Open Access Published by De Gruyter Open Access

Volume 3 Issue 2

June 2013

Issue of Journal of Geodetic Science

Contents
Journal Overview

Open Access September 7, 2013

Various parameterizations of “latitude” equation – Cartesian to geodetic coordinates transformation

M. Ligas

Page range: 87-110

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Abstract

The paper presents a solution to one of the basic problems of computational geodesy - conversion between Cartesian and geodetic coordinates on a biaxial ellipsoid. The solution is based on what is known in the literature as “latitude equation”. The equation is presented in three different parameterizations commonly used in geodesy - geodetic, parametric (reduced) and geocentric latitudes. Although the resulting equations may be derived in many ways, here, we present a very elegant one based on vectors orthogonality. As the “original latitude equations” are trigonometric ones, their representation has been changed into an irrational form after Fukushima (1999, 2006). Furthermore, in order to avoid division operations we have followed Fukushima’s strategy again and rewritten the equations in a fractional form (a pair of iterative formulas). The resulting formulas involving parametric latitude are essentially the same as those introduced by Fukushima (2006) (considered the most efficient today). All the resulting variants are solved with Newton’s second-order and Halley’s third-order formulas. It turns out that all parameterizations of the “latitude equation” show a comparable level of performance.

Open Access September 7, 2013

The effect of tunnelling on repeated precise levelling measurements for vertical deformation control of the Metro4 project

Cs. Égető, L. Földváry, T. Huszák

Page range: 95-102

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Abstract

The effect of the construction of the 4th subway line of Budapest (Metro4) on the potential surfaces of the gravity field has been simulated, using the prism modelling technique. In the study mass loss due to the excavation of the two tunnels and of the stations has been considered. Mass variations deform the level surfaces; as so, the vertical reference surface of the levelling measurements is changing by time. In this study, the effect of the mass loss on levelling measurements was determined at a level 1 m above the ground, roughly simulating common instrument heights. Subsequently, the effect of the actual deformations of the surface on the levelling measurements has also been determined. According to the results, under certain arrangements of the levelling line with respect to the position of the excavations, the error due to the change of the vertical reference is in the 1μm order of magnitude, thus negligible.

Open Access September 7, 2013

The geoid or quasigeoid – which reference surface should be preferred for a national height system?

L. E. Sjöberg

Page range: 103-109

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Abstract

Most European states use M. S. Molodensky’s concept of normal heights for their height systems with a quasigeoid model as the reference surface, while the rest of the world rely on orthometric heights with the geoid as the zero-level. Considering the advances in data caption and theory for geoid and quasigeoid determinations, the question is which system is the best choice for the future. It is reasonable to assume that the latter concept, in contrast to the former, will always suffer from some uncertainty in the topographic density distribution, while Molodensky’s approach to quasigeoid determination has a convergence problem. On the contrary, geoid and quasigeoid models computed by analytical continuation (e.g., rcr technique or KTH method) have no integration problem, and the quasigeoid can always be determined at least as accurate as the geoid. As the numerical instability of the analytical continuation is better controlled in the KTH method vs. the rcr method, we propose that any future height system be based on normal heights with a quasigeoid model computed similar to or directly based on the KTH method (Least squares modification of Stokes formula with additive corrections).

Open Access September 7, 2013

Errata to article Sjöberg, L.E. (2012), Journal of Geodetic Science 2: 162-171 entitled Solutions to the ellipsoidal Clairaut constant and the inverse geodetic problem by numerical integration

Lars E. Sjöberg

Page range: 110-110

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Open Access September 7, 2013

The effect of correlation on uncertainty estimates – with GPS examples

P. Jansson, C.-G. Persson

Page range: 111-120

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Abstract

This article deals with the effect of correlation on the estimates of measurement uncertainty, with some focus on Global Positioning Satellite (GPS) time series analysis. Analytical derivations and Monte Carlo simulations form the theoretical basis, which shows that uncompensated correlation produces unrealistic uncertainty estimates. Tools for handling correlation in connection with estimation of uncertainty, construction of confidence intervals, hypothesis testing, design of measurement strategies, and development of tolerances are outlined and demonstrated. The GPS observation time series used in the article has a short to medium range correlation, and can therefore be handled with the presented tools - based on a simple Location-model and stationary stochastic processes.

Open Access September 7, 2013

GPS monitoring of bedrock stability at Olkiluoto nuclear waste disposal site in Finland from 1996 to 2012

S. Nyberg, U. Kallio, H. Koivula

Page range: 121-126

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Abstract

The Finnish Geodetic Institute has studied crustal deformations at Olkiluoto nuclear waste disposal site since mid-90’s. Biannual GPS measurement has been carried out in two local GPS networks. This paper analyses the GPS data processing effects on the coordinate solutions and presents the results of GPS monitoring from 1996 to 2012. The GPS data was processed using Bernese GPS Software 5.0. The GPS data processing and baseline analysis showed a 1.0 mm (max RMS) level agreement of observation and high bedrock stability in the area. Most of the horizontal trends were smaller than 0.1 mm/a. The troposphere estimation strategy had a clear effect on the horizontal trends at some sites. The strain rates were all very small, but we could detect motions near the Olkiluoto permanent station.

Open Access September 7, 2013

Global sea level trends in the presence of variable sea level velocities, and variable accelerations

H. Bâki Iz, X.L. Ding, C.K. Shum

Page range: 127-135

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Abstract

This study investigates, using a new variable-acceleration model, the validity of the implicit assertion in previous studies regarding global constant sea level rise accelerations. Thirteen out of twenty seven globally distributed tide gauge stations, with records longer than 80 years, exhibit statistically significant quartic coefficients (p < 0.05) revealing the presence of variable sea level accelerations though not as a global phenomenon. Most of these stations initially exhibit decreasing negative velocities until early 20th century and increasing positive velocities after 1970’s following a period of constant velocities. It is shown that, for those locations experiencing statistically significant variable sea level accelerations, the estimates based on the conventional linear representation of linear sea level trends are not appropriate, and are notably biased for a number of stations. All solutions account for serial correlations, which otherwise induce biases in solution statistics. It is also demonstrated that the omission of non-linearities in sea level changes will bias the sea level trends for short records, such as those from satellite altimetry, as large as 3 mm/yr.

Open Access September 7, 2013

Accuracy assessment of test flights using the Turnkey Airborne Gravity System over Alabama in 2008

Y.M. Wang, S. Preaux, T. Diehl, V. Childers, D. Roman, D. Smith

Page range: 136-142

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Abstract

The National Geodetic Survey (NGS) performed a few test flights using Micro-g’s Turnkey Airborne Gravity System (TAGS) at altitude of 1700, 6300 and 11000 meters over Alabama in 2008. The cross-track spacing was 10 km for the two lower flights and 5 km for the highest flight. The test flights not only provided important information regarding the precision and accuracy of the TAGS but also revealed the impact of flight altitudes and track spacing on the collected gravity data. The gravity anomalies at three altitudes were modeled using 3-dimensional Fourier series, then compared at the three altitudes. The agreement was excellent - the gravity anomalies agree with each other from 1.4 to 3.3 mGal RMS at the three altitudes. When the bias was removed, the agreement was improved to better than 1.1 mGal. On the ground (h =0), the three gravity models agree from 1.9 to 3.8 mGal RMS. After removing the mean, the agreement improved to better than 1.7 mGal. Similar results were obtained in comparison with recent surface gravity which was of sub-mGal accuracy. The overall agreement between the downward continued airborne gravity and the surface gravity was better than 1.7 mGal after removing the mean values. As expected, the flight altitude had a direct impact on accuracy of the values of gravity downward continued to the Earth’s surface. The comparisons with terrestrial gravity show that gravity collected at 11000 m is having an accuracy of ±3 mGal on the ground. This accuracy is slightly worse than the other two altitudes most probably due to smaller signal/noise ratios and larger downward continuation effects. The RMS values of differences between the downward continued airborne gravity at altitude 1700 and 6300 meters and the surface gravity are 2.0 and 1.6 mGals, respectively. Based on these comparisons, airborne gravity data collected at altitudes below 6300 meters should result in accuracy better than ±2 mGals on the ground. Note, however, that the test area is flat and the accuracy of airborne gravity would likely be worse in more rugged mountainous regions.

About this journal

Journal of Geodetic Science is a peer-reviewed, electronic-only journal that publishes original, high-quality research on topics broadly related to Geodesy. The journal focuses on theoretical and application papers. The aim of the Journal is to become a premier source of knowledge and a worldwide-recognized platform of exchange for scientists of different disciplinary origins and backgrounds (e.g., Surveyors, Geodesists and Geophysicists). The journal publishes geodetic research from a broad range of topics and approaches including Geodetic Networks, Deformation analysis, Adjustment theory and application of mathematical statistics, Satellite Geodesy, Physical Geodesy, Geodynamics, Geometric Geodesy, (see the scope listed below for more). However, we will accept both theoretical and empirical contributions in all subfields of Geodesy as long as they contribute in a broad sense to the core theme.

The scope includes, but is not restricted to:

Surveying Engineering
Geodetic Networks
Deformation Analysis
Adjustment Theory and Mathematical Geodesy
Global Navigation Satellite Systems (GNSS)
Inertial Geodesy
Geoid determination and height systems
Marine Geodesy and Satellite Altimetry
Satellite Gravimetry
Geometric Geodesy
Numerical methods and software developments in Geodesy
Geodynamics
Geophysical Geodesy

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