联合多代卫星测高和多源重力数据的局部大地水准面精化方法

本文研究了基于泊松小波径向基函数融合多代卫星测高及多源重力数据精化大地水准面模型的方法.分别以沿轨垂线偏差和大地水准面高高差作为卫星测高观测量,研究了使用不同类型测高数据对于大地水准面建模精度的影响.针对全球潮汐模型在浅水区域及部分开阔海域精度较低的问题,引入局部潮汐模型研究了不同潮汐模型对于大地水准面的影响.数值分析表明:相比于使用沿轨垂线偏差作为测高观测量,基于沿轨大地水准面高高差解算得到的大地水准面模型的精度更高,特别是在海域区域,其精度提高了2.3cm.由于使用沿轨大地水准面高高差作为测高观测量削弱了潮汐模型长波误差的影响,采用不同潮汐模型对大地水准面解算的影响较小.总体而言,船载重力及测高观测数据在海洋重力场的确定中呈现互补性关系,联合两类重力场观测量可以提高局部重力场的建模精度.     

我国海域大地水准面的计算及其与大陆大地水准面拼接的研究和实施

研究和实施了由卫星测高数据计算垂线偏差，用莫洛 金斯基（Molodensky）公式反演 大地水准面高，由此求得我国海域大地水准面高. 为了检核，将测高垂线偏差利用逆维宁迈 纳斯（Vening Meinesz）公式反演重力异常，与海上船测重力值进行了外部检核；同时还用 司托克斯（Stokes）公式，将上述反演的重力异常计算大地水准面高，与莫洛金斯基公式直 接解得的相应结果进行比较作为内部检核. 在积分计算中充分应用了FFT的严格公式.由重力和GPS水准数据确定的陆地大地水准面，和主要由卫星测高数据确定的海洋大地水准 面，二者之间一般都存在以系统误差为主的拼接差，本文分析了产生这一现象的主要原因, 并结合我国在陆海大地水准面拼接区重力资料稀疏的实际，提出了新的拼接技术，最后将拟 合参数校正中国全部海域的重 力大地水准面，以最大限度地削弱拼接点和制约测高海洋大地水准面可能存在的系统误差.     

基于方差分量估计的局部似大地水准面精化拟合模型

局部似大地水准面精化中需要进行GPS水准与重力两种水准面的拟合,其中两种观测量精度的权比确定是关键问题,本文提出基于方差分量估计的方法解决这一问题.根据此思路,文中还利用某给定区域的实际资料,对常用的几种似大地水准面拟合方法——多项式拟合、多面函数拟合以及曲面样条插值的函数模型按不等权拟合似大地水准面进行试验.通过某3...     

应用GPS/重力数据确定(似)大地水准面

作为GPS/重力边值问题理论及方法的应用,本文在对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702个GPS重力数据以及52个高精度的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/水准方法确定的该地区似大地水准面的精度达到厘米级.     

基于泊松小波径向基函数融合多源数据的局部重力场建模

融合多源数据的高精度、高分辨率的局部重力场建模是物理大地测量学的前沿和热点问题.本文研究了基于径向基函数融合多源数据的局部重力场建模方法,利用Monte-Carlo方差分量估计实现了不同类型的观测数据的合理定权,引入了最小标准差法确定基函数的适宜网络,分析了地形因素对于基函数网络确定及局部重力场建模精度的影响.以泊松小波基函数为构造基函数,结合残差地形模型,融合实测的陆地重力异常、船载重力异常及航空重力扰动数据构建了局部区域陆海统一的似大地水准面模型.研究结果表明:引入残差地形模型平滑了地形质量引入的高频扰动信号,简化了基函数的网络设计;并提高了重力似大地水准面的精度,平原地区其精度提高了4mm,地形起伏较大的山区其精度提高了约5cm.总体而言,基于"三步法"构建的局部重力似大地水准面在荷兰、比利时及德国相关区域,其精度分别达到1.12cm、2.80cm以及2.92cm.     

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.     

基于卫星测高的海域大地水准面

利用测高数据的一次差分计算海域垂线偏差，有效降低了动力海面地形和系统残差对垂线偏差的影响；然后根据扰动场元间的协方差函数是具有各态历经性的平稳随机函数这一特征，提出了利用垂线偏差精确逼近海域大地水准面的协方差函数. 而海域大地水准面的精确确定，为从测高数据中精确分离动力海面地形提供了条件. 本文还利用Topex/Poseidon、ERS 1/2测高数据计算了全球海域大地水准面和动力海面地形，证明了本文所述方法是科学合理的.     

基于多种方法构建似大地水准面模型推估特性分析

针对构建似大地水准面中采用的重力水准法、EGM2008水准法、GPS水准法,结合地形复杂程度、面积大小、重力似大地水准面分辨率与精度等特点,首次评价了基于多种方法构建的似大地水准面模型的外推性与真实性.采用地形复杂区域S、平原区域N以及沿海区域Q构建区域似大地水准面模型.通过时各方法得到的似大地水准面模型推估特性分析比较,结果表明:就反应似大地水准面起伏的真实情况而言,重力水准法精度最高且外推能力最强;EGM2008水准法精度次之,外推能力较强外推范围在10 km左右;GPS水准法精度最弱,外推能力最差.构建高精度高分率1 cm级似大地水准面时须采用基于grave/level法.     

海域航空重力快速构建区域大地水准面

我国在海域开展了大规模的航空重力勘探,这些资料对构建高精度大地水准面具有重要价值.基于此,本文提出一种利用海域航空重力测量数据快速构建大地水准面的方法.该方法基于移去-恢复法思想,利用位场最小曲率方法对航空重力数据进行高精度向下延拓并获取相应的扰动位,实现航空重力测量快速构建海域大地水准面.与斯托克斯积分计算相比,采用了处理效率更高的频率域位场转换,解决了向下延拓及垂向积分时航空重力异常数据空白及扩边问题,具有较高的位场转换精度.本文应用EGM2008模拟航空重力数据进行模型验证,计算结果与其给出的水准面的精度相当;同时,也选取GRAV-D计划的航空重力数据进行实际验证,计算结果与xGEOID18B水准面模型精度基本一致.模型验证和实际应用验证了本方法的实用性.     

沿海雷达卫星测高波形重定多子波参数方法和重力异常恢复

雷达卫星测高数据质量是测高在大地测量学、地球物理学和海洋学等领域应用研究的关键。在沿海海域,测高波形受到地形和地球物理环境等污染,测高数据精度低于开阔海域的测高数据。提出了一种新的测高波形重定方法,即多子波参数重定方法（MSPR）,用于改善沿海海域的测高数据质量。由测高数据,利用最小二乘配置法解算沿海重力异常,给出了对应的方差-协方差矩阵。利用MSPR对台湾岛周边海域的Geosat／GM波形数据进行重定,与台湾岛大地水准面进行比较,MSPR重定结果精度要优于常用的β-5参数方法重定结果和GDR数据。利用重定后的测高数据,由最小二乘法计算了台湾岛近海海域的重力异常。与船测重力数据进行比较,由重定数据得到的结果精度优于GDR结果。     

Merging of Airborne Gravity and Gravity Derived from Satellite Altimetry: Test Cases Along the Coast of Greenland

The National Survey and Cadastre - Denmark (KMS) has for several years produced gravity anomaly maps over the oceans derived from satellite altimetry. During the last four years, KMS has also conducted airborne gravity surveys along the coast of Greenland dedicated to complement the existing onshore gravity coverage and fill in new data in the very-near coastal area, where altimetry data may contain gross errors. The airborne surveys extend from the coastline to approximately 100 km offshore, along 6000 km of coastline. An adequate merging of these different data sources is important for the use of gravity data especially, when computing geoid models in coastal regions.The presence of reliable marine gravity data for independent control offers an opportunity to study procedures for the merging of airborne and satellite data around Greenland. Two different merging techniques, both based on collocation, are investigated in this paper. Collocation offers a way of combining the individual airborne gravity observation with either the residual geoid observations derived from satellite altimetry or with gravity derived from these data using the inverse Stokes method implemented by Fast Fourier Transform (FFT).     

Update of the precision geoid determination in Korea

From the late 1990s, many studies on local geoid construction have been made in South Korea. However, the precision of the previous geoid has remained about 15 cm due to distribution and quality problems of gravity and GPS/levelling data. Since 2007, new land gravity data and GPS/levelling data have been obtained through many projects such as the Korean Land Spatilaization, Unified Control Point and Gravity survey on the Benchmark. The newly obtained data are regularly distributed to a certain degree and show much better improvement in their quality. In addition, an airborne gravity survey was conducted in 2008 to cover the Korean peninsula (South Korea only). Therefore, it is expected that the precision of the geoid could be improved. In this study, the new South Korean gravimetric geoid and hybrid geoid are presented based on land, airborne, ship‐borne, altimeter gravity data, geopotential model and topographic data. As for the methodology, the general remove‐restore approach was applied with the best chosen parameters in order to produce a precise local geoid. The global geopotential model EGM08 was used to remove the low‐frequency components using degree and order up to 360 and the short wavelength part of the gravity signal was dealt with by using the Shuttle Radar Topography Mission data. The parameters determined empirically in this study include for Stokes’ integral 0.5° and for Wong‐Gore kernel 110–120°, respectively and 10 km for both the Bjerhammar sphere depth and attenuation factor. The final gravimetric geoid in South Korea ranges from 20–31 m with a precision of 5.45 cm overall compared to 1096 GPS/levelling data. In addition, the South Korean hybrid geoid produces 3.46 cm and 3.92 cm for degrees of fitness and precision, respectively and a better statistic of 2.37 cm for plain and urban areas was achieved. The gravimetric and hybrid geoids are expected to improve further when the refined land gravity data are included in the near future.     

A new ellipsoidal gravimetric, satellite altimetry and astronomic boundary value problem, a case study: The geoid of Iran

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.

Contributions of terrestrial and GRACE data to the study of the secular geoid changes in North America

This paper tests and discusses different statistical methods for modelling secular rates of change of the geoid in North America. In particular, we use the method of principal component/empirical orthogonal functions (PC/EOF) analysis to model the geoid rates from Gravity Recovery and Climate Experiment (GRACE) satellite data. As demonstrated, the PC/EOF analysis is useful for studying the contributions from different signals (mainly residual hydrology signals and leakage effects) to the GRACE-derived geoid rates. The PC/EOF analysis leads to smaller geoid rates compared to the conventional least-squares fitting of a trend and annual and semi-annual cycles to the time series of the spherical harmonic coefficients. This is because we filter out particular spatiotemporal modes of the regional geoid changes.We apply the method of least-squares collocation with parameters to combine terrestrial data (GPS vertical velocities from the Canadian Base Network and terrestrial gravity rates from the Canadian Gravity Standardization Net) with the GRACE-derived vertical motion to obtain again the geoid rates. The combined model has a peak geoid rate of 1.4 mm/year in the southeastern area of Hudson Bay contrary to the GRACE-derived geoid rates that show a large peak of 1.6–1.7 mm/year west of Hudson Bay. We demonstrate that the terrestrial data, which have a longer time span than the GRACE data, are important for constraining the GRACE-derived secular signal in the areas that are well sampled by the data.     

Modelling the fine-structure of the geoid: Methods,data requirements and some results

The requirements for precise geoid models on local and regional scales have increased in recent years, primarily due to the ongoing developments in height determination by GPS on land, but also due to oceanographic requirements in using satellite altimetry for recovering dynamic sea-surface topography. Suitable methods for geoid computations from gravity data include Stokes integration, FFT methods, and least-squares collocation. Especially the FFT methods are efficient in handling large amounts of gravity data, and new variants of the methods taking earth curvature rigorously into account provide attractive methods for obtaining continental-scale, high-resolution geoid models. The accuracy of such models may be from 2–5 cm locally, to 50–100 cm on regional scales, depending on gravity data coverage, long wave-length gravity field errors, and datum problems. When approaching the cm-level geoid basic geoid definition questions (geoid or quasigeoid?) become very significant, especially in rugged areas. In the paper the geoid modelling methods and problems are reviewed, and some investigations on local data requirements for cm-level geoid prediction are presented. Some actual results are presented from Scandinavia, where a recent regional high-resolution geoid model yields apparent accuracies of 2–10 cm over GPS baselines of 50 to 2000 km.     

Local geoid determination based on airborne gravity data

A mathematical model used for determination of a local geoid model by combining airborne gravity disturbances and the Earth Gravitational Model 2008 (EGM08) is shortly reviewed. The precision of the estimated local geoid model of Taiwan is tested by its comparison with the “real” geoid at Global Satellite Navigation Systems (GNSS)/levelling points. The same comparison at GNSS/levelling points is done for the geoid evaluated only by using EGM08. Conclusions concerning a rate of improvement of the “global” geoid from EGM08 using the “local” geoid from airborne gravity data are presented.     

Geoid and Sea Surface Topography Derived from ERS-1 Altimeter Data by the Adjoint Method

A method for splitting sea surface height measurements from satellite altimetry into geoid undulations and sea surface topography is presented. The method is based on a combination of the information from altimeter data and a dynamic sea surface height model. The model consists of geoid undulations and a quasi-geostrophic model for expressing the sea surface topography. The goal is the estimation of those values of the parameters of the sea surface height model that provide a least-squares fit of the model to the data. The solution is accomplished by the adjoint method which makes use of the adjoint model for computing the gradient of the cost function of the least-squares adjustment and an optimization algorithm for obtaining improved parameters. The estimation is applied to the North Atlantic. ERS-1 altimeter data of the year 1993 are used. The resulting geoid agrees well with the geoid of the EGM96 gravity model.