On one method of solving the two-dimensional direct magnetic problem

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.     

On one method of solving the direct gravimetric problem

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     

Quasi-one-dimensional method for solving the inverse magnetotelluric problem

We consider the iterative numerical method for solving two-dimensional (2D) inverse problems of magnetotelluric sounding, which significantly reduces the computational burden of the inverse problem solution in the class of quasi-layered models. The idea of the method is to replace the operator of the direct 2D problem of calculating the low-frequency electromagnetic field in a quasi-layered medium by a quasi-one dimensional operator at each observation point. The method is applicable for solving the inverse problems of magnetotellurics with either the E- and H-polarized fields and in the case when the inverse problem is simultaneously solved using the impedance values for the fields with both polarizations. We describe the numerical method and present the examples of its application to the numerical solution of a number of model inverse problems of magnetotelluric sounding.     

On one formulation of the frontal wave problem

u nu m¶rt;a a u ¶rt; u amu ¶rt; au amm u a m amuu ma. ¶rt; au mam ¶rt; nma a¶rt;au.     

On the new approach to solving the inverse problem of gravimetry

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.     

On a spectral method of solving the Stokes equation

A method of solving the Stokes equation for a spherical mantle model by expansion in spherical harmonics was developed by Hager and O’Connell [1979]. However, this method is applicable only if the viscosity depends solely on depth. In this case, the Stokes equation reduces to a system of independent equations for each harmonic. Given lateral variations in viscosity, the Stokes equation contains terms in the form of products of harmonics, which invalidates all advantages of harmonic expansion. Zhang and Christensen [1993] developed a perturbation method for the case when terms containing products of lateral viscosity variations are small. These terms are first calculated from the preceding iteration and are then expanded in a series of harmonic functions. As a result, equations for harmonics remain independent. An evident advantage of the spectral method is the simplicity of the technique of incorporating the self-gravitation and compressibility effects. Moreover, this method partially eliminates difficulties related to the singularities at poles. As yet, it has not been applied in practice, possibly because the equations presented in [Zhang and Christensen, 1993] contain misprints that have not been elucidated in the literature. In the present work, a system of equations is derived for the spectral-iterative method of solving the Stokes equation and the errata present in formulas of Zhang and Christensen [1993] and significantly affecting results of calculations are analyzed.     

三维土-结构动力相互作用的一种时域直接分析方法

本文提出了一种分析三维土-结构动力相互作用的时域直接方法。该方法采用集中质量显式有限元和透射人工边界模拟无限域地基,通过编制的FORTRAN程序实现;采用ANSYS软件对上部结构进行建模分析,并通过FORTRAN程序对ANSYS软件的调用,实现了土与结构系统在地震作用下的整体分析。该方法为显隐式相结合的方法,地基和上部结构可采用不同的时间步距进行分析,可大大提高效率。通过两算例,验证了该方法的可行性。     

Pilot points method incorporating prior information for solving the groundwater flow inverse problem

The pilot points method is often used in nonlinear geostatistical calibration. The method consists of estimating the values of the hydraulic properties at a set of arbitrary (pilot) points so as to best fit the aquifer response as measured by available indirect observations (i.e., heads or drawdowns). Though this method remains general and appealing, no prior information of the hydraulic properties is usually included in the optimization process, which constrains the number of pilot points to ensure stability. In this paper, we present a modification of the pilot points method, including prior information in the optimization process by adding a plausibility term to the objective function to be minimized. This results from formulating the inverse problem in a maximum likelihood framework. The performance of the method is tested on a synthetic example. Results show that including the plausibility term improves the identification of heterogeneity. Furthermore, this term makes the inverse problem more stable and allows the use of larger number of pilot points, thus improving the identification of the heterogeneity as well. Therefore, the use of the plausibility term is recommended.     

An approximation method for solving the inverse MTS problem with the use of neural networks

The work develops the approximation approach to solving the inverse MTS problem with the use of neural networks. The inverse problem is considered in model classes of parametrized geoelectric structures, whose electric conductivity is controlled by a few hundreds of macroparameters (N ∼ 300). An approximate inverse operator of the problem is constructed for each model class as a neural network, whose coefficients are determined in the process of training on a representative sample of standard examples of forward problem solutions. The problem of determination of the model class of geolectric structures corresponding to the presented input MT data is solved with the use of the neural network classifier constructed for the available set of model classes of structures. Regularizing factors and errors of the neural network method are analyzed. The operation of the algorithm is illustrated by examples of the 2-D inversion of synthetic MT data.     

On the problem of generalizing Gerstner's trochoidal waves in a three-dimensional case

Summary It is shown that functions, which determine the position of a particle and which represent the solution of Euler's equations of motion in Lagrange's form, can be determined quite accurately from the differential equations established in the paper.     

中国数字地震台网数据管理中心Y2K问题的解决方法及getdata_new软件

叙述了中国数字地震台网 (CDSN)数据管理中心 (DMC)的计算机 2 0 0 0年问题 (Y2 K)的解决情况 ,着重介绍了为解决 Y2 K问题而编制的 getdata new软件的功能 ,特点 ,结构和工作原理 ,并结合几个典型实例 ,对用法和应用情况进行说明。另外 ,本文对 getdata new所涉及的部分 ASL的程序也作了简介。     

中国数字地震台网数据管理中心Y2K问题的解决方法及getda new软件

叙述了中国数字地震台网（ＣＤＳＮ）数据管理中心（ＤＭＣ）的计算机２０００年问题（Ｙ２Ｋ）的解决情况,着重介绍了为解闷Ｋ问题而编制的ｇｅｔｄａｔａ＿ｎｅｗ软件的功能,特点,结构和工作原理,并结合几个典型实例,对用法和应用情况进行说明,另外,本文对ｇｅｔｄａｔａ＿ｎｅｗ所涉及的部分ＡＳＬ的程序也作了简介。     

On the use of the fitting method in solving inverse problems of gravimetry and magnetometry

An analytical approach to the gravity and magnetic data inversion by the fitting method is described. The problems of the uniqueness of the solution and the convergence and stability of the iterative process are considered.     

On the problem of electron loss in the outer radiation belt during a magnetic storm

An abrupt change in the latitudinal profile of energetic electrons in the Earth’s outer radiation belt during magnetic storms is explained in many publications by a loss of electrons at L = 4–7 resulting from their departure to the atmosphere or to the magnetopause. In the present work, the loss of electrons is explained primarily by adiabatic transformation of the magnetic drift trajectories. For this purpose, the effect of dawnto- dusk asymmetry measured by low-orbit SERVIS-1 and KORONAS-F satellites is involved.     

On the application of the coupled finite-infinite element method to geodetic boundary-value problem

Our aim is to introduce the Coupled Finite-Infinite Element Method (CFIEM) as a new alternative approach to the Earth’s gravity field modelling. We show that if the computational domain is large enough in radial direction, one can obtain the qualitatively and quantitatively comparable solution to the solution by the Finite Element Method (FEM). We study the influence of the size of the computational domain on the final CFIEM solution as well as the successive refinement of the discretization and its convergence to the exact solution. As an input data we use the synthetic boundary conditions computed from a Synthetic Earth Gravity Model (SEGM) and we test the CFIEM solution by the data generated directly from SEGM and the solution by the FEM.     

Application of the method of numerical simulation of ionospheric filtration of Pc1 signals to solving the inverse problem of ionospheric modelling

Summary The numerical method of simulating ionospheric filtration of ULF signals in the range of Pc1 frequencies has been applied to French geomagnetically conjugate observations of ULF signals made by the GEOS-1 satellite and at the observatory of Husafell (Iceland) [2]. The experimentally obtained variable values of the transmissivity of the Pc1 signal through the ionosphere [5] in the course of the micropulsation distrubance of 13.7. 1977 have been compared with the results of the numerical simulation taking into consideration the fundamental physical parameters of the high-latitude external ionosphere. This approximate form of solving the inverse problem of ionospheric modelling yielded quantitative estimates of the rapid variations of the concentration of charged particles in connection with the expected changes of their temperature. It is assumed that nonstationary states of the ionospheric plasma are caused by the very ion-cyclotron waves penetrating the ionosphere at high latitudes ( 70°) along the plasmapause.     

A direct method of interpreting gravity and magnetic anomalies: The case of a horizontal cylinder

Summary A new method of interpreting the gravity and magnetic anomalies is introduced with special reference to the magnetic anomalies of a horizontal cylinder. The method consists of calculating the functions of the anomaly and its distance from an arbitrary point. These form a simple linear equation with coefficients related to the parameters defining the body. Since each observation forms a separate linear equation, the required normal equations are formed by the method of least squares and solved for the coefficients and hence for the various parameters defining the target. The discussion here is confined to the vertical magnetic anomalies. The application of the method to horizontal and total field anomalies of two dimensional bodies is also outlined.     

Structure and collapse of three-dimensional magnetic neutral points

Abstract

The structure and collapse of linear three-dimensional magnetic neutral points is studied by varying the four parameters (p, q,j_|,j_⊥ ) that define, in general, the linear field of a neutral point. The effect of these parameters on both the skeleton structure (i.e. the fan and spine) and the actual field line structure of the null is considered. It is found that one current component (j_⊥ ) causes the skeleton structure of the null to fold up from its potential state, whereas the other current component (j _|;) causes the field lines to bend. The two other parameters (p,q) determine the potential structure of the null and cause the null to transform from a three-dimensional null to a two-dimensional null and from a positive (type B) null to a negative (type A) null.

To investigate the collapse of three-dimensional nulls, solutions to the linear, low-β ideal magnetohydrodynamic equations are found. It is found that three-dimensional null points can collapse if the field line foot-points are free and energy can propagate into the system.     

Computation of magnetic gradients due to three-dimensional bodies

Thc expressions of magnetic gradients due to 3-D homogeneous magnetized polyhedra are systematically derived and presented, fronr which the forward problem of magnetic gradients of an arbitrary shaped geological body is solved. It is shown that in the rotation of coordinate systems there is an essential difference between the transformation of magnetic fields and that of their gradients. In a 2-D coordinate system a unified transformation formula of any order gradients can he derived, hut cannot in the 3-D case. The calculations of synthetic models show the correctness of the expressioils or magnetic gradients. Project supported by the National Natural Science Foundation of China.