层状弹性介质的波阻抗反演

讨论层状弹性介质的纵波阻抗和横波阻抗的同时反演问题，由纵波线源激发产生的弹性波场，通过倾斜叠加可以得到其平面波分解，分解出来的平面波场对应于以不同倾角斜入射激发所产生的波场，它们满足由二维弹性波基本方程派生出的一维偏微分方程组。利用在地面同时接收的位移速度的水平和垂直分量，可以由每个特定角度斜入射产生的平面波场所满足的一维方程组反演层状弹性介质的两个参数，在已知密度情况下，可以反演纵波阻抗和横波阻     

非均匀各向异性介质中弹性波的传播

平面波分解法是研究地震波场简捷有效的方法,各种复杂的波场可用平面波合成的方法得到．文中采用平面波方法研究非均匀各向异性介质中的弹性波．对时空域非均匀各向异性介质波动方程,运用f-k变换,可得到频率空间域波动方程(Christoffel方程)．利用非均匀各向异性介质中,弹性参数及其空间变化率与Christoffel矩阵元素关系,提出非均匀各向异性介质Christoffel矩阵方程的求解方法,并运用于非均匀TIV介质和非均匀EDA介质．在连续介质条件下,当波沿速度增加方向传播时,振幅的方向导数小于零,即振幅衰减;当波沿速度减小方向传播时,振幅的方向导数大于零,即振幅增强．波的振幅强度是传播方向的函数(各向同性条件下也是如此),但并不总是衰减．若只研究波沿速度增加方向传播的情况即得出波在连续介质中传播振幅衰减的结论是不全面的．      

各向异性介质中地震波前面的偏微分方程

从含２１个弹性参数的各向异性介质中关于位移分量ｕ_ｘ、ｕ_ｙ与ｕ_ｚ的偏微分波动方程组出发，通过假定平面波位移函数解，导出准Ｐ波、准ＳＶ波与准ＳＨ波的波前面偏微分控制方程，进而对各类特殊各向异性介质（横向各向同性介质、椭圆及立方体各向异性介质）中地震波前面偏微分方程进行了讨论．以上结果为研究各向异性介质中地震波传播规律以及进行正、反演研究奠定了理论基础．     

各向异性介质qP波传播描述I：伪纯模式波动方程

地球介质相对于地震波波长尺度的定向非均匀性会导致波速的各向异性,进而影响地震波场的运动学与动力学特征．各向异性弹性波动方程是描述该类介质波场传播的基本工具,在正演模拟、偏移成像与参数反演中起着关键作用．为了面向实际应用构建灵活、简便的各向异性波场传播算子,人们一直在寻求简化的各向异性波动方程．本文借鉴各向异性弹性波波型分离思想,通过对平面波形式的弹性波方程(即Christoffel方程)实施一种代表向波矢量方向投影的相似变换,推导出了一种适应任意各向异性介质、运动学上与原始弹性波方程完全等价,在动力学上突出qP波的新方程,即qP波伪纯模式波动方程．文中以横向各向同性(TI)介质为例,给出了相应的qP波伪纯模式波动方程及其声学与各向同性近似,并在此基础上开展了正演模拟和逆时偏移试验,展示了这种描述各向异性波场传播的新方程的特点与优势．     

基于海底电缆数据的声弹耦合介质多参数最小二乘逆时偏移（英文）

在海洋地震勘探中,海底电缆技术采集的多分量地震数据,涉及到多参数的反演与成像问题,本文针对海底电缆多分量地震数据提出了一种弹性波多参数最小二乘逆时偏移方法。该方法的波场延拓算子为混合方程,即在海水介质中采用声波方程进行波场计算,而海底固体介质的波场由纵横波形分离的矢量弹性波方程得到。在海底界面中采用声弹耦合控制方程将两种类型的方程结合起来。通过推导纵横波形分离的弹性波偏移算子、反偏移算子和梯度公式实现基于纵横波形分离的弹性波最小二乘逆时偏移方法。通过模型试算证明了该方法能够得到高质量的纵波速度和横波速度分量的成像剖面,相比与传统弹性波最小二乘逆时偏移方法,多参数耦合造成的成像串扰噪音得到了很好地压制。     

时间域全波场各向异性性参数反演

从各向异性弹性波的有限元正演方程出发，导出了反问题中时间域雅可比矩阵求解的计算公式。它具有与时间域有限元正演方程相同的表达形式，故可通过有限元正演计算来获得雅可比矩阵。研究了有限元正演算法的效率和精度、吸收边界条件等的问题，以提高反演系统的效率和精度。在此基础上，实现了叠前全波场各向异性弹性参数反演。计算表明，在初始模型偏离真实模型较大的情况下，层状模型和横向不均匀模型的反演结果均能准确地收敛到真实模型上。     

饱和土中浅埋隧道耦合二维动力响应解答探讨

针对平面波耦合作用下饱和半空间中浅埋隧道二维动力响应的典型问题的解答进行探讨。首先基于Biot饱和孔隙介质理论建立饱和土场方程,并通过中间势函数的代入推导得到饱和土体中的快纵波、慢纵波及横波的Helmholtz势函数方程,随后引入柱坐标系下饱和土体和弹性衬砌的势函数通解,并代入边界条件中,建立以第n组参数为变量的多元一次齐次线性方程组。采用本文的推导思路,可以解决饱和土体中的浅埋隧道在地震作用时P波和S波耦合作用下的响应问题。     

对波达波夫和Pride震电波方程组的对比分析

用Biot介质参数说明了波达波夫震电波方程组中弹性动力学 参数的含义，解释了第一类和第二类震电效应的意义，在忽略第一类震电效应条件下将该方 程组与Pride方程组进行比较，说明了二者在描述第二类震电效应方面的异同点. 同时指出 ：波达波夫方程组忽略了流体与固体的耦合质量；方程中的黏性耗散项丢掉了一个孔隙度因 子，依据该方程组计算出的弹性波和转换电场的幅度将偏大；边界条件之一存在错误，会影 响对波在界面上的反射透射规律的描述.     

时间域全波场各向异性弹性参数反演

从各向异性弹性波的有限元正演方程出发 ,导出了反问题中时间域雅可比矩阵求解的计算公式 .它具有与时间域有限元正演方程相同的表达形式 ,故可通过有限元正演计算来获得雅可比矩阵 .研究了有限元正演算法的效率和精度、吸收边界条件等方面的问题 ,以提高反演系统的效率和精度 .在此基础上 ,实现了叠前全波场各向异性弹性参数反演 .计算表明 ,在初始模型偏离真实模型较大的情况下 ,层状模型和横向不均匀模型的反演结果均能准确地收敛到真实模型上 .     

三维各向异性介质弹性波模拟的透射边界条件

在弹性波数值模拟中,为了压制人工边界反射,需要使用边界条件.本文从三维各向异性介质中弹性渡方程出发,在边界入射波为平面波的假设前提下,利用特征值分解以及坐标系旋转,导出人工边界处质点位移矢量计算公式,实现了在边界处为任意倾斜入射时的透射边界条件.并显示了边界条件的使用效果.     

Constraining the anisotropy structure of the crust by joint inversion of seismic reflection travel times and wave polarizations

In the context of wide-angle seismic profiling, the determination of the physical properties of the Earth crust, such as the elastic layer depth and seismic velocity, is often performed by inversion of P- and/or S-phases propagation data supplying the geometry of the medium (reflector depths) or any other structural parameter (P- or S-wave velocity, density...). Moreover, the inversion for velocity structure and interfaces is commonly performed using only seismic reflection travel times and/or crustal phase amplitudes in isotropic media. But it is very important to utilize more available information to constrain the non-uniqueness of the solution. In this paper, we present a simultaneous inversion method of seismic reflection travel times and polarizations data of transient elastic waves in stratified media to reconstruct not only layer depth and vertical P-wave velocity but also the anisotropy feature of the crust based on the estimation of the Thomsen’s parameters. We carry out a checking with synthetic data, comparing the inversion results obtained by anisotropic travel-time inversion to the results derived by joint inversion of seismic reflection travel times and polarizations data. The comparison proves that the first procedure leads to biased anisotropic models, while the second one fits nearly the real model. This makes the joint inversion method feasible. Finally, we investigate the geometry, P-wave velocity structure and anisotropy of the crust beneath Southeastern China by applying the proposed inversion method to previously acquired wide-angle seismic data. In this case, the anisotropy signature provides clear evidence that the Jiangshan-Shaoxing fault is the natural boundary between the Yangtze and Cathaysia blocks.     

Elastic one-return boundary element method and hybrid elastic thin-slab propagator for strong-contrast media with sharp boundaries

In this paper, we developed the theory and algorithm of an elastic one-way boundary element method(BEM) and a corresponding hybrid elastic thin-slab propagator for earth media with sharp boundaries between strong contrast media. This approach can takes the advantage of accurate boundary condition of BEM and completely overcomes the weak contrast limitation of the perturbationtheory based one-way operator approach. The one-way BEM is a smooth boundary approximation, which avoids huge matrix operations in exact full BEM. In addition, the one-way BEM can model the primary-only transmitted and reflected waves and therefore is a valuable tool in elastic imaging and inversion. Through numerical tests for some simple models,we proved the validity and efficiency of the proposed method.     

Computing the Sensitivity Kernels for 2.5-D Seismic Waveform Inversion in Heterogeneous,Anisotropic Media

2.5-D modeling and inversion techniques are much closer to reality than the simple and traditional 2-D seismic wave modeling and inversion. The sensitivity kernels required in full waveform seismic tomographic inversion are the Fréchet derivatives of the displacement vector with respect to the independent anisotropic model parameters of the subsurface. They give the sensitivity of the seismograms to changes in the model parameters. This paper applies two methods, called ‘the perturbation method’ and ‘the matrix method’, to derive the sensitivity kernels for 2.5-D seismic waveform inversion. We show that the two methods yield the same explicit expressions for the Fréchet derivatives using a constant-block model parameterization, and are available for both the line-source (2-D) and the point-source (2.5-D) cases. The method involves two Green’s function vectors and their gradients, as well as the derivatives of the elastic modulus tensor with respect to the independent model parameters. The two Green’s function vectors are the responses of the displacement vector to the two directed unit vectors located at the source and geophone positions, respectively; they can be generally obtained by numerical methods. The gradients of the Green’s function vectors may be approximated in the same manner as the differential computations in the forward modeling. The derivatives of the elastic modulus tensor with respect to the independent model parameters can be obtained analytically, dependent on the class of medium anisotropy. Explicit expressions are given for two special cases—isotropic and tilted transversely isotropic (TTI) media. Numerical examples are given for the latter case, which involves five independent elastic moduli (or Thomsen parameters) plus one angle defining the symmetry axis.     

Exact elastic impedance tensor for isotropic media

The existing expressions of elastic impedance,as the generalized form of acoustic impedance,represent the resistance of subsurface media to seismic waves of non-normal incidence,and thus include information on the shear-wave velocity.In this sense,conventional elastic impedance is an attribute of the seismic reflection and not an intrinsic physical property of the subsurface media.The derivation of these expressions shares the approximations made for reflectivity,such as weak impedance contrast andisotropic or weakly anisotropic media,which limits the accuracy of reflectivity reconstruction and seismic inversion.In this paper,we derive exact elastic impedance tensors of seismic P-and S-waves for isotropic media based on the stress-velocity law.Each componentof the impedance tensor represents a unique mechanical property of the medium.Approximations of P-wave elastic impedance tensor components are discussed for seismic inversion and interpretation.Application to synthetic data and real data shows the accuracy and robust interpretation capability of the derived elastic impedance in lithology characterizations.     

层状介质弹性参数反演问题研究综述

地震波动方程反问题的研究具有重要的理论意义和实践意义。由于高维波动方程反演问题理论研究的困难和巨大的计算量,层次介质弹性参数研究在数学界和地球物理学引起了广泛的关注。经过前人近三十年的努力,一维声波方程的单参数反演理论已趋成熟,并已逐步实用化。基于矢量波动方程的多参数反演,非脉冲响应对应的反问题是层状介质弹性参数反演需要进一步深入研究的问题。     

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.     

Joint inversion of travel times and waveforms by means of annealing algorithms. Application to a seismic refraction experiment

An algorithm of annealing is applied to a joint inversion of travel times and waveforms belonging to a synthetically generated seismic refraction experiment. The medium (crust and upper mantle) is modelled by a set of plane stratified layers and a halfspace. The obtained structure (elastic parameters and depth of layers) shows that, in spite of contaminating seismic noise and poor knowledge of the seismic source, annealing methods are a good tool in these kinds of inversion problems. We think that many characteristics of the annealing process described here could be used with real data and more sophisticated media for the crust and upper mantle of the earth than the present example.     

非均匀流-固边界耦合介质多参数全波形反演方法

海洋勘探环境可以抽象为下伏固体与上覆流体相互耦合的介质,本文针对流-固边界耦合介质提出了一种高效、稳定的多参数（速度和密度）全波形反演方法.本文采用弹性波一阶位移-应力方程作为过渡层耦合声波压力方程与弹性波位移方程来模拟耦合环境,相比于传统的交错网格建模方法或者构建连续性条件,本文提出的方法在正演精度和稳定性上凸显出很大优势,极大降低了计算内存.反演策略对多参数全波形反演至关重要,由于不同参数之间的相互耦合使得密度在多参数全波形反演中较难获得,因此本文将非均匀流-固边界耦合介质多参数全波形反演分为两个步骤完成：第一步利用变密度声波方程结合推导出的密度梯度算子进行纵波速度和密度的双参数反演;第二步根据链式法则求取横波速度的梯度,结合第一步的反演结果使用流-固边界耦合方程反演横波速度.最后通过与声波动方程数值模拟结果对比证明正演算法的准确性;上覆流体的Marmousi-2模型的数值试验测试说明反演方法的有效性和适应性.     

横观各向同性饱和土的基本方程组

两相饱和多孔介质的基本方程组和计算参数的选取在一定程度上是混乱的.本文利用连续介质力学理论，结合空间平均化方法，根据应力-应变关系、运动学关系、连续性方程及广义Darcy定律，建立了横观各向同性液体饱和多孔介质的基本方程组；通过将该基本方程组与Biot理论的基本方程组进行比较，确定了Biot方程组中的弹性常数Bi与弹性常数cij的关系，并得到了确定Biot参数mi和ri的计算公式——Biot参数与渗透率、孔隙率及黏性系数的关系；最后对几种特殊情形进行了讨论，给出了简化方程组.     

A new method to directly invert the elastic parameters

IntroductionMoreandmoreevidencesshowthatstratapropertiesareanisotropic.Itisveryimportanttoutilizegeophysicalwaystouncoverthepropertiesofstratainpetroleumsurveyandcoalbedmethaneexplorationaswellasearthquakeforecasting.Becauseofdetectablecharacteristicsofseismicvelocityanisotropy,itissuccessfulinpastyearsthatlayersareshiftedcorrectlytotheoriginalpositioninmigrationprocessionofseismicwaves.Anewwayofdirectinversionofstrataelasticparametersisputforthinthepaper.Itusesmultiple-wavesdatatodiscoverorp…