The Iceland 1986 GPS geodetic survey: tectonic goals and data processing results

Summary The 1986 GPS survey of Iceland aimed to: (1) establish geodetic control in the South Iceland Seismic Zone (SISZ), to study destructive earthquakes there, (2) measure a country-wide network to form the basis of a new first order national network. 51 points were surveyed, with 20–30 km spacings within the SISZ and 100 km spacings elsewhere. The data were processed using the Bernese GPS software Version 3. Analysis was difficult due to poor satellite geometry and short-period ionospheric variations. However, an ambiguity-fixed, ionosphere-free solution gave accuracies of 1–2 cm in the horizontal and 2–3 cm in the vertical for the SISZ network and an ambiguity-free, ionosphere-free solution yielded accuracies of about 5 cm for the country-wide network. An ionosphere-free solution for the total survey with ambiguities fixed for the SISZ network only gave marginal additional improvements over the two separate solutions. GPS surveying has continued annually in Iceland with measurements in South Iceland in 1989 and 1992 (Hackman 1991; Sigmundsson 1992) and in North Iceland in 1987, 1990 and 1992 (Jahn et al. 1992; Foulger et al. 1992).     

Trip making, induced travel demand, and accessibility

Traditional transportation planning practice rests on the premise that the demand for transportation is derived. On the other hand, economic theory advances that enhancement to the transportation system leads to lower travel cost and hence to induced demand. Such an argument lends support to the view that the rate at which trips are generated is linked to the ease of making trips to potential destinations. Rather conflicting evidence has so far come out of aggregate trip generation modeling applications. This paper revisits this issue with proper characterization of integral accessibility. Poisson regression models of automobile trip generation by trip purpose are estimated on travel survey data in Minneapolis–St. Paul, MN. Alternative measures of accessibility are tested for statistical significance. Conclusions are drawn on the role of accessibility in trip making and on the comparison of integral accessibility measures.The first author gratefully acknowledges the financial support of NSF grant SBR- 9308394. We are particularly indebted to Rick Gelbmann, Robert Paddock, and Mark Philippi at the Metropolitan Council, Minneapolis–St. Paul, and William Barrett at the Office of Transportation Data Analysis, Minnesota Department of Transportation for their availability to answer all our data-related questions.     

Improvement of inertial surveys through post-mission network adjustment and self-calibration

Present day inertial surveys are limited to single traverse runs in which the number of unknown system parameters to be determined are few, depending on the number of control points available along the traverse. Further, conventional inertial surveys are generally restricted to the determination of coordinates with no possibility for a rigorous post-mission adjustment of the observations. The consequence is the continued presence of systematic trends in the residuals, even after the use of error models such as those proposed by Ball, Gregerson or Kouba. Future work aiming at higher accuracies obviously requires more comprehensive models and rigorous adjustment procedures. These can be accomplished by the development of such error models and by the use of “area surveys”, instead of the single traverses, together with rigorous adjustment procedures suitable for the network of criss-crossing lines inertially surveyed. In such a network the cross-over points serve as constraints for the geodetic parameters (latitude, longitude, height, gravity anomaly, deflection components) and allow the addition of hardware and software related error parameters. Thus an opportunity is provided to effectively self-calibrate the system—a concept successfully used, for example, in photogrammetry or in satellite tracking. The number and the strength of such parameters depend on the number of control and cross-over points. The adjustment, of course, also provides the necessary statistical information on the adjusted parameters, such as their precision and the correlation between them. The presentation will describe current work at OSU in this area. Presented at the Second International Symposium on Inertial Technology for Surveying and Geodesy, Banff, Canada, June 1–5, 1981.     

Prospects for gradiometric aiding of inertial survey systems

The state of current and proposed moving-base gravity gradiometer instruments is briefly reviewed. The review perspective is directed toward their deployment as a source of additional gravimetric data during inertial surveys. In such gradiometer-aided surveys, the additional gravity gradient information could be used to:

1. Improve surveyed gravity vector accuracy
2. Extend the interval between zero velocity update stops
3. Accomplish varying combinations of the above.

The paper examines potential survey improvements associated with gradiometers having noise levels observed in laboratory prototypes. The additional improvements possible with future gradiometers are also discussed. These results are interpreted in light of present and likely future inertial survey system technology.     

The Italian North-South GPS Traverse and a proposal for a “first order” Italian geoidal net

Some time ago it was agreed to set up a European GPS Traverse from Tromsö (Norway) to Syracuse (Sicily), to improve the definition of the European geoid.An outline of the Italian portion of this Traverse is summarized here, with special reference to the sections from the Brenner Pass to Taranto — carried out in 1989 — and for those from Taranto to Syracuse-Noto, recently completed.The observing procedures and results are reported here. A comparison with the results of the ITALGEO '90 geoid, and a tentative profile of the Italian geoid along the whole traverse are also sketched.Furthermore, a net of similar traverses, a first order geoidal net in Italy is proposed, in order to support the existing and new geoid determinations. In such a way a sub-decimetric accuracy in the Italian GPS derived orthometric heights may probably be achievedPaper presented at the XVII General Assembly of the IUGG Vienna, 12–23 August 1991     

Super Cyclone Induces a Mesoscale Phytoplankton Bloom in the Bay of Bengal

Tropical cyclones when on land create havoc, but over the oceans they can trigger a very strong biological response, giving rise to phytoplankton blooms. The Super Cyclone (TC) 05B that occurred during October 25–29, 1999, in the Bay of Bengal over the tropical Indian ocean was one of the most significant tropical cyclones on record to affect India, with maximum winds of 240 km/h, and the worst since 1971. Using satellite data, it is found that this tropical super cyclone helped spawn a notable mesoscale phytoplankton bloom in the domain (17 $^{circ}$–20$^{circ} hbox{N}$; 87$^{circ}$–90 $^{circ} hbox{E}$), which persisted for over a month. The bloom spanned 440 km zonally and 330 km meridonally, enhanced the chlorophyll-$a$ concentrations to a maximum of 10 $hbox{mg/m}^{3}$ and the net primary productivity by 200%. Furthermore, a cyclonic eddy over the bloom region is revealed from an ocean general circulation model simulation, helping the bloom to last for over month.      

The Rolling Pig or How does a surveyor creep through a pipeline?

The inspection of a pipeline from the inside becomes more and more widespread. An inspection tool, called Geometry Pig, carries a variety of sensors, among which a strapdown inertial system provides essential geometric information on the pipeline. In this paper the inspection pig is described as a surveying tool, which delivers information on centre line, shape and features of the pipe. After some background information it is explained, why the inertial system is the optimal instrument to deliver some structural parameters of the pipeline. The interaction between data evaluation and measurement procedure is discussed in view of the very few possibilities to vary the procedure. One of them is a forced rotation about the forward axis. Analogies are shown to traditional surveying procedures. Finally some results of actual surveys are presented. A positioning accuracy of 1:2500 is achieved with respect to tie points.     

Impact of GPS satellite and pseudolite geometry on structural deformation monitoring: analytical and empirical studies

Global positioning systems (GPS) have in recent years been increasingly used to monitor the deformations of large structures, particularly the deflections of long suspension bridges. When appropriately employed, and with the presence of a strong satellite geometry, GPS can supply timely and accurate structural deformation information. However, the three-dimensional (3-D) positioning accuracies in a local coordinate system are uneven. For instance, the vertical component of 3-D coordinates is less accurate than the horizontal component. In addition, GPS satellite availability tends to be a function of the latitude of the observation site and its surrounding obstructions. As a consequence, the accuracy of the north–south component is typically worse than that of the east–west component in mid-latitude areas (>45), and in some of the worst situations the horizontal positioning accuracy could even degrade to the same level as that of the vertical component. With such measurements it might not be possible to correctly interpret the real structural deformations. Furthermore, an insufficient number of satellites, caused by signal obstruction, could make it impossible to use GPS alone for kinematic positioning, even when integrated with other sensors such as triaxial accelerometers. With the aim of improving 3-D positioning accuracies for the monitoring of structural deflections, especially in vertical and northern directions, the optimal location selection of an array of ground-based pseudolites to augment GPS satellite geometry using an analytical simulation technique proposed by the authors is considered. Achievable 3-D positioning accuracies are estimated by simulating a real bridge deformation scenario using augmented transmitter geometry and compared with actual positioning accuracies calculated from the measurements gathered from a bridge trial. The results show that with an augmented satellite geometry and multipath mitigation it is possible to achieve uniform 3-D positioning accuracies of a few millimetres.     

The Geoid Slope Validation Survey 2014 and GRAV-D airborne gravity enhanced geoid comparison results in Iowa

Three Geoid Slope Validation Surveys were planned by the National Geodetic Survey for validating geoid improvement gained by incorporating airborne gravity data collected by the “Gravity for the Redefinition of the American Vertical Datum” (GRAV-D) project in flat, medium and rough topographic areas, respectively. The first survey GSVS11 over a flat topographic area in Texas confirmed that a 1-cm differential accuracy geoid over baseline lengths between 0.4 and 320 km is achievable with GRAV-D data included (Smith et al. in J Geod 87:885–907, 2013). The second survey, Geoid Slope Validation Survey 2014 (GSVS14) took place in Iowa in an area with moderate topography but significant gravity variation. Two sets of geoidal heights were computed from GPS/leveling data and observed astrogeodetic deflections of the vertical at 204 GSVS14 official marks. They agree with each other at a \({\pm }1.2\,\, \hbox {cm}\) level, which attests to the high quality of the GSVS14 data. In total, four geoid models were computed. Three models combined the GOCO03/5S satellite gravity model with terrestrial and GRAV-D gravity with different strategies. The fourth model, called xGEOID15A, had no airborne gravity data and served as the benchmark to quantify the contribution of GRAV-D to the geoid improvement. The comparisons show that each model agrees with the GPS/leveling geoid height by 1.5 cm in mark-by-mark comparisons. In differential comparisons, all geoid models have a predicted accuracy of 1–2 cm at baseline lengths from 1.6 to 247 km. The contribution of GRAV-D is not apparent due to a 9-cm slope in the western 50-km section of the traverse for all gravimetric geoid models, and it was determined that the slopes have been caused by a 5 mGal bias in the terrestrial gravity data. If that western 50-km section of the testing line is excluded in the comparisons, then the improvement with GRAV-D is clearly evident. In that case, 1-cm differential accuracy on baselines of any length is achieved with the GRAV-D-enhanced geoid models and exhibits a clear improvement over the geoid models without GRAV-D data. GSVS14 confirmed that the geoid differential accuracies are in the 1–2 cm range at various baseline lengths. The accuracy increases to 1 cm with GRAV-D gravity when the west 50 km line is not included. The data collected by the surveys have high accuracy and have the potential to be used for validation of other geodetic techniques, e.g., the chronometric leveling. To reach the 1-cm height differences of the GSVS data, a clock with frequency accuracy of \(10^{-18}\) is required. Using the GSVS data, the accuracy of ellipsoidal height differences can also be estimated.     

Geoid determination in Turkey (TG-91)

It is considered that precise geoid determination is one of the main current geodetic problems in Turkey since GPS defined coordinates require geoidal heights in practice. In order to determine the geoid by least squares collocation (LSC) the area covering Turkey was divided into 114 blocks of size 1° × 1°. LSC approximation to the geoid based upon the tailored geopotential model GPM2-T1 is constructed within each block. The model GPM2-T1 complete to degree and order 200 has been developed by tailoring of the model GPM2 to mean free-air anomalies and mean heights of one degree blocks in Turkey. Terrain effect reduced point gravity data spaced 5 × 5 within each block which the sides extended 0°.5 were used in LSC. Residual terrain model (RTM) depends on point heights at 15×20 griding and 5×5 and 15×15 mean heights has been carried out in terrain effect reduction. Indirect effect of RTM on geoid is also taken into account. The geoid, called Turkish Geoid 1991 (TG-91), referenced to GRS-80 ellipsoid has been computed at 3 × 3 griding nodes within each block. The quality of the TG-91 is also evaluated by comparing computed and GPS derived geoidal height differences, and 2.1 – 2.6 ppm accuracy for average baseline lenght of 45 km is obtained.     

Ionospheric TEC predictions over a local area GPS reference network

Single layer ionosphere models are frequently used for ionospheric modeling and estimation using GPS measurements from a network of GPS reference stations. However, the accuracies of single layer models are inherently constrained by the assumption that the ionospheric electrons are concentrated in a thin shell located at an altitude of about 350 km above Earths surface. This assumption is only an approximation to the physical truth because the electrons are distributed in the entire ionosphere region approximately from 50 to 1,000 km. To provide instantaneous ionospheric corrections for the real-time GPS positioning applications, the ionospheric corrections need to be predicted in advance to eliminate the latency caused by the correction computation. This paper will investigate ionospheric total electron content (TEC) predictions using a multiple-layer tomographic method for ionospheric modeling over a local area GPS reference network. The data analysis focuses on the accuracy evaluation of short-term (5 min in this study) TEC predictions. The results have indicated that the obtainable TEC prediction accuracy is at a level of about 2.8 TECU in the zenith direction and 95% of the total electron content can be recovered using the proposed tomography-based ionosphere model.     

Minimization and estimation of geoid undulation errors

The objective of this paper is to minimize the geoid undulation errors by focusing on the contribution of the global geopotential model and regional gravity anomalies, and to estimate the accuracy of the predicted gravimetric geoid.The geopotential model's contribution is improved by (a) tailoring it using the regional gravity anomalies and (b) introducing a weighting function to the geopotential coefficients. The tailoring and the weighting function reduced the difference (1) between the geopotential model and the GPS/levelling-derived geoid undulations in British Columbia by about 55% and more than 10%, respectively.Geoid undulations computed in an area of 40° by 120° by Stokes' integral with different kernel functions are analyzed. The use of the approximated kernels results in about 25 cm () and 190 cm (maximum) geoid errors. As compared with the geoid derived by GPS/levelling, the gravimetric geoid gives relative differences of about 0.3 to 1.4 ppm in flat areas, and 1 to 2.5 ppm in mountainous areas for distances of 30 to 200 km, while the absolute difference (1) is about 5 cm and 20 cm, respectively.A optimal Wiener filter is introduced for filtering of the gravity anomaly noise, and the performance is investigated by numerical examples. The internal accuracy of the gravimetric geoid is studied by propagating the errors of the gravity anomalies and the geopotential coefficients into the geoid undulations. Numerical computations indicate that the propagated geoid errors can reasonably reflect the differences between the gravimetric and GPS/levelling-derived geoid undulations in flat areas, such as Alberta, and is over optimistic in the Rocky Mountains of British Columbia.Paper presented at the IAG General Meeting, Beijing, China, August 8–13, 1993.     

Setting-up local “mapping geoids” with the aid of GPS/LEV traverses. Application to the geoids of Sardinia and Calabria

The problem of fitting a pre-existing geoid on local GPS/LEV points is first taken into account, a possible way for its solution is proposed, based on techniques similar to the aerophotogrammetric absolute orientation.This approach is then used to compute themapping geoids of Sardinia and Calabria i.e. geoids with decimetric accuracy, needed for the heigthing of large scale maps. The pre-existing geoids EAGGI by Brennecke et al. (1983), and EGG2 by Denker et al (1993) are utilized, fitted on points of GPS/LEV traverses.The complete input-output data, the contour maps of both geoids, and a substantial checking on some Calabrian GPS/TRIG points of the entreprise IGM.95 are finally reported.     

Confirming regional 1 cm differential geoid accuracy from airborne gravimetry: the Geoid Slope Validation Survey of 2011

A terrestrial survey, called the Geoid Slope Validation Survey of 2011 (GSVS11), encompassing leveling, GPS, astrogeodetic deflections of the vertical (DOV) and surface gravity was performed in the United States. The general purpose of that survey was to evaluate the current accuracy of gravimetric geoid models, and also to determine the impact of introducing new airborne gravity data from the ‘Gravity for the Redefinition of the American Vertical Datum’ (GRAV-D) project. More specifically, the GSVS11 survey was performed to determine whether or not the GRAV-D airborne gravimetry, flown at 11 km altitude, can reduce differential geoid error to below 1 cm in a low, flat gravimetrically uncomplicated region. GSVS11 comprises a 325 km traverse from Austin to Rockport in Southern Texas, and includes 218 GPS stations ( $\sigma _{\Delta h }= 0.4$ cm over any distance from 0.4 to 325 km) co-located with first-order spirit leveled orthometric heights ( $\sigma _{\Delta H }= 1.3$ cm end-to-end), including new surface gravimetry, and 216 astronomically determined vertical deflections $(\sigma _{\mathrm{DOV}}= 0.1^{\prime \prime })$ . The terrestrial survey data were compared in various ways to specific geoid models, including analysis of RMS residuals between all pairs of points on the line, direct comparison of DOVs to geoid slopes, and a harmonic analysis of the differences between the terrestrial data and various geoid models. These comparisons of the terrestrial survey data with specific geoid models showed conclusively that, in this type of region (low, flat) the geoid models computed using existing terrestrial gravity, combined with digital elevation models (DEMs) and GRACE and GOCE data, differential geoid accuracy of 1 to 3 cm (1 $\sigma )$ over distances from 0.4 to 325 km were currently being achieved. However, the addition of a contemporaneous airborne gravity data set, flown at 11 km altitude, brought the estimated differential geoid accuracy down to 1 cm over nearly all distances from 0.4 to 325 km.     

A new isostatic model of the lithosphere and gravity field

Based on the analysis of various factors controlling isostatic gravity anomalies and geoid undulations, it is concluded that it is essential to model the lithospheric density structure as accurately as possible. Otherwise, if computed in the classical way (i.e. based on the surface topography and the simple Airy compensation scheme), isostatic anomalies mostly reflect differences of the real lithosphere structure from the simplified compensation model, and not necessarily the deviations from isostatic equilibrium. Starting with global gravity, topography and crustal density models, isostatic gravity anomalies and geoid undulations have been determined. The initial crust and upper-mantle density structure has been corrected in a least squares adjustment using gravity. To model the long-wavelength (>2000 km) features in the gravity field, the isostatic condition (i.e. equal mass for all columns above the compensation level) is applied in the adjustment to uncover the signals from the deep-Earth interior, including dynamic deformations of the Earths surface. The isostatic gravity anomalies and geoid undulations, rather than the observed fields, then represent the signals from mantle convection and deep density inhomogeneities including remnants of subducted slabs. The long-wavelength non-isostatic (i.e. the dynamic) topography was estimated to range from –0.4 to 0.5 km. For shorter wavelengths (<2000 km), the isostatic condition is not applied in the adjustment in order to obtain the non-isostatic topography due to regional deviations from classical Airy isostasy. The maximum deviations from Airy isostasy (–1.5 to 1 km) occur at currently active plate boundaries. As another result, a new global model of the lithosphere density distribution is generated. The most pronounced negative density anomalies in the upper mantle are found near large plume provinces, such as Iceland and East Africa, and in the vicinity of the mid-ocean ridge axes. Positive density anomalies in the upper mantle under the continents are not correlated with the cold and thick lithosphere of cratons, indicating a compensation mechanism due to thermal and compositional density.     

Evaluation of the accuracy of the EIGEN-1S and -2 CHAMP-derived gravity field models by satellite crossover altimetry

Since the advent of CHAMP, the first in a series of low-altitude satellites being almost continuously and precisely tracked by GPS, a new generation of long-wavelength gravitational geopotential models can be derived. The accuracy evaluation of these models depends to a large extent on the comparison with external data of comparable quality. Here, two CHAMP-derived models, EIGEN-1S and EIGEN-2, are tested with independent long-term-averaged single satellite crossover (SSC) sea heights from three altimetric satellites (ERS-1, ERS-2 and Geosat). The analyses show that long-term averages of crossover residuals still are powerful data to test CHAMP gravity field models. The new models are tested in the spatial domain with the aid of ERS-1/-2 and Geosat SSCs, and in the spectral domain with latitude-lumped coefficient (LLC) corrections derived from the SSCs. The LLC corrections allow a representation of the satellite-orbit-specific error spectra per order of the models spherical harmonic coefficients. These observed LLC corrections are compared to the LLC projections from the models variance–covariance matrix. The excessively large LLC errors at order 2 found in the case of EIGEN-2 with the ERS data are discussed. The degree-dependent scaling factors for the variance-covariance matrices of EIGEN-1S and –2, applied to obtain more realistic error estimates of the solved-for coefficients, are compatible with the results found here.     

Ellipsoidal terrain correction based on multi-cylindrical equal-area map projection of the reference ellipsoid

An operational algorithm for computation of terrain correction (or local gravity field modeling) based on application of closed-form solution of the Newton integral in terms of Cartesian coordinates in multi-cylindrical equal-area map projection of the reference ellipsoid is presented. Multi-cylindrical equal-area map projection of the reference ellipsoid has been derived and is described in detail for the first time. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid are selected and the gravitational potential and vector of gravitational intensity (i.e. gravitational acceleration) of the mass elements are computed via numerical solution of the Newton integral in terms of geodetic coordinates {,,h}. Four base- edge points of the ellipsoidal mass elements are transformed into a multi-cylindrical equal-area map projection surface to build Cartesian mass elements by associating the height of the corresponding ellipsoidal mass elements to the transformed area elements. Using the closed-form solution of the Newton integral in terms of Cartesian coordinates, the gravitational potential and vector of gravitational intensity of the transformed Cartesian mass elements are computed and compared with those of the numerical solution of the Newton integral for the ellipsoidal mass elements in terms of geodetic coordinates. Numerical tests indicate that the difference between the two computations, i.e. numerical solution of the Newton integral for ellipsoidal mass elements in terms of geodetic coordinates and closed-form solution of the Newton integral in terms of Cartesian coordinates, in a multi-cylindrical equal-area map projection, is less than 1.6×10^–8 m²/s² for a mass element with a cross section area of 10×10 m and a height of 10,000 m. For a mass element with a cross section area of 1×1 km and a height of 10,000 m the difference is less than 1.5×10^–4m²/s². Since 1.5× 10^–4 m²/s² is equivalent to 1.5×10^–5m in the vertical direction, it can be concluded that a method for terrain correction (or local gravity field modeling) based on closed-form solution of the Newton integral in terms of Cartesian coordinates of a multi-cylindrical equal-area map projection of the reference ellipsoid has been developed which has the accuracy of terrain correction (or local gravity field modeling) based on the Newton integral in terms of ellipsoidal coordinates.Acknowledgments. This research has been financially supported by the University of Tehran based on grant number 621/4/859. This support is gratefully acknowledged. The authors are also grateful for the comments and corrections made to the initial version of the paper by Dr. S. Petrovic from GFZ Potsdam and the other two anonymous reviewers. Their comments helped to improve the structure of the paper significantly.     

Ellipsoidal corrections to order e 2 of geopotential coefficients and Stokes’ formula

Assuming that the gravity anomaly and disturbing potential are given on a reference ellipsoid, the result of Sjöberg (1988, Bull Geod 62:93–101) is applied to derive the potential coefficients on the bounding sphere of the ellipsoid to order e ² (i.e. the square of the eccentricity of the ellipsoid). By adding the potential coefficients and continuing the potential downward to the reference ellipsoid, the spherical Stokes formula and its ellipsoidal correction are obtained. The correction is presented in terms of an integral over the unit sphere with the spherical approximation of geoidal height as the argument and only three well-known kernel functions, namely those of Stokes, Vening-Meinesz and the inverse Stokes, lending the correction to practical computations. Finally, the ellipsoidal correction is presented also in terms of spherical harmonic functions. The frequently applied and sometimes questioned approximation of the constant m, a convenient abbreviation in normal gravity field representations, by e ²/2, as introduced by Moritz, is also discussed. It is concluded that this approximation does not significantly affect the ellipsoidal corrections to potential coefficients and Stokes formula. However, whether this standard approach to correct the gravity anomaly agrees with the pure ellipsoidal solution to Stokes formula is still an open question.     

Channels of synthesis forty years on: integrated analysis of spatial economic systems

Isards vision of integrated modeling that was laid out in the 1960s book Methods of Regional Science provided a road map for the development of more sophisticated analysis of spatial economic systems. Some forty years later, we look back at this vision and trace developments in a sample of three areas – demographic-econometric integrated modeling, spatial interaction modeling, and environmental-economic modeling. Attention will be focused on methodological advances and their motivation by new developments in theory as well as innovations in the applications of these models to address new policy challenges. Underlying the discussion will be an evaluation of the way in which spatial issues have been addressed, ranging from concerns with regionalization to issues of spillovers and spatial correlation.