Magneto-elastic waves and disturbances in initially stressed conducting media: II

Summary The paper is concerned with the investigation of the magneto-elastic waves and disturbances in initially stressed conducting media. Firstly, (a) the steady state response to moving loads in a magneto-elastic initially stressed conducting medium under an uniaxial tension has been discussed. Secondly, (b) the Lamb's problem corresponding to a line load suddenly applied in a magneto-elastic initially stressed conducting half-space bounded by a plane under uniaxial tension has been investigated. The final results obtained in both cases are in agreement with the corresponding classical problems when the initial tension is zero and the magnetic field is absent.     

贴井壁声波测井仪的有限差分模拟研究

贴井壁声波测井仪在石油勘探开发中具有广泛的应用.它能够避开泥浆的影响而直接检测井壁附近的地层性质.但目前对此进行的数值模拟研究还仅局限于比较简单的模型.有限差分法可以模拟比较复杂的井眼模型,然而贴井壁声源的频率较高（80kHz左右）,使有限差分法计算量过大.本文应用局部加密交错网格有限差分方法解决了这类数值模拟中计算精度和计算量之间的矛盾.用这种算法模拟了井中有仪器时贴井壁声源激发的声场,并将其与无仪器时的声场作了比较.对模拟结果的验证和分析显示,该有限差分方法能够正确模拟贴井壁声源激发的声场.通过考察井中仪器本体对贴井壁声源激发声场的影响发现,测井仪器本体能够对直达波进行衰减而对环绕井壁传播的面波影响不大.     

Effect of surface stress on magneto-elastic surface waves in finitely conducting media

This paper deals with the investigation of the effect of surface stress and conductivity on the propagation of surface wave in isotropic, homogeneous, elastic media under the action of a primary magnetic field. Formulation of the general surface wave propagation problem has been made, and the corresponding frequency equation has been derived. Frequency equations for Rayleigh wave, surface shear wave and Stoneley wave have been deduced from that of general surface wave as special cases. The effects of surface stress and magnetic field on the wave velocities and attenuation factors of Rayleigh wave and surface shear wave are shown by numerical calculations and graphs. Some important wave velocity equations, as obtained by other authors, have been deduced as special cases from the wave velocity equation for Stoneley wave. It is found that the combined effect of surface stress and magnetic field modulates the wave velocity ratios and attenuation factors of Rayleigh wave and surface shear wave to a considerable extent.     

Magneto-elastic waves and disturbances in initially stressed conducting media

Summary The object of the present paper is to investigate magneto-elastic waves and disturbances in initially stressed conducting media. Firstly, the theory of magneto-elastic surface waves in a conducting medium under an initial uniaxial tension has been deduced and then it has been employed to investigate the particular cases of surface waves such as Rayleigh, Love and Stoneley waves. Secondly, propagation of waves in an elastic layer has been considered using the fundamental equations of motion for magneto-elastic waves in conductors under an initial uniaxial tension or compression. This is followed by the case of plane Lamb's problem in a magneto-elastic semi-space under the same initial tension. The final results obtained in the above cases are in agreement with the corresponding classical problems when the initial tension is zero and the magnetic field is absent.     

A Least-squares Approach to Depth Determination from Numerical Horizontal Self-potential Gradients

We have developed a least-squares minimization approach to depth determination of a buried ore deposit from numerical horizontal gradients obtained from self-potential (SP) data using filters of successive window lengths (graticule spacings). The problem of depth determination from SP gradients has been transformed into the problem of finding a solution to a nonlinear equation of the form f(z)=0. Formulas have been derived for vertical and horizontal cylinders and spheres. Procedures are also formulated to estimate the electrical dipole moment and the polarization angle. The method is applied to synthetic data with and without random noise. Finally, the validity of the method is tested on two field examples. In both cases, the depth obtained is found to be in a very good agreement with that obtained from drilling information.     

Prediction of the median IDA curve by employing a limited number of ground motion records

A methodology has been proposed which can be used to reduce the number of ground motion records needed for the reliable prediction of the median seismic response of structures by means of incremental dynamic analysis (IDA). This methodology is presently limited to predictions of the median IDA curve only. The reduction in the number of ground motion records needed to predict the median IDA curve is achieved by introducing a precedence list of ground motion records. The determination of such a list is an optimization problem, which is solved in the paper by means of (1) a genetic algorithm and (2) a proposed simple procedure. The seismic response of a simple, computationally non‐demanding structural model has been used as input data for the optimization problem. The presented example is a three‐storey‐reinforced concrete building, subjected to two sets of ground motion records, one a free‐field set and the other a near‐field set. It is shown that the median IDA curves can be predicted with acceptable accuracy by employing only four ground motion records instead of the 24 or 30 records, which are the total number of ground motion records for the free‐field and near‐field sets, respectively. Copyright © 2007 John Wiley & Sons, Ltd.     

EQUIVALENCE IN ELECTROMAGNETIC (FREQUENCY) SOUNDING*

An analysis of the equivalence phenomenon, analogous to that encountered in resistivity sounding, has been made for electromagnetic (frequency) sounding with the following systems: horizontal coplanar coils, perpendicular coils, vertical coplanar coils, and vertical coaxial coils. Cases analyzed are three-layer H and K type resistivity distributions. The theoretical responses for the EM sounding systems have been computed by the digital linear filter method using short filters. An analysis has been made of the resolution by the four EM systems considered f the equivalence effect. It is concluded that from the equivalence point of view electromagnetic (frequency) sounding has relatively better resolution compared to resistivity sounding for the H type three-layer cases. For the K type three-layer cases electromagnetic (frequency) sounding provides a serious problem in resolution similar to that encountered in resistivity sounding. Empirical relationships have been established for the H and K type cases respectively in order to numerically quantify the equivalence involved in electromagnetic (frequency) sounding.     

Analytical configurations of a force-free magnetic cylinder in the solar wind

The problem of a smooth field configuration, which should be an initial configuration in modeling (using the method of coarse particles) the problem of a stationary solar wind flow around a magnetic cloud in the case of a spatially two-dimensional statement (when a magnetic cloud is considered as a force-free magnetic cylinder with a finite radius) is considered. It has been indicated that such a statement is possible only when the magnetic field in the solar wind is parallel to the cylinder axis. The method for finding the magnetic field of a force-free cylinder with a finite radius, when some field component is specified and another component is determined based on this one (which makes it possible to construct fields with preassigned properties), has been proposed. The variant for constructing the initial field configuration in the transition region around a cylinder has been proposed. This variant makes it possible to gradually pass from homogeneous crossed fields in the solar wind to a force-free magnetic and zero electric fields within a cylinder, an electric field being potential and orthogonal to a magnetic field (in the reference system related to a magnetic cloud).     

Magnetohydrodynamic disturbances in the earth's core,II

Summary In paper I, (Mohandis [2]²)), the author contributes to the discussion of the origin of the secular variation of the earth's magnetic field. A mathematical solution of magnetohydrodynamic disturbances and fluid motion due to the sudden introduction of an oscillating dipole in the earth's core has been obtained. Only the symmetrical case of the problem, where the axis of the dipole is placed perpendicular to the mantle and parallel to a poloidal field, has been discussed.In this paper, the source of disturbance is still considered to be the oscillating dipole, but the exciting field is taken as a toroidal field always parallel to the mantle. Two unsymmetric different cases of the problem are considered but the disturbed field is sonsidered only in the mantle. It is worth to note here that simpler results can be obtained by applying more conditions than those used in the present work. The new method will be illustrated in a forthcoming paper of this series, Magnetolydrodynamic disturbances in the earth's core, IV where another case of the problem will be discussed.     

起伏地形上的位场转换

根据起伏地形上观测的异常场分量（沿任一方向的分量）换算出垂直与水平分量,本文提供了二维情况下的转换方法。其算法是:（1）通过共形映照,将w平面上的地形曲线L的上部映照为z平面的上半平面,将曲线L映照成z平面上的实轴。（2）求解边界为实轴的Hilbert边值问题。 通过理论模型的计算,验证了该方法的正确性。     

A New Algorithm for Depth Determination from Total Magnetic Anomalies due to Spheres

We have developed an automatic method to determine the depth of a buried sphere from numerical second horizontal derivative anomalies obtained from total field magnetic data. The method is based on using a relationship between the depth and a combination of observations at symmetric points with respect to the coordinate of the projection of the center of the source in the plane of the measurement points with a free parameter (graticule spacing). The problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of f(z) = 0. Procedures are also formulated to determine the magnetic moment and the effective angle of magnetization. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal. In all cases, the depth solutions are in good agreement with the actual ones.     

Quantitative Interpretation of Self-Potential Anomalies of Some Simple Geometric Bodies

We have developed a new numerical method to determine the shape (shape factor), depth, polarization angle, and electric dipole moment of a buried structure from residual self-potential (SP) anomalies. The method is based on defining the anomaly value at the origin and four characteristic points and their corresponding distances on the anomaly profile. The problem of shape determination from residual SP anomaly has been transformed into the problem of finding a solution to a nonlinear equation of the form q = f (q). Knowing the shape, the depth, polarization angle and the electric dipole moment are determined individually using three linear equations. Formulas have been derived for spheres and cylinders. By using all possible combinations of the four characteristic points and their corresponding distances, a procedure is developed for automated determination of the best-fit-model parameters of the buried structure from SP anomalies. The method was applied to synthetic data with 5% random errors and tested on a field example from Colorado. In both cases, the model parameters obtained by the present method, particularly the shape and depth of the buried structures are found in good agreement with the actual ones. The present method has the capability of avoiding highly noisy data points and enforcing the incorporation of points of the least random errors to enhance the interpretation results.     

HIDDEN LAYER PROBLEM IN SEISMIC REFRACTION WORK*

The hidden layer problem in seismic refraction work has been studied for three velocity configurations – the intermediate layer having (a) lower, (b) intermediate and (c) higher velocity than the underlying and overlying beds. It has been shown that conventional methods fail to locate the presence of the intermediate layer for the cases (a) and (c) and lead to errors in calculating the depth to the bedrock. For the case (b), it is possible to interpret the first arrival travel time analytically as an alternative to Green's graphical approach. It has been suggested that the hidden layer may be detected in all the three cases if converted S waves are also recorded in the seismogram.     

The INGV software for the automatic scaling of foF2 and MUF(3000)F2 from ionograms: A performance comparison with ARTIST 4.01 from Rome data

The performance of a computer program, called Autoscala, for the automatic scaling of foF2 and MUF(3000)F2 from ionograms has been extensively tested. Results of comparisons between automatically and manually scaled data are shown both for Autoscala and for ARTIST (release 4.01). Particular attention has been paid to the cases in which the ionograms have a truncated trace. The problem of the rejection of bad quality ionograms has been also considered. The analysis of data shows that the reliability of values automatically given as output by Autoscala is good. For the data set considered Autoscala seems to operate better than ARTIST.     

瞬变电磁场时域格林函数解

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.     

Robust inversion of vertical electrical sounding data using a multiple reweighted least-squares method

The root cause of the instability problem of the least-squares (LS) solution of the resistivity inverse problem is the ill-conditioning of the sensitivity matrix. To circumvent this problem a new LS approach has been investigated in this paper. At each iteration, the sensitivity matrix is weighted in multiple ways generating a set of systems of linear equations. By solving each system, several candidate models are obtained. As a consequence, the space of models is explored in a more extensive and effective way resulting in a more robust and stable LS approach to solving the resistivity inverse problem. This new approach is called the multiple reweighted LS method (MRLS). The problems encountered when using the L ₁- or L ₂-norm are discussed and the advantages of working with the MRLS method are highlighted. A five-layer earth model which generates an ill-conditioned matrix due to equivalence is used to generate a synthetic data set for the Schlumberger configuration. The data are randomly corrupted by noise and then inverted by using L ₂, L ₁ and the MRLS algorithm. The stabilized solutions, even though blurred, could only be obtained by using a heavy ridge regression parameter in L ₂- and L ₁-norms. On the other hand, the MRLS solution is stable without regression factors and is superior and clearer. For a better appraisal the same initial model was used in all cases. The MRLS algorithm is also demonstrated for a field data set: a stable solution is obtained.     

Penetration of Nonstationary Ionospheric Electric Fields into Lower Atmospheric Layers in the Global Electric Circuit Model

The problem of the penetration of nonstationary ionospheric electric fields into the lower atmospheric layers is considered based on the model of the global electric circuit in the Earth’s atmosphere. For the equation of the electric field potential, a solution that takes into account exponential variation in the electrical conductivity with height has been obtained. Analysis of the solution made it possible to reveal three cases of the dependence of the solution on height. The first case (the case of high frequencies) corresponds to the Coulomb approximation, when the electrical conductivity of the atmosphere can be neglected. In the case of low frequencies (when the frequency of changes in the ionosphere potential is less than the quantity reciprocal to the time of electric relaxation of the atmosphere), a quasi-stationary regime, in which the variation in the electric potential of the atmosphere is determined by the electric conduction currents, occurs. In the third case, due to the increase in the electrical conductivity of the atmosphere, two spherical regions appear: with the Coulomb approximation in the lower region and conduction currents in the upper one. For these three cases, formulas for estimating the electric field strength near the Earth’s surface have been obtained.     

A note on three-dimensional scattering and diffraction by a hemispherical canyon–I: Vertically incident plane P-wave

The three-dimensional scattering by a hemi-spherical canyon in an elastic half-space subjected to seismic plane and spherical waves has long been a challenging boundary-value problem. It has been studied by earthquake engineers and strong-motion seismologists to understand the amplification effects caused by surface topography. The scattered and diffracted waves will, in all cases, consist of both longitudinal (P-) and shear (S-) shear waves. Together, at the half-space surface, these waves are not orthogonal over the infinite plane boundary of the half-space. Thus, to simultaneously satisfy both zero normal and shear stresses on the plane boundary numerical approximation of the geometry and/or wave functions were required, or in some cases, relaxed (disregarded). This paper re-examines this boundary-value problem from the applied mathematics point of view, and aims to redefine the proper form of the orthogonal spherical-wave functions for both the longitudinal and shear waves, so that they can together simultaneously satisfy the zero-stress boundary conditions at the half-space surface. With the zero-stress boundary conditions satisfied at the half-space surface, the most difficult part of the problem will be solved, and the remaining boundary conditions at the finite canyon surface will be easy to satisfy.     

EFFECTS OF DATA ERRORS AND ACCURACY IN SECOND DERIVATIVE COMPUTATION BY RATIONAL APPROXIMATION*

The effects of systematic (constant) and random errors in the observed data have been investigated analytically for rational approximation method of computing second derivative involving a summation of the products of the averages of the gravity field with the corresponding weight coefficients, both in numerator as well as in denominator. A theoretical gravity anomaly over three spheres has been analyzed to demonstrate the high accuracy in the approximation. Since the sums of the weight coefficients in numerator and denominator are zero and one respectively, the regional gravity anomaly, even though approximated by a constant value over the entire area under computation, can produce substantially large error in the calculated derivative value. This is happening because of the contribution of the regional field in the denominator. Thus, inspite of the high accuracy in rational approximation, the method has limited application to field cases where a combined gravity field consisting of regional and residual anomalies is usually used. Master curves are presented for the constant and random errors by which a rough estimate of the percentage of error in second derivative computation can be made provided one has some idea of the magnitudes of the regional field and random error.     

接地源瞬变电磁短偏移深部探测技术

对于接地源时间域瞬变电磁法,当选取适当的激励波形后,可将辐射场与自有场分离开来, 实现频率域电磁法无法实现的近源深部勘探;水平分层大地的解析分析表明,随着偏移距的缩短,接地导线源的场对地层的反映变得更为灵敏;时间域瞬变电磁法的探测深度主要由观测时长决定.基于接地源近场测深的优越性,作者提出短偏移瞬变电磁探测技术并首次命名为SOTEM, 采用了1000 m的偏移距对埋深为1400 m的某盐矿溶腔进行探测, 在全期视电阻率-深度剖面上圈定的溶腔分布被钻孔所揭露, 验证了SOTEM方法的探测能力.该方法为大深度、高分辨探测地下矿产资源提供了新的技术手段.