Study On The Recovery Of Gravitational Potential Model With Dynamical Method

With the application of satellite gravimetry, static as well as time-variant information of middle and long wavelength gravity field of the Earth can be fast acquired, which has made satellite gravimetry one high-tech tool in the research of geophysics, geodesy and oceanography. Therefore, the recovery of the Earth's gravity field using satellite techniques has become a hot issue for the research of geodesy in recent years. Dynamic method is one of the earliest applied methods for the recovery of the Earth's gravity field. The earliest and current widely used gravity field models were mostly acquired using the Dynamic method. With the successful implementation of satellite gravity missions like CHAMP, GRACE, some new methods, say, the Energy method, etc., attract more attention, however the Dynamic method is still one basic method that plays an important role. The dissertation covered the principle of the recovery of the Earth's gravity field using the Dynamic method with new types of observations, discussed the characteristics of satellite gravimetry observations and made practical computations using CHAMP data. At the same time, due to the enormous increasing of satellite gravimetry observations, there are more and more gravity field models of the Earth that were established by a lot of research institutions. The models make less difference when compared with real ground gravity observations, but their coefficients differs a lot, especially the higher degree, for which the inter-difference reaches 30%-100% of the coefficient itself and some to a higher extent. Therefore, the stability problem of gravity field model coefficients arises. From the fundamental of related contemporary sciences, the dissertation studied the recovery of the Earth's gravity field using the Dynamic method.The main work is as follows:1. The basic theory for satellite gravimetry was systematically presented. Perturbing forces that affect satellite gravimetry were categorized and discussed in detail and practical formulae were also presented.2. The effect of the Earth center movement on satellite orbit was studied using numerical methods.3. The spherical harmonic expressions of gravitational potential within the Earth Fixed System was provided. For the practical computations of satellite gravity, the expressions of gravity potential, gravity vector and gravity gradient tensor were also provided.4. The features of the Earth's gravity potential as well as the physical meanings of lower-degree coefficients were discussed. Power spectral constraint of the gravity field was also analyzed. The influence of the arrangement of gravity potential model coefficients on the structure of normal equations was analyzed, from which the optimal arrangement of model coefficients was determined that can be applied in satellite gravity solution.5. Precise Orbit Determination (POD) using the Dynamic method was researched, in which the partial derivatives for different observations were obtained. The specific math model and procedure for the Earth's gravity field solution were presented aiming at SST-HL and SST-LL model in current satellite gravimetry.6. Data of space-borne accelerometer as orbit of CHAMP were analyzed, along with the a priori gravity field model and integral arc length. Based on CHAMP data, practical computations were made, from which gravity field model G-Model S1(up to 50 degree) was derived. And then the model was assessed by making comparisons in computing gravity field elements with four models, i.e. GGM02S, DQM2000d, UGM05 and EGM2008.7. When used as constants, the gravity field model coefficients have certain physical meanings, which were analyzed in the dissertation. Based on the physical meanings of model coefficients, the expression of model coefficients in terms of point masses was presented, and the relation between C n 0, C nk ,S nk and the global mass integral was analyzed.8. C n 0, C nk ,S nk were studied based on the characteristics of zonal harmonics. From the analysis, different C n0 is totally insensitive to the mass layer and mass variation of n latitudes, and when n??, C n0 converges to the integral or inter-difference that includes two polar masses. Due to the infinitesimally small value, approximately C n0?0 can be taken. Similar points holds for coefficients C nk ,S nk.9. From the principle of the Theory of Relativity, the problem that gravity field recovery using the Dynamic method encounters was qualitatively analyzed. According to the Generalized Theory of Relativity, the Earth's gravity field model of Newton gravitational potential that people are used to is the subtle description of the gravitational field within 3-D Cartesian system; however, it is the approximation of the curved space that surrounds the Earth. Due to the different scale, the limit mean accuracy reaches 10-9 for the geoid computed at the mean radius of the Earth using the Earth's gravity field model that is solved with no post-Newton effect taken into account.10. The nature of the near integrable nonlinear dynamic system as well as its internal randomness was discussed from the viewpoint of the Chaos Theory. The randomness manifests that there exist bias between coefficients of different gravity field models, but the total accuracy between different models make less difference.