地面重力数据结合GPS/水准数据精化兴城物探实验区大地水准面

区域大地水准面的确定是GPS测量常需解决的问题。目前确定大地水准面的方法主要包括重力法、GPS水准几何法及组合法,其中组合法因其精度和可靠性都较高,常用于计算高精度区域大地水准面。高精度的大地水准面模型是组合法确定区域大地水准面的关键。在我国,EGM2008全球重力场模型精度和分辨率均高于此前的所有模型,研究基于该模型的组合法大地水准面精化具有重要的实践意义。笔者以吉林大学兴城教学实习基地物探实验区为例,基于实测重力数据、EGM2008重力场模型和GPS水准数据,采用组合法精化了区域大地水准面,比较了组合法大地水准面模型和无重力实测数据的几何法大地水准面模型的精度差异,分析了该方法在物探测量中的适用性。结果表明,实验区组合法大地水准面模型精度最高达到1.2 cm,并且误差分布区间较小,总体上精度和可靠性高于对比的几何方法,并且组合法和几何法获取的两种大地水准面模型均能满足大比例尺物探测量要求。EGM2008模型精度较高,故平坦地区使用组合法时,高密度的实测重力数据可能带来高频扰动,有可能降低EGM2008重力场模型本身的精度,所以重力数据采集过程中要顾及重力点的密度和空间分布。本文方法更适用于地形复杂的地区。     

基于EGM2008模型的GPS高程转换法

GPS求得的高程是地面点在WGS84坐标系中的大地高,而我国采用正常高系统的高程,是通过该点的大地高减去该点的高程异常获得。高程异常的获取,惯用的做法是曲面拟合法,这种方法在水准点稀少的测区（特别是山区）实施起来比较困难。EGM2008模型是迄今为止分辨率最高、精度最好、阶次最多的全球重力场模型。首先利用EGM20081′×1′的大地水准面模型计算各点的高程异常,再通过联测一个一等水准点,获取EGM2008模型所表示的全球似大地水准面与我国高程基准面之间的差异,即可将GPS大地高转换为1985国家高程基准的正常高。兴城测区实例表明,EGM2008模型高程转换法在山区仅用一个水准点即可实现GPS大地高到正常高的转换,且高效率、高精度。     

GPS高程控制网在1:5万重力调查高程异常改正问题中的应用

在没有精细大地水准面模型的地区开展1:5万重力调查工作时,采用布设GPS高程控制网的形式,求得高程异常改正模型,解决高程异常改正问题。布设GPS控制网时已知高程控制点要多于6个,适当地选用某种数学模型(多项式曲线拟合、多项式曲面拟合,多面函数拟合等)拟合出测区的大地水准面,然后用插值的方法再推算出其它GPS点和正常高程值,提高重力测点的高程精度。     

带状区域GPS大地高转换成正常高的研究

在对GPS测高与水准测量理论及其异同分析的基础上,阐述了确定似大地水准面的原理与方法,分析了用数学模型法和少量GPS高程点与水准点重合,将GPS大地高直接转换为具有厘米量级正常高的实现方法。实验结合黑龙江省虎林地区的地形特点,提出了用线性内插法、平面模型法和二次曲面模型法等来转换GPS高程,证明在该地区可以通过少量且分布合理的水准点来直接求出具有厘米量级的正常高,且精度可以达到四等水准测量的精度要求,满足一般工程的需要。     

应用GPS数据与重力数据确定大地水准面

作为GPS/重力边值问题理论及方法的应用,在对GPS/重力方法确定(似)大地水准面的原理进行简要介绍与分析的基础上,利用收集到的N区的600个GPS/重力数据和48个高精度GPS水准数据,计算出该区域的(似)大地水准面。通过拟合法和系统差直接改正法进行的精度分析表明,应用GPS/重力数据结合水准方法确定的该地区(似)大地水准面的精度达到厘米级精度。     

大比例尺重力勘探GPS高程转换

在大比例尺重力勘探工作中,当布格重力异常设计总精度提高到0.025×10-5 m/s2时,要求测点高程均方误差为0.05 m。为使GPS高程能够达到该精度要求,提出利用EGM2008模型和GPS水准数据拟合局部似大地水准面的方法以实现测点GPS高程的转换,并利用某地区GPS水准资料,对转换方法的可行性进行验证分析。结果表明,这种方法完全适用于大比例尺重力勘探工作。     

利用GPS水准控制山区高程——以陕西丁家林金矿区为例

应用GPS水准控制山区高程的基本原理是当GPS点布设成一定区域时，可以用数学曲面拟合法求待定点的正常高，根据测区中已知点的平面坐标或大地坐标和高程异常值，用数字拟合法求出该区似大地水准面，得出等求点的正常高。在陕西丁家林金矿区实验结果表明，该方法与传统的三角高程控制法相比，无论在平原或在山区都能获得较好精度。因此，用GPS水准可替代几何水准。     

基于地球重力场模型的区域高程转换方法

利用多项式分区拟合与EGM96地球重力场模型相结合的数学方法,使少量的水准点与GPS点重合,对GPS测得的大地高直接转换为具有厘米量级正常高的重力模型区域高程转换方法作了讨论,将该方法得到的正常高与单独利用多项式分区拟合和EGM96地球重力场模型得到的结果进行了比较,其差值的标准差为±2.9 cm。     

基于EGM2008模型的重力观测点GPS高程转换

在重力勘探工作中,重力成果的精度受重力观测点高程的影响尤为明显。在分析了EGM2008模型的精度基础上,提出一种基于该模型的重力观测点GPS高程转换方法,并利用某地区GPS水准资料,对转换方法的可行性进行验证分析,结果表明,这种方法完全适用于中小比例尺重力勘探工作。     

GPS高程拟合的方式及可靠性分析

在范围不大的区域中，高程异常具有一定的几何相关性，GPS高程拟合就是利用这一原理，求解正常高。在解析法求解过程中，首先用最小二乘法确定拟合数学模型的系数，在此基础上计算出待测点的高程异常值。通过实例验证：GPS高程拟合的精度主要取决于GPS大地高的精度、重合点正常高的精度、重合点的分布及拟模型的选择。一般在重合点数量充足且分布均匀的情况下，GPS高程拟合的精度可达到四等水准网的精度要求。     

High-resolution regional gravity field model of Pakistan based on best residual terrain model (RTM) of topography and interpolation techniques

This study focuses on the development of absolute gravity model for Pakistan based on best possible residual terrain model of gravity using residual terrain modeling technique. The datasets used for the development of model are observed gravity, global gravity models, and Shuttle Radar Topographic Mission (SRTM30) elevation data. The residual terrain modeling technique has been used in the remove-restore procedure for smoothing the observed gravity field. Different topographic elevation models were tested in the model selection and one best possible model with minimum mean and standard deviation was selected for residual terrain effects. Least square collocation technique has been used for quality control and error estimates. The best possible covariance model was established from residual gravity for onward prediction of gravity anomalies at the earth surface for error and prediction analysis. The residual terrain effect of gravity, value of free air anomaly from EGM96, and observed free air anomaly are added to normal gravity to compute the absolute gravity at earth surface. The prediction of these parameters is made by employing Lagrange interpolation with least square adjustment. The results are compared with ～5% randomly selected data points not utilized for the development of covariance function and/or model development. Spline interpolation technique has also been used for the prediction of gravity field-related parameters. Lagrange interpolation exhibits relatively superior results over spline-based interpolation. This is as per expectation due to the reason that additional gridding for spline interpolation filters the signal part as well. This fact is evident from the results of spline interpolation of Grid-I and Grid-II with relatively better prediction results in Grid-I. This version of the model is capable of prediction having limiting error of 30 mGal. The predicted results show that 96.16% of prediction data falls within above-mentioned limit with Lagrange interpolation technique with least square adjustment for whole Pakistan area. The adverse effect of gridding is absent in case of Grid-I due to relatively flat areas and predicted data matches totally with control values for both spline as well as Lagrange interpolations. However, in case of Grid-II which includes high mountains of Himalaya, gridding effect is present and the accuracy of the predicted results falls to ～92%. The computed results have been compared with absolute values predicted using EGM96 and EGM2008 models as well. The gravity field recovered with PAKGM model is much better, i.e., ～ 96.16%, than both with EGM96 and EGM2008 which is about 85% only.     

Constrained Smoothing of Noisy Data Using Splines in?Tension

A method of fitting a smooth cubic spline curve through noisy data points is presented. Overshoots of the spline curve between data points were prevented by applying tension to the fit using a quadratic spring approximation, which allowed a linear inverse theory approach to be adopted. Error-bars in the measured data were mapped through the inversion process to give the covariance of the fitted curve. This is an improvement over previous methods, which largely neglect the effect of data errors on the fit. Another improvement is to impose fixed constraints on the fit by simultaneously applying the method of Lagrange multipliers. The effect of these constraints on the covariance of the fitted curve is quantified using results from linear algebra. Example applications to synthetic data and a record of magnetic inclination from Hawaii are given.     

Constrained Smoothing of Noisy Data Using Splines in Tension

A method of fitting a smooth cubic spline curve through noisy data points is presented. Overshoots of the spline curve between data points were prevented by applying tension to the fit using a quadratic spring approximation, which allowed a linear inverse theory approach to be adopted. Error-bars in the measured data were mapped through the inversion process to give the covariance of the fitted curve. This is an improvement over previous methods, which largely neglect the effect of data errors on the fit. Another improvement is to impose fixed constraints on the fit by simultaneously applying the method of Lagrange multipliers. The effect of these constraints on the covariance of the fitted curve is quantified using results from linear algebra. Example applications to synthetic data and a record of magnetic inclination from Hawaii are given.     

EGY-HGM2016: an improved hybrid local geoid model for Egypt based on the combination of GOCE-based geopotential model with gravimetric and GNSS/levelling measurements

An improved hybrid gravimetric geoid model for Egypt, EGY-HGM2016, has been recently computed implementing the least-squares collocation (LSC) method through the remove-compute-restore (RCR) procedure. The computation of EGY-HGM2016 involves different datasets in terms of gravity anomalies determined from the GOCE (gravity field and steady-state ocean circulation explorer)-based global geopotential model (SPW-R4) up to d/o 200 and EGM2008 from d/o 201 to 720 combined with terrestrial gravity datasets in terms of 2140 gravity field anomalies and about 121,480 marine surface gravity anomalies. In addition, orthometric heights from 17 GPS/levelling measurements have been considered during the modelling process to improve the determination of the hybrid gravimetric geoid over the Egyptian region. The EGY-HGM2016 model estimated over Egypt provides geoid heights that are ranging from 7.677 to 21.095 m with a standard deviation (st. dev.) of about 2.534 m in the northwest of the country excluding the involvement of the orthometric heights from GPS/levelling measurements. When the later dataset is considered during the implementation of LSC process, hybrid residual height anomalies ranging from ?1.5 to +0.9 m, with a mean of 0.22 m and a st. dev. of 0.17 m, are obtained. Comparison of the predicted hybrid gravimetric geoid with the corresponding ones obtained from EGM2008, GOCE-based SPW R4 model, and GPS/levelling reveals considerable improvements of our EGY-HGM2016 model over Egypt.     

斜轴高斯投影在跨带物探长剖面测量中的应用

在高精度物探重力测量中,需要提供高精度的平面位置和高程。在物探长剖面测量中,对东西跨度较大的线路进行控制测量时,高斯-克吕格投影分带和高程引起的投影变形较大,不能满足长距离重力测量对精度的要求。基于高斯-克吕格投影的基本理论,采用斜轴变形椭球高斯投影方法,结合最小二乘法、坐标转换理论及椭球变换,将原始椭球构建斜轴变形椭球,可以减小高斯投影横坐标和高程投影变形的影响,避免高斯投影分带过多对应用的影响。以漠河—呼和浩特物探长剖面测地数据为例,利用GPS快速静态测量获得平面和高程位置,测点距离约1km,通过斜轴高斯投影进行投影,最大平面精度为67.87mm/km,最大高程精度为53.039mm/km,最大投影综合变形的中误差为88.51 mm/km,大大减小了投影变形,提高了地图投影精度。因此,该投影在跨度物探长剖面测量中的应用具有一定优势。     

综合地球物理勘探在夏日哈木矿区的应用研究

文章通过选用高精度磁测剖面测量、激电中梯剖面测量、高精度重力剖面测量、可控源音频大地电磁测深等方法对青海省夏日哈木铜镍矿床开展地球物理方面的研究,探讨各种物探手段对该区矿床勘查的有效性及适用性,丰富区内物探资料,为区内同类型矿床勘查提供借鉴.研究表明,高精度磁测剖面测量在大范围寻找矿体较为有效,但难以表达矿体的形态特征...     

Utilisation of Fast Fourier Transform and Least-squares Modification of Stokes formula to compile a gravimetric geoid model over Khartoum State: Sudan

We use Fast Fourier Transform (FFT) and least-squares modification (LSM) of Stokes formula to compute the geoid over Khartoum State in Sudan. The two methods (FFT and LSM) have been utilised to test their efficiency with respect to EGM08 and the local GPS-levelling data. The FFT method has many advantages, it is fast and it reduces the computational complexity. The modification of Stokes formula is widely used in geoid modelling; however, its implementation based on point-wise summation requires a considerable amount of time. In FFT, we combine the terrestrial gravity data and the global geopotential model (GGM) by means of a remove-compute-restore procedure and we successfully apply the modification of the Stokes formula in the least-squares sense. FFT and LSM geoid solutions are evaluated against EGM2008 and the GPS-levelling data. The analysis of the undulation differences shows that the LSM solution is more compatible with EGM08 and GPS-levelling data. The discrepancies of the differences are removed using a 4-parameter model, the standard deviation (STD) of the undulation differences of LSM decreased from 0.41 to 0.37 m and from 0.48 to 0.39 m for FFT solution. There is no significant impact to the LSM geoid when adding the additive corrections, while the FFT geoid solution is slightly improved when terrain correction is applied.     

面波基模式频散曲线提取解精度对比研究

针对不同方法提取面波基模式频散曲线精度问题,笔者分别采用τ-p变换、频率分解法、F-K变换、高分辨率线性拉东变换(High-Resolution Linear Radon Transform,简称HRLRT)对六层递增型地质模型合成瑞雷波记录进行频散能量成像,并按频散能量最大值拾取基模式频散曲线。为定量评价理论模型基模式频散曲线提取解与解析解的接近程度,引入了均方差与相关系数两种评价参数。评价结果表明,高分辨率线性拉东变换提取基模式频散曲线精度最高,均方差为11.167 8,相关系数为0.994 9;F-K变换提取基模式频散曲线精度最低,均方差为195.274,相关系数为0.515 2。