引用本文: 陈欣, 翟国君, 暴景阳, 欧阳永忠, 陆秀平, 邓凯亮. 航空重力向下延拓的最小二乘配置Tikhonov正则化法[J]. 武汉大学学报 ( 信息科学版), 2018, 43(4): 578-585.
CHEN Xin, ZHAI Guojun, BAO Jingyang, OUYANG Yongzhong, LU Xiuping, DENG Kailiang. Least Squares Collocation-Tikhonov Regularization Method for the Downward Continuation of Airborne Gravity Data[J]. Geomatics and Information Science of Wuhan University, 2018, 43(4): 578-585.
 Citation: CHEN Xin, ZHAI Guojun, BAO Jingyang, OUYANG Yongzhong, LU Xiuping, DENG Kailiang. Least Squares Collocation-Tikhonov Regularization Method for the Downward Continuation of Airborne Gravity Data[J]. Geomatics and Information Science of Wuhan University, 2018, 43(4): 578-585.

## Least Squares Collocation-Tikhonov Regularization Method for the Downward Continuation of Airborne Gravity Data

• 摘要: 基于最小二乘配置法向下延拓航空重力的过程中，由于协方差矩阵严重病态，影响延拓结果的稳定性和精度。针对这一问题，提出了航空重力向下延拓的最小二乘配置Tikhonov正则化法。基于全球协方差函数模型建立航空重力数据与地面重力数据的协方差关系，引入基于广义交叉验证法，选择正则化参数的Tikhonov正则化法改善协方差矩阵的病态性，抑制观测噪声对延拓结果的放大影响。基于EGM2008重力场模型，设计了山区、丘陵和海域3种不同地形区域的航空重力数据向下延拓的仿真实验，实验结果验证了该方法的有效性。

Abstract: The covariance matrix that least-squares collocation is used to the downward continuation of airborne gravity data is ill-conditioned, which influences the reliability and precision of computation results. To solve this problem, the least squares collocation-Tikhonov regularization method for the downward continuation of airborne gravity data is proposed. The functional relationship between airborne gravity data and ground gravity data is established by using the global covariance function model, and the Tikhonov regularization method that the Generalized Cross-Validation (GCV) method is used to select the regularization parameter is introduced, which can improve the ill conditioned covariance matrix and inhibit the amplification impact of ill matrix on observational error. Based on the EGM2008 gravity model, the simulation experiments that airborne gravity anomalies are downward continued to calculate corresponding ground gravity anomalies in mountainous, hill, and sea areas are designed, and the results validate the effectiveness of the proposed method.

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