On the boundary condition of the gravity disturbing potential

Summary The boundary condition for the gravity disturbing potential was derived upto the second-order terms and the influence of the second-order terms was investigated.Dedicated to 90th Birthday of Professor Frantiek Fiala     

On the problem of determining the vertical gradients of gravity anomalies

Summary Green's theorem on harmonic functions makes it possible to determine the integral relationship between the harmonic function and its derivative with respect to the normal on a closed Lyapunov surface. The conditions of solvability are given by Fredholm's theory of integral equations. The solution for a sphere was presented by Molodenskii[3] and the general solution with the help of Molodenskii's parameter k by Ostach[4]. The present paper indicates a possibility of solving this problem with the help of a system of linear algebraic equations, a simplified modification of the Ostach-Molodenskii solution and, finally, a method, based on Eremeev's solution of the fundamental integral equation[5].     

On the colocation iterative solution model and algorithm for gravity anomaly

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Calculation of the second vertical derivative of gravity field

Summary Two formulas, using Taylor's series expansion method, have been developed by means of which the second vertical derivative of gravity field may be computed at any point in the horizontal plane of observation. A comparative study of the resolving powers of different approaches by performing numerical and filter response tests suggests that the formulas provide a definite improvement over many existing methods.NGRI Contribution No. 69-130.     

基于总水平导数改进的密度界面快速反演方法

直接迭代法是利用重力异常反演密度界面的一种重要方法,对迭代公式分析的结果表明,可在反演公式中添加加速收敛因子以减少反演的迭代次数从而提高效率.对于平缓的密度界面采用较小的加速收敛因子、而对起伏较大的界面采用较大的加速收敛因子可有效减少反演迭代次数.为此,本文利用重力异常总水平导数判断待反演界面起伏平缓和起伏较大的区域,...     

Accuracy of deflections of vertical determined from discrete solution of the geodetic boundary value problem

Summary The general problem of determining the figure of the earth leads to the solution of the geodetic boundary value problem. By its discrete approximation we obtain the discrete disturbing potential that maintains all properties of the original problem. Thus, the discrete approximation of the disturbing potential can be used in studying the behaviour of the earth's gravity field outside the disturbing masses. The deflections of the vertical are one of the quantities describing the behaviour of the earth's gravity field. A method for their computation from the discrete solution of the geodetic boundary value problem is put forth and estimates for its accuracy are given.     

On the solution of the Molodenskii boundary value problem using successive approximations

Gravimetric methods of determining the figure of the Earth can be divided into two groups. The first employs an auxiliary surface—the geoid. The second employs the so-called quasigeoid as an auxiliary surface. Its main advantage is in that it only uses surface measurements and that it does not require knowledge of the structure of the Earth's crust. This method was treated in [1]. The results display an accuracy of the order of the Earth's flattening. The purpose of this paper is to show that this method can be applied theoretically to reach an arbitrary accuracy.     

On the interpretation of vertical gravity gradients produced by magmatic intrusions

A method for the computation and interpretation of gravity and height changes and vertical gravity gradients produced by magmatic intrusions in a layered elastic–gravitational medium is presented. The methodology assumes a planar medium geometry, which consists of welded layers overlying a half-space. The medium is elastic and gravitating. The intrusion is treated as a point source and can be located at any depth inside the medium. The theoretical elastic–gravitational model allows the computation of the so-called geometric and orthometric vertical displacements as well as gravity changes of different types. The corresponding vertical gravity gradients can also be computed. We present several examples of theoretical computations and study different types of these geometric and orthometric gravity gradients and the information we can get from the application of the methodology described. The results presented show that the use of these gradients is a useful tool to obtain information on the dynamics of the injection processes, including the detection of new magma recharge. We show that using the elastic–gravitational deformation model we can explain non-linear gravity–height relationships that appear in volcanic areas. We also present the application of the methodology to Mayon volcano, Philippines, delineating the intrusion of new magma, consistent with the produced eruptions after the observation period.     

On the correction of gravity tides observation and the indication analysis of gravity anomaly

The problems of correcting gravity tidal observations and indicating of the gravity anomalies used in earthquake prediction in China are systematically studied in this paper. The correcting problems of the rheological model of the instrument, inertia of the earth and the effects of the ocean loading, air pressure, underground water on gravity tidal recording data are also discussed in details, the related results are also given in the paper. The problem of the indicating non-tidal information in stational gravity data is dicussed. The properties of the several different data processing filters are compared in theoretical point of view.     

磁异常模量垂向一阶导数的特征及应用

磁异常转换模量(magnitude magnetic transforms,简称MMTs)相比传统的数据处理方法如化极、总梯度模等,其产生的异常更接近实际磁性异常体的水平位置,以便进行磁法解释.本文基于转换模量,提出了磁异常模量的垂向一阶导数的处理方法.进一步分析模量垂向一阶导数的特征可知,对于2D异常体其完全不依赖于...     

重力垂直梯度的测定及其应用与潜力

近年来,随着重力垂直梯度测量精度的提高及间接推求方法的改善,它在地球科学的研究中的作用日益扩大,本文叙述了利用高精度重力仪直接测量垂直梯度的方法与注意事项,阐明了垂直梯度在地学研究中的意义与作用,其中包括(1)可以更精确测定大地水准面与正高;(2)可以更好探测地下的物质的分布及界面起伏;(3)可根据垂直梯度及形变资料反演场源及解释引起上述变化的动力机制.关于如何进一步发掘其潜力,这里也提出了建议.     

重力异常垂向梯度严密改化模型及应用

积分奇异性和数值不连续性是改化重力异常垂向梯度全球积分模型面临的两大主要难题.本文研究并指出了积分模型传统改化方法存在的理论缺陷,同时依据实测数据保障条件,联合采用积分恒等式转换和移去恢复运算技术,分别推出了计算地球外部及地面重力异常垂向梯度全球积分模型的分步改化公式,提出了补偿传统改化模型理论缺陷的修正公式.以超高阶地球位模型EGM2008作为数值试验标准场,分别开展改化模型精度比对分析和向下延拓应用效能评估试验,从不同侧面验证了采用严密改化模型的必要性和有效性.

     

Location of secondary faults from cross-correlation of the second vertical derivative of gravity anomalies1

A method is described to locate secondary faults, which can be difficult to identify on the Bouguer gravity map. The method is based on cross-correlation between the theoretical anomaly due to a vertical step and the second vertical derivative of the Bouguer anomaly. Faults are located from the closed maxima and minima on the cross-correlation contour map calculated for two perpendicular directions. One-dimensional model computations show that the magnitude of the extremum of the cross-correlation is related to the depth to the top of the hanging wall and the throw of the fault. Application of the method to the Bouguer gravity map of the former mouth of the Yellow River in the Shengli Oilfield area near the Bo Hai Sea shows the effectiveness of the method.     

On mapping an irregular boundary by means of reflected-wave measurements

Summary A method, using seismic data, is presented for the mapping of the irregular boundary of an elastic half-space. It furnishes the shape of the corrugations in terms of the measured displacement field generated by plane dilatational or shear waves reflected from the boundary.Support of this investigation by the National Science Foundation under grant NSF-GP-2722 is gratefully acknowledged.     

The isostatic gravity anomaly: key to the evolution of the ocean-continent boundary at passive continental margins

Isostatic gravity highs bordering the passive continental margins are interpreted as resulting from oceanic basement highs. These basement elevations are relics of the transient phenomenon of a higher ridge axis elevation during early rifting. The steep landward gradient in the isostatic gravity field, generally associated with a magnetic edge effect anomaly, delineates the boundary between oceanic and continental basement.     

利用2009年日全食的精细重力观测探寻“引力异常”

日全食期间在是否存在"引力异常"现象是一个关系到引力本质的重大问题,也是一个十分具有现实意义的科学问题.近一个世纪来,许多科学工作者作了大量的观测和实验,研究日全食期间的"引力异常"现象.肯定的、否定的结果并存,更多的是难以确定的结果.在学习、总结和发展了前人工作的基础之上,本文利用7台LaCoste-Romberg重力仪和1台SG-053超导重力仪,对2009年7月22日日全食期间的重力变化进行了精细的观测.研究利用了目前最好的观测环境和观测仪器,无论观测规模还是观测质量在近百年来日全食的重力观测研究中都是首屈一指的.在经过详细的数据处理和图像分析后,可以确定,日全食期间不存在现有观测能力之上的引力异常,以往发现的异常现象受剧烈的气象变化影响可能性极大.另外,在处理重力观测数据时,本文合理的利用了最小二乘多项式拟合法去除理论潮汐值,使计算得以简化,结论更加可靠.     

位场垂向导数零值位置空间变化规律研究(英文)

本文推导了简单规则形体(单一边界、双边界和多边界)重力异常垂向一阶导数和重力异常垂向二阶导数零值位置的解析表达式,并研究了其空间变化规律;对难以得到其零值位置解析表达式的简单规则形体,利用其剖面图和断面图上的零值位置来研究其空间变化规律。研究结果表明,重力异常垂向二阶导数与重力异常垂向一阶导数零值位置的空间变化规律基本一致,只是重力异常垂向二阶导数零值位置比重力异常垂向一阶导数的零值位置更靠近地质体上顶面边缘位置,且其分辨能力更强。对于单边界模型,随着埋深的增加,重力异常垂向导数的零值位置均自形体上顶边缘位置向外侧偏移,但最终均能收敛于某一固定值;对于双边界模型,随着埋深的增加,重力异常垂向导数的零值位置自形体上顶边缘位置一直向外侧偏移;对于多边界模型,随着埋深的增加,重力异常垂向导数零值位置自形体上顶边缘位置向外侧收敛,部分边界的零值位置重合并消失。最后通过实际资料检验了方法的有效性和可靠性。