强磁性三度体内部磁化强度的分布

本文讨论稳定磁化场中强磁性三度体内部磁化强度的数值解法。展示了由于退磁作用而造成的不均匀性,并以长方体内一些典型截面为例,较详细地讨论了磁化强度的特征,作了分布图;推导了较均匀磁化体磁化强度分布的近似公式,并计算了一组长方体的视退磁系数。     

Love waves in an inhomogeneous interstratum

Summary The propagation of Love waves in an inhomogeneous interstratum, whose rigidity and density follow generalized power law variation, lying between two homogeneous half-spaces has been considered. The characteristic frequency equations have been obtained. The computational results for some special cases are presented in the form of dispersion curves showing the variation of phase and group velocity of Love waves with wave number.     

INTERPRETATION AND DEPTH OF INVESTIGATION OF GRADIENT MEASUREMENTS IN DIRECT CURRENT GEOELECTRICS*

Gradient measurements in a homogeneous electrical primary field can easily be interpreted for simple models. The simplified solution (conducting or resistant body in a homogeneous space in a homogeneous electrical field) is often sufficiently accurate, as comparisons with the exact solution (body of finite resistivity in a homogeneous half-space in a quasihomogeneous electrical field) show. The exact geometry of the body cannot be determined by gradient measurements; the same anomaly of apparent resistivity can be caused by different bodies. In particular, the similarity between a sphere and a cube of the same volume is very high. There is a distinct influence of the resistivity of the overburden: the higher this resistivity is, the stronger is the effect caused by a buried body. If a deviation of 10% of the apparent resistivity is assumed as the lower boundary at which a buried body can be detected by gradient measurements, the depth of investigation for a three-dimensional body is approximately equal to its width; in the two-dimensional case the thickness of the overburden can be twice the width. If the overburden has a resistivity which is higher than the resistivity of the substratum, these depths are greater. The greatest possible depth is approximately three times the width of the body.     

导电率随时间变化的导电球的电磁响应问题

本文采用非齐次麦克斯韦方程组,给出了导电率随时间变化时均匀的和非均匀的导电球,在均匀的和非均匀的外激励场的作用下的电磁响应问题的解析解。并简单讨论了这类电磁响应问题在地球物理学中的可能应用。     

A New Theory of Love Waves in Multi-layered Media with Irregular Interfaces

In this article, we have derived a new and more general formulation of Love waves in arbitrarily irregular multi-layered media by using the global generalized reflection/transmission (abbreviated to R/T thereafter) matrices method developed earlier by Chen [17~20]. From the basic principle that the modal solutions are the non-trivial solutions of the free elastodynamic equation under appropriate boundary conditions, we naturally derived the characteristic frequencies and the corresponding distorted modes of Love wave in irregular multi-layered media. Moreover, we have derived the corresponding excitation formulation of Love waves in such laterally heterogeneous media by using the general solution of elastodynamic equation [17~20]. Similar to the result for laterally homogeneous layered structure, the Love waves radiated from a point source in irregular multi-layered media can be expressed as a superposition of distorted modes. Since the structure model used here is quite arbitrary, it can be used for so     

上地幔各向异性介质对固体潮及负荷潮的影响

讨论了上地幔各向异性介质中的潮汐运动方程,根据Deiewonski提供的地球模型参数,利用经典的Runge－Kutta数值积分方法,计算了固体潮勒夫数和负荷勒夫数．结果表明,考虑上地幔介质各向异性与否对固体潮勒夫数的影响较小（约为0．06％）,而对负荷勒夫数的影响较大（2．5％）,进一步说明了中低阶负荷勒大数对上地慢介质特性的敏感性．     

上地幔各向异性介质对固体潮及负荷潮的影响

讨论了上地幔各向异性介质中的潮汐运动方程,根据Deiewonski提供的地球模型参数,利用经典的Runge－Kutta数值积分方法,计算了固体潮勒夫数和负荷勒夫数．结果表明,考虑上地幔介质各向异性与否对固体潮勒夫数的影响较小（约为0．06％）,而对负荷勒夫数的影响较大（2．5％）,进一步说明了中低阶负荷勒大数对上地慢介质特性的敏感性．     

GRAVITY INTERPRETATION USING THE HANKEL TRANSFORM*

The Hankel transform theorem can be applied to the inversion of gravity data for the buried sphere, the horizontal cylinder, and the vertical rod. This new approach leads to exact solutions of the transforms for the assumed bodies. A comparison with the classical procedure by Fourier transform reveals that for the sphere and the vertical rod, the Hankel transform is preferable.     

A NOTE ON THE USE OF A NOMOGRAM FOR SELF-POTENTIAL ANOMALIES*

A nomogram has been devised for situations, in which the source of a self-potential anomaly can be approximated by an obliquely polarized sphere or horizontal cylinder embedded in a homogeneous half space. The nomogram can be used for rapid determination of three parameters of the target: (1) depth to the centre, (2) angle between the axis of polarization and the horizontal, (3) shift of the point vertically above the centre of the body from zero potential value. The nomogram has been tested and the parameters determined for SP results obtained over ore bodies Weiss and Süleymanköy in the Ergani Copper district, Turkey. The curves computed for the estimated parameters match the field curves well.     

Influence of viscosity on the phase of earth tides

The effect of viscosity on the phase of earth tides is computed. Computations are based on the general theory of the effect of viscosity of the mantle considered as a Maxwell body as it has been elaborated by Molodensky (1963). The problem is solved by the method of variation of constants, starting from the solution for the case of an ideally elastic, spherically symmetrical globe. The computations presented here cover the cases of the earth models B₁ and B₂ of Bullen and Haddon (1967). Love numbers k, l, h were computed for tides of second and third order, and values of phase delay due to viscosity were computed for tides of second order.     

关于用有限元法作磁法勘探正演计算的理论问题

本文提出用有限元法解磁法勘探的正问题,不再需要引入均匀磁化假定。 传统的正演计算方法是在均匀磁化的假定下建立的,它不能适应解释复杂磁异常的需要。近几年来,国外学者提出了用迭代方法作非均匀磁化条件下的正演计算,对形状比较简单的磁性体取得了较好的效果。但随着磁性体的形状变得比较复杂,计算所需时间很快增加,精度和稳定性也明显降低。以求能量函数极小的变分原理为依据,用有限元法作非均匀磁化条件下的正演计算,得到的磁位势函数满足磁性体内外的偏微分方程和全部界面条件（文中对此作了证明）。因此,这种方法可以研究各种复杂因素的影响,宜于计算非均匀磁化磁性体的有效磁化强度和磁异常。     

考虑关断时间的回线源激发TEM三维时域有限差分正演

从麦克斯韦旋度方程出发可以直接导出瞬变电磁场扩散方程,然而扩散方程不含电场对时间的一阶导数,不能构成显式的时域有限差分方程,借鉴du Fort-Frankel有限差分离散方法引入虚拟位移电流项构建显式时域有限差分方程.对Wang和Hohmann的经典时域算法进行了两点改进:第一,通过将矩形回线源电流密度加入麦克斯韦方程组的安培环路定理方程,实现回线源瞬变电磁激发源加入;第二,在计算中考虑关断时间.第一点改进使时域有限差分方程考虑了一次场的计算,并且源的计算不再依赖均匀半空间模型响应作为初始条件,使算法能够适应表层电阻率不均匀时的三维复杂模型.由于实际观测中不可能出现阶跃电流的关断形式,第二点改进可以方便设置发射电流下降沿.采用改进的三维时域有限差分正演算法对均匀半空间模型、四类三层模型、均匀半空间中含有低阻块体模型进行了计算并分别与解析解、线性数字滤波解、积分方程解和Wang的三维时域有限差分解进行了对比验证.以H模型为例,采用建立的三维时域有限差分正演算法计算了不同关断时间的斜阶跃脉冲回线源瞬变电磁中心点感应电动势衰减曲线.以实际地质资料为基础,构建包含两层采空区的三维复杂模型,以1 μs的极短关断时间进行了复杂模型定回线源瞬变电磁响应计算,并计算了该复杂模型的视电阻率曲线.     

On the electrical reflectivity tensor in d.c. electric field modelling

We use the integral equation for a d.c. electric field, published in the literature, to introduce the concept of the electrical reflectivity tensor into d.c. electric field modelling. It is shown that in d.c. electric field modelling, the electric reflectivity tensor can be obtained in exactly the same way as in electromagnetic modelling. As a result, for a d.c. electric field, the quasi‐linear and the quasi‐analytical approximations, as well as the quasi‐analytical series, can be constructed in exactly the same way as in electromagnetic modelling. If the primary field is uniform, and if the anomalous body is a uniform circular cylinder or a uniform sphere, the reflectivity tensor is zero order (constant), relating to the free surface charge density. Thus, for some homogeneous bodies that have simple shapes and are embedded in a uniform primary field, the electrical reflectivity tensor is not only a mathematical mechanism for obtaining approximate solutions, but also a physical reality. Indeed, the free surface charge density is defined as the change of the electric displacement vector across the boundary surface under consideration. If the primary field is caused by a point source, and if the anomalous body is a uniform sphere, the reflectivity tensor is second order, varying slowly within the sphere. The relationship to the free surface charge density can be established only when both the reflectivity tensor and the free surface charge density are approximated by the first terms of their series solutions. If the point source is far from the centre of the sphere, the corresponding reflectivity tensor reduces to zero order, and is independent of the observation position within the sphere, i.e. it is a constant. Therefore, the basic idea of the quasi‐analytical approximation, i.e. taking the reflectivity tensor outside the integral operator, is justified in the case considered here.     

RAPID DETERMINATION OF CUBE'S GRAVITY FIELD *

Gravity modeling involves the evaluation of gravity field due to bodies of irregular shape. This is commonly accomplished by dividing the body into smaller units of regular shape whose field can be determined analytically. Cubes are ideal building blocks for constructing bodies of irregular shape. However, the exact expression defining the gravity field of a cube-shaped body is very long and requires tedious numerical work. Approximation formulas for rapid evaluation of the cube's gravity field are presented and discussed in detail. Their use for computing the field for small distances leads to large errors in the results; on the other hand, using the exact formula for large distances where approximation formulas yield practically identical results, is waste of time. After a detailed analysis about the nature of the cube's gravity field, certain criteria are established for suitably combining the two alternatives. This results in tremendous reduction in the task of computations without affecting the accuracy of data.     

气压变化及其对地壳形变和深井水位的影响

根据北京塔院地区1984和1985年的微气压计记录采用频谱分析和调和分析两种方法得出了大气潮谱的详细结构;用负荷勒甫数代替潮汐勒甫数,仿照固体潮的有关公式,导出了大气潮引起的地壳应变和地倾斜公式;使用北京塔院井的水位观测资料结合当地的气压资料,分析了气压变化对深井水位的影响.理论计算和实测资料的分析结果基本相符,特别是两种结果都得出S_2大气潮引起的体膨胀约为S_2固体潮体膨胀的20％.     

气压变化及其对地壳形变和深井水位的影响

根据北京塔院地区1984和1985年的微气压计记录采用频谱分析和调和分析两种方法得出了大气潮谱的详细结构;用负荷勒甫数代替潮汐勒甫数,仿照固体潮的有关公式,导出了大气潮引起的地壳应变和地倾斜公式;使用北京塔院井的水位观测资料结合当地的气压资料,分析了气压变化对深井水位的影响.理论计算和实测资料的分析结果基本相符,特别是两种结果都得出S₂大气潮引起的体膨胀约为S₂固体潮体膨胀的20％.     

Love wave propagation in anisotropic inhomogeneous medium: Elastic parameters for equivalent isotropic case

Summary It is shown that the problem of Love wave propagation in an anisotropic inhomogeneous medium can be studied alternatively by defining elastic parameters in the equivalent isotropic case. An example is considered to illustrate the application of the method in obtaining the frequency equation of Love waves, propagating in an anisotropic inhomogeneous layer embedded between two isotropic homogeneous half spaces.     

Mechanical problems in geodynamics and work done in China

The subject of geodynamics concerns the dynamics of the global motion of the earth, of the motion in the earth's interior and its interaction with surface features, together with mechanical processes in the deformation and rupture of geological structures. A brief historical review is given from Sir I. Newton, Maclauwin, Jacobi, Poincaré, Poisson, Lamé, Darwin, Rayleigh, and Love, who dealt with the homogeneous sphere, to Leibenson, Takeuchi, and Meinesz, concentrating on layered spheres, and after the advent of plate tectonics, on the use of numerical simulation, to the analyses of tectonic features, earthquake mechanism, the application of nonlinear dynamics. By discussing the forward and inverse mechanical problems, and the questions facing the inverse problems of searching for the structural parameters, driving forces, etc. are raised in more detail. Thereafter, some works accomplished in China on the global and regional stress fields analyses; tectonic features' analyses, mantle flow studies; experimental studies of rocks and their constitutive relations are presented. Finally, the interdisciplinary nature of the subject is emphasized, and the main mechanical problems that need special attention are then proposed.     

ANALYTICAL EXPRESSIONS FOR GRAVITY DUE TO HOMOGENEOUS REVOLUTIONAL COMPARTMENTS IN THE GAUSSIAN DIVERGENCE APPROACH*

Complete analytical expressions are developed for the first and second derivatives of the Newtonian gravitational potential in arbitrary directions due to the homogeneous revolutional compartment with a polygonal vertical section by applying the Gaussian divergence theorem in the cylindrical coordinate system. Elementary solutions presented can easily be translated into magnetic anomalies caused by a uniformly magnetized body. The divergence approach in the polar coordinate system is also described, and gravity attractions in the radial direction are presented in closed form associated with a homogeneous cap compartment. The explicit solutions are tested against well-known formulae for a cylinder, cone, infinite plate, and sphere.     

Global tidal parameters

Summary Global tidal parameters are shown to have recently increased in accuracy, after more than twenty years of LLR and a decade of superconducting gravimetry, whereas the numerical values for the Earth have not changed substantially. Numerical values of Love numbers for terrestrial planets and the moon are also given for degrees higher than four as load numbers are basically linear combinations of Love numbers, at least for spherical non-rotation approximations. Numerical values for planetary moons, as far as they are known, have also been included in the paper. The static and dynamic behaviour of long-period and pole tide is discussed. Inner solid and outer fluid core effects are critically reviewed, also in view of a century of terrestrial tide observations of the classical type. The separation of long-period tides from secular effects (on a rotating Earth) such as J_n (n<5), is considered.Dedicated to the Memory of M. S. Molodensky