scholarly journals Fitting a triaxial ellipsoid to a geoid model

2020 ◽  
Vol 10 (1) ◽  
pp. 69-82 ◽  
Author(s):  
G. Panou ◽  
R. Korakitis ◽  
G. Pantazis
Keyword(s):  
Spherical Harmonic ◽  
Oblate Spheroid ◽  
Triaxial Ellipsoid ◽  
Data Sets ◽  
Geoid Model ◽  
Geometric Fitting ◽  
Mathematical Background ◽  
Major Semi Axis ◽  
Degenerate Cases

AbstractThe aim of this work is the determination of the parameters of Earth’s triaxiality through a geometric fitting of a triaxial ellipsoid to a set of given points in space, as they are derived from a geoid model. Starting from a Cartesian equation of an ellipsoid in an arbitrary reference system, we develop a transformation of its coefficients into the coordinates of the ellipsoid center, of the three rotation angles and the three ellipsoid semi-axes. Furthermore, we present different mathematical models for some special and degenerate cases of the triaxial ellipsoid. We also present the required mathematical background of the theory of least-squares, under the condition of minimization of the sum of squares of geoid heights. Also, we describe a method for the determination of the foot points of the set of given space points. Then, we prepare suitable data sets and we derive results for various geoid models, which were proposed in the last fifty years. Among the results, we report the semi-axes of the triaxial ellipsoid of geometric fitting with four unknowns to be 6378171.92 m, 6378102.06 m and 6356752.17 m and the equatorial longitude of the major semi-axis –14.9367 degrees. Also, the parameters of Earth’s triaxiality are directly estimated from the spherical harmonic coefficients of degree and order two. Finally, the results indicate that the geoid heights with reference to the triaxial ellipsoid are smaller than those with reference to the oblate spheroid and the improvement in the corresponding rms value is about 20 per cent.

scholarly journals On the determination of a locally optimized Ellipsoidal model of the Geoid surface in sea areas

2021 ◽  
Vol 906 (1) ◽  
pp. 012036
Author(s):  
Persephone Galani ◽  
Sotiris Lycourghiotis ◽  
Foteini Kariotou
Keyword(s):  
Data Acquisition ◽  
Sea Level ◽  
Reference Ellipsoid ◽  
Triaxial Ellipsoid ◽  
Geoid Model ◽  
Orthometric Heights ◽  
The One ◽  
Best Fit ◽  
Local Geoid

Abstract Deriving a local geoid model has drawn much research interest in the last decade, in an endeavour to minimize the errors in orthometric heights calculations, inherited by the use of global geoid reference models. In most parts of the earth, the local geoid surface may be tens of meters away from the Global Reference biaxial Ellipsoid (WGS84), which create numerus problems in topographic, environmental and navigational applications. Several methods have been developed for optimizing the precision of the calculation of the geoid heights undulations and the accuracy of the corresponding orthometric heights calculations. The optimization refers either to the method used for data acquisition, or to the geometrical method used for the determination of the best fit local geoid model. In the present work, we focus on the reference ellipsoid used for the geometric and geoid heights determination and develop a method to provide the one that fits best to the local geoid surface. Moreover, we consider relatively small sea regions and near to coast areas, where the usual methods for data acquisition fail more or less, and we pay attention in two directions: To obtain accurate measured data and to have the best possible reference ellipsoid for the area at hand. In this due, we use the “GNSS-on-boat” methodology to obtain direct sea level data, which we induce in a Moore Penrose pseudoinverse procedure to calculate the best fit triaxial ellipsoid. This locally optimized reference ellipsoid minimizes the geometric heights in the region at hand. The method is applied in two closed sea areas in Greece, namely Corinthian and Patra’s gulf and also in four regions in the Ionian Sea, which exhibit significant geoid alterations. Taking into account all factors of uncertainty, the precision of the mean sea level surface, produced by the “GNSS on boat” methodology, had been estimated at 5.43 cm for the gulf of Patras, at 3.76 cm for the Corinthian gulf and at 3.31 for the Ionian and Adriatic Sea areas. The average difference of this surface and the local triaxial reference ellipsoid, calculated in this work, is found to be less than 15 cm, whereas the corresponding difference with respect to WGS84 is of the order of 30m.

scholarly journals Towards worldwide height system unification using ocean information

2012 ◽  
Vol 2 (4) ◽  
pp. 302-318 ◽  
Author(s):  
P.L. Woodworth ◽  
C.W. Hughes ◽  
R.J. Bingham ◽  
T. Gruber
Keyword(s):  
North Atlantic ◽  
Pacific Coast ◽  
Data Sets ◽  
Dynamic Topography ◽  
Model Accuracy ◽  
Geoid Model ◽  
Height System ◽  
The Mean ◽  
Height System Unification

AbstractWe describe the application of ocean levelling to worldwide height system unification. The study involves a comparison of ‘geodetic’ and ‘ocean’ approaches to determination of the mean dynamic topography (MDT) at the coast, from which confidence in the accuracy of stateof- the-art ocean and geoid models can be obtained. We conclude that models are consistent at the sub-decimetre level for the regions that we have studied (North Atlantic coastlines and islands, North American Pacific coast and Mediterranean). That level of consistency provides an estimate of the accuracy of using the ocean models to provide an MDT correction to the national datums of countries with coastlines, and thereby of achieving unification. It also provides a validation of geoid model accuracy for application to height system unification in general. We show how our methods can be applied worldwide, as long as the necessary data sets are available, and explain why such an extension of the present study is necessary if worldwide height system unification is to be realised.

Direct phase determination in electron crystallography: small organic molecules

1992 ◽  
Vol 50 (2) ◽  
pp. 1166-1167
Author(s):  
Douglas L. Dorset
Keyword(s):  
Organic Molecules ◽  
Data Sets ◽  
Temperature Structure ◽  
3D Analysis ◽  
Intensity Data ◽  
Electron Crystallography ◽  
Phase Determination ◽  
Measured Intensity ◽  
3D Data

The quantitative use of electron diffraction intensity data for the determination of crystal structures represents the pioneering achievement in the electron crystallography of organic molecules, an effort largely begun by B. K. Vainshtein and his co-workers. However, despite numerous representative structure analyses yielding results consistent with X-ray determination, this entire effort was viewed with considerable mistrust by many crystallographers. This was no doubt due to the rather high crystallographic R-factors reported for some structures and, more importantly, the failure to convince many skeptics that the measured intensity data were adequate for ab initio structure determinations.We have recently demonstrated the utility of these data sets for structure analyses by direct phase determination based on the probabilistic estimate of three- and four-phase structure invariant sums. Examples include the structure of diketopiperazine using Vainshtein's 3D data, a similar 3D analysis of the room temperature structure of thiourea, and a zonal determination of the urea structure, the latter also based on data collected by the Moscow group.

scholarly journals Constraints on neutrino non-standard interactions from LHC data with large missing transverse momentum

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
DianYu Liu ◽  
ChuanLe Sun ◽  
Jun Gao
Keyword(s):  
Transverse Momentum ◽  
Neutral Current ◽  
Data Sets ◽  
Leading Order ◽  
Missing Transverse Momentum ◽  
Upper Limit ◽  
Theoretical Predictions ◽  
Parton Showering ◽  
Single Jet

Abstract The possible non-standard interactions (NSIs) of neutrinos with matter plays important role in the global determination of neutrino properties. In our study we select various data sets from LHC measurements at 13 TeV with integrated luminosities of 35 ∼ 139 fb−1, including production of a single jet, photon, W/Z boson, or charged lepton accompanied with large missing transverse momentum. We derive constraints on neutral-current NSIs with quarks imposed by different data sets in a framework of either effective operators or simplified Z′ models. We use theoretical predictions of productions induced by NSIs at next-to-leading order in QCD matched with parton showering which stabilize the theory predictions and result in more robust constraints. In a simplified Z′ model we obtain a 95% CLs upper limit on the conventional NSI strength ϵ of 0.042 and 0.0028 for a Z′ mass of 0.2 and 2 TeV respectively. We also discuss possible improvements from future runs of LHC with higher luminosities.

scholarly journals Evaluation of hydrological and cryospheric angular momentum estimates based on GRACE, GRACE-FO and SLR data for their contributions to polar motion excitation

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Justyna Śliwińska ◽  
Jolanta Nastula ◽  
Małgorzata Wińska
Keyword(s):  
Angular Momentum ◽  
Spherical Harmonic ◽  
Polar Motion ◽  
Spectral Band ◽  
Water Storage ◽  
Terrestrial Water Storage ◽  
Terrestrial Water ◽  
High Consistency ◽  
Polar Motion Excitation

AbstractIn geodesy, a key application of data from the Gravity Recovery and Climate Experiment (GRACE), GRACE Follow-On (GRACE-FO), and Satellite Laser Ranging (SLR) is an interpretation of changes in polar motion excitation due to variations in the Earth’s surficial fluids, especially in the continental water, snow, and ice. Such impacts are usually examined by computing hydrological and cryospheric polar motion excitation (hydrological and cryospheric angular momentum, HAM/CAM). Three types of GRACE and GRACE-FO data can be used to determine HAM/CAM, namely degree-2 order-1 spherical harmonic coefficients of geopotential, gridded terrestrial water storage anomalies computed from spherical harmonic coefficients, and terrestrial water storage anomalies obtained from mascon solutions. This study compares HAM/CAM computed from these three kinds of gravimetric data. A comparison of GRACE-based excitation series with HAM/CAM obtained from SLR is also provided. A validation of different HAM/CAM estimates is conducted here using the so-called geodetic residual time series (GAO), which describes the hydrological and cryospheric signal in the observed polar motion excitation. Our analysis of GRACE mission data indicates that the use of mascon solutions provides higher consistency between HAM/CAM and GAO than the use of other datasets, especially in the seasonal spectral band. These conclusions are confirmed by the results obtained for data from first 2 years of GRACE-FO. Overall, after 2 years from the start of GRACE-FO, the high consistency between HAM/CAM and GAO that was achieved during the best GRACE period has not yet been repeated. However, it should be remembered that with the systematic appearance of subsequent GRACE-FO observations, this quality can be expected to increase. SLR data can be used for determination of HAM/CAM to fill the one-year-long data gap between the end of GRACE and the start of the GRACE-FO mission. In addition, SLR series could be particularly useful in determination of HAM/CAM in the non-seasonal spectral band. Despite its low seasonal amplitudes, SLR-based HAM/CAM provides high phase consistency with GAO for annual and semiannual oscillation.

Archiving of Food Samples from Restaurants and Caterers—Quantitative Profiling of Outbreaks of Foodborne Salmonellosis in Japan

2004 ◽  
Vol 67 (9) ◽  
pp. 2024-2032 ◽  
Author(s):  
FUMIKO KASUGA ◽  
MASAMITSU HIROTA ◽  
MASAMICHI WADA ◽  
TOSHIHIKO YUNOKAWA ◽  
HAJIME TOYOFUKU ◽  
...  
Keyword(s):  
Dose Response ◽  
Storage System ◽  
Epidemiological Data ◽  
Food Samples ◽  
Food Storage ◽  
Disease Rate ◽  
Data Sets ◽  
Response Data ◽  
Quantitative Profiling

The Ministry of Health, Labor and Welfare (former MHW) of Japan issued a Directive in 1997 advising restaurants and caterers to freeze portions of both raw food and cooked dishes for at least 2 weeks. This system has been useful for determining vehicle foods at outbreaks. Enumeration of bacteria in samples of stored food provide data about pathogen concentrations in the implicated food. Data on Salmonella concentrations in vehicle foods associated with salmonellosis outbreaks were collected in Japan between 1989 and 1998. The 39 outbreaks that occurred during this period were categorized by the settings where the outbreaks took place, and epidemiological data from each outbreak were summarized. Characteristics of outbreak groups were analyzed and compared. The effect of new food-storage system on determination of bacterial concentration was evaluated. Freezing and nonfreezing conditions prior to microbial examination were compared in the dose-response relationship. Data from outbreaks in which implicated foods had been kept frozen suggested apparent correlation between the Salmonella dose ingested and the disease rate. Combined with results of epidemiological investigation, quantitative data from the ingested pathogen could provide complete dose-response data sets.

A Reliability-Based Approach to Assess Fatigue Behaviour Based on Small Incomplete Data Sets

2008 ◽  
Vol 44-46 ◽  
pp. 871-878 ◽  
Author(s):  
Chu Yang Luo ◽  
Jun Jiang Xiong ◽  
R.A. Shenoi
Keyword(s):  
Incomplete Data ◽  
Standard Procedure ◽  
Fatigue Behaviour ◽  
Fatigue Tests ◽  
Small Sample ◽  
Data Sets ◽  
Safe Life ◽  
A New Technique ◽  
And Performance

This paper outlines a new technique to address the paucity of data in determining fatigue life and performance based on reliability concepts. Two new randomized models are presented for estimating the safe life and pS-N curve, by using the standard procedure for statistical analysis and dealing with small sample numbers of incomplete data. The confidence level formulations for the safe and p-S-N curve are also given. The concepts are then applied for the determination of the safe life and p-S-N curve. Two sets of fatigue tests for the safe life and p-S-N curve are conducted to validate the presented method, demonstrating the practical use of the proposed technique.

scholarly journals LOWER BOUNDS OF CHARACTERISTIC SCALE OF TOPOLOGICAL MODIFICATION OF THE NEWTONIAN GRAVITATION

2012 ◽  
Vol 21 (05) ◽  
pp. 1250048
Author(s):  
L. IORIO
Keyword(s):  
Semimajor Axis ◽  
Data Sets ◽  
Orbital Elements ◽  
Dynamical Models ◽  
Spatial Direction ◽  
Newtonian Gravitation ◽  
Complementary Approach ◽  
Local Modification

We analytically work out the long-term orbital perturbations induced by the leading order of perturbing potential arising from the local modification of the Newton's inverse square law due to a topology ℝ2 × 𝕊1 with a compactified dimension of radius R recently proposed by Floratos and Leontaris. We neither restrict to any specific spatial direction [Formula: see text] for the asymmetry axis nor to particular orbital configurations of the test particle. Thus, our results are quite general. Nonvanishing long-term variations occur for all the usual osculating Keplerian orbital elements, apart from the semimajor axis which is left unaffected. By using recent improvements in the determination of the orbital motion of Saturn from Cassini data, we preliminarily inferred R ≳ 4-6 kau . As a complementary approach, the putative topological effects should be explicitly modeled and solved-for with a modified version of the ephemerides dynamical models with which the same data sets should be reprocessed.

scholarly journals The seven sisters DANCe

2018 ◽  
Vol 612 ◽  
pp. A70 ◽  
Author(s):  
J. Olivares ◽  
E. Moraux ◽  
L. M. Sarro ◽  
H. Bouy ◽  
A. Berihuete ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Model Comparison ◽  
Precise Determination ◽  
Model Parameters ◽  
Data Sets ◽  
Adequate Model ◽  
Comparison Results ◽  
Bayesian Evidence ◽  
Mass Segregation

Context. Membership analyses of the DANCe and Tycho + DANCe data sets provide the largest and least contaminated sample of Pleiades candidate members to date. Aims. We aim at reassessing the different proposals for the number surface density of the Pleiades in the light of the new and most complete list of candidate members, and inferring the parameters of the most adequate model. Methods. We compute the Bayesian evidence and Bayes Factors for variations of the classical radial models. These include elliptical symmetry, and luminosity segregation. As a by-product of the model comparison, we obtain posterior distributions for each set of model parameters. Results. We find that the model comparison results depend on the spatial extent of the region used for the analysis. For a circle of 11.5 parsecs around the cluster centre (the most homogeneous and complete region), we find no compelling reason to abandon King’s model, although the Generalised King model introduced here has slightly better fitting properties. Furthermore, we find strong evidence against radially symmetric models when compared to the elliptic extensions. Finally, we find that including mass segregation in the form of luminosity segregation in the J band is strongly supported in all our models. Conclusions. We have put the question of the projected spatial distribution of the Pleiades cluster on a solid probabilistic framework, and inferred its properties using the most exhaustive and least contaminated list of Pleiades candidate members available to date. Our results suggest however that this sample may still lack about 20% of the expected number of cluster members. Therefore, this study should be revised when the completeness and homogeneity of the data can be extended beyond the 11.5 parsecs limit. Such a study will allow for more precise determination of the Pleiades spatial distribution, its tidal radius, ellipticity, number of objects and total mass.

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