综合半参数核估计与正则化方法的航空重力向下延拓模型分析

Analysis of Downward Continuation Model of Airborne Gravity Based on Comprehensive Semi-parametric Kernel Estimation and Regularization Method

在航空重力向下延拓过程中,将重力数据中的系统误差和离散化造成的模型误差用非参数分量表达。在无外部数据的情况下,建立基于半参数核估计方法的重力向下延拓模型,为了改善泊松积分离散后的设计矩阵的病态影响,引入正则化方法,提出了综合半参数核估计和正则化方法的逆泊松积分延拓方法。基于EGM2008(earth gravity model 2008)模型计算了某地空中重力异常,采用线性项和周期项系统误差进行仿真实验,以及美国某地实测重力异常数据,验证了本文方法在改善病态性和分离系统误差方面的有效性。结果表明,本文方法在无外部数据时,能有效地分离系统误差并具有较高的精度。

In the process of downward continuation(DWC) of airborne gravity, the model error caused by discretization and systematic error in gravity data is expressed by non-parametric components. This paper proposes an inverse Poisson integral DWC method based on regularization method and semi-parametric kernel estimation, establishes gravity DWC model based on semi-parametric kernel estimation method without external data, reduces the ill-conditioned influence of the design matrix after Poisson integral discretization and introduces regularization method. It calculates the simulated airborne gravity anomaly based on the EGM2008 model and performs the simulation experiment using linear term and periodic term systematic error. The simulation experiment and the measured gravity anomaly data in the United States show the effectiveness of the proposed method in improving the ill-conditioned and separation system errors. The results show that the proposed method can effectively separate systematic errors and has high precision when there is no external data.