的实用性，该方法最的特点是充分地利用了透射波资料中所含的界面位置的信息。界面位置的分辩率与界面两边的速度反差有关，速度判别越大，则分辨率越高。     

三维复杂介质中转换波走时快速计算

复杂介质中转换波走时计算是多波勘探地震学中重要内容之一.本项研究利用惠更斯原理和费玛原理,获得了三维复杂介质中转换波快速计算的改进型最小走时树方法.其中,在保证精度的条件下,为了提高三维转换波走时计算效率,首先对初至波最小走时树基本算法进行了改进.本方法通过将转换波分为上、下行波分别进行射线追踪以实现三维转换波走时的快速计算.模型计算表明,方法的计算速度快,而且稳定性强,对多波地震勘探具有较大的应用价值.     

Transformation of spatial and perturbation derivatives of travel time at a curved interface between two arbitrary media

We consider the partial derivatives of travel time with respect to both spatial coordinates and perturbation parameters. These derivatives are very important in studying wave propagation and have already found various applications in smooth media without interfaces. In order to extend the applications to media composed of layers and blocks, we derive the explicit equations for transforming these travel–time derivatives of arbitrary orders at a general smooth curved interface between two arbitrary media. The equations are applicable to both real–valued and complex–valued travel time. The equations are expressed in terms of a general Hamiltonian function and are applicable to the transformation of travel–time derivatives in both isotropic and anisotropic media. The interface is specified by an implicit equation. No local coordinates are needed for the transformation.     

P-wave Tomography in Inhomogeneous Orthorhombic Media

— A P-wave tomographic method for 3-D complex media (3-D distribution of elastic parameters and curved interfaces) with orthorhombic symmetry is presented in this paper. The technique uses an iterative linear approach to the nonlinear travel-time inversion problem. The hypothesis of orthorhombic anisotropy and 3-D inhomogeneity increases the set of parameters describing the model dramatically compared to the isotropic case. Assuming a Factorized Anisotropic Inhomogeneous (FAI) medium and weak anisotropy, we solve the forward problem by a perturbation approach. We use a finite element approach in which the FAI medium is divided into a set of elements with polynomial elastic parameter distributions. Inside each element, analytical expressions for rays and travel times, valid to first-order, are given for P waves in orthorhombic inhomogeneous media. More complex media can be modeled by introducing interfaces separating FAI media with different elastic properties. Simple formulae are given for the Fréchet derivatives of the travel time with respect to the elastic parameters and the interface parameters. In the weak anisotropy hypothesis the P-wave travel times are sensitive only to a subset of the orthorhombic parameters: the six P-wave elastic parameters and the three Euler angles defining the orientation of the mirror planes of symmetry. The P-wave travel times are inverted by minimizing in terms of least-squares the misfit between the observed and calculated travel times. The solution is approached using a Singular Value Decomposition (SVD). The stability of the inversion is ensured by making use of suitable a priori information and/or by applying regularization. The technique is applied to two synthetic data sets, simulating simple Vertical Seismic Profile (VSP) experiments. The examples demonstrate the necessity of good 3-D ray coverage when considering complex anisotropic symmetry.     

Simultaneous inversion of velocity distribution and interface positions

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3-D seismic tomography for velocity and interface structure of the crust and upper mantle (theoretical part)

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Grid travel-time tracing: Second-order method for the first arrivals in smooth media

A new computational scheme for calculating the first-arrival travel times on a rectangular grid of points is proposed. The new proposed method is of second-order accuracy. This means that the error of the calculated travel time is proportional to the second power of the grid spacing. The method should be sufficiently accurate for all applications in smooth seismic models. On the other hand, the method is not, in its present form, proposed for models with structural interfaces which make the method unstable and generate travel-time errors of the first order. Equations are also presented for the appropriate evaluation of the errors of calculated travel times to check their accuracy, and the proposed method is compared with other numerical methods. The method is developed, described and demonstrated in 2-D, but may also be extended to 3-D models and to general models with structural interfaces.     

各向异性介质中S波接收函数成像方法

岩石圈各向异性主要由上地幔矿物晶格优势排列方向和上地壳内裂缝、裂隙的定向分布造成.在各向异性特征显著区域,利用SKS震相剪切波分裂获得的延迟时间高达1.5s以上.本文根据方位各向异性,利用广义反射透射系数矩阵方法正演S波接收函数,研究各向异性对不同反方位角接收函数转换震相走时的影响.我们发展了基于HTI模型各向异性走时校正的方法,成功的在单层和多层(快轴方向相同或不同)的各向异性介质中对齐不同反方位角接收函数的Moho面和LAB的转换震相走时.我们将该方法应用于在青藏高原东北缘的流动台站,试图在各向异性强度较大区域对实测数据转换震相走时的校正效果进行测试.结果表明:各向异性走时校正能够加强单台接收函数转换震相的可追踪性,能量增强的叠后转换震相在时深转换后更利于对界面深度的识别与判断;在考虑三维成像的情况下,我们的各向异性校正方法对提高成像结果的准确性有重要意义.     

Ray path of head waves with irregular interfaces

Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity. However, the path that the rays travel along in media with irregular interfaces is not clear. Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements (SEMO) that can accurately evaluate waves traveling along an irregular interface. Consequently, the head waves are separated from interface waves by a time window. Thus, their energy and arrival time changes can be analyzed independently. These analyses demonstrate that, contrary to the case for head waves propagating along a flat interface, there are two mechanisms for head waves traveling along an irregular interface: a refraction mechanism and transmission mechanism. That is, the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media. Such knowledge will be helpful in constructing a more accurate inversion method, such as head wave travel-time tomography, and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas, such as the Tibetan Plateau.     

利用单程波算子进行叠前时间偏移走时计算(英文)

传统的叠前时间偏移公式都是基于水平层状模型的假设而推导而来,在速度横向变化剧烈的介质中则不能够达到理想的聚焦效果。本文基于李代数积分方程以及拟微分算子等理论推导了非对称走时公式,计算公式由于包含有速度横向导数项,在速度横向变化大的介质中,也能有较高的聚焦效果,而且也为走时计算提供了精确的相对振幅保持权系数。本文对推导的方法进行模型测试并进行实际数据的试算,其结果证明非对称走时方法的成像精度远高于对称走时计算方法。