测绘学报

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航空重力向下延拓病态问题的求解

蒋涛1,李建成2,王正涛1,张守建3   

  1. 1. 武汉大学测绘学院
    2. 武汉大学 测绘学院
    3. 武汉大学
  • 收稿日期:2010-11-01 修回日期:2011-04-11 出版日期:2011-12-25 发布日期:2011-12-25
  • 通讯作者: 蒋涛

Solution of Ill-posed Problem in Downward Continuation of Airborne Gravity

  • Received:2010-11-01 Revised:2011-04-11 Online:2011-12-25 Published:2011-12-25

摘要: 提出将广义岭估计用于求解航空重力向下延拓病态问题,研究了求解逆Poisson积分问题的3种正则化方法:Tikhonov正则化、岭估计和广义岭估计。利用EGM2008地球位模型设计模拟数值实验,将飞行高度处含白噪声的2.5′×2.5′重力扰动向下延拓至大地水准面上,与参考值作外部检验,全面检验、比较了各向下延拓方法的可靠性、精度和稳定性,数值结果表明基于多个最优正则化参数的广义岭估计在延拓精度、稳定性和抗差性等方面要显著优于基于单个正则化参数的Tikhonov法和岭估计。

Abstract: Generalized ridge estimate was suggested for solving the ill-posed problem in downward continuation (DWC) of airborne gravity, three regularization methods were studied to solve the inverse Poisson problem, which are Tikhonov regularization, ridge estimate and generalized ridge estimate. By conducting a simulated numerical experiment designed based on EGM2008 Earth gravitational model, the 2.5′×2.5′gravity disturbances with white noise at the flight levels were downward continued to the Geoid, the accuracy and stability of the DWC methods were tested and compared, the numerical results show that, in terms of continued accuracy, stability and robustness, the generalized ridge estimate based on multiple optimal regularization parameters performs significantly better than Tikhonov regularization and ridge estimate which based on single regularization parameter.