GPS vector configuration design for monitoring deformation networks

 The performance of geodetic monitoring networks is heavily influenced by the configuration of the measured GPS vectors. As an effective design of the GPS measurements will decrease GPS campaign costs and increase the accuracy and reliability of the entire network, the identification of the preferred GPS vectors for measurement has been highlighted as a core problem in the process of deformation monitoring. An algorithm based on a sensitivity analysis of the network, as dependent upon a postulated velocity field, is suggested for the selection of the optimal GPS vectors. Relevant mathematical and statistical concepts are presented as the basis for an improved method of vector configuration design. A sensitivity analysis of the geodetic geodynamic network in the north of Israel is presented, where the method is examined against two deformation models, the Simple Transform Fault and the Locked Fault. The proposed method is suggested as a means for the improvement of the design of monitoring networks, a common practice worldwide. Received: 30 July 2001 / Accepted: 3 June 2002 Acknowledgments. It is my pleasant duty to thank the Survey of Israel and Dr. E. Ostrovsky for providing the variance–covariance matrix of the G1 network in northern Israel. I would like to thank the reviewers of this paper for their constructive and helpful remarks.     

Bringing GPS into harsh environments for fully automated deformation monitoring

Engineering projects that require deformation monitoring frequently utilize geodetic sensors to measure displacements of target points located in the deformation zone. In situations where control stations and targets are separated by a kilometer or more, GPS can offer higher precision position updates at more frequent intervals than can normally be achieved using total station technology. For large-scale deformation projects requiring the highest precision, it is therefore advisable to use a combination of the two sensors. In response to the need for high precision, continuous GPS position updates in harsh deformation monitoring environments, a software has been developed that employs triple-differenced carrier-phase measurements in a delayed-state Kalman filter. Two data sets were analyzed to test the capabilities of the software. In the first test, a GPS antenna was displaced using a translation stage to mimic slow deformation. In the second test, data collected at a large open pit mine were processed. It was shown that the delayed-state Kalman filter developed could detect millimeter-level displacements of a GPS antenna. The actual precision attained depends upon the amount of process noise infused at each epoch to accommodate the antenna displacements. Higher process noise values result in quicker detection times, but at the same time increase the noise in the solutions. A slow, 25 mm displacement was detected within 30 min of the full displacement with sigma values in E, N and U of ±10 mm or better. The same displacement could also be detected in less than 5 h with sigma values in E, N and U of ±5 mm or better. The software works best for detecting long period deformations (e.g., 20 mm per day or less) for which sigma values of 1–2 mm are attained in all three solution components. It was also shown that the triple-differenced carrier-phase observation can be used to significantly reduce the effects of residual tropospheric delay that would normally plague double-differenced observations in harsh GPS environments.

Surface deformation analysis of dense GPS networks based on intrinsic geometry: deterministic and stochastic aspects

In this contribution, the regularized Earth’s surface is considered as a graded 2D surface, namely a curved surface, embedded in a Euclidean space . Thus, the deformation of the surface could be completely specified by the change of the metric and curvature tensors, namely strain tensor and tensor of change of curvature (TCC). The curvature tensor, however, is responsible for the detection of vertical displacements on the surface. Dealing with eigenspace components, e.g., principal components and principal directions of 2D symmetric random tensors of second order is of central importance in this study. Namely, we introduce an eigenspace analysis or a principal component analysis of strain tensor and TCC. However, due to the intricate relations between elements of tensors on one side and eigenspace components on other side, we will convert these relations to simple equations, by simultaneous diagonalization. This will provide simple synthesis equations of eigenspace components (e.g., applicable in stochastic aspects). The last part of this research is devoted to stochastic aspects of deformation analysis. In the presence of errors in measuring a random displacement field (under the normal distribution assumption of displacement field), the stochastic behaviors of eigenspace components of strain tensor and TCC are discussed. It is applied by a numerical example with the crustal deformation field, through the Pacific Northwest Geodetic Array permanent solutions in period January 1999 to January 2004, in Cascadia Subduction Zone. Due to the earthquake which occurred on 28 February 2001 in Puget Sound (M _w > 6.8), we performed computations in two steps: the coseismic effect and the postseismic effect of this event. A comparison of patterns of eigenspace components of deformation tensors (corresponding the seismic events) reflects that: among the estimated eigenspace components, near the earthquake region, the eigenvalues have significant variations, but eigendirections have insignificant variations.     

GPS精确定位技术在小湾水电站工程变形测量中的应用

为保障电站建设和运行安全,小湾电站构建了全国规模最大的工程安全监测系统——基于GPS精确定位技术的工程变形监测系统,先后成功应用于小湾电站枢纽区工程边坡、大坝和水库库岸滑坡体的变形监测。介绍布设于上述工程部位的的GPS变形监测系统的架构组成、技术特点和监测成果,为水电工程建设GPS变形监测系统提供参考和借鉴。     

Decomposition of deformation primitives of horizontal geodetic networks: application to Taiwan’s GPS network

The contribution to each component of the deformation vector due to a marginally undetected blunder in an observation is split into two parts, and so are the deformation measures at a point. The first part, called the local component (or self component), signifies the contribution due to the redundancy-related multiplier belonging to the observation itself, while the second part, called the complementary component, shows the contribution due to the non-redundancy-related multipliers belonging to the observation. A larger redundancy results in a smaller local component for each component of the deformation vector. However, robustness due to an observation at a point is correlated with redundancy to a significant extent. The first-order global positioning system (GPS)-geodetic network of Taiwan was examined for its robustness. The experiments seem to indicate that: (1) large deformations tend to be found at points where the group redundancies are small; (2) the local components monopolize deformation measures at the perimeter stations of the network where very small redundancy numbers are found; (3) the largest deformation at a point may be due to an observation not directly tied to the point of interest; and (4) except for local twisting, deformation measures and mean positional precisions at individual points are highly correlated.Acknowledgement The authors thank Drs. A.A. Simkooei, M. Schmidt, and M.R. Craymer greatly for their constructive comments and suggestions, which improved the quality of the paper. This research was supported by National Science Council of Taiwan (contract number NSC-91-2211- E-002-085).     

Ground deformation of Papandayan volcano before, during, and after the 2002 eruption as detected by GPS surveys

Papandayan is an A-type active volcano located in the southern part of Garut Regency, about 70 km southeast of Bandung, Indonesia. Its earliest recorded eruption, and the most violent and devastating outburst, occurred in 1772. The latest eruptions occurred in the period from 11 November–8 December 2002, and consisted of phreatic, freatomagmatic, and magmatic types of eruption. During the latest eruption period, GPS surveys were conducted at several points inside and around the crater in a radial mode, using the reference point located at the Papandayan observatory, about 10 km from the crater. At the points closest to the erupting craters, GPS displacements up to a few decimeters were detected, whereas at the points outside the crater, the displacements were at the centimeter level. The magnitude of displacements observed at each point also showed a temporal variation according to the eruption characteristics. The results show that deformation during eruption tends to be local, e.g. just around the crater. The pressure source is difficult to be properly modeled from GPS results, due to the limited GPS data available and differences in topography, geological structure, and/or rheology related to each GPS station.     

GPS技术在滑坡变形监测中的应用

介绍了GPS技术用于滑坡变形监测的方法,并通过三峡库区某滑坡的变形监测介绍了GPS用于滑坡变形监测的整个过程,包括监测网的技术设计、外业观测、数据处理、变形分析等内容。监测结果表明,GPS静态定位技术可以达到mm级的精度,在变形监测方面有很好优越性,完全可以满足高精度滑坡监测的要求。     

东海大桥GPS天线阵列变形监测方案设计

介绍了自主研制的GPS天线阵列变形监测系统。根据东海大桥的具体情况,给出两个东海大桥GPS天线阵列变形监测的设计方案。采用该设计方案,建设东海大桥变形监测系统的成本仅为隔河岩模式的31%。     

三角钢标对GPS测量影响的试验分析

GPS测量控制网为了与地面国家控制网进行联合的平差，必须与国家坐标系进行联测，GPS接收机有时也必须安置在有三角钢标的旧有控制点上。通过对此分析研究了三角钢标对GPS测量的影响，对设计和实施GPS测量的用户具有一定的参考价值。     

Atmospheric turbulence theory applied to GPS carrier-phase data

Turbulent irregularities in the lower atmosphere cause physical correlations between Global Positioning System (GPS) carrier-phase measurements. Based on turbulence theory, a variance–covariance model is developed in this paper that reflects these correlations. The main result shows that the obtained fully-populated variance–covariance matrices depend not only on the satellite-station geometry, but also on the prevailing atmospheric conditions, which are parameterised by, e.g., the von Karman spectrum of refractivity fluctuations and the wind velocity vector. It is shown that the amount of the correlation between two GPS carrier-phase observations is inversely related to the separation distance of the corresponding ray paths through the turbulent atmosphere. Furthermore, the wind velocity and direction play a key role in the correlation.     

苏通大桥形变的GPS动态监测

针对目前大桥监测的现状及各种监测方法的优缺点,该文结合苏通大桥运营情况,研究了GPS动态监测的原理、系统组成、坐标转换及监测注意事项,并对其进行了GPS动态监测试验。采集了桥面沿轴线方向、横向及竖向位移数据,对大桥在温度、风荷、车载等因素影响下的运营期大桥响应情况进行了分析。表明大桥轴线方向位移与温度正相关,1/4跨处相关系数为0.859;竖向位移与温度负相关,1/4跨处相关系数-0.817。并对数据进行了频谱分析,分析结果表明频谱没有明显变化;大桥各方向振幅在安全范围内,表明运营期的大桥十分健康;同时也表明GPS动态系统监测结果是可靠的。     

GPS高程拟合法在高程测量中的应用试验

采用多种拟合方式对小测区首级高程控制测量进行GPS高程转换工程试验。通过其结果精度和GPS高程拟合法的适用性分析研究,探讨GPS高程转换工作应遵循的原则和GPS、RTK技术应用于大比例尺地形图测绘高程测量的有效方法。     

Applications of graph theory to gross error detection for GPS geodetic control networks

This paper describes a broad perspective of the application of graph theory to establishment of GPS control networks whereby the GPS network is considered as a connected and directed graph with three components. In this algorithm the gross error detection is undertaken through loops of different spanning trees using the “Loop Law” in which the individual components ΔX, ΔY and ΔZ sum up to zero. If the sum of the respective vector components ΩX, ΩY and ΩZ in a loop is not zero and if the error is beyond the tolerable limit (ε>ω), it indicates the existence of gross errors in one of the baselines in the loop and therefore the baseline must be removed or re-observed. After successful screening of errors by graph theory, network adjustment can be carried out. In this paper, the GPS data from the control network established as refence system for the HP Dam at Baishan county in Liaoning province is presented to illustrate the algorithm.     

Applications of graph theory to gross error detection for GPS geodetic control networks

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GPS动态监测数据优化分析及变形特征的提取

GPS变形监测系统中的监测点的观测资料是与时间有关的信号序列,本文研究应用小波分析优化流程,结合苏通大桥GPS变形监测系统获取的监测点数据序列进行分析。结果表明,选择合适的小波基函数,对数据信号进行小波分解与重构,可以有效地从受到强噪声干扰的监测数据序列中提取有用的特征信号,较好解决了传统处理技术对GPS动态观测数据去噪以及特征信息提取的局限性。     

青岛海湾大桥变形监测方案及应用分析

在众多变形监测的方法中,GPS无疑是最有效的手段之一,特别是在像海湾大桥这样需要连续监测的建筑中。但是由于GPS成本过高,而限制其发展,本文中通过分析几种监测的方法,选择GPS多天线阵列变形监测系统能很好地解决这一问题。此系统拥有与常规GPS监测方法相当的精度,但是大大地降低了成本。可以应用于青岛海湾大桥的变形监测中。     

GPS构造沉降监测数据处理及变形分析

为了防洪防灾及对水患区的治理,在洞庭湖区建立了高精度的GPS构造沉降监测网。顾及到对流层延迟的影响,实测了每个测站处的气象数据。基线解算采用了高精度的解算软件GAMIT,监测网平差使用了GLOBK软件。解算出的起算点的坐标精度为±3.0mm。由两期GPS观测数据所计算的各个监测点的南北方向和东西方向的中误差都小于1mm,垂直方向的精度都优于3.0mm。研究和计算结果表明,洞庭湖区的构造沉降变形是很显著的。两期GPS监测获得的每个监测点的垂直变形值显著可信,可直接用于沉降变形分析和地壳运动研究。     

On the adjustment of combined GPS/levelling/geoid networks

A detailed treatment of adjustment problems in combined global positioning system (GPS)/levelling/geoid networks is given. The two main types of `unknowns' in this kind of multi-data 1D networks are usually the gravimetric geoid accuracy and a 2D spatial field that describes all the datum/systematic distortions among the available height data sets. An accurate knowledge of the latter becomes especially important when we consider employing GPS techniques for levelling purposes with respect to a local vertical datum. Two modelling alternatives for the correction field are presented, namely a pure deterministic parametric model, and a hybrid deterministic and stochastic model. The concept of variance component estimation is also proposed as an important statistical tool for assessing the actual gravimetric geoid noise level and/or testing a priori determined geoid error models. Finally, conclusions are drawn and recommendations for further study are suggested. Received: 9 September 1998 / Accepted: 8 June 1999     

On the sensitivity of the location, size and shape of the GPS ambiguity search space to certain changes in the stochastic model

In this contribution we analyse in a qualitative sense for the geometry-free model the dependency of the location, the size and the shape of the ambiguity search space on different factors of the stochastic model. For this purpose a rather general stochastic model is used. It includes time-correlation, cross-correlation, satellite elevation dependency and the use of an a priori weighted ionospheric model, having the ionosphere-fixed model and the ionosphere-float model as special cases. It is shown that the location is invariant for changes in the cofactor matrix of the phase observables. This also holds true for the cofactor matrix of the code observables in the ionosphere-float case. As for time-correlation and satellite elevation dependency, it is shown that they only affect the size of the search space, but not its shape and orientation. It is also shown that the least-squares ambiguities, their variance matrix and its determinant, for, respectively, the ionosphere-fixed model, the ionosphere-float model and the ionosphere-weighted model, are all related through the same scalar weighted mean, the weight of which is governed by the variance ratio of the ionospheric delays and the code observables. A closed-form expression is given for the area of the search space in which all contributing factors are easily recognized. From it one can infer by how much the area gets blown up when the ionospheric spatial decorrelation increases. This multiplication factor is largest when one switches from the ionosphere-fixed model to the ionosphere-float model, in which case it is approximately equal to the ratio of the standard deviation of phase with that of code. The area gives an indication of the number of grid points inside the search space. Received: 11 November 1996 / Accepted: 21 March 1997     

GPS城市地壳变形监测网的数据处理及精度分析

应用GPS定位技术进行城市或区域地壳变形监测,研究了GPS监测的数据处理和精度分析的理论和方法.使用高精度的定位分析软件GAMIT,对某城市地壳变形监测网的试验观测数据进行数据处理,并对解算得到的基线向量和坐标分别进行精度分析,结果表明:在100km范围内,GPS基线重复率在平面上比例误差可以达到10-8,垂直方向比例误差可以达到10-7;GPS监测点的三维坐标重复率精度可达到3mm左右,能满足城市或区域地壳变形监测的精度要求.