评估航空重力系统误差及向下延拓的逆泊松半参数方法

摘要

The existing systematic errors processing method of airborne gravity demands external gravity data, but many areas do not have external gravity data.However, semi-parameter model can estimate the systematic errors without external data.Firstly, the systematic errors were modeled by using natural spline function.Then the compensation least squares method was used to estimate the parameter and the natural spline function.The smooth parameter was used to balance them.More importantly, the generalized cross validation method to determine the smooth parameter does not need prior information.Therefore, the semi-parameter model was applied in the inverse Poisson integral to estimate systematic errors and downward continuation in one step.The numerical test results show that the inverse Poisson integral and least square collocation cannot estimate the systematic errors.The regularization method based on the inverse Poisson integral can reduce systematic error effect.The semi-parameter combine inverse Poisson integral model can estimate the systematic errors and improve downward continuation accuracy at the same time without external gravity data.%常用航空重力系统误差事后处理方法需外部重力数据,但很多地区无外部重力数据.研究发现,半参数模型可在无外部数据时估计系统误差.先用自然样条函数为系统误差建模,后用补偿最小二乘法和光滑参数求解,最后用广义交叉核实法(不需要先验信息)选取光滑参数.将半参数模型用于向下延拓逆泊松积分,建立逆泊松半参数混合模型,既可无外部重力时估计系统误差,又可向下延拓.实验结果表明:无外部重力时逆泊松积分和最小二乘配置法受系统误差影响最大,向下延拓精度最差;正则化算法可减弱系统误差影响,向下延拓精度较好;逆泊松半参数混合模型可估计系统误差,向下延拓精度最好.