共查询到20条相似文献，搜索用时 640 毫秒
1.
Summary. In the present paper, we give an approximate analytic solution of the Dirichlet and Neumann problems in the two-dimensional case for a contour of any shape. The formalism is based on a representation of potential functions as a sum of elementary interpolating functions and uses the theory of generalized inverse matrices. Formulae are given in the cases of Cartesian, polar and elliptic co-ordinates. The fact that an analytic expression for continuation is obtained enables one to compute and draw equipotential lines as well as field lines; besides, any further computations that one might want to perform on either the field or the potential can be handled in an analytic way. The formalism can be extended from the Laplace to the Helmholtz equation.
We give examples in the case of magnetostatics, treating in more detail the problem of the distortion of magnetic field lines by an inclusion. We also show how the method allows the computation of conformal mappings in otherwise intricate situations. 相似文献
We give examples in the case of magnetostatics, treating in more detail the problem of the distortion of magnetic field lines by an inclusion. We also show how the method allows the computation of conformal mappings in otherwise intricate situations. 相似文献
2.
When marine magnetic-anomaly data are used to construct geomagnetic polarity timescales, the usual assumption of a smooth spreading-rate function at one seafloor spreading ridge forces much more erratic rate functions at other ridges. To eliminate this problem, we propose a formalism for the timescale problem that penalizes non-smooth spreading behaviour equally for all ridges. Specifically, we establish a non-linear Lagrange multiplier optimization problem for finding the timescale that (1) agrees with known chron ages and with anomaly-interval distance data from multiple ridges and (2) allows the rate functions for each ridge to be as nearly constant as possible, according to a cumulative penalty function. The method is applied to a synthetic data set reconstructed from the timescale and rate functions for seven ridges, derived by Cande & Kent (1992) under the assumption of smooth spreading in the South Atlantic. We find that only modest changes in the timescale (less than 5 per cent for each reversal) are needed if no one ridge is singled out for the preferential assumption of smoothness. Future implementation of this non-prejudicial treatment of spreading-rate data from multiple ridges to large anomaly-distance data sets should lead to the next incremental improvement to the pre-Quaternary geomagnetic polarity timescale, as well as allow a more accurate assessment of global and local changes in seafloor spreading rates over time. 相似文献
3.
Upward and downward continuation as inverse problems 总被引：2，自引：0，他引：2
Summary . The formalism of Backus & Gilbert is applied to the problems of upward and downward continuation of harmonic functions. We first treat downward continuation of a two-dimensional field to a level surface everywhere below the observation locations; the calculation of resolving widths and solution estimates is a straightforward application of Backus—Gilbert theory. The extension to the downward continuation of a three-dimensional field uses a delta criterion giving resolving areas rather than widths. A feature not encountered in conventional Backus—Gilbert problems is the requirement of an additional constraint to guarantee the existence of the resolution integrals. Finally, we consider upward continuation of a two-dimensional field to a level above all observations. We find that solution estimates must be weighted averages of the field not only on this level, but also on a line passing between the observations and sources. Weighting on the lower line may be traded off against resolution on the upper level. 相似文献
4.
5.
S. V. Goldin 《Geophysical Journal International》1984,79(1):327-337
Summary. This paper discusses the inverse (downward) continuation of a wavefield into a medium, as a means of estimating seismic velocities and the imaging of the geometry of reflecting objects. The notion of a kinematically equivalent (K-equivalent) operator of the field continuation is introduced, which allows both the possibility of replacing the initial Lamé equation by a simpler one (for example, a wave equation) and also the existence of an infinite set of continuation operators which permit us to construct a wavefield with proper characteristics. Any of the K-equivalent operators can be used in the task of imaging of reflectors given the known velocities. If velocities are unknown and reflectors are irregular, it is possible to improve the regularity of reflections by continuing the field downward to a fictitious surface in the media with a velocity Vo , that differs from the true velocity V . The conditions needed to untie loops in the true patterns in the continued field are also given.
Another approach is connected with calculations of dynamic sections using different values of velocity (say, an extremal velocity) under which the amplitudes of reflectors on sections are brought to a maximum due to the phenomena of focusing. Extremal velocities can be also used for solving inverse kinematical problems. 相似文献
Another approach is connected with calculations of dynamic sections using different values of velocity (say, an extremal velocity) under which the amplitudes of reflectors on sections are brought to a maximum due to the phenomena of focusing. Extremal velocities can be also used for solving inverse kinematical problems. 相似文献
6.
气候重建研究中,重建数据有限的特点对研究造成很大影响。对于解决这个问题,区域优化平均法是一个很有效的重建方法。区域优化平均法可以通过最优权值和有限的温度数据计算目标区域平均温度的一种方法。应用区域优化平均法时,首先利用均方差最小化的优化加权机制和拉格朗日乘子法计算得到最优权值,然后最优权值结合温度数据计算得到区域平均温度。现阶段的区域优化平均在计算大范围区域的平均温度时有其自身弱点。为克服这一弱点,使其可以计算大范围区域的平均温度,例如北半球平均温度,本文对区域优化平均法做如下改进：不再使用网格划分求和的方式求解协方差模式,利用Haar小波函数和矩阵算子求得协方差模式;利用全选主元高斯消去法求解线性代数方程组得到最优权值。结果表明,Haar小波函数和矩阵算子用于计算中,使协方差模式的计算结果更精确。计算所用数据源于气候研究中心（CRU）,CRU被认为是最权威的数据来源之一。以计算北半球1961~1990年平均温度为例,发现改进后的区域优化平均法的计算所得结果与CRU已有结果的相关性较改进之前有所提高。因此,针对古气候重建过程中代用数据记录有限的问题,改进后的区域优化平均法提供了一个更为合理可行的计算方法。 相似文献
7.
V. S. Geyko 《Geophysical Journal International》1981,67(3):529-545
Summary. A general theory of inversion of the reflected travel-time curve is developed. The properties of the travel-time curve and its analytical continuation are examined. The inversion formulae are presented and the structure of the set of velocity—depth functions is studied in detail. The inverse problem or a finite number of reflectors and the problem of separation of the reflected and multiple travel-time curves are both considered. 相似文献
8.
M. A. Brodsky 《Geophysical Journal International》1981,66(3):727-732
Summary. The inverse gravity potential problem consists in the determination of the form and the density of the body by its exterior gravity potential. We describe two similar classes of bodies for which this problem has a unique constructive solution.
(1) The first class contains the cylindrical bodies with finite length, arbitrary form of section and ρ( R , ø, z) =ρ1 ( z )ρ2 ( R , ø) density distribution, where z is the cylindrical coordinate; R , ø are the polar coordinates in a section plane. This class is important for prospecting geophysics in that it allows us to determine in a unique and constructive way, the function ρ1 ( R , ø), the length, form and orientation of the cylinder if we know the function ρ1 ( z ) and the exterior potential. The classical moment problem of functions is the basis for the solution of this problem.
(2) The analogous problem for the class of the spherical cylinders, or bodies bounded by arbitrary similar sections of two different concentric spheres and the radial lateral surface, appears when bodies of planetary size are studied. (An example of these bodies would be the Moon mascons.) The density distribution of these cylinders is ρ(τ, θ, ø) =ρ1 (τ)ρ2 (θ, ø) where τ, θ, ø are the spherical coordinates. The function ρ1 (θ, ø), length and form of spherical sections can be uniquely determined by exterior potential if we know the function ρ1 (τ). We propose a new constructive method for harmonic continuation of the gravity potential into the region containing the perturbing masses for the solution of the problem. 相似文献
(1) The first class contains the cylindrical bodies with finite length, arbitrary form of section and ρ( R , ø, z) =ρ
(2) The analogous problem for the class of the spherical cylinders, or bodies bounded by arbitrary similar sections of two different concentric spheres and the radial lateral surface, appears when bodies of planetary size are studied. (An example of these bodies would be the Moon mascons.) The density distribution of these cylinders is ρ(τ, θ, ø) =ρ
9.
地理学多视角研究方法——Braess网络车流分配过程的理论分析与数值计算 总被引：1，自引：0，他引：1
对复杂的地理系统采用多种方法从不同的视角开展分析,可以降低错误结论的概率。本文以Braess交通网络为例,提出一个地理系统多视角分析的研究案例。首先借助La氏乘数法预测奇对称Braess网络的车流优化分配的结果。然后采用数值计算和模拟方法论证,在该网络中,车流会通过自组织过程自动向着优化分配的方向演化,并且利用Markov链预测各个阶段的车流分配数值。最后借助最大熵原理从理论上证明,上述最优化过程的本质是地理系统的熵最大化;运用对偶规划和对称思想揭示,熵最大化的实质是车流运行的耗时总量最小。不同的方法给出的结果殊途同归、互相印证。这一套研究方法可以推广到多维不对称的交通网络,进而推广应用于地理学其他方面的理论分析和应用研究。 相似文献
10.
Summary. Due to the non-uniqueness of traveltime inversion of seismic data, it is more appropriate to determine a velocity-depth ( v-z ) envelope, rather than just a v-z function. Several methods of obtaining a v-z envelope by extremal inversion have been proposed, all of which invert the data primarily from either x-p , or T-p , or both domains. These extremal inversion methods may be divided into two groups: linear extremal and non-linear extremal. There is some debate whether the linearized perturbation techniques should be applied to the inherently non-linear problem of traveltime inversion. We have obtained a v-z envelope by extremal inversion in T-p with the constraint that the inversion paths also satisfy x-p observations. Thus we use data jointly in r-p and x-p , and yet avoid the linearity assumptions.
This joint, non-linear extremal inversion method has been applied to obtain a v-z envelope down to a depth of about 30 km in the Baltimore Canyon trough using x-t data from an Expanding Spread Profile acquired during the LASE project. We have found that the area enclosed by the v-z envelope is reduced by about 15 per cent using x-p control on the T-p inversion paths, compared to the inversion without x-p control. 相似文献
This joint, non-linear extremal inversion method has been applied to obtain a v-z envelope down to a depth of about 30 km in the Baltimore Canyon trough using x-t data from an Expanding Spread Profile acquired during the LASE project. We have found that the area enclosed by the v-z envelope is reduced by about 15 per cent using x-p control on the T-p inversion paths, compared to the inversion without x-p control. 相似文献
11.
Spherical Slepian functions and the polar gap in geodesy 总被引：4，自引：0，他引：4
The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an ill-posed inverse problem. We show that this potential-field estimation problem has deep-seated connections to Slepian's spatiospectral localization problem which seeks bandlimited spherical functions whose energy is optimally concentrated in some closed portion of the unit sphere. This allows us to formulate an alternative solution to the traditional damped least-squares spherical harmonic approach in geodesy, whereby the source field is now expanded in a truncated Slepian function basis set. We discuss the relative performance of both methods with regard to standard statistical measures such as bias, variance and mean squared error, and pay special attention to the algorithmic efficiency of computing the Slepian functions on the region complementary to the axisymmetric polar gap characteristic of satellite surveys. The ease, speed, and accuracy of our method make the use of spherical Slepian functions in earth and planetary geodesy practical. 相似文献
12.
Stephen P. Huestis 《Geophysical Journal International》1981,65(1):165-170
Summary. The formalism of Huestis for placing bounds on subsurface temperatures is generalized to the case of heat flow measurements on a surface which is neither flat nor isothermal. The strip extending between the surface and the depth of interest is imbedded in a larger flat strip extending to a horizontal level everywhere above the topography. Using linear programming, heat sources within and temperatures on the boundary of this simpler region are found such that the heat flow data and temperatures on the Earth's surface are fit, heat production constraints are met, and the extremal bound is achieved. 相似文献
13.
Choice of norm for the density distribution of the Earth 总被引：1，自引：0，他引：1
Summary. The determination of the density distribution of the Earth from gravity data is called the inverse gravimetric problem. A unique solution to this problem may be obtained by introducing a priori data concerning the covariance of density anomalies. This is equivalent to requiring the density to fulfil a minimum norm condition. The generally used norm is the one equal to the integral of the square of the density distribution ( L2 -norm), the use of which implies that blocks of constant density are uncorrelated. It is shown that for harmonic anomalous density distributions this leads to an external gravity field with a power spectrum (degree-variances) which tends too slowly to zero, i.e. implying gravity anomalies much less correlated than actually observed. It is proposed to use a stronger norm, equal to the integral of the square sum of the derivatives of the density distribution. As a consequence of this, base functions which are constant within blocks, are no longer a natural choice when solving the inverse gravimetric problem. Instead a block with a linearly varying density may be used. A formula for the potential of such a block is derived. 相似文献
14.
Three-dimensional inversion without blocks 总被引：12，自引：0，他引：12
Summary. We propose a method for solving non-linear inverse problems in the case where the unknown is a function of the spatial coordinates and the data set is discrete and finite. The method is based on a generalized leastsquares criterion, it is defined directly for non-linear problems (without previous linearization of the forward problem), and in the particular linear case it gives the same results (although slightly more general) than the Backus & Gilbert approach. As an example, we apply the method to the three-dimensional seismic velocity inverse problem, using as data the arrival times of seismic waves. The following paper (Nercessian et al .) shows some esults obtained using the present method. 相似文献
15.
Summary . The spectral function of a perfectly elastic, horizontally stratified medium has been demonstrated previously to provide an attractive formulation to describe the properties of the one-dimensional synthetic seismogram (Robinson & Treitel). Here we examine the mathematical framework of the Model in still greater detail. Knowledge of this fine structure of the synthetic seismogram leads to the solution of two particular seismic inverse problems. First, we consider a layered medium with an arbitrary surface reflection coefficient c o , where | c o |<1, and which contains an impulsive source immediately above the surface. Given the corresponding synthetic seismogram, we develop an inverse, or backward recursion formalism which recovers the entire series of original reflection coefficients. Second, we consider a similar problem for an impulsive source located just below the surface. Both inversion procedures constitute a continuation of the work of Goupillaud and of Sherwood & Trorey, and represent a generalization of the classical technique originally proposed by Kunetz which, however, only holds for the marine case, co =±1. The present approach is not so constrained and thereby becomes applicable to land seismograms as well.
If products of third or higher order in the reflection coefficients can be neglected, significant simplifications arise in the theory. In that event the usual representation of the synthetic seismogram as a ratio of two polynomials in the complex variable z becomes particularly revealing. The numerator polynomial is then approximately equal to the z transform of the reflection coefficient series, while the denominator polynomial is approximately equal to the z transform of the autocorrelation of these reflection coefficients. The resulting simplified theory affords important computational savings in the appropriate backward recursion algorithms. 相似文献
If products of third or higher order in the reflection coefficients can be neglected, significant simplifications arise in the theory. In that event the usual representation of the synthetic seismogram as a ratio of two polynomials in the complex variable z becomes particularly revealing. The numerator polynomial is then approximately equal to the z transform of the reflection coefficient series, while the denominator polynomial is approximately equal to the z transform of the autocorrelation of these reflection coefficients. The resulting simplified theory affords important computational savings in the appropriate backward recursion algorithms. 相似文献
16.
D. W. Vasco 《Geophysical Journal International》2000,142(3):970-990
Many geophysical inverse problems derive from governing partial differential equations with unknown coefficients. Alternatively, inverse problems often arise from integral equations associated with a Green's function solution to a governing differential equation. In their discrete form such equations reduce to systems of polynomial equations, known as algebraic equations. Using techniques from computational algebra one can address questions of the existence of solutions to such equations as well as the uniqueness of the solutions. The techniques are enumerative and exhaustive, requiring a finite number of computer operations. For example, calculating a bound to the total number of solutions reduces to computing the dimension of a linear vector space. The solution set itself may be constructed through the solution of an eigenvalue problem. The techniques are applied to a set of synthetic magnetotelluric values generated by conductivity variations within a layer. We find that the estimation of the conductivity and the electric field in the subsurface, based upon single-frequency magnetotelluric field values, is equivalent to a linear inverse problem. The techniques are also illustrated by an application to a magnetotelluric data set gathered at Battle Mountain, Nevada. Surface observations of the electric ( E y ) and magnetic ( H x ) fields are used to construct a model of subsurface electrical structure. Using techniques for algebraic equations it is shown that solutions exist, and that the set of solutions is finite. The total number of solutions is bounded above at 134 217 728. A numerical solution of the algebraic equations generates a conductivity structure in accordance with the current geological model for the area. 相似文献
17.
Summary. The Backus–Gilbert theory is extended to the case when the models are piecewise continuous vector functions of depth with variable discontinuity locations. In addition, some of the layers may be represented by linear combinations of known functions. For such layers only a finite number of discrete parameters is to be determined. The iterative process for obtaining a model satisfying the data is convergent, the numerical procedure by which the iterations are performed being equivalent to the method of spectral decomposition for continuous structures. The method of obtaining the Fréchet kernels by using the first perturbation of the differential system satisfied by the corresponding functionals is shown to be valid.
The theory is applied to the magnetotelluric problem, Fréchet kernels being calculated for isotropic and non-isotropic structures.
A few numerical examples are described. 相似文献
The theory is applied to the magnetotelluric problem, Fréchet kernels being calculated for isotropic and non-isotropic structures.
A few numerical examples are described. 相似文献
18.
New techniques for improving both the computational and imaging performance of the three-dimensional (3-D) electromagnetic inverse problem are presented. A non-linear conjugate gradient algorithm is the framework of the inversion scheme. Full wave equation modelling for controlled sources is utilized for data simulation along with an efficient gradient computation approach for the model update. Improving the modelling efficiency of the 3-D finite difference (FD) method involves the separation of the potentially large modelling mesh, defining the set of model parameters, from the computational FD meshes used for field simulation. Grid spacings and thus overall grid sizes can be reduced and optimized according to source frequencies and source–receiver offsets of a given input data set. Further computational efficiency is obtained by combining different levels of parallelization. While the parallel scheme allows for an arbitrarily large number of parallel tasks, the relative amount of message passing is kept constant. Image enhancement is achieved by model parameter transformation functions, which enforce bounded conductivity parameters and thus prevent parameter overshoots. Further, a remedy for treating distorted data within the inversion process is presented. Data distortions simulated here include positioning errors and a highly conductive overburden, hiding the desired target signal. The methods are demonstrated using both synthetic and field data. 相似文献
19.
1960-2010年中国西北地区水分盈亏量时空特征 总被引：4，自引：1，他引：3
基于1960-2010年中国西北地区126个国家气象站点实测数据,应用Morlet小波函数、Kendall趋势系数、Mann-Kendall突变检验等方法分析西北地区水分盈亏量时空变化特征。结果表明:西北地区大部分区域水分盈亏量为负值,呈由东南和西北两侧向中部逐渐减小的空间格局。在研究时段内水分盈亏量总体呈上升趋势,但各季节水分盈亏量变化存在一定的差异性,其中春夏冬三个季节水分盈亏量呈上升趋势,而在秋季呈下降趋势。西北地区水分盈亏量变化存在3.5~5 a左右的主周期,其中夏季周期变化以强振荡为主,年际波动大,而其它三个季节以弱振荡周期为主。位于西风带气候区与高原气候区的站点水分盈亏量呈上升趋势,且多发生突变;水分盈亏量呈下降趋势的站点主要位于东南季风区及其边缘区。 相似文献
20.
Summary. The geodetic boundary value problem is solved by taking temporal changes of geometry and gravity into account. It is aimed to get complete information about the mechanical response of the Earth to an external tidal force which is only imperfectly known. The information is used to solve the inverse Love-Shida problem, e.g. by computing the Love -Shida operators. The general solution (4.25), (4.26) is specialized for a perfectly known external gravity field and for a free fixed boundary of the Earth. 相似文献