共查询到20条相似文献，搜索用时 610 毫秒
1.
An inverse gravity problem is solved for a geological model consisting of bodies of Sretenskii’s class. The position of the
middle plane is fixed for each body. It is required to determine the upper and lower boundaries of a body, which are described
by analytical functions and are parameterized. The solution of the problem is illustrated by an example. 相似文献
2.
Jaroslava Sisáková 《Studia Geophysica et Geodaetica》1990,34(1):32-36
Summary In this paper the solution of the direct magnetic problem for two-dimensional bodies, founded on the application of Green's theorem is derived. This solution is derived under the assumption that the components of the magnetization vector have continuous derivatives with respect to the coordinates and that they are continuous within the body. The problem is solved in terms of Green-type integrals for the scalar and vector potential of the magnetostatic field and it may serve the purpose of solving the problem of the analytical continuation of the external field into the body. 相似文献
3.
Roland Karcol 《Studia Geophysica et Geodaetica》2011,55(1):21-34
Solutions to the direct problem in gravimetric interpretation are well-known for wide class of source bodies with constant
density contrast. On the other hand, sources with non-uniform density can lead to relatively complicated formalisms. This
is probably why analytical solutions for this type of sources are rather rare although utilization of these bodies can sometimes
be very effective in gravity modeling. I demonstrate an analytical solution to that problem for a spherical shell with radial
polynomial density distribution, and illustrate this result when applied to a special case of 5th degree polynomial. As a
practical example, attraction of the normal atmosphere is calculated. 相似文献
4.
Summary The general solution of the direct gravimetric problem for homogeneous and inhomogeneous bodies was derived in[1] in the form of Green-type integrals. In the present paper it is proved that this solution simplifies considerably, if the solution of the external Dirichlet problem, defined by conditions(2), is known for a closed surface bounding the attracting body.Dedicated to RNDr Jan Pícha, CSc., on his 60th Birthday 相似文献
5.
Roland Karcol 《Studia Geophysica et Geodaetica》2018,62(3):427-449
The direct gravity problem and its solution belong to the basis of the gravimetry. The solutions of this problem are well known for wide class of the source bodies with the constant density contrast. The non-uniform density approximation leads to the relatively complicated mathematical formalism. The analytical solutions for this type of sources are rare and currently these bodies are very useful in the gravimetrical modeling. The solution for the vertical component of the gravitational attraction vector for the 3D right rectangular prism is known in the geophysical literature for the density variations described by the 3-rd degree polynomial. We generalized this solution for an n-th degree, not only for the vertical component, but for the horizontal components, the second-order derivatives and the potential as well. The 2D modifications of all given formulae are presented, too. The presented general solutions, which involve a hypergeometric functions, can be used as they are, or as an auxiliary tool to derive desired solution for the given degree of the density polynomial as a sum of the elementary functions. The pros-and-cons of these approaches (the complexity of the programming codes, runtimes) are discussed, too. 相似文献
6.
全张量磁梯度数据具有高精度、高分辨率、多参量的优点,能更加清晰地刻画地质体的分布特征,综合利用磁张量梯度数据准确地获得地质体水平位置和深度信息是解释的主要目的.磁张量数据的方向解析信号具有减小倾斜磁化干扰的优点,常被用来圈定磁源体的水平位置,但解析信号强度随着地质体埋深的增加急剧衰减,难以有效识别较深的地质体.张量数据均衡边界识别技术,利用不同方向解析信号的比值函数,能有效地均衡不同深度地质体的响应,同时显示不同深度地质体的边界,提高了对较深地质体的分辨率.磁张量数据深度成像技术根据实测张量数据与假定模型张量数据的相关系数来给定地质体的深度,综合利用多参量数据联合反演提高了反演结果的准确性,且无需进行复杂的反演运算,是大数据量张量数据解释的有效方法.理论模型试验证明：磁张量数据均衡边界识别技术可清晰和准确地识别地质体的水平范围,受倾斜磁化干扰小;磁张量数据深度成像技术可准确地获得地质体的深度信息,具有较强的抗噪性.将上述方法应用于铁矿区实测航磁张量梯度数据解释,获得了铁矿体水平分布与埋深,深度结果与张量欧拉反褶积法计算结果一致. 相似文献
7.
A new finite element model to analyze the seismic response of deformable rocking bodies and rocking structures is presented. The model comprises a set of beam elements to represent the rocking body and zero‐length fiber cross‐section elements at the ends of the rocking body to represent the rocking surfaces. The energy dissipation during rocking motion is modeled using a Hilber–Hughes–Taylor numerically dissipative time step integration scheme. The model is verified through correct prediction of the horizontal and vertical displacements of a rigid rocking block and validated against the analytical Housner model solution for the rocking response of rigid bodies subjected to ground motion excitation. The proposed model is augmented by a dissipative model of the ground under the rocking surface to facilitate modeling of the rocking response of deformable bodies and structures. The augmented model is used to compute the overturning and uplift rocking response spectra for a deformable rocking frame structure to symmetric and anti‐symmetric Ricker pulse ground motion excitation. It is found that the deformability of the columns of a rocking frame does not jeopardize its stability under Ricker pulse ground motion excitation. In fact, there are cases where a deformable rocking frame is more stable than its rigid counterpart. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
Summary
A solution of the direct gravity problem for a finite body with variable density is given. The method is based on Green's formula and is applicable when a particular solution of Poisson's equation is known. The attraction due to the body is expressed by integrals over its surface
The exact solution of the direct gravity problem, as known from the theory of two-dimensional fields [1–3], is closely connected with the problem of the analytic continuation of the exterior field of the attracting mass system into its interior. In the first place, this is a problem of determining the singularities of the exterior field, their distribution within the system and their nature. This approach to the solution of the direct problem is also meaningful from the point of view of determining the characteristics of the attracting system and, therefore, also of solving the inverse problem. In the case of two-dimensional fields the methods of analytical continuation were widely developed in a series of well-known papers by V. N. Strakhov, and they are mainly based on the methods of the theory of the functions of the complex variable. These methods were also successfully applied by Tsirulskii and Golizdra [1, 2] in treating the homogeneous and inhomogeneous, two-dimensional direct problem by means of Cauchy's integrals. However, as regards three-dimensional fields a number of fundamental problems has not been solved in this respect.Dedicated to 90th Birthday of Professor Frantiek Fiala 相似文献
9.
Z. Z. Arsanukaev 《Izvestiya Physics of the Solid Earth》2017,53(1):140-146
The results of the studies within the new approach to solving the inverse problem of gravimetry are considered. This approach consists in direct (analytical) continuation of the anomalous gravitational field specified on the Earth’s surface into the lower half-space with the use of the method of discrete approximations. The solution of the problem of analytical continuation is demonstrated by the model example. In the solution of the problem of analytical continuation, the developed algorithms and computer programs were implemented in two program packages which are used both in the model computations and in practice. 相似文献
10.
This paper deals with an analysis method for the response and motion of soil-like rigid-plastic bodies under seismic loading conditions. A continuity condition to determine the acceleration distribution within the rigid-plastic body when the failure occurs during seismic motions is proposed. Combining this continuity condition of acceleration and the ‘Generalized Limit Equilibrium Method (GLEM)’, the responses of the earth structure during seismic motions as well as the permanent displacements can be obtained, where GLEM is one of the limit equilibrium methods proposed by the authors for static problems and providing the approximate solution for Kötter's equation. The theoretical formulation of the method, the illustrative examples, and some comparisons between the analytical and experimental results are demonstrated. 相似文献
11.
A. V. Gotovtsev 《Water Resources》2014,41(3):330-334
An analytical solution of a modified system of Streeter-Phelps equations in the absence of aeration of the water body is given. Such solution is of interest in calculating the dynamics of biochemical oxidation of organic matter in a water body or a river channel covered by ice. The same solution can be used to describe processes taking place in a sealed flask in the determination of biochemical demand of the examined water sample over some period. The analytical solution of the modified system of Streeter-Phelps equations was used to derive formulas for calculating biochemical oxygen demand and the rate of biochemical oxidation. 相似文献
12.
Horizontal gravity filtration of groundwater in soil is considered. Under Boussinesq approximation, the problem is reduced to a one-dimensional nonlinear parabolic equation in phreatic water level. The problem of linearizing the original equation is discussed. The comparison of gravity-filtration problem solutions in the nonlinear and linearized formulations shows considerable discrepancies to exist between the solutions, especially, for boundary problems with mixed boundary conditions, when the value of the function is not fixed on the right boundary. An analytical solution is obtained for steady-state flow from a water body into the soil with subsequent leakage into underlying beds. Two regimes are shown to exist: one with an infinite exponential tail, and another in the form of a finite groundwater mound. A new approach is proposed to the linearization problem—quasilinearization with the use of the Burgers equation. 相似文献
13.
Apparent fracture toughness in Mode I of microcracking materials such as rocks under confining pressure is analyzed based
on a cohesive crack model. In rocks, the apparent fracture toughness for crack propagation varies with the confining pressure.
This study provides analytical solutions for the apparent fracture toughness using a cohesive crack model, which is a model
for the fracture process zone. The problem analyzed in this study is a fluid-driven fracture of a two-dimensional crack with
a cohesive zone under confining pressure. The size of the cohesive zone is assumed to be negligibly small in comparison to
the crack length. The analyses are performed for two types of cohesive stress distribution, namely the constant cohesive stress
(Dugdale model) and the linearly decreasing cohesive stress. Furthermore, the problem for a more general cohesive stress distribution
is analyzed based on the fracture energy concept. The analytical solutions are confirmed by comparing them with the results
of numerical computations performed using the body force method. The analytical solution suggests a substantial increase in
the apparent fracture toughness due to increased confining pressures, even if the size of the fracture process zone is small. 相似文献
14.
An analytical solution for calculating the residence time of fluid flowing toward a pumping well in an unconfined aquifer has been developed. The analytical solution was derived based on a radial, steady-state, Dupuit-Forchheimer flow model. The resulting integral expression involved computing the imaginary error function, for which a simple series expansion is proposed. The validity of the analytical expression is demonstrated by testing its results against numerical results for an example problem. The analytical solution compared favorably with the numerical approximation. 相似文献
15.
A versatile integral equation technique for magnetic modelling 总被引：1，自引：0，他引：1
Peter Furness 《Journal of Applied Geophysics》1999,41(4):737
A requirement currently exists in both mineral exploration and environmental or engineering geophysics for a technique to model the magnetic fields caused by bodies with large to extreme susceptibilities in which both induced and remanent magnetizations are significant. It is well known that modelling such magnetic fields is not amenable to any known approximation. It is a significantly difficult task that requires the solution of a magnetostatic boundary value problem. Analytical solutions to the problem are extremely useful for providing insight but generally of limited application in practical interpretation due to the geometrical complexity of real situations. Available numerical solutions include both volume and surface integral equation formulations. However neither of these are particularly efficient for the purpose. An alternative surface integral equation formulation is presented here which represents the required magnetic field in terms of a double layer over the surface of the body. The technique accommodates both remanent and induced magnetization and is generally applicable to any 3D body in a magnetic environment for which the Green's function is available. The present technique has significant advantages over other integral equation solutions in the geophysical literature. It is particularly economic in terms of the density of the surface discretization and consequently the computational effort. Moreover, it is extremely robust. It is found to yield accurate solutions for the type of thin bodies that cause numerical instability with other surface integral equation approaches. 相似文献
16.
圆弧状凹陷地形对平面P波的散射:高频解答 总被引：2，自引：1，他引：1
利用波函数的Fourier-Bessel级数展开,推导了具有不同深宽比的圆弧状凹陷地形对入射平面P波二维散射问题的解析解.与现有解析解不同之处在于,为了使该解析解适用于更高的入射波频率,本文利用了柱函数的渐进性质,使得散射波的待定系数可以直接确定,避免了线性方程组的求解以及相关的数值计算问题,从而拓展了该解析解适用的频带范围.通过与现有解析解的比较,论证了该解析解的正确性,进而在一个较宽的频带范围内分析了圆弧状凹陷地形对入射平面P波的散射效应. 相似文献
17.
Yang Caihong 《中国地震研究》2010,24(2):155-166
Through the Fourier-Bessel series expansion of wave functions,the analytical solution to the two-dimensional scattering problem of incidental plane P waves by circular-arc canyon topography with different depth-to-width ratio is deduced.Unlike other existing analytical solutions,in order to ensure that the analytical solution is valid for higher frequency incident waves,the asymptotic properties of cylindrical functions are in this paper introduced to directly determine the unknown coefficients of scattering waves,avoiding the solution of linear equation systems and corresponding numerical issues,which in turn expand the frequency band in which the analytical solution is valid.Comparison with other existing analytical solutions demonstrates that the proposed analytical solution is correct.Furthermore,the scattering effects of a circular-arc canyon on the incident plane P wave are analyzed in a comparatively broad frequency band. 相似文献
18.
The spectrum of a magnetic or a gravity anomaly due to a body of a given shape with either homogeneous magnetization or uniform density distribution can be expressed as a product of the Fourier transforms of the source geometry and the Green's function. The transform of the source geometry for any irregularly-shaped body can be accurately determined by representing the body as closely as possible by a number of prismatic bodies. The Green's function is not dependent upon the source geometry. So the analytical expression for its transform remains the same for all causative bodies. It is, therefore, not difficult to obtain the spectrum of an anomaly by multiplying the transform of the source geometry by that of the Green's function. Then the inverse of this spectrum, which yields the anomaly in the space domain, is calculated by using the Fast Fourier Transform algorithm. Many examples show the reliability and accuracy of the method for calculating potential field anomalies. 相似文献
19.
从电偶源三维地电断面可控源电磁法的二次电场边值问题及其变分问题出发,采用任意六面体单元对研究区域进行剖分,并且在单元分析中同时对电导率及二次电场进行三线性插值,实现电导率分块连续变化情况下,基于二次场的可控源电磁三维有限元数值模拟.这个新的可控源电磁三维正演方法可以模拟实际勘探中地下任意形状及电性参数连续变化的复杂模型.理论模型的计算结果表明,均匀大地计算的视电阻率误差和相位误差分别为0.002%和0.0005°.分层连续变化模型的有限元计算结果表明,其与对应的分层均匀模型解析结果有明显差异.三维异常体组合模型以及倾斜异常体等复杂模型的有限元计算结果也有效地反映了异常形态. 相似文献
20.
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