共查询到20条相似文献，搜索用时 46 毫秒
1.
E. S. SAMPAIO 《Geophysical Prospecting》1976,24(1):112-122
The solution for the potential distribution about a point source of current placed at the surface of a continuous half-space is obtained for two cases: (1) the resistivity increases linearly with depth; (2) the conductivity increases linearly with depth. In each case, an expression for the apparent resistivity is established and master curves are presented for both the Wenner and the Schlumberger configurations. The results can be used in the interpretation of electrical sounding data in specified geologic situations. Furthermore, they may be used as a first step in the development of solutions for the more complex electric sounding problems. 相似文献
2.
Time harmonic point load and dynamic contact problem of contacting fluid and poroelastic half-spaces
The dynamic response of contacting fluid and fluid-saturated poroelastic half- spaces to a time-harmonic vertical point force or a point pore pressure is investigated. The solutions are formulated using the boundary conditions at the fluid-porous medium interface. The point load solutions are then used to solve the dynamic problem of the vertical vibration of a rigid disc (both permeable and impermeable discs are included) on the surface of the poroelastic half-space. The contact problems are solved by integrating the point force and point pore pressure solutions over the contact area with unknown discontinuous force and pore pressure distributions, which are determined from the boundary conditions. The solutions are expressed in terms of dual integral equations, which are converted to Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the vertical dynamic compliance coefficient for the cases with or without fluid overlying the poroelastic half-space are presented to show the effects of the fluid. The influence of the permeability condition of the disc on the compliance of the poroelastic half-space is investigated. The displacement, vertical stress, pore pressure in the poroelastic half-space and water pressure in the fluid half-space are also examined for different poroelastic materials and frequencies of excitation. The present results are helpful in the study of the dynamic response of foundations on the seabed under seawater. 相似文献
3.
从麦克斯韦旋度方程出发可以直接导出瞬变电磁场扩散方程,然而扩散方程不含电场对时间的一阶导数,不能构成显式的时域有限差分方程,借鉴du Fort-Frankel有限差分离散方法引入虚拟位移电流项构建显式时域有限差分方程.对Wang和Hohmann的经典时域算法进行了两点改进:第一,通过将矩形回线源电流密度加入麦克斯韦方程组的安培环路定理方程,实现回线源瞬变电磁激发源加入;第二,在计算中考虑关断时间.第一点改进使时域有限差分方程考虑了一次场的计算,并且源的计算不再依赖均匀半空间模型响应作为初始条件,使算法能够适应表层电阻率不均匀时的三维复杂模型.由于实际观测中不可能出现阶跃电流的关断形式,第二点改进可以方便设置发射电流下降沿.采用改进的三维时域有限差分正演算法对均匀半空间模型、四类三层模型、均匀半空间中含有低阻块体模型进行了计算并分别与解析解、线性数字滤波解、积分方程解和Wang的三维时域有限差分解进行了对比验证.以H模型为例,采用建立的三维时域有限差分正演算法计算了不同关断时间的斜阶跃脉冲回线源瞬变电磁中心点感应电动势衰减曲线.以实际地质资料为基础,构建包含两层采空区的三维复杂模型,以1 μs的极短关断时间进行了复杂模型定回线源瞬变电磁响应计算,并计算了该复杂模型的视电阻率曲线. 相似文献
4.
This paper considers the vertical dynamic response of a disk on a saturated poroelastic half-space. Firstly the pressure-solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. These equations are solved by a new method. Then the mixed boundary value problem for the vertical harmonic vibration of a disk on a poroelastic half-space is studied. The two types of drainage conditions at the surface of the poroelastic half-space are considered: (a) the surface of the poroelastic half-space is assumed to be completely pervious both within and exterior to the plate; (b) The interface between the plate and the poroelastic half-space is assumed to be impervious and the exterior region is assumed to be pervious. By using the Hankel transform techniques, the paper develops the governing dual integral equations. These governing integral equations are further reduced to systems of standard Fredholm integral equations of the second kind by Abel transform. 相似文献
5.
The paper first studies the analytical expression of electrical potential by a point current source in a uniform half-space medium,and then focuses on the distribution of electrical potential in a horizontally layered half-space model by a point current source within the surface layer or the bottom layer.Finally,the electrical potential by a source electrode in any layer of a layered half-space model is presented. 相似文献
6.
A transversely isotropic material in the sense of Green is considered. Using a series of potential functions proposed in [Eskandari-Ghadi M. A complete solution of the wave equations for transversely isotropic media. J Elasticity 2005; 81:1–19], the solutions of the transient wave equations within a half-space under surface load are obtained in the Laplace–Hankel domain for axisymmetric problems. The solutions are investigated in detail in the special case of a surface point force pulse varying with time as Heaviside function. Using Cagniard–De Hoop method, the inverse Laplace transform and inverse Hankel transform of the solutions are then obtained in the form of integrals with finite limits. For validity of the analytical results, the final formulations for surface waves are degenerated for an isotropic material and compared with the existing formulation obtained by Pekeris [The seismic surface pulse. Proc Natl Acad Sci USA 1955;41:469–80], to show that they are exactly the same. The numerical evaluations of the integrals for some transversely isotropic materials as well as an isotropic one are obtained. The present approach is then numerically verified by comparing a particular case of displacements for the surface of an isotropic half-space subjected to a point load of Heaviside function with the solutions obtained by Pekeris [The seismic surface pulse. Proc Natl Acad Sci USA 1955;41:469–80]. In addition, the wave equations for the mentioned medium are obtained on the vertical line directly under the applied surface load. The final formulations are degenerated for an isotropic material and compared with the existing formulation given in Graff [Wave motion in elastic solids. New York: Dover Publications Inc; 1975 [New Ed edition, November 1991]], to show that they are also exactly the same. Then equations are presented in graphical forms using an appropriate numerical evaluation. 相似文献
7.
Th. Triantafyllidis 《地震工程与结构动力学》1986,14(3):391-411
The dynamic soil–structure interaction of a rigid rectangular foundation with the subsoil represents a mixed-boundary value problem. This problem is formulated in terms of a system of coupled Fredholm integral equations of the first kind. The subsoil is modelled by a homogeneous, linear-elastic and isotropic half-space which is perfectly bonded to the rigid, rectangular foundation. An approximate solution for the resultant loads between the foundation and the half-space due to a unit forced displacement or rotation is obtained using the Bubnov–Galerkin method. Using this method the displacement boundary value conditions are exactly satisfied and the contact stress distributions between the foundation and the half-space are approximated by series expansions of Chebyshev polynomials. This method provides a simple means of studying the soil-structure interaction of rectangular foundations with different inertia properties. 相似文献
8.
Gin-Show Liou 《地震工程与结构动力学》1991,20(12):1115-1125
Presented is a systematic procedure for generating impedance (or compliance) matrices for foundations with arbitrary shapes, resting on an elastic half-space medium. A technique to decompose prescribed harmonic tractions on the half-space medium is employed to solve analytically the differential wave equations in cylindrical coordinates. However, the interaction stresses due to the vibration of a foundation with arbitrary shape are described in rectangular coordinates, and assumed to be piecewise constant in the region of the arbitrary shape. A coordinate transformation matrix is introduced for the piecewise constant tractions in order to use the solution of the differential wave equations in cylindrical coordinates. Finite element modelling is assumed in rectangular coordinates for the foundation itself. The impedance matrix is then obtained for the finite element model, using a variational principle and the reciprocal theorem. A simple example of a rigid square plate resting on a half-space medium and subjected to vertical excitation is used to demonstrate the efficiency and effectiveness of the procedure. Some numerical aspects are investigated and some possible extensions of the procedure are also discussed. 相似文献
9.
This paper analytically examines the horizontal vibration of a rigid disk on a saturated poroelastic half-space. The pressure-solid displacement form of the harmonic equations of motion for asymmetric dynamic problem are developed from the form of the equations originally presented by Biot. Making use of a new method the solution of the above equations is obtained. According to the mixed boundary -value conditions, the dual integral equations of the horizontal vibration of a rigid disk on a saturated poroelastic half-space are established. By appropriate transforms, it is shown that the dual integral equations can be reduced to a pair of Fredholm integral equations of the second kind, whose solutions are then computed. Numerical results for the horizontal dynamic compliance coefficient are given at the end of this paper. 相似文献
10.
Estimation of Elastic Moduli in a Compressible Gibson Half-space by Inverting Rayleigh-wave Phase Velocity 总被引：3，自引：1，他引：3
A Gibson half-space model (a non-layered Earth model) has the shear modulus varying linearly with depth in an inhomogeneous
elastic half-space. In a half-space of sedimentary granular soil under a geostatic state of initial stress, the density and
the Poisson’s ratio do not vary considerably with depth. In such an Earth body, the dynamic shear modulus is the parameter
that mainly affects the dispersion of propagating waves. We have estimated shear-wave velocities in the compressible Gibson
half-space by inverting Rayleigh-wave phase velocities. An analytical dispersion law of Rayleigh-type waves in a compressible
Gibson half-space is given in an algebraic form, which makes our inversion process extremely simple and fast. The convergence
of the weighted damping solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method.
Calculation efficiency is achieved by reconstructing a weighted damping solution using singular value decomposition techniques.
The main advantage of this algorithm is that only three parameters define the compressible Gibson half-space model. Theoretically,
to determine the model by the inversion, only three Rayleigh-wave phase velocities at different frequencies are required.
This is useful in practice where Rayleigh-wave energy is only developed in a limited frequency range or at certain frequencies
as data acquired at manmade structures such as dams and levees. Two real examples are presented and verified by borehole S-wave
velocity measurements. The results of these real examples are also compared with the results of the layered-Earth model. 相似文献
11.
A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section in a half-space is studied using the wave functions expansion method. The solution is reduced to solving infinite linear algebraic equations using the Graf's addition theorem in an appropriate form. Numerical results of the solution are obtained by truncation of the infinite equations and accuracies of the truncation are checked by the extent to which the numerical results fit the boundary condition and by convergence of the numerical results with the truncation order. Complicated effects of the depth-to-width ratio of the canyon on surface ground motion are shown by the numerical results for typical cases. 相似文献
12.
采用波函数展开方法，提出弹性半空间埋藏的圆形弹性夹塞区对平面ＳＨ波二维散射的封闭级数解答．利用内域型Ｇｒａｆ加法公式，将解答归结为一组无穷代数方程组的求解．通过对无穷方程组的截断计算，得到了解答的数值结果；并通过边值条件的收敛，检验了截断计算的精度．最后给出若干典型算例说明夹塞区产生的散射场对地表运动的复杂影响． 相似文献
13.
When an electric current is introduced to the earth, it sets up a distribution of charges both on and beneath the earth's surface. These charges give rise to the anomalous potential measured in the d. c. resistivity experiment. We investigate different aspects of charge accumulation and its fundamental role in d. c. experiments. The basic equations and boundary conditions for the d. c. problem are first presented with emphasis on the terms involving accumulated charges which occur wherever there is a non-zero component of electric field parallel to the gradient of conductivity. In the case of a polarizable medium, the polarization charges are also present due to the applied electric field, yet they do not change the final field distribution. We investigate the precise role of the permittivity of the medium. The charge buildup alters the electric fields and causes the refraction of current lines; this results in the well-known phenomenon of current channelling. We demonstrate this by using charge density to derive the refraction formula at a boundary. An integral equation for charge density is presented for whole-space models where the upper half-space is treated as an in-homogeneity with zero conductivity. The integral equation provides a tool with which the charge accumulation can be examined quantitatively and employed in the practical forward modelling. With the aid of this equation, we investigate the effect of accumulated charges on the earth's surface and show the equivalence between the half-space and whole-space formulations of the problem. Two analytic examples are presented to illustrate the charge accumulation and its role in the d. c. problem. We investigate the relationship between the solution for the potential via the image method and via the charge density. We show that the essence of the image method solution to the potential problem is to derive a set of fictitious sources which produce the same potential as does the true charge distribution. It follows that the image method is viable only when the conductivity structure is such that the effect of the accumulated charge can be represented by a set of point images. As numerical examples, we evaluate quantitatively the charge density on the earth's surface that arises because of topography and the charge density on a buried conductive prism. By these means, we demonstrate the use of the boundary element technique and charge density in d. c. forward modelling problems. 相似文献
14.
SH波对圆弧形凸起地形的散射 总被引：20，自引：3，他引：17
本文采用“契合”的方法,给出了一个求解平面ＳＨ波对圆弧形凸起形散射的新方法。利用包括圆绵形凸起上边界线在内的一个圆域中预先构造的满足凸起边界应力为零。其余边界应力待定的级数解和其余下的具有圆弧形凹陷的半空间中的解答。通过在其结合面上完成“契合”的过程中分别确定出圆域和半空间听解答。给出了问题的最终结果。利用上述方法,问题的求解仍归结为对一个无穷代数方程组的求解。最后,本文给出了数值结果并对其进行了 相似文献
15.
Diffraction of anti-plane SH waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel 总被引：8，自引：3，他引：5
A closed-form analytic solution of two-dimensional scattering and diffraction of plane SH waves by a semicylindrical hill with a semi-cylindrical concentric tunnel inside an elastic half-space is presented using the cylindrical wave functions expansion method. The solution is reduced to solving a set of infinite linear algebraic equations. Fourier expansion theorem with the form of complex exponential function and cosine function is used. Numerical solutions are obtained by truncation of the infinite equations. The accuracy of the presented numerical results is carefully verified. 相似文献
16.
A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section in a half-space is presented using the wave functions expansion. The solution is reduced to solving a set of infinite linear algebraic equations using the exterior region form of Graf's addition theorem. Numerical solutions are obtained by truncation of the infinite equations and their accuracies are demonstrated by convergence of the numerical results to the exact boundary condition with the increasing of the truncation order. The present solution is compared with the existing one presented by Todorovska and Lee for the same problem and their differences are analysed. Complicated effects of the depth-to-width ratio of the alluvial valley on surface ground motion are finally illustrated. 相似文献
17.
The boundary element method is used to obtain dynamic stiffness functions of rigid cylindrical foundations embedded in a uniform or layered viscoelastic half-space. Dynamic stiffness functions of hemispherical foundations embedded in a uniform half-space are also computed. The direct integral equation formulation is used in combination with the complete space point load fundamental solution that is integrated numerically along the azimuthal coordinate. The approach is easy to implement because of the simplicity of the fundamental solution. The numerical results obtained by this method for cylindrical and hemispherical foundations are very close to corresponding published results obtained by different procedures. A parametric study shows the important effects of the Poisson's ratio on the dynamic stiffness functions of cylindrical foundations embedded in a uniform viscoelastic half-space. The effect of the bedrock compliance on the stiffness functions is also shown in the case of cylindrical foundations embedded in a soil layer that rests on a bedrock. 相似文献
18.
圆弧型沉积盆地对平面SH波的散射 总被引：19，自引：0，他引：19
采用波函数展开方法给出圆弧型沉积盆地对面ＳＨ波二维散射问题的封闭级数解答。利用外域Ｇｒａｆ加法公式将解答归结为无穷代数方程组的求解。通过截断计算得到解答的数值结果，并通过连续条件的满足程度检验了截断计算的精度。将本文结果已有的近似解析解进行比较，指出了近似解答的误差来源和适用范围。给出一些典型算例说明盆地深度比对地震动的复杂作用。 相似文献
19.
A mathematical formulation for the electric potential from point current-sources coaxial with a metal casing has been obtained. The excitation caused by the axial point-sources will produce currents in the pipe. By assuming that the pipe can be divided into many cylindrical ring segments with constant axially-directed current, the solution of the fields inside and outside the pipe can be formulated in an integral form. The integral equation applied to the segmented pipe yields a set of simultaneous linear equations which are solved for the currents in the pipe; these are then used to calculate the potentials anywhere outside the pipe in the medium. This solution has been used to study the distribution of the potentials in a half-space for a single current-source at and beyond the bottom of a finite length of casing. For a casing 0.1 m in radius and 0.006 m in wall thickness with a conductivity of 106 S/m, in a half-space of 10-2 S/m, it was found that only in a region very near the pipe does the pipe exert substantial influence on the fields of a point-source 100 casing diameters beyond the end of the pipe. It appears that cross-hole resistivity surveys can be implemented without corrections for the casing if the source is located at least 50–100 casing diameters beyond the end of the casing. Hole-to-surface surveys are much more affected by the pipe. For a pipe-source separation of 100 casing diameters, the surface measurements must not be closer than a half pipe length for a 5% or less field distortion. 相似文献
20.
K. Gopalsamy 《Pure and Applied Geophysics》1974,112(1):240-252
Summary This paper deals with the determination of the pressure distribution in an acoustic half-space excited by a pressure pulse randomly moving along a line on the surface. When the random motion of the pressure pulse is a stationary stochastic process, the expectation of the random acoustic pressure field in the excited half-space is obtained using transform techniques. 相似文献