Showing papers on "Geodetic datum published in 2007"

Short Note: A global model of pressure and temperature for geodetic applications

Abstract: The empirical model GPT (Global Pressure and Temperature), which is based on spherical harmonics up to degree and order nine, provides pressure and temperature at any site in the vicinity of the Earth’s surface. It can be used for geodetic applications such as the determination of a priori hydrostatic zenith delays, reference pressure values for atmospheric loading, or thermal deformation of Very Long Baseline Interferometry (VLBI) radio telescopes. Input parameters of GPT are the station coordinates and the day of the year, thus also allowing one to model the annual variations of the parameters. As an improvement compared with previous models, it reproduces the large pressure anomaly over Antarctica, which can cause station height errors in the analysis of space-geodetic data of up to 1 cm if not considered properly in troposphere modelling. First tests at selected geodetic observing stations show that the pressure biases considerably decrease when using GPT instead of the very simple approaches applied to various Global Navigation Satellite Systems (GNSS) software packages so far. GPT also provides an appropriate model for the annual variability of global temperature.

Interferometric Synthetic Aperture Radar Geodesy

Abstract: Satellite-based interferometric synthetic aperture radar (InSAR) provides a synoptic high spatial resolution perspective of Earth’s deforming surface, permitting one to view large areas quickly and efficiently. We review basic InSAR theory for geodetic applications and attempt to provide an overview of what processing and analysis schemes are currently used and a glimpse of what the future may hold. As part of this discussion, we present a biased view of what constitutes best practices for use of InSAR observations in geodetic modeling. Finally, we provide a basic primer on the ties between different mission design parameters and their relationship to the character of the resulting observations.

Earth Rotation Variations – Long Period

Abstract: The solid Earth is subject to a wide variety of forces including external forces due to the gravitational attraction of the Sun, Moon, and planets; surficial forces due to the action of the atmosphere, oceans, and water stored on land; and internal forces due to earthquakes and tectonic motions, mantle convection, and coupling between the mantle and both the fluid outer core and the solid inner core. The solid Earth responds to these forces by displacing its mass, deforming its shape, and changing its rotation. Geodetic observing systems can measure the change in the Earth's gravity caused by mass displacement, the change in the Earth's shape, and the change in the Earth's rotation. Consequently, geodetic observing systems can be used to study both the mechanisms causing the Earth's shape, rotation, and gravity to change and the response of the solid Earth to these forcing mechanisms. As a result, geodetic observing systems can be used to gain greater understanding of the Earth's interior structure and of the nature of the forcing mechanisms including their temporal evolution. In this chapter, the variations in the Earth's rotation that occur on timescales greater than a day are discussed. The standard theory used to study the variations is reviewed, the techniques by which the variations are observed are described, and the causes of the observed variations are discussed.

Second-order ionospheric term in GPS : Implementation and impact on geodetic estimates

Abstract: [1] In this paper, different aspects of the application of the second-order ionospheric term (abbreviated as I2) and its impact on geodetic estimates are studied. A method to correct the GPS observations from this effect is proposed. This method provides a more accurate correction to the GPS measurements (in some cases, it can even be 50% better) with respect to other ways of computing such effect. Moreover, this method can be applied routinely to estimate geodetic parameters. Applying the I2 correction to subdaily differential positioning, several relationships between the deviation of the parameter estimates and the I2 term are derived in the context of a new global approach to the problem. In particular, it is shown that the effect in receiver position mainly depends on the differential value of this term between GPS receivers, while the satellite clocks are directly affected by the undifferenced values. Data from the International GNSS Service (IGS) global network of receivers have been gathered over a period of 21 months. These data have been used to study the I2 effect on the geodetic estimates, such as receiver positions, satellite clocks, and orbits. The most important effect appears for the satellite clocks, and it can be greater than 1 cm depending on the geographical location, comparable to the IGS nominal accuracies. The effect on orbits consists of a global contribution of several millimeters (which confirms the geocenter displacement detected by other authors) plus a subdaily contribution, also of several millimeters, that is geographically dependent, also comparable to the IGS nominal accuracies. As for the position of receivers, the obtained shifts are, in general, at submillimeter level and are directed southward for low-latitude receivers and northward for high-latitude receivers. These results will be explained in detail since they are not completely in agreement with the ones presented in previous works.

On the link between GPS pseudorange noise and day-boundary discontinuities in geodetic time transfer solutions

Abstract: When neglecting calibration issues, the accuracy of GPS-based time and frequency transfer using a combined analysis of code and carrier phase measurements highly depends on the noise of the GPS codes. In particular, the pseudorange noise is responsible for day-boundary discontinuities which can reach more than 1 ns in the time transfer results obtained from geodetic analysis. These discontinuities are caused by the fact that the data are analyzed in daily data batches where the absolute clock offset is determined by the mean code value during the daily data batch. This pseudorange noise is not a white noise, in particular due to multipath and variations of instrumental delays. In this paper, the pseudorange noise behavior is characterized in order to improve the understanding of the origin of the large day-boundary discontinuities in the geodetic time transfer results. In a first step, the effect of short-term noise and multipath is estimated, and shown to be responsible for only a maximum of 150 ps (picoseconds) of the day-boundary jumps, with only one exception at NRC1 where the correction provides a jump reduction of 300 ps. In a second step, a combination of time transfer results obtained with pseudoranges only and geodetic time transfer results is used to characterize the long-term evolution of pseudorange errors. It demonstrates that the day-boundary jumps, especially those of large amplitude, can be explained by an instrumental effect imposing a common behavior on all the satellite pseudoranges. Using known influences as temperature variations at ALGO or cable damages at HOB2, it is shown that the approach developed in this study can be used to look for the origin of the day-boundary discontinuities in other stations.

System and method for deriving a hierarchical event based database optimized for analysis of biological systems

Abstract: A computer implemented method, apparatus, and computer usable program code for inferring a probability of a first inference absent from a database at which a query regarding the inference is received. Each datum of the database is conformed to the dimensions of the database. Each datum of the plurality of data has associated metadata and an associated key. The associated metadata includes data regarding cohorts associated with the corresponding datum, data regarding hierarchies associated with the corresponding datum, data regarding a corresponding source of the datum, and data regarding probabilities associated with integrity, reliability, and importance of each associated datum. The query is used as a frame of reference for the search. The database returns a probability of the correctness of the first inference based on the query and on the data.

System and method for deriving a hierarchical event based database optimized for pharmaceutical analysis

Abstract: A computer implemented method, apparatus, and computer usable program code for inferring a probability of a first inference absent from a database at which a query regarding the inference is received. Each datum of the database is conformed to the dimensions of the database. Each datum of the plurality of data has associated metadata and an associated key. The associated metadata includes data regarding cohorts associated with the corresponding datum, data regarding hierarchies associated with the corresponding datum, data regarding a corresponding source of the datum, and data regarding probabilities associated with integrity, reliability, and importance of each associated datum. The query is used as a frame of reference for the search. The database returns a probability of the correctness of the first inference based on the query and on the data.

System and method for deriving a hierarchical event based database optimized for analysis of complex accidents

Abstract: A computer implemented method, apparatus, and computer usable program code for inferring a probability of a first inference absent from a database at which a query regarding the inference is received. Each datum of the database is conformed to the dimensions of the database. Each datum of the plurality of data has associated metadata and an associated key. The associated metadata includes data regarding cohorts associated with the corresponding datum, data regarding hierarchies associated with the corresponding datum, data regarding a corresponding source of the datum, and data regarding probabilities associated with integrity, reliability, and importance of each associated datum. The query is used as a frame of reference for the search. The database returns a probability of the correctness of the first inference based on the query and on the data.

System and method for deriving a hierarchical event based database optimized for clinical applications

Abstract: A computer implemented method, apparatus, and computer usable program code for inferring a probability of a first inference absent from a database at which a query regarding the inference is received. Each datum of the database is conformed to the dimensions of the database. Each datum of the plurality of data has associated metadata and an associated key. The associated metadata includes data regarding cohorts associated with the corresponding datum, data regarding hierarchies associated with the corresponding datum, data regarding a corresponding source of the datum, and data regarding probabilities associated with integrity, reliability, and importance of each associated datum. The query is used as a frame of reference for the search. The database returns a probability of the correctness of the first inference based on the query and on the data.

System and method for deriving a hierarchical event based database optimized for analysis of criminal and security information

Abstract: A computer implemented method, apparatus, and computer usable program code for inferring a probability of a first inference absent from a database at which a query regarding the inference is received. Each datum of the database is conformed to the dimensions of the database. Each datum of the plurality of data has associated metadata and an associated key. The associated metadata includes data regarding cohorts associated with the corresponding datum, data regarding hierarchies associated with the corresponding datum, data regarding a corresponding source of the datum, and data regarding probabilities associated with integrity, reliability, and importance of each associated datum. The query is used as a frame of reference for the search. The database returns a probability of the correctness of the first inference based on the query and on the data.

System and method for deriving a hierarchical event based database optimized for privacy and security filtering

Abstract: Inferring a probability of a first inference absent from a database. Each datum of the database is conformed to the dimensions of the database. Each datum of the plurality of data has associated metadata and an associated key. The associated metadata includes data regarding cohorts associated with the corresponding datum, data regarding hierarchies associated with the corresponding datum, data regarding a corresponding source of the datum, and data regarding probabilities associated with integrity, reliability, and importance of each associated datum. The query is used as a frame of reference for the search. The database returns a probability of the correctness of the first inference based on the query and on the data. Security filtering is performed based on at least one of a significance level of the probability of the first inference, the probability itself exceeding a pre-selected value, and a security level possessed by a user.

Present motion and deformation of the Caribbean plate: Constraints from new GPS geodetic measurements from Honduras and Nicaragua

Abstract: Velocities from six continuous and 14 campaign sites within the boundaries of the Caribbean plate, including eight new sites from previously unsampled areas of Honduras and Nicaragua at the western edge of the Caribbean plate, are described and tested for their consistency with Caribbean–North America plate motion and a rigid Caribbean plate model. Sites in central Honduras and Guatemala move 3–8 mm yr−1 westward with respect to the Caribbean plate interior, consistent with distributed east-to-west extension in Guatemala and the western two-thirds of Honduras. A site in southern Jamaica moves 8 ± 1 mm yr−1 westward relative to the Caribbean plate interior, indicating that most or all of Jamaica is unsuitable for estimating Caribbean plate motion. Two sites in southern Hispaniola also exhibit anomalous motions relative to the plate interior, consistent with a tectonic bias at those sites. An inversion of the velocities for 15 sites nominally located in the plate interior yields a well-constrained Caribbean plate angular velocity vector that predicts motion similar to previously published models. Data bootstrapping indicates that the solution is robust to better than 1 mm yr−1 with respect to both the site velocities that are used *chuck@geology.wisc.edu DeMets, C., Mattioli, G., Jansma, P., Rogers, R., Tenorio, C., and Turner, H.L., 2007, Present motion and deformation of the Caribbean plate: Constraints from new GPS geodetic measurements from Honduras and Nicaragua, in Mann, P., ed., Geologic and Tectonic Development of the Caribbean Plate in Northern Central America: Geological Society of America Special Paper 428, p. 21–36, doi: 10.1130/2007.2428(02). For permission to copy, contact editing@geosociety.org. ©2007 The Geological Society of America. All rights reserved. spe 428-02 page 21

GPS and Space-Based Geodetic Methods

Abstract: Space-based geodetic methods such as the Global Positioning System (GPS) have revolutionized our view of the Earth, enabling us to observe plate tectonics in progress, right now as it happens. The relative positions between any pair of geodetic stations in the world can be determined with a precision measured in millimeters; thus, the long-term movement of the Earth's surface can be monitored to within 1 mm Year − 1 . Dense networks of GPS stations are now being used to map the rate of strain in the Earth's crust in plate boundary regions. The Earth's geometric and gravitational shapes and its orientation in space are being monitored and inverted to determine the redistribution of geophysical fluids on or near the Earth's surface, including the ocean and atmosphere, cryosphere, and the terrestrial hydrosphere. All of this has been made possible since the development of space-based geodetic techniques in the 1970s and 1980s, starting with satellite laser ranging and very long baseline interferometry. This chapter provides a summary of the developments that led to this astonishing new geophysical tool and also introduces the fundamentals of space geodesy and how it is being applied to geophysical research, with examples provided from plate tectonics, the earthquake cycle, and surface mass redistribution.

Definition and realisation of the SIRGAS Vertical Reference System within a globally unified height system

Abstract: The new SIRGAS vertical reference system is based on the determination of an equipotential reference surface W 0 within a global definition, i.e. optimally fitting the worldwide mean sea surface. The corresponding W 0 value (mean geopotential value over the total ocean surface) is empirically estimated using different combinations of global gravity models (EGM96, TEG4, GGM02S, EIGEN-CG03C) and mean sea surface models (CLS01, KMS04, GFSC00.1 and a series of annual models from 1993 to 2001 derived at DGFI from T/P). The results show the W 0 dependence on the GGM’s degree n, on the latitudinal extension, and on time. The recommended W 0 value (62 636 853,4 m 2 s −2) is derived from EIGEN-CG03C (n = 120) and referred to the epoch 2000.0. It differs from previous computations by 3 m 2 s −2 (e.g. Bursa et al. 2002, Bursa et al. 2004). A preliminary realisation of this new reference level is accomplished by transforming the existing South American classical height datums (defined individually at different tide gauges) through the combination of GNSS positioning, high resolution (quasi)geoid models and physical heights derived from spirit levelling and terrestrial gravity data.

Application of a Back-Propagation Artificial Neural Network to Regional Grid-Based Geoid Model Generation Using GPS and Leveling Data

Abstract: The height difference between the ellipsoidal height h and the orthometric height H is called undulation N. The key issue in transforming the global positioning system GPS-derived ellipsoidal height to the orthometric height is to determine the undulation value accurately. If the undulation N for a point whose position is determined by a GPS receiver can be estimated in the field, then the GPS-derived three-dimensional geocentric coordinate in WGS-84 can be transformed into a local coordinate system and the orthometric height in real-time. In this paper, algorithms of applying a back-propagation artificial neural network BP ANN to develop a regional grid-based geoid model using GPS data e.g., ellipsoidal height and geodetic leveling data e.g., orthometric height are proposed. In brief, the proposed algorithms include the following steps: 1 establish the functional relationship between the point's plane coordinates and its undulation using the BP ANN according to the measured GPS data and leveling data; 2 develop a regional grid-based geoid model using the imaginary grid plane coordinates with a fixed grid interval and the trained BP ANN; 3 develop an undulation interpolation algorithm to estimate a specific point's undulation using the generated grid-based geoid model; and 4 estimate the point's undulation in the field and transform the GPS ellipsoidal height into the orthometric height in real-time. Three data sets from the Taiwan region are used to test the proposed algorithms. The test results show that the undulation interpolation estimation accuracy using the generated grid-based geoid is in the order of 2-4 cm. The proposed algorithms and the detailed test results are presented in this paper.

Edge geodetic number of a graph

Abstract: For a non-trivial connected graph G, a set S⊆V(G) is called an edge geodetic cover of G if every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g 1 (G) of G is the minimum order of its edge geodetic covers and any edge geodetic cover of order g 1 (G) is an edge geodetic basis. Connected graphs of order p with edge geodetic number 2 are characterized. Various necessary conditions for the edge geodetic number of a graph to be p−1 and p are given. A geodetic graph of order p with edge geodetic number p is characterized. It is shown that every pair k, p of integers with 2≤k≤p is realizable as the edge geodetic number and order of some connected graph. For positive integers r, d and k≥2 with r

Second-order ionospheric term in GPS: implementation and impact on geodetic estimates. J Geophys Res 112:B08417

Abstract: [1] In this paper, different aspects of the application of the second-order ionospheric term (abbreviated as I2) and its impact on geodetic estimates are studied. A method to correct the GPS observations from this effect is proposed. This method provides a more accurate correction to the GPS measurements (in some cases, it can even be 50% better) with respect to other ways of computing such effect. Moreover, this method can be applied routinely to estimate geodetic parameters. Applying the I2 correction to subdaily differential positioning, several relationships between the deviation of the parameter estimates and the I2 term are derived in the context of a new global approach to the problem. In particular, it is shown that the effect in receiver position mainly depends on the differential value of this term between GPS receivers, while the satellite clocks are directly affected by the undifferenced values. Data from the International GNSS Service (IGS) global network of receivers have been gathered over a period of 21 months. These data have been used to study the I2 effect on the geodetic estimates, such as receiver positions, satellite clocks, and orbits. The most important effect appears for the satellite clocks, and it can be greater than 1 cm depending on the geographical location, comparable to the IGS nominal accuracies. The effect on orbits consists of a global contribution of several millimeters (which confirms the geocenter displacement detected by other authors) plus a subdaily contribution, also of several millimeters, that is geographically dependent, also comparable to the IGS nominal accuracies. As for the position of receivers, the obtained shifts are, in general, at submillimeter level and are directed southward for low-latitude receivers and northward for high-latitude receivers. These results will be explained in detail since they are not completely in agreement with the ones presented in previous works.

Toward a direct combination of space‐geodetic techniques at the measurement level: Methodology and main issues

Abstract: [1] In the framework of the activities of the Combination Research Centers (CRC) of the International Earth Rotation and Reference Systems Service (IERS), the French Groupe de Recherche en Geodesie Spatiale (GRGS) studies the benefit of combining space-geodetic techniques (Doppler orbitography and radiopositioning integrated by satellite, GPS, satellite laser ranging, and very long baseline interferometry) at the observational level. This combination aims to produce a global and consistent solution for Earth orientation parameters (EOPs), polar motion xp and yp, and universal time UT1 with a 1-day or a 6-hour sampling, as well as weekly station positions. In this paper we present a methodology for multitechnique combination at the observational level. We process the measurements of the four techniques over a 1-year period (the year 2002) in order to illustrate and validate our method. All techniques are processed with the same computational framework, thus with the same models and a priori values for parameters. By using the same software and conventions, we avoid inconsistencies in individual computations. We process each technique individually and inside the combination. The comparison between these solutions is a way of analyzing the power of our method even if the actual status of our software does not reproduce the state-of-the-art analyses of each technique. However, we produce an analysis of the quality of our individual computations so that readers can get an informed appreciation of the current capabilities of our software. Finally, we present the capability of such combinations in terms of accuracy and precision, we underline the main issues of our method and propose solutions to solve them in the future.

3.06 – Earth Tides

Abstract: The tidal deformation of the solid Earth has become increasingly important in geodesy as the precision of geodetic measurements has increased, to the point that for some quantities, uncertainties in tidal effects are a major source of inaccuracy. Fortunately, our models for the tidal driving forces, the response of the Earth to them, and the effect of loading by ocean tides have all improved significantly over the last 20 years. This chapter describes the theories and methodologies used in computing all these effects and also those used in analyzing and predicting observed tidal series. It also summarizes some of the observations of Earth tides, particularly in the last two decades, when the traditional measurements of tidal effects in gravity, tilt, and strain have been supplemented by direct measurements of displacement using space geodetic methods.

GPS as a geodetic tool for geodynamics in northern Victoria Land, Antarctica

Abstract: The VLNDEF (Victoria Land Network for DEFormation control) project started in 1999 with the aim of detecting crustal deformation in Northern Victoria Land (Antarctica) over an area that had never been surveyed by a dense GPS network before. After a brief summary of the Italian geodetic activities carried out since 1991, the paper presents the results obtained from the processing of data collected from 1999 to 2003. In particular, processing strategies were dealt with, in order to produce horizontal and vertical displacement maps through GPS observations. Absolute motions in a global reference frame have been investigated using a double approach, which allowed us to make considerable progress in detecting movements and standardizing the data analysis. The analyses provide absolute horizontal velocities ranging between 17 mm yr−1 and 8 mm yr−1, with greater motions in the northernmost area. The subtraction of the rigid plate motion provides relative displacements, which may contribute to the understanding of neotectonics and geology, whereas the pattern of the vertical crustal motions detected, with average values of +1.3 mm yr−1, is essential to detect the effect of Glacial Isostatic Adjustment (GIA) and other geophysical signals, and to redefine theory and numerical models used without any direct measurements.

A new methodology for incorporating tide gauge data in sea surface topography models

Abstract: As part of the Vertical Offshore Reference Frames (VORF) project sponsored by the U K Hydrographic Office, a new model for Sea Surface Topography (SST) around the British Isles has been developed For offshore areas (greater than 30 km from the coast), this model is largely derived from satellite altimetry However, its accuracy and level of detail have been enhanced in coastal areas by the inclusion of not only the 60 PSMSL tide gauges with long-term records around the coasts of the United Kingdom and Ireland but also some 385 gauges established at different epochs and for different observation spans by the U K Admiralty All tide gauge data were brought into a common reference frame by a combination of datum models and direct GPS observations, but a more significant challenge was to bring all short-term sea level observations to an unbiased value at a common epoch This was achieved through developing a spatial-temporal correlation model for the variations in mean sea level around the British Isles,

Quasigeoid modelling in New Zealand to unify multiple local vertical datums

Abstract: One goal of modern geodesy is the global unification of vertical datums so that height data from them can be properly integrated. This thesis studies the unification of the 13 disparate levellingand tide-gauge-based vertical datums in New Zealand (NZ). It proposes a new NZ-wide single vertical datum based on a gravimetric quasigeoid model to unify the existing local vertical datums. This will also include methods to transform height data in terms of the existing datums to the new datum and vice versa. After defining and comparing the main types of height system and vertical datum used around to world, the system of heights used in NZ was shown to be normalorthometric. Consequently, datum unification was achieved using a quasigeoid model, as opposed to a geoid model. The quasigeoid was computed by combining the GRACE-based GGM02 and EGM96 global geopotential models with land gravity data (40,737 observations) and a 56-m resolution digital elevation model (DEM). Marine gravity data came from a least-squares collocation combination of 1,300,266 crossover-adjusted ship track observations and gravity anomalies derived from multi-mission satellite altimetry. To ensure that the best quasigeoid was computed for the NZ datasets, a number of computation processes were compared and contrasted. The Hammer chart, fast Fourier transform (FFT) and prism integration methods of computing terrain corrections (TCs) were compared. This showed that the prism integration TC is the most realistic in NZ. The mean Helmert gravity anomalies, required for numerical integration of Stokes’s formula, were computed via refined Bouguer anomalies with the prism TCs, and reconstruction with heights from the DEM used to ‘reconstruct’ more representative mean anomalies. In addition, five deterministic modifications to Stokes’s formula were compared. There was little difference between three of them, so the Featherstone et al. (1998) modification ( 0 ψ = 1.5°, M = 40) was chosen because it is theoretically better than its predecessors. The global geopotential, gravimetric geoid, sea surface topography and geodetic boundary-value problem approaches to vertical datum unification were then contrasted. As none was likely to be effective in NZ, a new iterative quasigeoid

Radio source instability in VLBI analysis

Abstract: The source position time-series for many of the frequently observed radio sources in the NASA geodetic very long baseline interferometry (VLBI) program show systematic linear and non-linear variations of as much as 0.5 mas (milli-arc-seconds) to 1.0 mas, due mainly to source structure changes. In standard terrestrial reference frame (TRF) geodetic solutions, it is a common practice to only estimate a global source position for each source over the entire history of VLBI observing sessions. If apparent source position variations are not modeled, they produce corresponding systematic variations in estimated Earth orientation parameters (EOPs) at the level of 0.02–0.04 mas in nutation and 0.01–0.02 mas in polar motion. We examine the stability of position time-series of the 107 radio sources in the current NASA geodetic source catalog since these sources have relatively dense observing histories from which it is possible to detect systematic variations. We consider different strategies for handling source instabilities where we (1) estimate the positions of unstable sources for each session they are observed, or (2) estimate spline parameters or rate parameters for sources chosen to fit the specific variation seen in the position-time series. We found that some strategies improve VLBI EOP accuracy by reducing the biases and weighted root mean square differences between measurements from independent VLBI networks operating simultaneously. We discuss the problem of identifying frequently observed unstable sources and how to identify new sources to replace these unstable sources in the NASA VLBI geodetic source catalog.

Device for and method of authenticated cryptography

Abstract: A device for and method of authenticated encryption by concatenating a first user-datum with a second datum, concatenating the first datum with a third datum, encrypting the results, concatenating the encrypted results, concatenating the result with a message and a fifth user-definable datum, hashing the result, concatenating the result with the message, dividing the result into blocks, concatenating the first datum with a sixth datum, generating key-stream blocks from the result using a block cipher in counter mode, combining the blocks and key-stream blocks, concatenating the result with the first datum and the fifth datum, and transmitting the result to a recipient. The recipient extracts the hash value from the received ciphertext, generates a hash value from the first through fifth datums and plaintext derived from the ciphertext, and compares the two. If they match then the plaintext and fifth datum are as the sender intended.

Global estimates for the schrödinger maximal operator

Abstract: The Schrodinger equation, i∂ t u + Δu = 0, with initial datum f contained in a Sobolev space H s (R n ), has solution e itΔ f. We give sharp conditions under which sup t |e itΔ f| is bounded from H s (R) to L q (R) for all q, and give sharp conditions under which sup 0 1 2 - 1 2(n+1).

VLBI2010: A Vision for Future Geodetic VLBI

Abstract: This article summarizes the results of IVS Working Group 3 ‘VLBI2010’, which was charged with creating a vision for a new geodetic VLBI instrument that will meet requirements for the coming decades. This comes at a time when problems with aging antennas, a deteriorating radio frequency environment due to interference, obsolete electronics, and high operating costs are making it difficult to achieve the required level of performance. Fortunately, recent advances in antenna manufacture, digital electronics, and data transmission technology are enabling the development of systems and modes of operation unimaginable only a few years ago, along with much reduced costs. A set of criteria to be met by a future geodetic VLBI system was established based on recommendations in reports compiled by IVS, GGOS, and NASA. These criteria are: 1 mm measurement accuracy on global baselines, continuous measurements for time series of station positions and Earth orientation parameters, and turnaround time to initial geodetic results of less than 24 hrs.

Statistical analysis of the eigenspace components of the two-dimensional, symmetric rank-two strain rate tensor derived from the space geodetic measurements (ITRF92-ITRF2000 data sets) in central Mediterranean and Western Europe

Abstract: SUMMARY In the deformation analysis with a 2-D (or planar and horizontal), symmetric rank-two deformation tensor in geosciences (geodesy, geophysics and geology), the eigenspace components of these random deformation tensors (principal components, principal directions) are of focal interest. With the new development of space-geodetic techniques, such as GPS, VLBI, SLR and DORIS, the components of deformation measures (such as the stress or strain tensor, etc.) can be estimated from their highly accurate regular measurement of positions and change rates and analysed by means of the proper statistical testing procedures. In this paper we begin with a review of the results of statistical inference of eigenspace components of the 2-D symmetric, rank-two random tensor (‘random matrix’), that is, the best linear uniformly unbiased estimation (BLUUE) of the eigenspace elements and the best invariant quadratic uniformly unbiased estimate (BIQUUE) of its variance–covariance matrix. Then the geodynamic setting of the Earth and especially the selected investigated region—the central Mediterranean and Western Europe will be discussed. Thirdly, the ITRF sites are selected according to the history and quality of the ITRF realization series, and the related incremental velocities of selected ITRF sites are computed. Fourthly, the methods of derivation for the 2-D geodetic strain rates are introduced in order to obtain these strain rates from the incremental velocities. In the case study, both BLUUE and BIQUUE models as well as related hypothesis tests are applied to the eigenspace components of the 2-D strain rate tensor observations in the area of the central Mediterranean and Western Europe, as derived from the ITRF92 to ITRF2000 sequential station positions and velocities. The interpretation and comparison of these results with the geodynamic feature are followed. Furthermore the statistical inference of the eigenspace components provides us with not only the confidence regions of these estimated, but also the visual presentation of the possible magnitude and the directions of the extension and contraction of the strain rate, which is important for the prediction of the tectonic activity including the possible deformation trend and directions.