Point Mass Method Applied to the Regional Gravimetric Determination of the Geoid

The determination of the local gravity field by means of the point mass inversion method can be performed as an alternative to conventional numerical methods, such as the least-squares collocation. Based on the first derivative of the inverse-distance Newtonian potential for the representation of the gravity anomaly data, it is possible to compute any wavelength component of the geoid in planar approximation with sufficient accuracy. In order to exemplify the theoretical concept, two applications are presented of the computation of two different wavelength components of the geoid, the long wavelength component in a local solution and the short wavelength component in a regional solution. The results are compared with corresponding least-squares collocation solutions, using a global geopotential model to remove and to restore the long wavelength component.     

A second derivative method of interpretation of gravity anomalies of anticlines

Summary A simple method for the interpretation of second derivative gravity anomalies of an anticline is presented. The method utilises only three readily measurable distances, from the origin to the points of half maximum second derivative anomaly, zero anomaly and minimum second derivative anomaly. Charts for the computation of the various parameters are constructed.     

重力位谱分析及重力异常导数换算新方法——余弦变换

为了提高重力异常导数换算的精度,真实有效地反映地质体的异常特征,提出用余弦变换计算异常导数的新方法. 给出并证明了两个定理,利用它们推导出重力位余弦谱一般表达式以及重力异常各阶导数计算公式,建立了位场余弦谱分析理论. 模型实验中发现,用Fourier变换计算的一阶导数与理论导数偏差很大,而余弦变换计算的导数与理论异常导数拟合效果非常好,除边界几个数据因重力异常的有限截断产生的吉布斯效应残留使误差较大外,数据的计算精度均很高,误差为-0.09%～5%.     

基于GIS的区域重磁空间信息集成研究

根据区域重磁场的特点，利用其水平一导峰谷值线可确定异常体的线性构造，垂向二阶导数可确定异常体的环形构造的基本原理，在计算机上自动完成重磁数据处理及成图；并基于GIS"空间分析"功能对图形进行模式识别；实现区域重磁构造的自动提取与空间信息的自动集成.通过对我国东昆仑1:100万重力资料的实际应用，表明其结果具有实用性，其信息集成技术可用于改造以往计算机成图并借助透明纸叠置的人工重磁资料解释工作模式.     

基于GIS的区域重磁空间信息集成研究

根据区域重磁场的特点,利用其水平一导峰谷值线可确定异常体的线性构造,垂向二阶导数可确定异常体的环形构造的基本原理,在计算机上自动完成重磁数据处理及成图;并基于GIS"空间分析"功能对图形进行模式识别;实现区域重磁构造的自动提取与空间信息的自动集成.通过对我国东昆仑1:100万重力资料的实际应用,表明其结果具有实用性,其信息集成技术可用于改造以往计算机成图并借助透明纸叠置的人工重磁资料解释工作模式.     

Atmospheric effects in the derivation of geoid-generated gravity anomalies

Parameters of the gravity field harmonics outside the geoid are sought in solving the Stokes boundary-value problem while harmonics outside the Earth in solving the Molodensky boundary-value problem. The gravitational field generated by the atmosphere is subtracted from the Earth’s gravity field in solving either the Stokes or Molodensky problem. The computation of the atmospheric effect on the ground gravity anomaly is of a particular interest in this study. In this paper in particular the effect of atmospheric masses is discussed for the Stokes problem. In this case the effect comprises two components, specifically the direct and secondary indirect atmospheric effects. The numerical investigation is conducted at the territory of Canada. Numerical results reveal that the complete effect of atmosphere on the ground gravity anomaly varies between 1.75 and 1.81 mGal. The error propagation indicates that precise determination of the atmospheric effect on the gravity anomaly depends mainly on the accuracy of the atmospheric mass density distribution model used for the computation.     

APPLICATION OF 3D HIGH PRECISION GRAVITY METHOD TO THE EXPLORATION OF DEEP BURIED HILL

Due to the influence of volcanic rock or weathering crust coverage, the quality of deep seismic data is often not reliable and it is difficult to identify small deep buried hill structure beneath the cover. However, the gravity exploration technology can use the remarkable density differences between the object and the overlying strata to identify this special geological reservoir. Although recently several rounds of seismic exploration have been carried out in Raoyang depression, Huabei Oilfield, North China to determine the existence of Hu 8 north deep buried hill, whether the buried hill really exists or not as well as its scale is still in controversial. In this paper, based on the information of seismic data and formation density, deep processing of 3D high precision ground gravity data has been carried out for 3D forward and inversion computation. The dimensional gravity forward calculation results show that the density of the deep anomaly body forms a relatively low gravity anomaly in the earth's surface. By using the potential processing method of vertical second derivative, and sliding filtering, the residual anomaly is separated from regional or background field, which illustrates the existence of a local high gravity anomaly at Hu 8 north area. According to the amplitude of residual gravity anomaly and formation density difference modeling, through a number of 3D forward calculations and 3D inversion of gravity data, the existence of Hu 8 north buried hill and its possible scale are basically determined. The results prove that the 3D high precision gravity method is effective in determining the deep buried hill structure in case that seismic data is not reliable.     

THE USE OF FOURIER SERIES METHOD IN UPWARD CONTINUATION WITH NEW IMPROVEMENTS*

This paper shows how to reduce the errors near edges of potential field data that result from using Fourier series in the computation of upward continuation of potential field anomalies. This kind of error, if uncorrected, can lead to erroneous geological interpretation. The errors that occur at both edges of potential field data after upward continuation originate from the representation of data by using Fourier series from which data becomes periodic with discontinuities or sharp changes between each period. In order to reduce this type of error, we propose, either 1) to use only the cosine series, or 2) to add a certain number of constant data to both edges of the original data before continuation. Using these new schemes, we have demonstrated the improvement on the accuracy near edges of continued anomalies with profiles of magnetic anomaly computed from an assumed model.     

Explicit formula for the geoid-quasigeoid separation

The explicit formula for the geoid-to-quasigeoid correction is derived in this paper. On comparing the geoidal height and height anomaly, this correction is found to be a function of the mean value of gravity disturbance along the plumbline within the topography. To evaluate the mean gravity disturbance, the gravity field of the Earth is decomposed into components generated by masses within the geoid, topography and atmosphere. Newton’s integration is then used for the computation of topography-and atmosphere-generated components of the mean gravity, while the combined solution for the downward continuation of gravity anomalies and Stokes’ boundary-value problem is utilized in computing the component of mean gravity disturbance generated by mass irregularities within the geoid. On application of this explicit formulism a theoretical accuracy of a few millimetres can be achieved in evaluation of the geoid-to-quasigeoid correction. However, the real accuracy could be lower due to deficiencies within the numerical methods and to errors within the input data (digital terrain and density models and gravity observations).     

Regional gravity field modeling based on rectangular harmonic analysis

Regional gravity field modeling with high-precision and high-resolution is one of the most important scientific objectives in geodesy,and can provide fundamental information for geophysics,geodynamics,seismology,and mineral exploration.Rectangular harmonic analysis(RHA)is proposed for regional gravity field modeling in this paper.By solving the Laplace’s equation of gravitational potential in local Cartesian coordinate system,the rectangular harmonic expansions of disturbing potential,gravity anomaly,gravity disturbance,geoid undulation and deflection of the vertical are derived,and so are the formula for signal degree variance and error degree variance of the rectangular harmonic coefficients(RHC).We also present the mathematical model and detailed algorithm for the solution of RHC using RHA from gravity observations.In order to reduce the edge effects caused by periodic continuation in RHA,we propose the strategy of extending the size of computation domain.The RHA-based modeling method is validated by conducting numerical experiments based on simulated ground and airborne gravity data that are generated from geopotential model EGM2008 and contaminated by Gauss white noise with standard deviation of 2 mGal.The accuracy of the 2.5′×2.5′geoid undulations computed from ground and airborne gravity data is 1 and 1.4cm,respectively.The standard error of the gravity disturbances that downward continued from the flight height of 4 km to the geoid is only 3.1 mGal.Numerical results confirm that RHA is able to provide a reliable and accurate regional gravity field model,which may be a new option for the representation of the fine structure of regional gravity field.     

THE ANALYSIS AND DESIGN OF TWO-DIMENSIONAL FILTERS FOR TWO-DIMENSIONAL DATA *

Some of the methods such as regional removal and second derivative calculations which can be used to outline anomalies on potential data maps can be thought of as a filtering operation. The analysis and design of such two-dimensional filters by means of direct and inverse two-dimensional Fourier transforms have been considered. An analysis of several published sets of second derivative coefficient sets indicates that, in general, they are not a good approximation to the theoretical second derivative filter. Alternate methods of designing regional removal and second derivative filters are discussed. The properties of various two-dimensional filters are further illustrated by means of maps obtained from the convolution of several of these filters with a set of observed field data. These maps show the large changes in anomaly shape which can result from the inclusion or rejection of various wavelength components.     

Numerical aspects of EGM08-based geoid computations in Fennoscandia regarding the applied reference surface and error propagation

So far the recent Earth's gravity model, EGM08, has been successfully applied for different geophysical and geodetic purposes. In this paper, we show that the computation of geoid and gravity anomaly on the reference ellipsoid is of essential importance but error propagation of EGM08 on this surface is not successful due to downward continuation of the errors. Also we illustrate that some artefacts appear in the computed geoid and gravity anomaly to lower degree and order than 2190. This means that the role of higher degree harmonics than 2160 is to remove these artefacts from the results. Consequently, EGM08 must be always used to degree and order 2190 to avoid the numerical problems.     

基于重力梯度张量数据的欧拉反演在梅山铁矿的应用

随着在石油勘查、矿产勘查、构造研究等地质工作中提出的应用位场异常研究规模相对较小的地质体及其细节的要求不断提高,传统重力方法在精度和分辨率方面已不能满足要求.重力梯度张量作为重力位二次导数,较之重力异常,能够更直观地反映地下密度体的赋存状态,基于重力梯度张量数据的反演能够提高地质体的定量模拟质量.但是由于受国内仪器的发展水平限制,直接获取实测的重力张量数据难度较大,目前对于重力张量数据的获取主要是通过数值计算的方法,把重力异常测量值变换成张量信息.本文是在样条理论的基础上,提出新的重力梯度张量计算方法,利用三次样条插值方法拟合重力异常,进一步地通过积分导数关系求取样条函数系数,实现了由重力异常求取重力梯度张量的数据计算.在此基础上,利用张量数据进行欧拉反演计算,对比常规欧拉反演结果,进一步分析张量欧拉反演精度.球体及水平板状体模型试验结果显示,张量欧拉反演更能有效地完成目标体的反演,其结果更加准确.最后,将张量欧拉反演应用到梅山铁矿区重力实测数据解释中,准确地反演出梅山主矿体的水平投影范围及矿体中心埋深.同时,相比常规欧拉反演,张量欧拉反演在刘家村附近、梅山村南部及黄林库—吴家洼地段显...     

位场解析信号振幅极值位置空间变化规律研究

通过对单一边界、双边界、多边界以及点(线)质量模型重力异常解析信号振幅和重力异常垂向导数解析信号振幅的极值位置空间变化规律研究表明,重力异常垂向导数解析信号振幅和化极磁力异常解析信号振幅的极值位置相同,且与重力异常解析信号振幅的极值位置空间变化规律相似.利用位场解析信号振幅极大值位置能够准确识别单一直立边界地质体的边缘位置,但不能准确识别其它任何形体的边缘位置,其识别结果的偏移量大小随地质体的埋深、水平尺寸以及倾斜程度等变化.虽然重力异常垂向导数解析信号振幅比重力异常解析信号振幅的峰值更加尖锐、横向识别能力更强,其极大值位置更靠近地质体上顶面边缘位置,但均受地质体埋深的影响较大;随着埋深的增加,位场解析信号振幅的极大值位置会快速收敛到形体的"中心位置",其轨迹类似"叉子状";且对多边界模型会出现"极大值位置盲区"而无法识别其边缘位置.通过这些理论研究表明,位场解析信号振幅只能识别单一边界地质体的边缘位置;而不宜用来识别多边界地质体的边缘位置,但可以用来识别多边界地质体的"中心位置".     

Conforming Falcon‡ gravity and the global gravity anomaly

Gravity derived only from airborne gravity gradient measurements with a normal error distribution will have an error that increases with wavelength. It is straightforward in principle to use sparsely sampled regional gravimeter data to provide the long wavelength information, thereby conforming the derived gravity to the regional gravity. Regional surface or airborne gravimeter data are not always available and can be difficult and expensive to collect in many of the areas where an airborne gravity gradiometer survey is flown. However the recent release by the Danish National Space Centre of the DNSC08 global gravity anomaly data has provided regional gravity data for the entire earth of adequate quality for this purpose. Studies over three areas, including comparisons with ground, marine and airborne gravimetry, demonstrate the validity of this approach. Future improvements in global gravity anomaly data are expected, particularly as the product from the recently launched Gravity field and steady‐state Ocean Circulation Explorer (GOCE) satellite becomes available and these will lead directly to an improvement in the very wide bandwidth gravity available after conforming gravity derived from gravity gradiometry with the global gravity.     

Ellipsoidal area mean gravity anomalies — precise computation of gravity anomaly reference fields for remove-compute-restore geoid determination

Gravity anomaly reference fields, required e.g. in remove-compute-restore (RCR) geoid computation, are obtained from global geopotential models (GGM) through harmonic synthesis. Usually, the gravity anomalies are computed as point values or area mean values in spherical approximation, or point values in ellipsoidal approximation. The present study proposes a method for computation of area mean gravity anomalies in ellipsoidal approximation (‘ellipsoidal area means’) by applying a simple ellipsoidal correction to area means in spherical approximation. Ellipsoidal area means offer better consistency with GGM quasigeoid heights. The method is numerically validated with ellipsoidal area mean gravity derived from very fine grids of gravity point values in ellipsoidal approximation. Signal strengths of (i) the ellipsoidal effect (i.e., difference ellipsoidal vs. spherical approximation), (ii) the area mean effect (i.e., difference area mean vs. point gravity) and (iii) the ellipsoidal area mean effect (i.e., differences between ellipsoidal area means and point gravity in spherical approximation) are investigated in test areas in New Zealand and the Himalaya mountains. The impact of both the area mean and the ellipsoidal effect on quasigeoid heights is in the order of several centimetres. The proposed new gravity data type not only allows more accurate RCR-based geoid computation, but may also be of some value for the GGM validation using terrestrial gravity anomalies that are available as area mean values.     

A GENERALIZED METHOD OF COMPUTING SECOND DERIVATIVE OF GRAVITY FIELD*

The unsuitability of a particular method of computation of second derivative to varying types of field problems evinces the need of a method by which it may be possible to obtain a wide range of filters. This requirement is achieved by incorporating a mathematical smoothing operator, e^-λρ2, λ and ρ being the smoothing parameter and radial frequency respectively, in the theoretical frequency response of second derivative operation. A few sets of weights for various smoothing parameters, are presented. The analysis of Bouguer gravity anomaly map of Los Angeles Basin, California, U.S.A., is carried out by Elkins's (1951) and Rosenbach's (1953) methods and the sets of weights given in this paper which clearly establishes their filtering equivalence.     

GRACE月时变模型缺失值的填补方法与精度分析

长时间序列的GRACE时变重力场对研究全球地表质量变化具有重要的意义.部分月份的GRACE卫星观测数据质量不佳导致了相应月份的时变重力场模型缺失,为了保持时变重力场模型的连续性,可采用一定的插值方法填补.本文以ITSG-Grace2016时变重力场模型序列为研究对象,详细分析了三次样条插值、三次埃尔米特插值和三次多项式插值等3种方法用于填补GRACE时变模型序列的精度,实验结果表明:(1)利用3种插值方法获取空缺1个月或连续空缺2个月的时变重力场模型时,插值时变模型与实测时变模型比较,阶误差均较小,且三次埃尔米特插值的精度稍好;(2)利用插值时变模型分析区域质量变化时,在空缺1个月数据的情况下,插值时变模型与实测时变模型符合度较高,但在连续空缺2个月数据的情况下,插值时变模型与实测时变模型的计算结果差异较大,说明利用阶误差评定模型精度具有一定局限性;(3)对区域质量变化的趋势项进行分析时,区域质量变化的复杂程度决定了模型内插的精度,当时间序列的长度在3年或3年以上时,插值时变模型的精度对区域质量变化分析的影响较小.在分析区域质量变化时,三次样条插值方法的插值结果与实测结果更为接近,建议...     

基于重力异常分离方法寻找深部隐伏铁矿 ——以安徽泥河铁矿为例

重力异常是地下不同规模、不同形态和不同埋深的不均匀地质体的综合响应,重力勘探主要通过从重力异常中提取感兴趣的局部异常,以便探测深部结构,寻找隐伏矿床.为探讨重力异常分离原则并检验方法效果,本文从各方法原理入手,加上模型试验以及在安徽省泥河矿区深部隐伏铁矿的探寻实践检验,阐明:趋势分析法是整体拟合不同于最小二乘圆滑的局部拟合,由于是多项式拟合区域场,趋势分析法不适宜范围大、地质情况复杂的测区;插值切割法以计算点场值与四点圆周平均值的插值运算为切割算子,通过连续切割,得到重力异常的切割区域场和局部场,插值切割法对于小测区单个异常的分离效果较好,切割次数选择1到2次即可;匹配滤波法通过分析实测异常功率谱曲线、选择合适的滤波段、建造适宜的低通和带通滤波器进行滤波,从而提取不同波数成分的异常场,匹配滤波更适合垂向叠加的异常分离;解析延拓是根据一个面上的一组位场数据确定另一个不同高度面上位场值,应用中要把握延拓高度;垂向二阶导数法可以起到突出浅源异常,区分水平叠加异常,确定异常体的边界,消除或削弱背景场的作用.通过安徽泥河铁矿重力异常分离实验,发现三阶趋势分析、向上延拓以及插值切割法能很好地分离出矿体异常和背景场,同时发现在泥河矿区东南部和东北部还存在剩余重力异常,可为泥河铁矿扩大规模提供新的线索.     

利用重力异常匹配技术实现潜艇导航

潜艇的惯性导航误差是随时间积累的,利用重力异常数据进行辅助导航可以对惯性导航的漂移误差进行校正.首先利用2′×2′重力异常数据库作为基础信息,结合Kalman滤波算法对某区域进行了模拟计算,模拟过程采用了增益系数和信息更新序列的新方法进行Kalman 滤波的处理,结果表明在重力异常变化幅度较大的地区,重力异常可以进行潜艇的辅助导航.