Volume 1, Issue 3 -

GPS Landslide Monitoring: Single Base vs. Network Solutions — A case study based on the Puerto Rico and Virgin Islands Permanent GPS Network This study demonstrated an approach to using permanent GPS stations from a local continuous GPS network as no-cost references in conducting long-term millimeter-level landslide monitoring. Accuracy and outliers from a series of single-base and network GPS measurements of a creeping landslide were studied. The criterion for accuracy was the weighted root-mean-square (RMS) of residuals of GPS measurements with respect to true landslide displacements over a period of 14 months. This investigation indicated that the current Puerto Rico and Virgin Islands GPS network, as a reference frame, can provide accuracy of 1 to 2 mm horizontally and 6 mm vertically for local 24-hour continuous landslide monitoring with few outliers (<1%). The accuracy degraded by a factor of two for 6-hour sessions, and more for shorter sessions. This study indicated that adding a few reference stations to GPS data processing can reduce the number of outliers and increase the accuracy and robustness of landslide surveying, even if these references are far from the study site. This improvement was particularly significant for short sessions and vertical components. The accuracy of network solutions depended slightly on the number of reference stations, but the dependence on the distance and geometric distribution of the references was weak. For long-term landslide monitoring, accuracy under 5 mm horizontally and 15 mm vertically are often expected. Accuracy at this level can be stably achieved in the Puerto Rico and Virgin Islands region by performing field observations for 4 hours or longer, and applying 3 or more reference stations for solving a network solution. This study also indicated that rainfall events can play a crucial rule in high-precision GPS measurements. GPS data collected during heavy rainfall events should be cautiously analyzed in landslide studies.

A new Approach for GNSS Analysis in a Multi-GNSS and Multi-Signal Environment Over the coming years GPS and GLONASS will be modernised, whilst at the same time new systems like QZSS, Galileo, and Compass are launched. The modernisations of the existing and the deployment of new Global Naviagation Satellite Systems (GNSS) will make a whole range of new signals available to the users. The anticipated improvements will strongly depend on our understanding and handling of the biases that will inevitably exist between the different systems and signals. Furthermore the extremely high stability of the future satellite clocks means, that any form of differencing observations to cancel out the satellite clock offsets, effectively leads to a very significant loss of information. The fundamentally new aspect of our approach for GNSS analysis in a multi-GNSS and multi-signal environment is that it avoids the formation of differences as well as of linear combinations. Thus all available observations from all GNSS systems as observed by all the receivers in a network are incorporated in the parameter estimation. The fact that all observations are analysed without any pre-selection of observation types, needed for linear combinations or observation differences, leads to an enormous simplification of the processing.

Estimation of Crustal Motions at the Permanent GPS Station SVEA, Antarctica from 2005 to 2009 In November 2004 the permanent GPS station SVEA (Latitude: 74°34' 34" S, Longitude: 11° 13' 31" W, Height 1261.2 m) was installed in Drottning Maud's Land, Antarctica. The main aim of this paper is to evaluate the collected data for on-going crustal motions. About 40% ("3-days weekly") of the continuous four years GPS data from 2005 to 2009 was processed together with the simultaneous data of five IGS reference stations using Bernese GPS software V 5.0. A linear regression analysis was used to estimate the linear motion of the station, yielding the estimated velocities' components (in mm/year) of 6.6± 0.4 North, -1.4 ± 0.2 East and 4.4 ± 0.6 Up. Although all components appear highly significant, the abnormal development of the E-W component needs further analyses. Post-glacial rebound is estimated to contribute only to 0.2-0.3 mm/yr (James and Ivin, 1998) of the vertical uplift rate, suggesting that the observed vertical motion mainly has another origin, possibly tectonic. The crustal motion results should be regarded as preliminary, and they need both further data and analyses to be confirmed. It is also concluded that the remote continuously running GPS station SVEA works well after more than five years of operation with only annual checks and data retrieval in the harsh environment of Antarctica.

Empirical Modeling and Impact of Transient Effects on the Mean Sea Level Trend Estimates from the Global Tide Gauge Data The mean sea level trend estimates from shorter records (less than 50 years) are easily influenced by a number of additional transient effects including atmospheric pressure variations, interannual and decadal changes in the mean sea level or various station dependent disturbances, which are not always accounted for in previous studies because their influences may be negligible for stations longer than 100 years or simply such information may not have been available. In this study, we detected and modeled 8,072 transient changes (a nearly periodic, or non-periodic variation, a shift or an episodic change in the mean sea level that may last several months or longer) from all of the globally distributed 1,862 tide gauge stations with approximately 47,000 years of tide gauge data in the Permanent Service Mean Sea Level repository. It was shown that 1,264 out of 1,862 globally distributed tide gauge station solutions were affected significantly by modeling transient changes in the mean sea level. The solutionsR2 values improved at a 95% confidence level with the inclusion of new empirical model parameters representing transient changes as mean shifts as well as the trend estimates that fall within [-1 to +3] mm/year interval.

Assessment Study of Using Online (CSRS) GPS-PPP Service for Mapping Applications in Egypt Many applications in navigation, land surveying, land title definitions and mapping have been made simpler and more precise due to accessibility of Global Positioning System (GPS) data, and thus the demand for using advanced GPS techniques in surveying applications has become essential. The differential technique was the only source of accurate positioning for many years, and remained in use despite of its cost. The precise point positioning (PPP) technique is a viable alternative to the differential positioning method in which a user with a single receiver can attain positioning accuracy at the centimeter or decimeter scale. In recent years, many organizations introduced online (GPS-PPP) processing services capable of determining accurate geocentric positions using GPS observations. These services provide the user with receiver coordinates in free and unlimited access formats via the internet. This paper investigates the accuracy of the Canadian Spatial Reference System (CSRS) Precise Point Positioning (PPP) (CSRS-PPP) service supervised by the Geodetic Survey Division (GSD), Canada. Single frequency static GPS observations have been collected at three points covering time spans of 60, 90 and 120 minutes. These three observed sites form baselines of 1.6, 7, and 10 km, respectively. In order to assess the CSRS-PPP accuracy, the discrepancies between the CSRS-PPP estimates and the regular differential GPS solutions were computed. The obtained results illustrate that the PPP produces a horizontal error at the scale of a few decimeters; this is accurate enough to serve many mapping applications in developing countries with a savings in both cost and experienced labor.

Digital Images with 3D Geometry from Data Compression by Multi-scale Representations of B-Spline Surfaces To build up a 3D (three-dimensional) model of the surface of an object, the heights of points on the surface are measured, for instance, by a laser scanner. The intensities of the reflected laser beam of the points can be used to visualize the 3D model as range image. It is proposed here to fit a two-dimensional B-spline surface to the measured heights and intensities by the lofting method. To fully use the geometric information of the laser scanning, points on the fitted surface with their intensities are computed with a density higher than that of the measurements. This gives a 3D model of high resolution which is visualized by the intensities of the points on the B-spline surface. For a realistic view of the 3D model, the coordinates of a digital photo of the object are transformed to the coordinate system of the 3D model so that the points get the colors of the digital image. To efficiently compute and store the 3D model, data compression is applied. It is derived from the multi-scale representation of the dense grid of points on the B-spline surface. The proposed method is demonstrated for an example.

Discrete Spherical Harmonic Transforms of Nearly Equidistributed Global Data Discrete Spherical Harmonic Transforms (SHTs) are commonly defined for equiangular grids on the sphere. However, when global array data exhibit near equidistributed patterns rather than equiangular grids, discrete SHTs require appropriate adaptations for analysis and synthesis. Computational efficiency and reliability impose structural constraints on possible equidistribution characteristics of data patterns such as for instance with Chebychev quadratures and Fast Fourier Transforms (FFTs). Following some general introduction to discrete SHTs and equidistributions on the sphere, equitriangular (near equiareal) lattices based on the octahedron and the icosahedron are introduced for SHT analysis and synthesis. The developed formulations are described and implemented using simulated data and geopotential models such as the Earth Geopotential Model EGM 2008. Comparative results for analysis and synthesis at different levels of resolution show the potential of the spherical equitriangular approach for geodetic and other applications with nearly equidistributed global data.

Application of Molodensky's Method for Precise Determination of Geoid in Iran Determination of the geoid with a high accuracy is a challenging task among geodesists. Its precise determination is usually carried out by combining a global geopotential model with terrestrial gravity anomalies measured in the region of interest along with some topographic information. In this paper, Molodensky's approach is used for precise determination of height anomaly. To do this, optimum combination of global geopotential models with the validated terrestrial surface gravity anomalies and some deterministic modification schemes are investigated. Special attention is paid on the strict modelling of the geoidal height and height anomaly difference. The accuracy of the determined geoid is tested on the 513 points of Iranian height network the geoidal height of which are determined by the GPS observations.

Crustal Deformation due to Atmospheric Pressure Loading in New Zealand We investigate atmospheric pressure loading displacements in New Zealand using global and regional air-pressure data collected over a period of 50 years (1960-2009). The elastic response of the Earth to atmospheric loading is calculated by adopting mass loading Love numbers based on the parameters of the Preliminary Reference Earth Model (PREM). The ocean response to atmospheric loading is computed utilising a modified inverted barometer theory. The results reveal that the atmospheric loading vertical displacements are typically smallest along coastal regions, while gradually increasing inland with the maximum peak-to-peak displacement of 13.1 mm for this study period. In contrast, the largest horizontal displacements are found along coastal regions, where the maximum peak-to-peak displacement reaches 2.7 mm. The vertical displacements have a high spatial correlation, whereas the spatial correlation of the horizontal displacement components is much smaller. A spectral decomposition of the atmospheric loading time series shows that the signal is a broad band with most energy between 1 week and annual periods, and with a couple of peaks corresponding to approximately annual forcing and its overtones. The largest amplitudes in the atmospheric loading time series have an annual and semi-annual period.

On the Best Quadratic Minimum Bias Non-Negative Estimator of a Two-Variance Component Model Variance components (VCs) in linear adjustment models are usually successfully computed by unbiased estimators. However, for many unbiased VC techniques estimated variance components might be negative, a result that cannot be tolerated by the user. This is, for example, the case with the simple additive VC model aσ2/1 + bσ2/2 with known coefficients a and b , where either of the unbiasedly estimated variance components σ2/1 + σ2/2 may frequently come out negative. This fact calls for so-called non-negative VC estimators. Here the Best Quadratic Minimum Bias Non-negative Estimator (BQMBNE) of a two-variance component model is derived. A special case with independent observations is explicitly presented.