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Kronometrik Nivelman Yöntemi ile Yüksekliklerin Belirlenmesi
Abstract
Genel Görelilik teorisinin bir sonucu olarak, kütleçkimsel alanlar gözlemci zaman akışını etkilemektedir. Zaman akışının aynı hıza sahip olduğu yüzeyler, Newton potansiyeli ile tariflenen eşpotansiyel yüzey kavramı ile aynı yüzeyleri tarif etmektedir. Eşpotansiyel yüzeyler klasik anlamda uzun yıllardır gravite ve yükseklik ölçmelerine bağlı olarak belirleniyordu.
Yükseklik belirleme için kullanılan geleneksel yöntemler bütünsel açıdan bakıldığında ölçme sonuçlarını etkileyebilecek önemli hata kaynakları barındırmaktadır. Bunlardan biri nokta üzerindeki potansiyel değerlerin doğrudan ölçülememesi nedeni ile yükseklik taşınması ile artan derecelerde hata birikmesidir. Ortalama deniz seviyeleri farklı olarak belirlenen karasal kütleler arasındaki yükseklik entegrasyonunun zorluğu da ayrı bir sorun oluşturmaktadır. Gözlemlerin yatay düzlemde gerçekleşmesi ve arazi zorlukları nedeniyle engebeli arazilerde işgücü, ekipman gücü ve yol uzunluğunun artması ile klasik yöntemlerde büyük zorluklar yaşanabilmektedir. Bu ciddi olumsuzlukları aşabilmek açısından, son yıllarda uydu teknolojileri önde gelen çözümlerden birisi olarak kullanılmaktadır. Fakat son 10 yıldır, temelleri 20. yüzyılın ikinci yarısına dayanan bir yöntem olan kronometrik nivelman, doğrulukları artan saatler ve ağ teknolojilerinin kullanıldığı test gözlemleri sonucunda önemli sonuçlar ortaya koymaya başlamıştır.
Zaman bilgisi atomik saat teknolojilerindeki gelişmeler ile birlikte atomik frekans standardında optik spektrumda yüksek frekansta gözlemler yapılarak artan ölçüde doğruluklarla belirlenebilmektedir. Bugüne kadar kullanılan mikrodalga atom saatlerinin daha düşük düzeydeki doğruluk ve kararlılıklarına karşı 100 kat daha iyileştirilmiş olan optik atomik saatler yükseklik belirlenmesinde yeni bir yöntem olarak kronometrik nivelman yönteminin önünü açmaktadır. Ayrıca fiber iletim teknolojileri ile birlikte optik atomik saat karşılaştırmaları 10−19 mertebelerinde bir hassasiyetle yapılabilmektedir. Yerçekimi ivmesi g≈10 m/s2 ve c≈ 300 000 000 m/s olmak üzere; 1 santimetrelik yükseklik değişimlerinde Δ𝑣𝑣≈10−18 frekans kayması oranı elde edilebilmektedir. Böylece optik atomik saatlerin 1 santimetrelik yükseklik farklarını belirleyebilecek hassasiyette olduğu söylenebilir.
Bu kapsamda, bu tez çalışmasında atom saatleri arasında yapılan frekans karşılaştırmaları neticesinde kütle-çekimsel Doppler etkisi ile ortaya çıkan farktan yararlanılarak potansiyel farkların belirlenmesi konusundaki teorik temellere, yöntemin genel çerçevesine ve güncel atomik saat test ağlarına değinilmektedir.
Bu bağlamda kronometrik nivelman yönteminin teorik temelleri ve güncel çalışmalar incelenmekte, uluslararası yükseklik referans sistemine olabilecek katkıları, sistemin çalışma mekanizmaları ve geoit belirleme yöntemlerine katkıları tartışılmaktadır.
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A new paradigm views the recently launched Gravity Recovery and Climate Experiment (GRACE) follow‐on mission as a gradiometer system, outside the mission's design concept, promising potentially major implications in geosciences. We develop an innovative and straightforward concept, the “GRACE gradiometer mode,” to process future GRACE follow‐on measurements to derive three‐dimensional gravitational gradients. Using positions, accelerations, and attitude measurements from the identical predecessor mission GRACE, we generate common and differential accelerations. We validate GRACE differential accelerations using Gravity field and steady‐state Ocean Circulation Explorer (GOCE) mission gradiometer measurements and we demonstrate an important and promising agreement between GRACE and GOCE. Consequently, we estimate gravitational gradients in full and we confirm their ability to detect geophysical signals over three example regions, namely, the Himalayas, Indonesia, and Canada. Coherence analysis between GOCE and GRACE gradients reveals a strong match that reaches up to 80%. GRACE gradiometer mode gradients are also compared with GRACE level 2‐ derived gradients, and results show that the new method captures smaller spatial‐scale signals than GOCE with the trade‐off being at higher noise level. We argue that future enhancements of the proposed proof‐of‐concept method will expand and enhance the GRACE follow‐on objectives that will lead to new insights, discoveries, and applications in the Earth system and the geosciences.
In this paper we investigate the stability of solutions of difference equation x n+1 = x n−1 x n−4 − 1. We also study periodic solutions of related difference equation especially asymptotic periodicity.
A high-resolution gravimetric quasigeoid model for Vietnam and its surrounding areas was determined based on new gravity data. A set of 29,121 land gravity measurements was used in combination with fill-in data where no gravity data existed. Global Gravity field Models plus Residual Terrain Model effects and gravity field derived from altimetry satellites were used to provide the fill-in information over land and marine areas. A mixed model up to degree/order 719 was used for the removal of the long and medium wavelengths and the calculation of the quasigeoid restore effects. The residual height anomalies have been determined employing the Stokes integral using the Fast Fourier Transform approach and deterministic kernel modification proposed by Wong–Gore, as well as by means of Least-Squares Collocation. The accuracy of the resulting quasigeoid models was evaluated by comparing with height anomalies derived from 812 co-located GNSS/levelling points. Results are very similar; both local quasigeoid models have a standard deviation of 9.7 cm and 50 cm in mean bias when compared to the GNSS/levelling points. This new local quasigeoid model for Vietnam represents a significant improvement over the global models EIGEN-6C4 and EGM2008, which have standard deviations of 19.2 and 29.1 cm, respectively, for this region.
The pursuit of ever more precise measures of time and frequency motivates redefinition of the second in terms of an optical atomic transition. To ensure continuity with the current definition, based on the microwave hyperfine transition in , it is necessary to measure the absolute frequency of candidate optical standards relative to primary cesium references. Armed with independent measurements, a stringent test of optical clocks can be made by comparing ratios of absolute frequency measurements against optical frequency ratios measured via direct optical comparison. Here we measure the transition of using satellite time and frequency transfer to compare the clock frequency to an international collection of national primary and secondary frequency standards. Our measurements consist of 79 runs spanning eight months, yielding the absolute frequency to be 518 295 836 590 863.71(11) Hz and corresponding to a fractional uncertainty of . This absolute frequency measurement, the most accurate reported for any transition, allows us to close the Cs-Yb-Sr-Cs frequency measurement loop at an uncertainty , limited for the first time by the current realization of the second in the International System of Units (SI). Doing so represents a key step towards an optical definition of the SI second, as well as future optical time scales and applications. Furthermore, these high accuracy measurements distributed over eight months are analyzed to tighten the constraints on variation of the electron-to-proton mass ratio, . Taken together with past Yb and Sr absolute frequency measurements, we infer new bounds on the coupling coefficient to gravitational potential of and a drift with respect to time of .
This paper compares the geoid heights from the Global Models-EGM2008, and EGM1996 against the GPS/Levelling-derived geoid heights in Tanzania. For the sake of comparison, the existing Preliminary African Geoid Model (AGP03) and the Tanzania Geoid Model (TZG13) are also tested against the GPS/levelling derived geoid heights at 13 benchmarks selected within the Tanzania Primary Levelling Network (TPLN). The comparisons of geoid heights obtained from these geoid models against the GPS/levelling geoid heights have been performed in absolute sense. Due to the fact that the ellipsoidal heights (h) obtained from the GPS do not provide the actual positions of points on the geoid, the orthometric heights (H) are needed. Broadly speaking, the orthometric heights are obtained through traditional sprit levelling which is a labour intensive work. In order to convert the ellipsoidal height (h) determined from GPS applications to orthometric height, the Geoid heights are needed. The spatial positions of these benchmarks have been recently determined at cm-level accuracy (with respect to ITRF2005) through a GPS campaign. The statistics of the differences between GPS/levelling-derived geoid heights (NGPS) and the corresponding geoid heights obtained from the available three geoid models (Nmodel) suggests that, AGP03 model is the most suitable at this moment. The Root Mean Square (RMS) fit of the AGP03 geoid model against the GPS/levelling data is 53.8 cm, which is a 2 times better fit compared to the Global Geopotential Models (EGM08 and EGM96) in the area of interest. On the other hand, the RMS of the height differences between the TZG13 and the GPS/leveling derived heights was 74.7cm. The study suggests that AGP03 geoid model is closer to the GPS/levelling geoid observations in comparison to EGM08 model in Tanzania.
The frequency stability and uncertainty of the latest generation of optical atomic clocks is now approaching the one part in level. Comparisons between earthbound clocks at rest must account for the relativistic redshift of the clock frequencies, which is proportional to the corresponding gravity (gravitational plus centrifugal) potential difference. For contributions to international timescales, the relativistic redshift correction must be computed with respect to a conventional zero potential value in order to be consistent with the definition of Terrestrial Time. To benefit fully from the uncertainty of the optical clocks, the gravity potential must be determined with an accuracy of about , equivalent to about 0.01 m in height. This contribution focuses on the static part of the gravity field, assuming that temporal variations are accounted for separately by appropriate reductions. Two geodetic approaches are investigated for the derivation of gravity potential values: geometric levelling and the Global Navigation Satellite Systems (GNSS)/geoid approach. Geometric levelling gives potential differences with millimetre uncertainty over shorter distances (several kilometres), but is susceptible to systematic errors at the decimetre level over large distances. The GNSS/geoid approach gives absolute gravity potential values, but with an uncertainty corresponding to about 2 cm in height. For large distances, the GNSS/geoid approach should therefore be better than geometric levelling. This is demonstrated by the results from practical investigations related to three clock sites in Germany and one in France. The estimated uncertainty for the relativistic redshift correction at each site is about .
Cambridge Core - Theoretical Physics and Mathematical Physics - Spacetime and Geometry - by Sean M. Carroll
In this thesis, I show how fundamental geodetic notions can be defined within a general relativistic framework. Among the concepts that are analyzed there are the relativistic gravity potential, the geoid, the normal gravity field and its potential, as well as the genuinely relativistic definition of chronometric height. Moreover, a simple procedure for the operational preservation of a chosen level surface of the relativistic gravity potential is investigated. For all these concepts, the respective Newtonian notions are recovered in the weak-field limit. In the first-order (parametrized) post-Newtonian expansion the results previously published in the literature are obtained and it is shown how they are embedded into the present framework. Magnitudes of leading-order relativistic corrections to the geoid as well as redshift and acceleration measurements are calculated in a simple gravity field model. After the most important geodetic notions are introduced, the theory of General Relativity and the mathematical formalism are briefly discussed. Emphasis lies on some exact solutions to Einstein's vacuum field equation. These spacetimes are used in the following to either estimate relativistic effects or generalize geodetic concepts. Proceeding to a relativistic theory of gravity changes the underlying stage on which all physics takes place. The involved mathematical structure, related to the description of a curved spacetime, causes conventional geodetic notions to become ill-defined in the framework of General Relativity. Here, it is shown how relativistic generalizations of these notions can be constructed, working without any kind of weak-field approximation. The approach is mainly based on a so-called redshift potential of which the level sets foliate a stationary spacetime into isochronometric surfaces. It gives rise to the definition of a relativistic gravity potential which is used intensively. In particular, using a parametrized post-Newtonian spacetime for the Earth, the magnitude of relativistic corrections to the geoid is investigated in a simple Earth model. In the last part, the relation between proper time on the geoid and the defining constant L g in the IAU resolutions is discussed and a consistent relativistic definition for chronometric heights is proposed. Finally, relativistic orbital effects are compared to non-gravitational perturbations of satellite orbits and relativistic gravity gradiometry is investigated to link geodesic deviation to the curvature of spacetime, which is determinable by geodetic measurements.