Theories And Methods For Determining Regional Gravity Field Model From Airborne Vector Gravimetry

Research on earth gravity field is one of the core missions of geodesy. With the development of global navigation system, airborne gravimetry has become a main and effective approach to determine earth's gravity information in the part of short and midium wavelength, and is also a complement to ground gravimetry, marine gravimetry and satellite gravimetry. Airborne gravimetry can be used to fill gravity data gaps where ground gravimetry has no access. Accuracy and resolution of gravity data, local gravity field and regional geoid determination, development of national economicy and military, construction of national defense, as well as relative earth sciences such as geophysics, oceanography, geodynamics and resource exploration, would all benefit from airborne gravimetry.Developed countries, such as United States, Canada, Denmark, have taken the lead in the research of airborne gravimetry, and a lot of flight tests have been done. Further more, Chinese airborne gravimetry system CHAGS has been developed successfully in2002. Numerous studies have proved that airborne scalar gravity data has a accuracy of1-3mGal on the scale of5-10km, it also means that airborne scalar gravimetry has reached a mature stage. Airborne vector gravimetry can not only get the values of the scalar gravity (the vertical component of the gravity vector), but can also measure the horizontal components of the gravity vector, and thus is currently one of the hot areas of geodesy. And so far there is no airborne vector gravimetry system in our country, and data processing of vector gravimetry is still in its infancy. Under the background of all scientific research about airborne gravimetry, the theories and methods to determine regional gravity field from airbone vector gravimetry data are studied in this dissertation, software packages for data processing of airbone vector gravimetry are developed, which is of great scientific significance and application value for the development of China's airborne vector gravimetry.The main work and contributions in the dissertation are as follows:(1) Stokes integral, Hotine integral and Possion integral are composed of near-zone contribution and far-zone contribution, and the key problem of computing far-zone contribution is how to solve kernel functions'truncation coefficients. Based on the universal formula of truncation coefficients, variable step-size Guass integral method for truncation coefficients is introduced. Since there are recursion methods of Stokes truncation coefficients and Hotine standard kernel fuction's truncation coefficients, the effectiveness of integral method is verified by comparing the results computed by the new algorithm and recursion methods.(2) Based on the researches of Jekeli(1979) and Li(1989), recursion algorithm for the modified Hotine kernel(series expand from2th degree) was implemented. By comparing the results from recursion method and those from variable step-size Guass integral, the correctness of the recursion algorithm is verified.(3) Two FIR lowpass digital filters are designed for airborne vector gravimetry using window function method and Chebyshev approximation method. Firstly, simulated height information is used to test the performance of the filters and secondly GPS static positioning data is processed by these two filters, during data processing phase delay and data cutoff is discussed explicitly. The conclusions are as follows:(a) With the same design parameters, Chebyshev approximation method gets better results than window function method;(b) The accuracies of the accelerations derived from GPS static positioning data are about±1-2mGal on vertical direction and better than±1mGal on horizontal directions when Chebyshev approximation method is used.(4) Data reduction methods for airborne vector gravimetry are studied, including reducing raw gravity observations along survey lines to average height level, compensating system errors by two-step crossover adjustment and gridding gravity data using weighted average (WA) method and Shepard surface fitting (SSF) method. In view of the horizontal components, simulated data is generated to verify the average-height-level reduction method, it turns out that the degrees and orders are of great importance among the elements that affect the accuracies of reduction, and that high order part of the reference model has more influence upon reduction accuracies than low degree part. When coming to vertical component, EN01data block released by NGS is processed according to the scheme, outputting5'x5'grid gravity disturbances covering a region of2°x3°with geodetic height6200m. Compared to reference values computed by EGM2008at the same locations, the accuracies of the output data from WA and SSF are±1.59mGal and±1.36mGal.(5) In the frame of Helmert's2nd condensation, formulae for band-limited topographical effect of airborne vector gravity observations and geoid undulations based on series-expanded Newton's kernel are studied, as well as those of topograhical effect based on analytical Newton's kernel, and formulae for band-limited topographical effect of horizotal components are deduced. Using a3"x3" digital elevation model, topographical effects are computed based on the analytical kernel along selected flight lines in western area of China with flight height of4000m, these values are processed by low-pass filter and compared to values computed using the band-limited formulae. It turns out that both topographical effects have a good consistence, the rms of differences between topographical effects on gravity vector and geoid is better than2.5mGal and3cm, then band-limted formulae can be used for topography reduction of airborne vector gravity data.(6) For vectical components of gravity disturbance vector, the formulae of inverse Possion integral, iteration method and analytical continuation by FFT are given in the spectral domain. Vectical components at flight level simulated from EGM2008are downward continued to geoid level using these method. A conclusion is reached that inverse Possion integral with Wiener filter is the stablest and the most reliable among three of all.(7) when coming to horizontal component of gravity disturbance vector, downward continuation using Input-output System is developed. The continued results of Single-input Single-output System and Double-input Single-output System are compared when the standard deviations of white noise are1.5mGal and6mGal respectively, it turns out that stable downward continuation of high precision horizontal components can be realized using both methods, that of lower precision horizontal components can only be realized using Double-input Single-output system.(8) Profile integration of relative geoid determination from horizontal components of gravity vector data is studied. Horizontal components at flight height of2km,3km,4km and5km are simulated using EGM2008and contamined by Gaussian white noise. When the standard deviation of the white noise is6mGal, the accuracies of relative geoid model is about10cm, at some points geoid errors can be up to40cm, and when the standard deviation of the white noise is1.5mGal, the accuracies of relative geoid model rise to3.31cm,4.79cm,5.16cm,5.64cm, which implies that a high-precision geoid can be determined from horizontal componts with less noise.(9) One-step method for geoid determination from vertical component of gravity data is studied. For vertical components at flight height of2km,3km,4km and5km simulated using EGM2008and contamined by Gaussian white noise with standard deviation of1.5mGal, the accuracies of regional geoid model obtained from one-step method are5.08cm,5.64cm,6.23cm,6.54cm.(10) When coming to geoid determination from all three components of gravity vector data, data fusion is realized using input-output system, the output of data fusion is vertical components in the air, then geoid is determined by one-step integration method. The precision of geoid is analyzed when the noise level of vertical components is1.5mGal, while the the noise levels of horizontal components are1.5mGal,3mGal, and6mGal respectively, at the flight height of2km to5km. Conclusions are drawed as follows:(a) when the precision of horizontal components is much lower than that of vertical components, the geoid can't be improved;(b) when the noise levels of all three components are nearly the same, the accuracies of the geoid are4.32cm,4.90cm,5.41cm,5.88cm at the flight height of2km to5km respectively, which are slightly better than those from vertical components only.