利用重力梯度张量等位面曲率的地质体定位

针对重力梯度张量曲率的研究, 前人的工作主要集中在重力张量曲率的解释及边缘检测中, 几乎没有涉及到地下密度异常体的定位.本文结合重力矢量和重力梯度张量提出了一套基于重力梯度张量等位面曲率的地下密度异常体位置估计策略.首先, 从重力梯度张量等位面曲率的基本定义出发, 计算重力梯度张量等位面曲率.然后, 通过寻找球面或圆形等位面的重力梯度张量曲率, 提出了利用最大主曲率定位地下密度异常体位置的源参数估计方法, 并详细推导了估计3D球体(质点)和2D水平线源位置信息的解析表达式.再者, 针对噪声和多源存在的情况, 提出了一套利用重力梯度张量等位面曲率获得密度异常体位置信息的稳健估计流程, 并利用模糊C均值聚类算法进一步确定地下密度异常体的中心位置.最后, 通过理论模型测试和文顿盐丘实测航空重力梯度数据测试, 验证了本文算法的可行性和可靠性.结果表明: 在满足曲率半径定义条件的情况下, 本文所提出的源参数估计方法可以定位单个或多个地下3D和2D密度异常体的空间位置, 具有较好的稳健性和抗噪能力.该方法拓展了重力梯度张量曲率的应用范围, 可为重力梯度张量的三维反演工作提供先验的空间位置信息.

     

地面扰动重力垂直梯度的确定

鉴于扰动重力垂直梯度在大地测量和物探中有重要作用,在未直接测量的情况下,对如何由地面重力异常及地形数据求取扰动垂直梯度进行了研究和分析,认为在被研点附近要求重力点分布密集,且精度不低于1×10-6ms-2;对中央区域积分奇异性问题也作了讨论;此外,扰动重力垂直梯度如何在大地测量和地球物理中进一步得到应用,以及为何用扰动重力垂直梯度代替重力异常垂直梯度也给予了简明的论述.     

基于重力梯度张量曲率的边界识别

重力梯度张量曲率目前广泛用于重力数据的处理和解释中.为了拓宽重力梯度张量曲率的应用,本文回顾了重力梯度张量曲率的定义,从等位面的曲率定义出发,讨论了正确计算曲率的测量参考系及局部旋转的相关理论,并以单个球体和棱柱体为例来说明曲率的正确计算方式.然后,在正确计算重力梯度张量曲率的基础上,将重力梯度张量曲率应用到重力数据的边界识别中,通过理论模型和实际数据详细分析和比较了各种曲率在重力边界识别中的应用效果.结果表明：基于等位面的局部旋转坐标系是各种曲率正确计算的先决条件,纠正了曲率计算的误区;在边界识别中,局部坐标系下所计算的高斯曲率进行边界识别能够较好的圈定地下地质体的边界.

     

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.     

地震重力观测技术的新发展方向:绝对重力与重力梯度一体化观测

高精度绝对重力与重力梯度一体化和阵列式观测可有效提高不同深度重力场源体的识别精度。本文基于中国地震局发布的《中国地球物理站网（重力）规划（2020—2030）》中绝对重力观测技术的不足和发展方向,提出了绝对重力与重力梯度一体化的观测技术思路。在监测中发现,强震孕育过程中壳—幔热物质运移引起的微重力变化信号,有利于提升破坏性地震的中、短期和临震预测能力。有必要进一步拓展重力站网绝对重力控制能力等方面的应用,为我国专业地震台站探索重力观测技术新发展方向。      

Experimental determination of the vertical gravity gradient below the sea level

The experiment for determining the vertical gravity gradient on a self-contained submersible instrument in the high latitudes with the use of the Chekan AM gravimetric complex is described.     

Allowance for the vertical gradient in an airborne gravity survey

When processing the results of an airborne gravity survey flown in the Arctic at flight heights of 2000 to 3000 m, the authors encountered conditions, when the values of the free-air anomaly of gravity exceeded the values taken from the anomaly map, with a trend towards “heavier” values. The formula for calculation of the vertical gradient as a function of the latitude of the locality has been refined. The tentative calculations reported in the paper also indicate that a free-air gravity anomaly above the mountainous areas will contain additional positive systematic components, since only the effect of the vertical gradient of the normal gravity field is taken into account here, and the flight’s height during an airborne gravity survey, above a mountainous area, should be held constant, otherwise it would be necessary to take into account additional systematic biases, obtained in different flights, which are caused by the different values of the vertical gradient at different heights.     

Computation of the vertical gradient of gravity for two dimensional bodies

Summary A method of computation of the vertical gradients of gravity, at different elevations, from the residual gravity profile due to a localised two dimensional causative body is presented. The vertical gradient at an elevation above a station has been expressed as a weighted summation of the gravity values at equally spaced stations along a profile. These weights (coefficients) depend only upon the positions of the individual stations, relative to the station of computation, and upon the ratio of the elevation at which the vertical gradient value is sought to the separation of the stations. Functional forms of these coefficients have been derived analytically and they have been computed for different relative positions of the individual stations and for different values for the ratio of elevation to separation.An analytical expression has been derived for the remainder term which is necessary when the above summation is performed over a finite length of the profile only. As this expression involves the parameters, (i) total mass per unit length and (ii) the positions of the centre of gravity of the causative body, a method has been developed separately for their accurate determination from the anomaly profile of finite length.The efficacy of the method has been assessed by applying it to an arbitrary theoretical model.     

The relation between the mean vector surface wind and the mean vector pressure gradient over the oceans

Summary Mean values of the angle of inclination between the mean vector surface wind and the mean isobars have been calculated as a function of latitude for a number of independent Marsden squares over the ocean. Mean values of the ratio between the mean vector surface wind velocity and the calculated geostrophic wind velocity have been computed in the same way. Some general inferences about the general circulation have been drawn from the results.     

精化大地水准面的一种间接方法——异常及其梯度在其中的应用

随着GPS/水准及全球重力测量的加密和扩展,获取高精度的似大地水准面或高程异常(ξ)已比较容易,如何进一步研究它和大地水准面或大地水准面高(N)之间的关系(即所谓间接的方法)使大地水准面得到精化,这就是本文的目的,文中对已推导的公式在模型作了验证,对如何利用地形等数据确定扰动重力垂直梯度也作了研究,结果表明:在海拔4000 m的高山地区,当似大地水准面的精度达到cm级时,大地水准面的精度也与之比较接近.     

The limitation of curvature gravity gradient tensor for edge detection and a method for overcoming it

Eigenvalues of the curvature gravity gradient tensor (CGGT) have been utilized to detect and outline edges of geologic bodies. In this paper, we analyzed and discussed the application scope and the limitation of CGGT using a complex synthetic model. We found that the large eigenvalue only can be used to outline edges of positive density bodies, and the small eigenvalue only can be used to delineate edges of negative density bodies. However, in the actual geological situation, the positive and negative density bodies usually coexist simultaneously. Therefore, it has certain limitations to detect edges using this method directly. In view of the limitations of the method, we combined the gravity anomaly with large eigenvalues, and proposed a new improved method for the eigenvalues of CGGT. The improved method can be utilized to outline edges of causative sources in any case. It was tested on synthetic model data and real field data. All of the results have shown that the new improved method is effective for edge detection.     

重力及其垂直梯度交叉约束联合密度结构反演方法

重力垂直梯度能突出浅部地质目标, 具有较高的水平分辨率, 而重力异常则可以更好地保留较深场源的信息, 重力与重力梯度联合勘探常用来获取不同深度场源的异常特征.本文提出重力及其垂直梯度交叉约束联合密度结构反演方法, 其采用交叉梯度实现重力与重力梯度数据联合反演, 并将二者单独反演结果作为归一化权函数约束联合反演过程.该方法可有效改善不同参量反演结果集中于异常变化较大区域的缺点, 提升不同深度场源的分辨率, 更加准确地揭示深部场源的分布.模型试验结果表明该方法能清晰恢复不同深度场源的密度结构分布特征, 且具有良好抗噪能力.针对辽源采空区勘查开展重力与其垂直梯度联合测量, 利用本文数据联合反演圈定出了6个采空区, 与以往已知矿点位置完全一致, 且与高密度电阻率法解释结果吻合良好, 为区域规划建设提供了准确的依据.此外, 我们还对长白山火山地区卫星重力及其梯度数据进行反演, 估计了岩浆囊的位置和范围, 且与前人地球物理勘探结果较为吻合, 进一步证明了本文方法的实用性.

     

Structural interpretation of the Erzurum Basin,eastern Turkey,using curvature gravity gradient tensor and gravity inversion of basement relief

The Erzurum Basin has received more attention in petroleum potential research because of its particularity in geographic and tectonic position. There remains debate on the basement structure of the basin since igneous rocks and faults make the structure and stratigraphy more complicated. We utilize gravity data to understand the structure of the Erzurum Basin. This study describes an edge enhancement technique based on the eigenvalues and determinant obtained from the curvature gravity gradient tensor (CGGT). The main goal of this technique is to delineate structural boundaries in complex geology and tectonic environment using CGGT. The results obtained from theoretical data, with and without Gaussian random noise, have been analyzed in determining the locations of the edges of the vertical-sided prism models. The zero contours of the smallest eigenvalue delineate the spatial location of the edges of the anomalous sources. In addition, 3-D gravity inversion of Bouguer anomalies has been used with purpose to estimate the structure of the substrata to allow modeling of the basement undulation in the Erzurum basin. For this reason, the Parker–Oldenburg algorithm helped to investigate this undulation and to evidence the main linear features. This algorithm reveals presence of basement depths between 3.45 and 9.06 km in the region bounded by NE–SW and E–W trending lineaments. We have also compared the smallest eigenvalue zero contours with the HGM images and Tilt derivative (TDR) of Bouguer anomaly map of the study area. All techniques have agreed closely in detecting the horizontal locations of geological features in the subsurface with good precision.     

基于激光干涉法的地表重力垂直梯度测量系统设计及试验

基于激光干涉法对新型地表重力垂直梯度测量系统进行了研究并初步构建了原理样机． 该测量系统利用双光路干涉测量法, 获取垂直向间距为50 cm且同步自由下落的两个落体相对于参考点的时间和位移信息, 并通过差分运算得到该测点的重力垂直梯度值． 在系统设计过程中, 主要解决了双落体自由下落的同步自动控制和双干涉测量光路的垂直性调节问题． 试验结果表明, 本套测量系统可以获取双落体同步自由下落运动时的干涉条纹信号, 并完成重力垂直梯度测量, 且梯度测量精度优于100 E．      

Anomalous curvature of equipotential surfaces due to variations in the Earth's rotation

Summary The anomalies of the Gaussian curvature of geopotential equipotential surfaces due to variations in the Earth's rotation vector have been derived theoretically.

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垂直重力梯度反演Moho面的频谱域公式及其应用

通过求解引力相等原则下的Fredholm积分方程,可以得到不规则单一密度界面(Moho面)的起伏.本文充分参考了前人的理论研究,推导出扰动垂直重力梯度确定Moho面深度的频谱域表达式,该式具有二次项迭代精度.运用此公式进行了全球Moho面的恢复计算,并将该结果与CRUST1.0模型和GEMMA Moho模型进行了对比和验证.     

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.

     

A study of regional gravity field recovery from GOCE vertical gravity gradient data in the Auvergne test area using collocation

Gravity field and steady-state Ocean Circulation Explorer (GOCE) is the first satellite mission that observes gravity gradients from the space, to be primarily used for the determination of high precision global gravity field models. However, the GOCE gradients, having a dense data distribution, may potentially provide better predictions of the regional gravity field than those obtained using a spherical harmonic Earth Geopotential Model (EGM). This is investigated in Auvergne test area using Least Squares Collocation (LSC) with GOCE vertical gravity gradient anomalies (T_zz), removing the long wavelength part from EGM2008 and the short wavelength part by residual terrain modelling (RTM). The results show that terrain effects on the vertical gravity gradient are significant at satellite altitude, reaching a level of 0.11 E?tv?s unit (E.U.) in the mountainous areas. Removing the RTM effects from GOCE T_zz leads to significant improvements on the LSC predictions of surface gravity anomalies and quasigeoid heights. Comparison with ground truth data shows that using LSC surface free air gravity anomalies and quasi-geoid heights are recovered from GOCE T_zz with standard deviations of 11 mGal and 18 cm, which is better than those obtained by using GOCE EGMs, demonstrating that information beyond the maximal degree of the GOCE EGMs is present. Investigation of using covariance functions created separately from GOCE T_zz and terrestrial free air gravity anomalies, suggests that both covariance functions give almost identical predictions. However, using covariance function obtained from GOCE T_zz has the effect that the predicted formal average error estimates are considerably larger than the standard deviations of predicted minus observed gravity anomalies. Therefore, GOCE T_zz should be used with caution to determine the covariance functions in areas where surface gravity anomalies are not available, if error estimates are needed.     

孕震过程中重力位、重力、重力梯度变化的数值模拟研究

简要介绍了为探索和解释地震前后重力变化的各种孕震模式,推导了由孕震引起的密度变化和位移与地面重力位、重力、重力梯度之间的变化关系。摸拟计算了孕震位移和密度变化引起的重力位、重力、重力梯度变化的空间分布并分析了重力位、重力、重力梯度变化的空间分布特征。与此同时,采用广义司托克斯云积分和有限差分方法对云南丽江7. 0级地震前重力位、重力、重力水平梯度进行了计算。结果表明,强震前重力位、重力、重力梯度有其自身的变化特征,这对预测强震有实际意义。     

Secular variations in the curvature of equipotential surfaces and directions of verticals due to geodynamic phenomena

Summary Formulae and numerical estimates are given for the non-periodical variations in the curvature of equipotential surfaces, horizontal forces and directions of the vertical, caused by the decrease in the second zonal geopotential harmonic, by the decrease in the angular velocity of the Earth's rotation and by secular polar motion.

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