航空重力测量数学模型及其测量精度分析

基于数学和分析力学角度分别推导了航空矢量重力测量的数学模型,得到了一致的模型公式;给出了矢量模型的3个分量形式,其中垂直方向的分量就是标量重力测量的数学模型;简要介绍了我国研制成功的航空标量重力测量系统CHAGS的数据处理的过程,分析了标量重力测量中测线交叉点和重复测线的重力异常的精度;根据实测数据计算的结果表明:测线交叉点重力异常不符值的标准差约为5×10-5ms-2左右,重复测线的内符合精度优于5×10-5ms-2,达到了预期的要求。     

Optimal Model for Geoid Determination from Airborne Gravity

Two different approaches for transformation of airborne gravity disturbances, derived from gravity observations at low-elevation flying platforms, into geoidal undulations are formulated, tested and discussed in this contribution. Their mathematical models are based on Green's integral equations. They are in these two approaches defined at two different levels and also applied in a mutually reversed order. While one of these approaches corresponds to the classical method commonly applied in processing of ground gravity data, the other approach represents a new method for processing of gravity data in geoid determination that is unique to airborne gravimetry. Although theoretically equivalent in the continuous sense, both approaches are tested numerically for possible numerical advantages, especially due to the inverse of discretized Fredholm's integral equation of the first kind applied on different data. High-frequency synthetic gravity data burdened by the 2-mGal random noise, that are expected from current airborne gravity systems, are used for numerical testing. The results show that both approaches can deliver for the given data a comparable cm-level accuracy of the geoidal undulations. The new approach has, however, significantly higher computational efficiency. It would be thus recommended for real life geoid computations. Additional errors related to regularization of gravity data and the geoid, and to accuracy of the reference field, that would further deteriorate the quality of estimated geoidal undulations, are not considered in this study.     

卫星测高问题的球谐级数解法

研究了球界面下卫星测高问题的解法，利用有限逼近方法得到了下列结论：若陆地部分是球冠，则卫星测高问题的解可以转换成关于球谐级数位系统的线性方程组。同时证明了常用的Stokes问题、Dirichlet问题、Neumann问题可以看成卫星测高问题的特殊情况。     

Gravity changes and present-day dynamics of the island of Pantelleria (Sicily Channel—Italy)

The island of Pantelleria is an active volcano located in the Sicily Channel (southern Italy), occurring in the middle of a continental rift system.Since the 1980's the island has been periodically surveyed by means of geodetic and geophysical methods to monitor the regional and local volcanic dynamics. Also, high-precision gravity measurements were started in 1990.The present paper is an analysis of the time-space gravity changes. Gravity measurements were carried out on a network presently formed by twenty stations. The gravity network was fully surveyed in June 1990 and June 1995 and partially surveyed in September 1993. Two absolute gravity stations were established in 1993 to provide a reference system and to check for long-term variations.The areal distribution of the gravity changes during the 1990–1995 time interval, obtained in the thirteen stations of the 1990 network, is strongly similar to the Bouguer anomaly field and to the large-scale features of the basement of the island. Otherwise, gravity changes are directly correlated with the Bouguer anomaly and inversely correlated with the altimetric variations. Comparison with the geological setting suggests that the present activity may be ascribed to the influence of the geodynamics of the Sicily Channel.     

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捷联式海洋重力数据的小波阈值滤波

基于捷联式海洋重力测量数据,对比不同小波、阈值及施加方式对滤波效果的影响。结果表明,db6、db7、db8、db9、db10、sym6、sym7、sym8、sym9、sym10、coif3、coif4和coif5小波较适用于海洋重力测量,小波分解层次可取至8层或9层,采用史坦无偏风险阈值滤波效果较好;小波分解至第8、9层时,阈值滤波结果与截止频率为0.005 Hz和0.003 3 Hz的Butterworth低通滤波器的滤波结果吻合较好,但小波阈值滤波结果更加平滑,两者差值的RMSE在0.25 mGal以内,且小波阈值滤波更容易分解出噪声成分,可以更有效地消除重力畸变。     

捷联式航空重力扰动矢量解算及误差补偿

介绍捷联式航空重力矢量测量的基本原理,利用波数相关滤波（WCF）、比力线性校正的方法对重力扰动的水平和垂向分量进行误差补偿,评定内符合精度。对国产捷联式航空重力矢量仪的某次试验数据进行处理,以验证和评估航空重力矢量仪的性能。结果表明,在半波长分辨率为7.5 km时,6条重复测线的重力扰动水平分量经波数相关滤波处理后,东、北向分量的平均内符合精度分别从9.77 mGal、9.18 mGal提高到5.95 mGal、3.83 mGal;对比力的垂向分量线性校正后,将解算的重力扰动垂向分量再用WCF方法处理,其平均内符合精度从1.27 mGal提高到0.59 mGal。     

用重复重力测量测定垂线偏差时变的精度

列举两种垂线偏差时变测定的微分公式,从理论上对用重复重力测量的方法测定垂线偏差时变的精度进行了探讨．在目前情况下,垂线偏差时变测定精度可以达到0．005＂．远区域的点对它的影响可以忽略不计,通过对重力网的模拟计算,进一步得到验证．探讨了有效积分半径对垂线偏差时变测量精度的影响,并在此基础上讨论了重力网优化的问题．