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利用积分方程法实现了均匀导电半空间三维大地电磁响应的数值模拟。求取张量格林函数积分时,采用二次剖分算法解决计算中奇异值问题,对于含有贝塞尔函数的积分项,利用结合连分式展开的高斯求积代替常规的快速汉克尔变换方法,确保了张量格林函数的正确计算并提高了计算精度。最后通过数值模拟结果的对比及模型试算验证了算法的正确性,所实现的三维大地电磁数值模拟算法为理论研究三维地电构造的大地电磁响应的分布规律提供了有效的工具,也为研究三维反演算法奠定了基础。 相似文献
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利用积分方程方法以及半空间并矢格林函数的快速算法对埋地目标体矢量电磁散射进行正演计算。首先,利用半空间电磁并矢格林函数建立起埋地目标体的体积分方程。然后通过将空间偏导转移至格林函数谱域积分的积分号之外,并采用离散复镜像方法来近似余下的零阶索末菲积分,进一步得到并矢格林函数各个分量的闭合形式。由于避免了对索末菲积分的繁琐数值计算,使得生成反应矩阵和计算散射场时由半空间并矢格林函数计算带来的瓶颈问题得到较好的克服,因而极大地提高了埋地目标体电磁响应正演计算效率,同时也能保证足够的精度。 相似文献
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本文在对称地震矩张量反演的基础上，进一步研究了非对称地震矩张量时间域反演的理论与方法，结果表明:非对称地震矩张量反演与对称地震矩张量反演类似，只需将对称地震矩张量反演方法略加改动，即增加3个待解参数，便可实现非对称地震矩张量反演.为了判断非对称地震矩张量反演相对于对称地震矩张量反演是否存在过度拟合，运用了AIC准则 (赤池信息准则).为了定量地描述地震矩张量之间的差异，引入了地震矩张量的矢量表示法.通过分析格林函数与地震矩张量各分量之间的关系，得出:在非对称地震矩张量反演时，若仅用垂直向地动位移数据，将无法区分Mxy与Myx这两个分量, 需要同时运用垂直向与水平向地动位移数据进行联合反演才能区分Mxy与Myx; 若采用不同的速度结构模型或不同的格林函数计算方法，则需重新评估地震矩张量各分量的分辨度问题.为检验非对称地震矩张量反演方法的可行性, 利用合成地震图进行了一系列数值试验.数值试验结果表明，在非对称地震矩张量反演中，有必要引入S波进行P波与S波联合反演以提高反演的准确性和判定断层面的能力. 相似文献
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近源时间域电磁场具有信号强、探测深度大、精度高等优点,但传统勘探电磁场理论中偶极子近似在近源会引起较大误差,导致这一优势的发挥受到了制约.开展直接时间域电磁场解析式研究,是解决这一问题的途径之一.本文提出在点电荷微元假设下,引入时域格林函数,求取瞬变电磁场时间域解析解.采用积分运算法,把电磁场阻尼波动方程的求解问题转化为求其格林函数积分形式解的问题;建立辅助路径解决奇点问题,利用复分析中的约当引理、留数定理和广义函数等理论和方法,推导计算出时间域格林函数的时空四重广义积分.得到达朗贝尔方程的直接时域格林函数精确解析式,与传统方法“比拟”出的公式具有相同的形式,验证了本文推导的时域格林函数解析公式的正确性;推导出扩散方程的直接时间域解析解.通过与时变点电荷源时间域的电磁响应近似表达式进行对比,得出本文所推导的公式计算精度较高的结论;建立了全空间回线源瞬变电磁场问题的直接时间域求解公式.为解决全场区瞬变电磁场精细探测直接时域解析问题提供了基础理论. 相似文献
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本文提出一种空间波数混合域磁异常场三维数值模拟方法.该方法利用磁位三维空间域积分为卷积的特点，沿水平方向进行二维傅里叶变换，把空间域磁位满足的三维积分问题转化为不同波数之间相互独立的垂向一维积分问题.保留垂向为空间域，优势之一在于便于浅层单元剖分可适当加密，随着深度增加，单元剖分适当稀疏，可以准确模拟任意复杂地形和磁性体的磁异常，兼顾了计算精度与计算效率；优势之二在于一维积分垂向可离散为多个单元积分之和，每个单元采用二次形函数表征磁化强度，可得出单元积分的解析表达式，计算精度高、效率高.该方法充分利用一维形函数积分的高效和高精度、快速傅里叶变换的高效性及算法高度并行性，实现了磁异常场高效、高精度的数值模拟.设计棱柱体模型，将模型解析解与空间波数混合域法的数值解对比，结果表明该方法计算精度高、效率高.设计了组合棱柱体复杂模型，对比分析了标准FFT扩边法与Gauss-FFT法的计算精度与计算效率，总结了标准FFT的扩边系数选取策略.针对任意复杂地形条件下的磁异常模拟问题，本文提出一种适用于起伏地形条件下的磁异常场快速计算方法，并对其有效性进行了验证. 相似文献
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Zhdanov提出的拟线性(QL)近似方法有效解决了积分方程计算速度慢、占用内存多的缺陷,但因为三维频谱激电(SIP)换源频繁,每次换源都需要重新计算剖分单元的并矢格林函数和一次场,所以用该方法模拟三维SIP的速度仍然缓慢.本文根据一次场及格林函数的空间对称性,提出了一种适用于多源电磁法的快速QL近似正演方法.在此基础上,实现了Cole-Cole参数范围约束的三维SIP共轭梯度反演方法.理论试算结果表明:快速QL近似方法适用于三维SIP正演模拟,计算速度较QL近似方法有了很大提高;Cole-Cole参数范围约束的三维SIP共轭梯度反演方法对零频电阻率、极化率等参数的反演效果良好,将异常区域剖分成2000块时迭代一次只需约0.2s的时间,占用内存大约为140 MB. 相似文献
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格林函数在解决电磁场和直流电场问题的积分方程法和边界单元法等方法中有着广泛的应用.在应用格林函数时会遇到格林函数奇异性的问题,即其在源区域的内部,当场点和源点重合时,会碰到对格林函数为无穷大,积分为奇异积分.对于不同问题中遇到的不同形式的格林函数奇异性问题的各种处理方法进行了分析和评述.对于标量格林函数奇异性问题处理方法有：挖去法、级数展开法、绕开法和解析法等.对于并矢格林函数奇异性问题处理方法有：分量处理法、源并矢法和拟源并矢法等处理方法.通过对实际工作中所遇到的新方法新问题中的不同形式的格林函数的研究,提供了奇异性问题的处理的方法和途径. 相似文献
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利用数字盒式磁带记录加速度仪组成的流动地震台网所记录的三分向近场加速度图,通过矩张量反演确定了1985年4月18日云南禄劝 Ms=6.1地震的部分余震的震源机制.以均匀半无限弹性介质的格林函数解释路径效应,并通过正演计算识别由两次积分得到的位移地震图中的直达 P 波、直达 S 波和 SP 转换波震相,然后用这些震相进行矩张量反演.反演结果表明,在解超定线性方程组时,采用适当的加权系数,可使上述直达波和转换波的理论计算值与观测值拟合得较好.尽管用以反演的三个余震大小不同(震级 ML48,3.2,3.5),震源位置也有差别,但它们的震源机制却非常接近,且与主震的震源机制相当一致.这一特征显示了余震的发生与主震发震构造的内在联系.这些实例说明,由震源球球面上分布适宜的数字地震台网取得的近场加速度资料,借助于即使是简单的介质模型,通过地震矩张量反演,不但可以得出这些地震震源的主要成份————剪切位错源,同时还可得出震源所含的其它成分,如膨胀源和补偿线性向量偶极. 相似文献
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基于Born散射理论的二维黏声介质高斯波束正演 总被引：1，自引：0，他引：1
Born散射理论可以通过省略高阶项实现针对一次散射波场的模拟.在这一理论的基础上,本文提出了一种针对二维黏声介质的一次散射波场高斯束Born正演方法.在该方法中,格林函数通过一系列不同初射方向的高斯波束累加获得,可以计算多至走时波场,保证了正演算法的计算精度.同时为了提高计算效率,正演方法使用了wavelet-bank方式合成局部平面波.区别于针对声波介质正演的wavelet-bank使用方法,文中将介质黏滞性信息融入了局部平面波的wavelet-bank合成方法中,以此实现针对黏声介质的快速一次散射波场模拟.两个模型的计算结果表明:本文提出的黏声介质高斯波束正演方法具有良好的计算精度以及较高的计算效率. 相似文献
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Kazuhito Yamasaki 《Acta Geophysica》2009,57(3):567-582
We consider the effect of the faults-defects (FD) field on the following quantum phenomena: (i) the motion of a particle expressed
by the Green function; (ii) thermodynamic phenomena expressed by the partition function. We use the path integral formulation
based on the extended deformation gradient (EDG) tensor. This formulation connects the Green function of (i) with the partition
function of (ii) to describe the thermodynamics in terms of a quantum particle motion. We obtain the following results: (a)
The Lagrangian in the Green function includes the new potential consisting of stress functions that shift the path of the
free particle from the shortest distance; (b) The solution of the partition function in one-dimensional space makes it possible
to deduce the thermodynamic relations in the FD field. Such results could not be obtained by taking the traditional mechanical
and quantum approaches, so the path integral formulation based on the EDG tensor is a useful tool. 相似文献
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Summary A method of determining simultaneously the moment tensor and source time function in the point source approximation is presented. For trial values of the moment tensor components and of the source time function, parametrized by the sum of overlapping triangles delayed in time, theoretical seismograms can be synthetized and compared with the recorded ones. The iterative procedure determines the adjustment of source parameters until a good correlation of both synthetic and observed records is reached. The Green functions in a horizontally stratified medium are constructed with the use of a modal summation method.The limits of applicability of the algorithm are illustrated by the inversion of four synthetic seismograms constructed for two horizontally stratified models of the structure in Friuli area, Italy. The records constructed for the same structural model as for which the Green functions were computed can be inverted even in the high-frequency range. In the opposite case, when the records and Green functions used corresponded to different structural models, a good correlation of the input records with the final synthetics was obtained for low - pass filtered data only.Additional tests performed with input seismograms contaminated with random noise yielded good resolution of the moment tensor and the duration of the source time function even for a high noise to signal ratio. 相似文献
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The coupling–ray–theory tensor Green function for electromagnetic waves or elastic S waves is frequency dependent, and is usually calculated for many frequencies. This frequency dependence represents no problem in calculating the Green function, but may pose a significant challenge in storing the Green function at the nodes of dense grids, typical for applications such as the Born approximation or non–linear source determination. Storing the Green function at the nodes of dense grids for too many frequencies may be impractical or even unrealistic. We have already proposed the approximation of the coupling–ray–theory tensor Green function, in the vicinity of a given prevailing frequency, by two coupling–ray–theory dyadic Green functions described by their coupling–ray–theory travel times and their coupling–ray–theory amplitudes. The above mentioned prevailing–frequency approximation of the coupling ray theory enables us to interpolate the coupling–ray–theory dyadic Green functions within ray cells, and to calculate them at the nodes of dense grids. For the interpolation within ray cells, we need to separate the pairs of prevailing–frequency coupling–ray–theory dyadic Green functions so that both the first Green function and the second Green function are continuous along rays and within ray cells. We describe the current progress in this field and outline the basic algorithms. The proposed method is equally applicable to both electromagnetic waves and elastic S waves. We demonstrate the preliminary numerical results using the coupling–ray–theory travel times of elastic S waves. 相似文献
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球体位错理论计算程序的总体设计与具体实现 总被引：3，自引：0，他引：3
本文详细介绍了球体位错理论计算程序的总体设计思想、 各类配套文件的具体内涵以及各类输出文件的物理含义, 同时介绍了程序的使用方法和注意事项, 为读者独立使用该程序提供参考。 球体位错理论计算程序主要由三部分组成: ① 位错格林函数计算程序, 基于具体的球对称地球模型提供离散的二维格林函数数值框架; ② 积分计算程序, 对离散的格林函数数值框架进行双二次样条插值运算, 并对四类独立位错源对应的格林函数进行适当组合, 从而计算出任意位置任意类型震源在地表产生的同震变形(含位移、 应变、 重力变化和大地水准面变化); ③ 辅助文件, 用于提供发震断层模型和计算点位信息。 一般情况下, 读者不需要理解位错格林函数计算程序和积分计算程序, 只需要对辅助文件提供的信息进行针对性改动, 就可以计算目标地震在目标观测站引起的同震变形。 相似文献
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S. S. Kevorkyants 《Izvestiya Physics of the Solid Earth》2006,42(8):702-711
Forward seismic problems are solved for elastic media by rigorous methods (i.e., methods with controllable accuracy). Analysis of the current state of research on this subject suggests that the most promising methods are based on integral and integro-differential equations, notwithstanding the rather modest results of their application to solving forward problems in the theory of elastic vibrations. The second Green integral theorem for seismic waves, formulated and proven in the paper, yields a system of two boundary (surface) integral equations for the displacement vector u(M 0) and the normal (to the boundary surface) vector component of the stress tensor tn(M 0). The integrands of the surface integrals in terms of which the function tn(M 0) is expressed on both sides of the interface between the medium and the heterogeneity contain the second derivatives of the Green’s tensor functions ? e (M 0, M) and ? i (M 0, M), respectively, which are responsible for a cubic singularity (third-order singularity) if the integration point M coincides with the observation point M 0. An original method of eliminating the cubic singularity proposed in the paper involves special tensor normalization of the integrals on the outer and inner sides of the interface and subsequent subtraction of one integral from another in order to construct the second integral equation. 相似文献
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We present a concept of the hybrid finite volume–integral equation technique for solving Maxwell's equation in a quasi-static form. The divergence correction was incorporated to improve the convergence and stability of the governing linear system equations which pose a challenge on the discretization of the curl–curl Helmholtz equation. A staggered finite volume approach is applied for discretizing the system of equations on a structured mesh and solved in a secondary field technique. The bi-conjugate gradient stabilizer was utilized with block incomplete lower-upper factorization preconditioner to solve the system of equation. To obtain the electric and magnetic fields at the receivers, we use the integral Green tensor scheme. We verify the strength of our hybrid technique with benchmark models relative to other numerical algorithms. Importantly, from the tested models, our scheme was in close agreement with the semi-analytical solution. It also revealed that the use of a quasi-analytical boundary condition helps to minimize the runtime for the linear system equation. Furthermore, the integral Green tensor approach to compute at the receivers demonstrates better accuracy compared with the conventional interpolation method. This adopted technique can be applied efficiently to the inversion procedure. 相似文献
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IntroductionThe wave propagation problems in saturated soil are very important for the civil engineering, geophysics and seismology. Biot (1956,1962) established the theory of wave propagation in saturated soil firstly, and hereafter many researchers have used Biot theory to study wave propagation problems in saturated soil. By using integral transform and potential function method, Philippacopoulos (1988) studied the Lamb(s problem of a vertical point force applied to the surface of saturate… 相似文献
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Electromagnetic induction of a three-dimensional conductivity inhomogeneity in the two-layered earth
Summary The calculation of the elements of Green's tensor function is presented for solving the problem of the electromagnetic induction by means of a vector integral equation. A two-layered Earth is considered as the medium, the surface layer including a three-dimensional conductivity inhomogeneity. Use is made of the boundary condition requiring the vertical component of the electric current to be zero at the Earth's surface which partly simplifies the theoretical computation. Long-period asymptotics of the individual complicated functions, occurring in Green's tensor function as well as in the tensor function required to calculate the components of the anomalous magnetic field at the surface of the halfspace, were effected. With the aid of these asymptotics one can obtain estimates of the functions occurring in the theoretical analysis of the problem. 相似文献