共查询到20条相似文献，搜索用时 42 毫秒
1.
位场向下与向上延拓之间存在固有的内在联系,向上延拓解算具有稳定可靠的优良特性,本文据此提出了借助向上延拓信息实现航空重力向下延拓稳定解算的两种方法,分别建立了点对点向下解析延拓模型和最小二乘向下解析延拓模型.其核心思想是,依据泰勒级数展开模型,将位场向下延拓解算过程转换为向上延拓计算和垂向偏导数解算两个步骤,通过第一步的处理有效抑制数据观测噪声对解算结果的干扰,通过第二步的处理成功实现向下延拓反问题的稳定解算,较好地解决了向下延拓解算固有的不适定性问题.分析研究了两种解析延拓模型的计算精度及适用条件,利用超高阶位模型EGM2008建立的模拟标准场数据对两种模型解算结果的合理性和有效性进行了数值验证,证明本文新方法实用易行,具有较高的应用价值. 相似文献
2.
Summary The solution of the direct magnetic problem is derived for three-dimensional bodies under the assumption that the components of the magnetization vector are analytical functions of the co-ordinates within the body being considered. The solution to the problem is given in the form of Green-type integrals and, much like with gravitational fields of inhomogeneous bodies, 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.
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
4.
本文从勘探地球物理的实际需要和特点出发,探讨了重磁位场解析延拓的数学提法,给出一套较为实用的数值解法。所论述的原理、方法适用于三维空间任意起伏地形条件下的重磁位场曲化平计算,可做“上延拓”计算,也可做“下延拓”计算。在一个比较复杂的理论模型上所做的方法检验表明“上延”和“下延”都取得了较好的效果。 相似文献
5.
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
6.
Thomas LUCKNER Ulrich ZANKE 《国际泥沙研究》2007,22(2):87-102
This paper presents an analytical solution for calculating the initiation of sediment motion and the risk of river bed movement. It thus deals with a fundamental problem in sediment transport, for which no complete analytical solution has yet been found. The analytical solution presented here is based on forces acting on a single grain in state of initiation of sediment motion. The previous procedures for calculating the initiation of sediment motion are complemented by an innovative combination of optical surface measurement technology for determining geometrical parameters and their statistical derivation as well as a novel approach for determining the turbulence effects of velocity fluctuations. This two aspects and the comparison of the solution functions presented here with the well known data and functions of different authors mainly differ the presented solution model for calculating the initiation of sediment motion from previous approaches. The defined values of required geometrical parameters are based on hydraulically laboratory tests with spheres. With this limitations the derivated solution functions permit the calculation of the effective critical transport parameters of a single grain, the calculation of averaged critical parameters for describing the state of initiation of sediment motion on the river bed, the calculation of the probability density of the effective critical velocity as well as the calculation of the risk of river bed movement. The main advantage of the presented model is the closed analytical solution from the equilibrium of forces on a single grain to the solution functions describing the initiation of sediment motion. 相似文献
7.
The quantitative analysis of the potential fields leads to the solution of some operational equations which sometimes have unstable solutions representing fictitious anomalies. A general method to find numerically stable solutions of such problems is presented in this paper. The subject of the downward analytical continuation is also discussed. The method has been checked on a theoretical model and applied to a gravity map. 相似文献
8.
The eigenvalue decomposition technique is used for analysis of conditionality of two alternative solutions for a determination
of the geoid from local gravity data. The first solution is based on the standard two-step approach utilising the inverse
of the Abel-Poisson integral equation (downward continuation) and consequently the Stokes/Hotine integration (gravity inversion).
The second solution is based on a single integral that combines the downward continuation and the gravity inversion in one
integral equation. Extreme eigenvalues and corresponding condition numbers of matrix operators are investigated to compare
the stability of inverse problems of the above-mentioned computational models. To preserve a dominantly diagonal structure
of the matrices for inverse solutions, the horizontal positions of the parameterised solution on the geoid and of data points
are identical. The numerical experiments using real data reveal that the direct gravity inversion is numerically more stable
than the downward continuation procedure in the two-step approach. 相似文献
9.
In this research, an analytical model is developed to estimate the hydrodynamic damping ratio of liquid sloshing for wall
bounded baffles using the velocity potential formulation and linear wave theory. Here, an analytical solution approach and
experimental investigations are conducted for describing the hydrodynamic damping which is provided by vertical and horizontal
baffles in partially filled rectangular liquid tanks. In order to evaluate the accuracy of the analytical solution which is
developed in present work, a series of experiments are carried out with a rectangular liquid tank excited by harmonic oscillation.
The parametric study is conducted on the damping efficiencies of both vertical and horizontal baffles with various dimensions
and locations. According to the results of the present investigations, the hydrodynamic damping is significantly affected
by the size and location of baffles. Furthermore, the validity of the developed analytical approach as well as the effectiveness
of various baffle configurations are discussed. Finally, a simple approach is proposed for estimating the damping ratios of
the baffles during earthquake motions. 相似文献
10.
Non-linear inversion of controlled source multi-receiver electromagnetic induction data for unexploded ordnance using a continuation method 总被引：1，自引：0，他引：1
This work adopts a continuation approach, based on path tracking in model space, to solve the non-linear least-squares problem for discrimination of unexploded ordnance (UXO) using multi-receiver electromagnetic induction (EMI) data. The forward model corresponds to a stretched-exponential decay of eddy currents induced in a magnetic spheroid. We formulate an over-determined, or under-parameterized, inverse problem. An example using synthetic multi-receiver EMI responses illustrates the efficiency of the method. The fast inversion of actual field multi-receiver EMI responses of inert, buried ordnances is also shown. Software based on the continuation method could be installed within a multi-receiver EMI sensor and used for near-real-time UXO decision-making purposes without the need for a highly-trained operator. 相似文献
11.
B. S. Svetov V. V. Ageev S. D. Karinskii O. A. Ageeva 《Izvestiya Physics of the Solid Earth》2013,49(6):836-843
In the first part of the paper, with some constraints, we find the analytical solution of the self-consistent problem of induced polarization (IP) for an electrokinetically polarized sphere. The stationary (on long time intervals) solution of the self-consistent problem is a set of the potential fields that are interconnected with each other: the exciting electric field, the extraneous hydrodynamical field (electroosmotic flow of a viscous incompressible fluid), and the resulting electromagnetic IP field. The extraneous field is the field of the osmotic flow of a charged liquid and the field of the charges that emerge due to the membrane effect in the narrowed segments of the pore channels. The calculations show that the IP fields derived by solving the self-consistent problem and by the Seigel-Komarov phenomenological approach are different. In the second part of the paper, by generalization of the obtained analytical solution, we formulate the self-consistent IP problem for isotropic σ-η media of arbitrary shape, which are bounded by a smooth surface. The problem can be solved by the numerical methods. 相似文献
12.
13.
针对位场向下延拓的不适定性,我们将位场向下延拓视为向上延拓的反问题,提出以位场最小曲率作为约束条件来求解稳定的下延位场.我们将剖面位场向上延拓表达式用傅里叶矩阵的形式表示,以矩阵乘法形式给出延拓的表达式,同时向待反演的下延位场引入最小曲率约束,得到向下延拓的最小曲率解,并利用正交变换给出了更为简洁的频率域解.随后,利用Kronecker积将上述全部结果拓展至三维位场,给出了三维位场向下延拓的最小曲率解.此外,我们将位场数据的填充、扩充问题与向下延拓问题统筹考虑,提出一种新的向下延拓迭代格式,该算法面向实际资料处理需求、无须预扩充或填补数据.下延迭代时,对原始数据直接向下延拓,而空白部分利用上一次下延位场估计的上延值替代其空白值并对其向下延拓,直至获得最小曲率约束下稳定的向下延拓结果.同时,我们也讨论了利用改进L曲线和广义交叉验证(GCV)计算正则参数最优估计的问题.对理论模型和实际航空重力资料进行了向下延拓检验,处理结果表明位场向下延拓的最小曲率方法解能满足实际位场资料对向下延拓处理的需求,具有较高的下延精度. 相似文献
14.
《Journal of Atmospheric and Solar》2002,64(5-6):639-644
Sequences of magnetostatic equilibria can often be used to model the quasi-static pre-eruptive energy storage phase of eruptive phenomena in e.g. Earth's magnetosphere or the solar corona. During these phases the systems evolve only due to slow changes in their environment, being practically in equilibrium on large scales. The eruption onset would then be identified with a bifurcation or catastrophe point in the solution diagram. Different energy storage mechanisms can be studied by different parameterizations of e.g. the boundary conditions. Also from the more fundamental point-of-view of the theory of dynamical systems, studying the possible stationary states and the bifurcation properties of plasma systems should be the first step towards a more thorough understanding of their full dynamical behaviour. In any case one will have to solve highly non-linear partial differential equations with the possibility of the existence of multiple solutions (or of none at all) for a given set of boundary conditions. Such problems can, in general, only be solved numerically. The most appropriate class of numerical algorithms for this type of problem are continuation methods which can calculate complete solution branches and detect bifurcation points. In this work a numerical bifurcation code based on a continuation method is presented. In addition to solving the non-linear magnetohydrostatic equations, the code can check a sufficient linear stability criterion for each solution. Some preliminary results for simple magnetohydrostatic equilibria are presented and potential future applications are discussed. 相似文献
15.
A solution conduit has a permeable wall allowing for water exchange and solute transfer between the conduit and its surrounding aquifer matrix. In this paper, we use Laplace Transform to solve a one‐dimensional equation constructed using the Euler approach to describe advective transport of solute in a conduit, a production‐value problem. Both nonuniform cross‐section of the conduit and nonuniform seepage at the conduit wall are considered in the solution. Physical analysis using the Lagrangian approach and a lumping method is performed to verify the solution. Two‐way transfer between conduit water and matrix water is also investigated by using the solution for the production‐value problem as a first‐order approximation. The approximate solution agrees well with the exact solution if dimensionless travel time in the conduit is an order of magnitude smaller than unity. Our analytical solution is based on the assumption that the spatial and/or temporal heterogeneity in the wall solute flux is the dominant factor in the spreading of spring‐breakthrough curves, and conduit dispersion is only a secondary mechanism. Such an approach can lead to the better understanding of water exchange and solute transfer between conduits and aquifer matrix. Highlights:
- 相似文献
16.
位场数据曲化平是位场数据处理解释中的重要运算,但是它的计算量和计算的复杂性影响了它在许多处理和解释方法技术中的应用.本文提出一种位场数据曲化平的迭代方法,即通过把位场数据曲化平视为平面位场数据向上延拓的反问题,得到曲化平的线性积分方程,再把曲面上位场数据视为曲面平均高程面上的位场数据,利用向下延拓的波数域广义逆算法把平均高程面上的位场数据向下延拓到设定平面上,再根据曲面和其平均高程面的相对起伏对设定平面上的向下延拓数据进行起伏校正,最后再把所得平面上的位场数据向上延拓得到曲面上的位场数据,并进行迭代.把这种方法用于三维理论模型数据和实际磁场数据的曲化平处理均获得了理想的结果. 相似文献
17.
P.W. France 《Journal of Hydrology》1974,21(4):381-398
A numerical method is presented for analysing either steady state or transient three-dimensional groundwater flow problems. The governing equation is formulated in terms of the finite element process using the Galerkin approach, and cubic isoparametric elements are used to simulate the flow domain as these permit accurate modelling of curved boundaries. Particular attention is paid to the time dependent movement of the phreatic surface where an iterative technique based on the replacement of the original transient problem by a discrete number of steady state problems is used to effect a solution. Furthermore, in tracing the movement of the surface use is made of the element formulation theory in order to compute the normal to the boundary.The validity of the technique is first established by analysing a radially symmetrical problem for which an alternative analytical solution is available. Finally, a general three-dimensional flow system is studied for which there is no known analytical solution. It is shown that relatively few elements are required to yield practical solutions. 相似文献
18.
An approximate solution of the classical eigenvalue problem governing the vibrations of a structure on an elastic soil is derived through the application of a perturbation analysis. For stiff soils, the full solution is obtained as the sum of the solution for a rigid-soil and small perturbing terms related to the inverse of the soil shear modulus. The procedure leads to approximate analytical expressions for the system frequencies, modal damping ratios and participation factors for all system modes that generalize those presented by other authors for the fundamental mode. The resulting approximate expressions for the system modal properties are validated by comparison with the corresponding quantities obtained by numerical solution of the eigenvalue problem for a nine-story building. The accuracy of the proposed approach and of the classical normal mode approach is assessed through comparison with the exact frequency response of the test structure. 相似文献
19.
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
20.
An approximate solution of the classical eigenvalue problem governing the vibrations of a relatively stiff structure on a soft elastic soil is derived through the application of a perturbation analysis. The full solution is obtained as the sum of the solution for an unconstrained elastic structure and small perturbing terms related to the ratio of the stiffness of the soil to that of the superstructure. The procedure leads to approximate analytical expressions for the system frequencies, modal damping ratios and participation factors for all system modes that generalize those presented earlier for the case of stiff soils. The resulting approximate expressions for the system modal properties are validated by comparison with the corresponding quantities obtained by numerical solution of the eigenvalue problem for a nine-story building. The accuracy of the proposed approach and of the classical normal mode approach is assessed through comparison with the exact frequency response of the test structure. 相似文献