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本文利用澳大利亚北领地West Arnhem Land 地区实测重力异常数据并联合DEM(9")和SRTM3(3")地形高程数据,使用移去-恢复技术和Stokes积分方法计算了该地区两条剖面的重力梯度及其功率谱密度,使用FFT方法解算了整个地区的重力梯度值,结果证明了联合重力异常数据和高分辨率地形高程数据能有效地提高重力梯度的解算精度;功率谱密度的计算结果与国外成熟的重力梯度功率谱密度模型相吻合,表明高于0.3 Hz频率范围的功率谱密度可看做噪声,为重力梯度数据处理中噪声的辨别和剔除提供了借鉴,另外对重力梯度辅助导航基准图的构建以及重力梯度测量系统的标定提供了有益的探索. 相似文献
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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。 相似文献
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通过联合全球重力位模型(EGM2008)、航空重力扰动数据和剩余地形模型(RTM)数据,基于频谱域(二维FFT变换)和空间域(Stokes数值积分)算法对毛乌素测区GT-2A航空重力测量系统采集的空中测线后处理重力扰动数据进行解算,构建了该地区的航空重力梯度扰动全张量.(1)残余航空重力扰动延拓结果表明:残余航空重力扰动经向下延拓至大地水准面,再向上延拓至航空高度后与原数据差值的标准差为1.0078 mGal,考虑边缘效应后,内缩计算范围得到的差值标准差减小至0.1269 mGal.(2)基于残余重力扰动数据(原航空高度数据及向下延拓数据),通过不同方案解算得到的梯度扰动结果表明:两种方案得到的研究区域重力梯度扰动各分量之差的最大标准差为6.4798E(Γ_(yz)分量),最小标准差为2.6968E(Γ_(xy)分量),内缩计算范围后得到的差值标准差最大值为1.8307E(Γ_(zz)分量),最小值为0.7223E(Γ_(yz)分量).本文的思路和方法可为未来我国自主构建航空重力梯度标定场提供参考. 相似文献
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《地震地质》2015,(4)
首先根据水平无限长圆柱形地质体的理论重力异常,在频率域使用余弦变换法,通过位场变换计算了水平方向的重力梯度,并与理论重力梯度做比较,发现余弦变换法计算得到的水平重力梯度是可靠的。其次,使用频率域中的余弦变换法计算了2010年9月至2012年10月芦山地震前的累积重力水平梯度,并求得沿龙门山断裂带走向和垂向的重力水平梯度。结果表明:沿断裂带走向和垂向的重力梯度能够以明显的条带状更好地显现出重力在断裂两侧的相对变化,并且芦山震中位于重力梯度高值区的中间地带;重力水平总梯度变化显示,在理县—芦山一带、康定—石棉一带为重力梯度高值区,且高值区位置及走向与区域断裂构造基本重合,并在理县、康定以及石棉附近重力水平梯度值为极值区。 相似文献
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本文设计了一种高-低卫星跟踪卫星、低-低卫星跟踪卫星和卫星重力梯度测量相结合的新型重力测量卫星系统,其可在一定程度上发挥卫星重力梯度和低低卫星跟踪卫星两种测量模式各自的优势.基于重力卫星系统指标设计的半解析法,深入分析了不同重力测量卫星系统配置和不同观测量及其不同白噪声水平情况下,新型卫星重力测量模式反演重力场模型的能力.数值模拟分析结果表明：在观测值精度和星间距离相同的条件下,轨道高度是影响重力场反演精度的关键因素;随着星间距离的增大,高频重力场信号反演精度会先提高后降低,轨道高度在200~350 km之间时,星间距离在150~180 km之间时反演精度最优;星间距离变率和卫星重力梯度两类观测值仅在某些精度配置时可达到优势互补,如果某一类观测值精度很高,则另一类观测值在联合解算时贡献非常小或者没有贡献.在300 km轨道高度,若以GRACE和GOCE任务的设计指标1 μm·s-1/√Hz和5 mE/√Hz来配置新型重力测量卫星系统中星间距离变率和引力梯度观测值的精度,联合两类观测值解算200阶次模型大地水准面的精度比独立解算分别提高1.2倍和2.8倍.如果以实现100 km空间分辨率1~2 cm精度大地水准面为科学目标,考虑卫星在轨寿命,建议轨道高度选择300 km,星间距离变率和卫星重力梯度的精度分别为0.1 μm·s-1/√Hz和1 mE/√Hz.本文的研究成果可为中国研制自主的重力测量卫星系统提供参考依据. 相似文献
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利用地球重力位模型计算重力和重力梯度 总被引：3，自引：0，他引：3
高阶高精度地球重力场模型具有广泛的用途。本文利用地球重力位模型计算重力和重力梯度在应用中很有实用阶值,同时也是计算重力场其它量的关键。利用伪局部笛卡尔坐标与球坐标的关系计算了重力与重力梯度在伪局部笛卡尔坐标系下的分量;利用张量变换的原理给出了已知重力与重力梯度在某一坐标系下的分量求它们在另一坐标系下分量的方法,并具体给出了重力与重力梯度在局部笛卡儿坐标系下的分量计算公式,同时还给出计算重力场五参量与垂线偏差的计算公式,本研究推进了地球重力场的可视化进程。 相似文献
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联合不同类型重力测量数据确定地球重力场模型的迭代法 总被引：1，自引：0，他引：1
不同的重力测量数据包含了不同波段的地球重力场信息,因此要恢复更高精度的地球重力场模型,就必须对不同类型的重力测量数据进行联合处理.以地面重力异常Δg为例,推导了利用迭代法联合不同类型重力测量数据反演地球重力场模型的基本原理公式,并给出了其具体实现步骤,接着采用全球的重力异常Δg数据和扰动位T数据,基于迭代法对卫星重力梯度SGG数据解算的重力场模型进行了进一步的精化.结果表明,初始的卫星重力梯度SGG模型和经过全球重力异常Δg数据精化后的模型,其对应的累计大地水准面误差分别达到1.128cm和0.048cm、累计重力异常误差分别达到0.416mGal和0.018mGal的精度;在经过全球扰动位T数据进一步精化后的模型,其对应的累计大地水准面误差达到0.043cm、累计重力异常误差达到0.016mGal的精度. 相似文献
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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. 相似文献
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YU JinHai & PENG FuQing Institute of Geodesy Geophysics Chinese Academy of Sciences Wuhan China College of Earth Scienc Graduate University of Chinese Academy of Sciences Beijing China Zhenghou Institute of Surveying Mapping Zhengzhou China 《中国科学D辑(英文版)》2007,50(4):555-562
A new solving method for Laplace equation with over-determined geodetic boundary conditions is pro- posed in the paper, with the help of minimizing some kinds of quadratic functional in calculus of variation. At first, the so-called variational solution for over-determined geodetic boundary value problem is defined in terms of principles in calculus of variation. Then theoretical properties related with the solution are derived, especially for its existence, uniqueness and optimal approximation. And then the computational method of the solution is discussed, and its expression is exhibited under the case that all boundaries are spheres. Finally an arithmetic example about EGM96 gravity field model is given, and the computational results show that the proposed method can efficiently raise accuracy to deal with gravity data. In all, the variational solution of over-determined geodetic boundary value problem can not only fit to deal with many kinds of gravity data in a united form, but also has strict mathematical basements. 相似文献
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A new gravimetric, satellite altimetry, astronomical ellipsoidal boundary value problem for geoid computations has been developed and successfully tested. This boundary value problem has been constructed for gravity observables of the type (i) gravity potential, (ii) gravity intensity (i.e. modulus of gravity acceleration), (iii) astronomical longitude, (iv) astronomical latitude and (v) satellite altimetry observations. The ellipsoidal coordinates of the observation points have been considered as known quantities in the set-up of the problem in the light of availability of GPS coordinates. The developed boundary value problem is ellipsoidal by nature and as such takes advantage of high precision GPS observations in the set-up. The algorithmic steps of the solution of the boundary value problem are as follows:
- - Application of the ellipsoidal harmonic expansion complete up to degree and order 360 and of the ellipsoidal centrifugal field for the removal of the effect of global gravity and the isostasy field from the gravity intensity and the astronomical observations at the surface of the Earth.
- - Application of the ellipsoidal Newton integral on the multi-cylindrical equal-area map projection surface for the removal from the gravity intensity and the astronomical observations at the surface of the Earth the effect of the residual masses at the radius of up to 55 km from the computational point.
- - Application of the ellipsoidal harmonic expansion complete up to degree and order 360 and ellipsoidal centrifugal field for the removal from the geoidal undulations derived from satellite altimetry the effect of the global gravity and isostasy on the geoidal undulations.
- - Application of the ellipsoidal Newton integral on the multi-cylindrical equal-area map projection surface for the removal from the geoidal undulations derived from satellite altimetry the effect of the water masses outside the reference ellipsoid within a radius of 55 km around the computational point.
- - Least squares solution of the observation equations of the incremental quantities derived from aforementioned steps in order to obtain the incremental gravity potential at the surface of the reference ellipsoid.
- - The removed effects at the application points are restored on the surface of reference ellipsoid.
- - Application of the ellipsoidal Bruns’ formula for converting the potential values on the surface of the reference ellipsoid into the geoidal heights with respect to the reference ellipsoid.
- - Computation of the geoid of Iran has successfully tested this new methodology.
Keywords: Geoid computations; Ellipsoidal approximation; Ellipsoidal boundary value problem; Ellipsoidal Bruns’ formula; Satellite altimetry; Astronomical observations 相似文献
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大陆上用重力数据和GPS水准数据确定(似)大地水准面,海洋上用卫星测高数据确定(似)大地水准面.由于沿海地区和近岸海域往往缺少完好的重力数据,近岸海域卫星测高数据质量相对较差,两类大地水准面在陆海相接区域精度偏低且存在拼合差.纯几何方法拟合陆海局部区域大地水准面,不能顾及大地水准面的物理特性,拟合结果不稳定.顾及到大地水准面的物理特性,依据其在局部所应满足的数学物理方程,拟合陆海局部区域大地水准面问题,转化为Laplace第一边值问题.讨论了有限元法衔接陆海局部区域大地水准面的数学思想,给出了相应的数学模型. 相似文献
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Jiří Nedoma 《Pure and Applied Geophysics》1977,115(3):639-645
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. 相似文献
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The undulation of the geoid, the gravity anomaly and the deflection of the vertical are the three basic observations describing the shape and the gravity field of the earth. The Stokes’ formula that computes the undulation of the geoid using the gravity anomaly on the geoid under spherical approximate conditions was first put forward by Stokes[1]. According to Stokes’ theory, The Vening-Meinesz formula that computes the meridian and the prime vertical components of the deflection of the ve… 相似文献
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Horizontal gravity filtration of groundwater in soil is considered. Under Boussinesq approximation, the problem is reduced to a one-dimensional nonlinear parabolic equation in phreatic water level. The problem of linearizing the original equation is discussed. The comparison of gravity-filtration problem solutions in the nonlinear and linearized formulations shows considerable discrepancies to exist between the solutions, especially, for boundary problems with mixed boundary conditions, when the value of the function is not fixed on the right boundary. An analytical solution is obtained for steady-state flow from a water body into the soil with subsequent leakage into underlying beds. Two regimes are shown to exist: one with an infinite exponential tail, and another in the form of a finite groundwater mound. A new approach is proposed to the linearization problem—quasilinearization with the use of the Burgers equation. 相似文献
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Roland Klees 《Surveys in Geophysics》1993,14(4-5):419-432
The Boundary Element Method (BEM), a numerical technique for solving boundary integral equations, is introduced to determine the earth's gravity field. After a short survey on its main principles, we apply this method to the fixed gravimetric boundary value problem (BVP), i.e. the determination of the earth's gravitational potential from measurements of the intensity of the gravity field in points on the earth's surface. We show how to linearize this nonlinear BVP using an implicit function theorem and how to transform the linearized BVP into a boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation into a linear system of equations. We discuss the major problems of this approach for setting up and solving the linear system. The BVP is numerically solved for a bounded part of the earth's surface using a high resolution reference gravity model, measured gravity values of high density, and a 50 50 m2 digital terrain model to describe the earth's surface. We obtain a gravity field resolution of 1 1 km2 with an accuracy of the order 10–3 to 10–4 in about 1 CPU-hour on a Siemens/Fujitsu SIMD vector pipeline machine using highly sophisticated numerical integration techniques and fast equation solvers. We conclude that BEM is a powerful numerical tool for solving boundary value problems and may be an alternative to classical geodetic techniques. 相似文献
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YU Jinhai & ZHANG Chuanding . Institute of Geodesy Geophysics of Chinese Academy of Sciences Wuhan China . Zhengzhou Information Engineering University Zhengzhou China 《中国科学D辑(英文版)》2005,48(3):398-405
Boundary value problem (BVP) plays a funda-mental role in physical geodesy that aims at determin-ing the earth’s shape and its external gravity field. TheMolodensky BVP and the Stokes BVP are typical inphysical geodesy, and the gravity anomaly is a kind ofbasic data. With the wide use of GPS, measurementaccuracy of the earth’s surface can reach one centime-ter, while that of the gravity measurement can reachμgals. Hence, it is necessary to establish a new kind ofBVP which can satisfy… 相似文献