共查询到20条相似文献，搜索用时 109 毫秒
1.
本文采用传播矩阵技术研究并建立了层状正交各向异性地层中多分量感应测井响应的有效算法.首先通过Fourier变换将频率空间域中的Maxwell方程组求解问题转化为频率波数域中关于电磁场水平分量常微分方程组的定解问题.利用该方程组系数矩阵的本征值和归一化本征向量将电磁场分解成上行波和下行波模式的组合,推导出均匀正交各向异性介质中由任意方向磁偶极子产生的电磁波模式解析表达式;在此基础上,利用叠加原理和边界条件研究了电磁波在层状正交各向异性地层中的反射和透射,给出各个界面上的广义反射系数和不同地层中电磁波振幅的递推公式,进而得到电磁波模式的解析解.为了有效确定频率空间域中的电磁场,采用二维Patterson自适应求积算法结合有限连分式展开技术计算傅氏逆变换.最后通过数值模拟结果证明了该算法的有效性,考察了不同各向异性系数、不同井眼倾角以及仪器长度和工作频率变化等情况下的多分量感应测井响应特征. 相似文献
2.
进一步提高瞬变电磁法对地探测的解释精度,提出了回线源瞬变电磁成像原理及数值计算方法. 讨论了频率域中水平层状介质中瞬变电磁响应,得到一个以波阻抗为积分核的双重积分式;然后对水平层介质下电磁场的解进行上、下行波分离,得到含有以反射系数序列为未知的线性方程组,并给出了求取波阻抗和反射系数的数值解法：对实测磁场值进行域的变换,以均匀半空间下的等效波阻抗代替积分核函数,经过线性数字滤波后,在频率域求出等效波阻抗;把频率域中的波阻抗转换到时间域,以此为参数,构建方程组,在时间域用线性规划法求出反射系数序列. 最终以反射系数为参数进行成像. 对理论模型的数值计算结果表明,用本文提出的成像方法可以增强瞬变电磁法识别地下电性分界面的能力. 相似文献
3.
4.
本文实现了2.5维电导率正交各向异性海洋可控源电磁等参有限元数值模拟.利用傅里叶变换导出了电导率正交各向异性2.5维海洋可控源电磁法波数域电磁场耦合方程,采用伽里金加权余量法推导了相应的有限元方程;采用任意四边形单元对研究区域进行剖分,在单元中进行双二次插值,将有限元方程化为线性代数方程组;最后,求解线性方程组并进行反傅里叶变换获得空间域电磁场值.这个方法可以模拟海底起伏地形条件下地下任意形状电导率正交各向异性的复杂模型.与一维模型的数值模拟结果对比表明,电磁场数值解与解析解吻合.二维模型的计算结果与二维自适应非结构有限元模拟结果也吻合.水平海底二维地电模型考察了不同各向异性系数对海洋可控源电磁响应的影响特征.海底起伏地形地电模型的数值结果表明,电导率各向异性对海洋可控源电磁响应影响明显,有可能淹没海底地形和高阻油气藏引起的异常. 相似文献
5.
提出直接在序率域内用Walsh变换实现引力场球谐综合的问题。给出球谐函数展开式的Walsh变换及快速算法,讨论了Walsh变换和Walsh-Fourier变换、Fourier变换之间的差异,分析了用地球重力场模型OSU81的位系数作出的Walsh变换和Fourier变换的结果。研究表明:Walsh变换与Walsh-Fourier变换、Fourier变换对应向量在数量方面的差值通常都小于士10~(-5);对于给定的阶数和飞行高度,3种方法求得的球谐综合值总是完全一致的;1°×1°等网格数据和Walsh函数形状相近。在重力场研究中Walsh级数会比Fourier级数收敛得更快;Walsh变换在计算速度、计算准确度、数据储存、收敛速度和方法简单方面都好于Fourier变换。 相似文献
6.
A time domain boundary element in a cylindrical co-ordinate system is developed for the analysis of wave propagation in a layered half-space. The field quantities (displacements and tractions) are expressed as products of Fourier series in the circumferential direction and as linear polynomials in the other spatial directions. An integral equation is written for each layer as an independent domain, and these equations are then assembled into a general equation by virtue of compatibility and equilibrium conditions between the interfaces. Examples of three-dimensional wave propagation in the layered half-spaces due to various forms of surface and inner-domain excitations are reported to demonstrate the accuracy and versatility of the method. 相似文献
7.
本文将普遍声逆散射微扰论应用于弹性波层析成像问题,在Born变换下推出了以旋转角为补偿参数的各阶微扰重建公式,实现了对非均匀各向同性散射体内3个参数（质量密度ρ和两个Lamé系数λ,μ）的同时重建. 对于层析成像问题,在弹性波的传播过程中P波与SV波有耦合,但它们不会和SH波发生耦合,于是可以得到3个形式相对简单的标量方程. 在Born变换下,在散射波中引入微扰参数,将散射体的3个参数分别按该微扰参数展开,然后利用二维自由空间的Green函数分别得到散射的P波、SV波和SH波的积分表示. 最后,经一维傅氏变换后,得到Born变换下散射体3个参数的各阶微扰重建公式. 相似文献
8.
随钻地质导向钻井的关键在于对边界的探测,为提高仪器探测深度,时谐源激励的电磁波测井方法通常采用降低频率、增大源距的方式.瞬变电磁波测井信号源的突然关断产生会产生感应涡流,涡流随时间向地层深部扩散,与时谐源激励方式相比,其探测深度更大且测量过程不受信号源的干扰.因此,本文提出一种时间域瞬变电磁波测井边界远探测方法,采用余弦变换的数值滤波算法,模拟层状地层同轴发射接收线圈的瞬变电磁波测井响应,结果显示,地层电导率越大,电磁波传播速度越慢,测量晚期感应电动势与地层电导率线性相关;通过定义层状介质总场与线圈系所在当前层背景场的差值可方便提取界面信息,对界面的探测距离可达数十米;瞬变电磁波测井响应受源距的影响很小,为利用短源距实现远探测提供了可能.瞬变电磁波测井与时谐源电磁波测井相比优势明显,在电磁波测井领域中应用前景广阔. 相似文献
9.
An exact stiffness matrix method is presented to evaluate the dynamic response of a multi-layered poroelastic medium due to time-harmonic loads and fluid sources applied in the interior of the layered medium. The system under consideration consists of N layers of different properties and thickness overlying a homogeneous half-plane or a rigid base. Fourier integral transform is used with respect to the x-co-ordinate and the formulation is presented in the frequency domain. Fourier transforms of average displacements of the solid matrix and pore pressure at layer interfaces are considered as the basic unknowns. Exact stiffness (impedance) matrices describing the relationship between generalized displacement and force vectors of a layer of finite thickness and a half-plane are derived explicitly in the Fourier-frequency space by using rigorous analytical solutions for Biot's elastodynamic theory for porous media. The global stiffness matrix and the force vector of a layered system is assembled by considering the continuity of tractions and fluid flow at layer interfaces. The numerical solution of the global equation system for discrete values of Fourier transform parameter together with the application of numerical quadrature to evaluate inverse Fourier transform integrals yield the solutions for poroelastic fields. Numerical results for displacements and stresses of a few layered systems and vertical impedance of a rigid strip bonded to layered poroelastic media are presented. The advantages of the present method when compared to existing approximate stiffness methods and other methods based on the determination of layer arbitrary coefficients are discussed. 相似文献
10.
11.
A transient Green function due to suddenly applied line loads in an isotropic and homogeneous half-space is reported in this paper. The derivation of the half-space Green function in the Laplace and the Fourier transform spaces is first reviewed. Following an explicit inversion of the Fourier transform, the inverse Laplace transform is implemented along the contour integral on the p-complex plane in an integral form. The half-space Green function consists of full-space Green functions and a singularity-free complementary term. It can be easily incorporated into current transient boundary elements using the transient full-space Green function. Combined with finite elements, the half-space Green function can be used in a hybrid procedure to solve transient half-space problems without discretization of the free surface. Numerical results are presented to illustrate transient wave propagation in a half-space. 相似文献
12.
T. LEE 《Geophysical Prospecting》1975,23(3):492-512
The Galerkin method of solving integral equations is well suited to the solution of the integral equations describing the transient response of a sphere embedded in a layered medium, which is excited by a large co-axial loop. The transient response is calculated by transforming the steady state solutions obtained in the frequency domain. The analysis shows that the scattering matrix is extremely diagonally dominant and the maximum number of modes required to obtain convergence does not rapidly increase with frequency. The number of modes required is about eight. This type of scattering matrix can be taken to be an expression of the principle of elementary superposition. This principle is reflected in the decay curves. These show that the early part of the decay curves asymptotically approach the decay curves to be expected for a layered structure without the sphere. The slope of the latter stages of the decay curve gives a decay constant that is the same as was obtained for spheres in free space excited by planar or dipolar sources. The point of departure in time of these curves from the layered ground curves is delayed either by placing the sphere at a greater depth or by placing a more conductive overburden above the sphere. 相似文献
13.
14.
地震的孕育是一复杂的物理和力学过程。对于一球型震源体,则会有裂隙由核向外而后液体由外向核的双重扩散过程;与此同时,介质的电磁性质亦相应地发生扩散运动。本从定解问题入手,求得ε、μ、σ的扩散解。根据麦克韦电场理论、求得震源体各向异性介质中麦克斯韦的等价方程与电磁场的基本方程。由此得出震源体介质的似异体性质。对球型导体电磁感应的定解问题,对其频域解分离,得到在外源场作用下震源体中的分量解,即感应场、 相似文献
15.
R. S. Sidhu 《Pure and Applied Geophysics》1971,85(1):125-139
Summary The wave equations of elasticity in the presence of body forces for a semi-infinite, isotropic, heterogeneous medium with exponentially varying material properties have been solved. Using double Fourier transform the equations are first transformed to linear second order differential equations. From the solution of these equations the displacements are obtained by the use of inversion theorem for double Fourier transform. The method followed resolves the disturbance into its constitutive parts—incident and reflectedP, SV andSH type waves. Surface displacements due to a single couple, double couple and various other sources have been calculated. 相似文献
16.
17.
Solutions to the problem of the point source field in a spherically layered medium are analyzed. For a three-layer waveguide model, a solution in the form of the Watson integral was used. A consideration of the singularities in the plane of the integration variable made it possible to represent the integral as a superposition of three waves. Two of them are connected with the interaction of the primary spherical wave with the lower convex and upper concave interfaces. The third wave is connected with the alternate action with both interfaces. The fourth wave is caused by the interaction between the primary wave and random inhomogeneities of the external medium (the ionosphere). Here, simulation was carried out based on Green equations. The considered unique data of flight measurements of the point source field strength indicate the efficiency of simulating the transhorizon propagation of decameter waves based on the superposition of all four aforesaid wave packets. 相似文献
18.
近源时域电磁场具有信号强、探测深度大和精度高等优点,但传统瞬变电磁场理论中偶极子近似在近源区会引起较大误差,推导瞬变电磁场直接时域解析式是解决这一问题的关键.本文在点电荷微元假设下通过时域格林函数,采用分离变量等方法推导出了上半空间一次有源波动场和反射波的时域解析式和下半空间二次无源波动场的时域解析式,结合均匀半空间瞬变电磁场的边界条件给出了均匀半空间瞬变电磁场的直接时域解析式,进而利用第一型曲线积分,通过沿回线源叠加推导出圆回线源在瞬变电磁场中的直接时域解析式.然后在半空间表面上,与传统的电偶极源假设下的表达式作了比较.数值结果表明两者在远源区的计算结果相差甚微,而近源区则存在很大误差.本文利用真正点元（点电荷）严密推导给出的均匀半空间表面上瞬变电磁场的直接时域解析式适用于全场区探测,克服了偶极子假设下只适用远场区的不足,为瞬变电磁法的进一步发展和实际勘探提供了新的理论基础. 相似文献
19.
在波场的正变换中,保证瞬变电磁场的计算精度的同时,应用两步最优化算法,成功地控制和减少了积分系数个数和离散数字积分的采样点个数,解决了在波场反变换式中,由于积分系数过多而产生的欠定方程组的问题,同时改善了第一类算子方程的不适定性.在波场反变换中,将正则化算法用于逆变换过程的计算中,通过采用偏差原理和Newton迭代格式选出最优的正则化参数,使得反变换所得到的波场稳定、可靠.通过对数值计算结果与已知波场函数对比,证明了该方法的有效性和实用性. 相似文献
20.
P. Novák 《Studia Geophysica et Geodaetica》2007,51(3):351-367
Satellite missions CHAMP and GRACE dedicated to global mapping of the Earth’s gravity field yield accurate satellite-to-satellite
tracking (SST) data used for recovery of global geopotential models usually in a form of a finite set of Stokes’s coefficients.
The US-German Gravity Recovery And Climate Experiment (GRACE) yields SST data in both the high-low and low-low mode. Observed
satellite positions and changes in the intersatellite range can be inverted through the Newtonian equation of motion into
values of the unknown geopotential. The geopotential is usually approximated in observation equations by a truncated harmonic
series with unknown coefficients. An alternative approach based on integral inversion of the SST data of type GRACE into discrete
values of the geopotential at a geocentric sphere is discussed in this article. In this approach, observation equations have
a form of Green’s surface integrals with scalar-valued integral kernels. Despite their higher complexity, the kernel functions
exhibit features typical for other integral kernels used in geodesy for inversion of gravity field data. The two approaches
are discussed and compared based on their relative advantages and intended applications. The combination of heterogeneous
gravity data through integral equations is also outlined in the article.
panovak@kma.zcu.cz 相似文献