On Key Technologies Of Data Processing For Air-sea Gravity Surveys

Sea and airborne gravimetries are two principal means to obtain Earth’s gravity field information. Data analysis and processing is an indispensable component of sea and airborne gravity surveys. With the aim of meeting the requirements of the department for guiding sea and airborne gravity surveys, based on previous studies, this thesis pays its attention to the analysis and investigation, research and study, experimental verification, mainly around several key technologies in the data processing of sea and airborne gravity measurements, such as precision positioning of motion carrier, dynamic environment effect corrections, data filtering, error analysis and accuracy assessment, downward continuation of airborne gravity data, multi-source data fusion, and so on. The main works, conclusions and contributions are summarized as follows.1. After a brief introduction to the background of this study, an overview of domestic and international developments and applications in sea and airborne gravimetries is given. The research progresses of data processing theory and method for sea and airborne gravity measurements are summarized and the problems to be resolved are pointed out And it is clear what should be focused on in this study.2. The observation models of sea and airborne gravimetries are studied. After a brief introduction to the space-time datum and their conversion methods involved in sea and airborne gravimetries, the basic principles and calculation models of differential GPS positioning (DGPS) and precise point positioning (PPP) techniques are described. Based on Newton’s second law of motion, the observation equations of sea and airborne vector and scalar gravimetries are derived respectively. The precision correction models of dynamic environmental effects are established one by one for the gravity measurements from L&R air-sea gravimeter. And the technical characteristics, suitable conditions and applicable scope of various computational models are analyzed and compared. The purpose is to lay the necessary theoretical foundation for the follow-up study.(1) The errors and omissions made by many scholars at home and abroad in their uses of different former and existing formulas of Eotvos corrections for airborne gravimetry are discovered and pointed out. A numeral comparison between the different formulas is accomplished. It is shown that the misuse of Eotvos correction formula can result in a calculation error of1～2mGal. The problems caused by the use of approximate formulas by our country’s scholars are pointed out, particularly. And the necessity of using rigorous formulas is emphasized. The above works provide a reliable theoretical support to uniform operation standards and for the next revision of existing rules for operations of airborne gravimetry. (2) The equivalence is proved theoretically among the three horizontal acceleration correction models recommended to use internationally, in a certain approximation. The performances of the three models are tested and compared using real data from airborne gravity survey. It is shown that the systematic differences of calculation results from two different forms of model can be up to1～2mGal, even larger due to the reasons of filtering. It cannot be ignored apparently.3. The technology of precision positioning of motion carrier for sea and airborne gravity surveys is studied. The choice of models is discussed for GPS PPP and three different models are analyzed and compared. The strategies of determining error corrections for corresponding positioning models are suggested. The solution methods of PPP models are investigated. And Kalman filtering and least squares parameter estimation methods are analyzed and compared. A recursive least squares estimation method is proposed by classifying the estimated parameters, which can significantly improve the computational efficiency. The methods of determining carrier velocity and acceleration using PPP technique are studied. And the calculation models of carrier velocity and acceleration are derived. A robust least squares estimation method is proposed to solve the velocity model. Then the acceleration of the carrier is determined by the differential velocity information. We focus our attention on the validity verification of determining the carrier motion parameters using PPP technique. First, two kinds of numerical calculation and analysis of PPP models are carried out using real data from sea and airborne gravity surveys. The results show that, based on robust least-squares estimation, the accuracies of velocity using PPP technique are superior to0.5cm/s in the horizontal and vertical directions, which completely meet the requirements of sea and airborne gravity surveys. The performances of the developed methodologies are further tested and compared using data acquired in the test of5air-sea gravimeters belong to4different types equipped onboard an aircraft. The differences of observations at surveying line network crossover points are used to assess PPP solutions. It is shown that the conformity of intersection gravity observations obtained by PPP solutions are almost the same with the results from DGPS mode. The differences of RMS between the two solutions do not exceed0.3mGal. They are at the same accuracy level. This indicates that the applications of PPP technique in sea and airborne gravity surveys are feasible and effective.4. The technology of air-sea gravity data filtering is studied. The matching relations of gravity data spatial resolution and low-pass filter cutoff frequency, flying or navigation speed and measurement accuracy are researched and analyzed. The spectrum analysis is made for various items of observation and correction using real data, respectively. And the spectrum window of valid information from air-sea gravity data is determined. It provides an important theoretical basis to solve the matching problem of filter design parameters. The design principles and operational models of low-pass differential filter are described for determining the vertical acceleration of carrier. A lot of numerical analysis are made with real data to verify the calculation results from various types of differentiator. It is shown that a simple form of two central differentiator can meet the accuracy requirements of air-sea gravity data processing.5. The technologies of error processing and accuracy assessment for air-sea gravity measurements are studied. A more comprehensive analysis and summary is made to the error sources of air-sea gravity measurements from nine aspects, such as the inherent characteristics of instrument, environmental effects, data processing strategy, external device conditions, and so on. The evaluation formulae of internal and external coincidence accuracy are given for air-sea gravity measurements. A new formula for multi-line overlapping measurements in air-sea gravity surveys is derived. The adjustment methods for air-sea gravity survey line networks are developed. And an adjusted model is proposed to compensate the CC effect correction for L&R air-sea gravimeter.(1) Through theoretical analysis and deduction, we find and point out an error in the existing formulas of accuracy evaluation for multi-line overlapping measurements in air-seea gravity surveys. And then a new set of accuracy evaluation formula with a unified form is put forward. The validity of the new formulae is tested using real data. When the number of repeated survey lines is2, the accuracy estimate from the existing formula is-(2) times less than the result from the new formula. The relative error is more than40%. So it cannot be ignored.(2) On the basis of a detailed analysis on the earlier integral adjustment of surveying line network, the recent self-calibration adjustment and other compensation methods, we breakthrough the traditional research ideas, in which the compensations of system errors in air-sea gravity surveys can be fulfilled only during the adjustment, and propose a method of two steps processing based on the theory of posteriori error compensation. The compensations of system errors are decomposed into crossover point condition adjustment, surveying line filtering and estimation, in which error compensations are fulfilled during the adjustment and after the adjustment step by step. The new method not only greatly simplifies the calculation process of gravity survey line network adjustment, but also effectively improves the stability and reliability of adjustment solutions.(3) For the reason that the current calculation model of CC effect correction supplied by the instrument manufacturer is not perfect, based on the basic principle that gravity observations has nothing to do with the motion state of carrier, and the modern theory of correlation analysis, an adjusted model of CC effect correction coefficients is constructed for L&R air-sea gravimeter. On this basis, it is suggested that the two-step processing method above be used to compensate the combined effects of various types of residual error. Thus all the steps above have made up a complete technology system of error processing for air-sea gravity measurements, which covers different stages of error compensations, including the ones before adjustment, during adjustment and after adjustment.6. The downward continuation technology of airborne gravity survey data is studied. After a brief introduction to the inverse problem, ill-posedness and regularization method, regularization of inverse Poisson integral is researched and improved. Two new methods of downward continuation are proposed, one is for sea surveying areas, in which the continuation corrections are calculated using ultra-high order gravity field model, the other is for land surveying areas, in which the continuation corrections are calculated by the joint uses of ultra-high gravity field models and terrain elevation information.(1) Using the singular value decomposition (SVD) method, the ill-posedness of traditional downward continuation model of inverse Poisson integral is analyzed. And the causes of instability by the downward continuation are pointed out. The truncated singular value (TSVD) regularization method is proposed to solve the downward continuation model of inverse Poisson integral, and the generalized cross-validation (GCV) criteria is used for selecting regularization parameters.(2) Taking into account the fact that there are still some degree of uncertainties in practice uses of existing downward continuation methods, including regularization method, we propose a new idea for downward continuation, which is based on external data sources and independent of observational data. According to the relatively flat change characteristics of marine gravity field, two methods is proposed to calculate the continuation corrections. In the first method, the continuation corrections are calculated by using the upward continuation of satellite gravity data, and in the other one, by using ultra-high order gravity field model. The notable features of the new idea are:the solving process avoids cleverly the inherent instability problem caused from the traditional method of solving the inverse Poisson integral, the solution accuracies are no longer dependent on the noise level of airborne gravity observation data, it effectively simplifies the calculation process and solving difficulty of downward continuation, and improves the solution accuracies. At the same time, the theoretical calculation accuracy using the new models is evaluated quantitatively. A satellite gravity data set, two sea-borne gravity data sets and an airborne gravity data set are used to accomplish actual numerical calculations and accuracy assessments. When the downward continuation height is5km, the theoretical estimated accuracy of the new models is better than4mGal, the external coincidence accuracy is better than2mGal.(3) Due to the fact that it is also difficult for ultra-high order gravity field model to fit the actual gravity field in land portions where the terrain changes are complicated, we continue using the new idea above and expand the downward continuation method used at sea to land portions. A new method is proposed to calculate the downward continuation corrections by joint uses of ultra-high order gravity field model and terrain information. The differential of local terrain corrections on flying height and corresponding ground points is added to the continuation correction from geopotential mdel, and it makes up the total continuation correction. The uniqueness of the new method is completely avoiding the drawbacks of traditional methods. It is to use ultra-high order gravity field model firstly to restore the long-wave part of continuation corrections, and then the terrain information to restore the high frequency components of ground gravity field, and it is ultimately realized to continue airborne gravity measurement data to the ground in full frequency extension. The continuation calculation in the new method can be carried out point-by-point for different flying heights. It is not necessary to pretreat observational data for a normalized height, gridding, eliminating edge effects and so on. It provides not only a reliable solution, but also a quick and easy solving process.7. The multi-source data fusion technologies of the Earth’s gravity field observations are studied. After a briefly analysis and summary on the technical characteristics of multi-source gravity data in sea surveying areas, a regularized least squares collocation (RLSC) model and a regularized point-mass (RPM) model are constructed for multi-source gravity data fusion processing, respectively. And an analytical fusion method is developed finally.(1) An analysis is made on the ill-posedness of traditional least squares collocation (TLSC) model. The Tikhonov regularization method is introduced to transform TLSC model. And then a RLSC model is established. A sea-borne gravity data set and an airborne gravity data set simulated by using EGM2008model are used to test the performances of the developed model. When the observation errors taken to be3mGal, the internal coincidence accuracy is4.12mGal for the fusion processing of airborne gravity data at5km altitude and the gravity data at ground.(2) Making a joint uses of the Tikhonov regularization method and the remove-restore technique, a regularized transformation is made to the traditional point-mass (TPM) model. And a corresponding RPM model is constructed. A sea-borne gravity data set and an airborne gravity data set simulated using EGM2008model are used to test the performances of the modified model. When the observation errors taken to be3mGal, the internal coincidence accuracy is3.71mGal for the fusion processing of airborne gravity data at5km altitude and the gravity data at ground.(3) The inherent relations and differences of statistics and analytical method for data fusion are analyzed and discussed. Especially for same kind of multi-source gravity data (refer to the gravity anomalies unified to the ground) fusion problem (here called the pure gravity data fusion problem), a pure analytical method is proposed for multi-source gravity data fusion. According to the heterogeneous characteristics of the gravity data obtained by different means, two new fusion processing models are established. The first one is called one-step fusion processing model where an interpolation formula is used to grid the multi-source gravity data with double weight factor. And the other one is called multi-step fusion processing model where the data management procedure is modified to a four steps processing based on the theories of adjustment, filtering, prediction and interpolation. A practical marine gravity measurements set and a satellite gravity data set are used as a case study to prove the efficiency of the two analytical data fusion processing models.8. In order to meet the requirements of the department for guiding sea and airborne gravity surveys, based on the studies on the key technologies in data processing above, an operation and data processing software system for sea and airborne gravity survey is designed synthetically and developed by optimizing and improving the existing operation and data processing software platform for marine gravity survey, through complementing and expanding the demand for airborne gravimetry, by which all the functions covering the whole processes of sea and airborne gravity surveys can be realized, from the designs before survey, navigation and positioning, information collection to data analysis and processing, making result maps and product output.