引用本文: 王乐洋, 谷旺旺, 赵雄, 许光煜, 高华. 利用偏差改正的方差分量估计方法确定联合反演相对权比[J]. 武汉大学学报 ( 信息科学版), 2022, 47(4): 508-516.
WANG Leyang, GU Wangwang, ZHAO Xiong, XU Guangyu, GAO Hua. Determination of Relative Weight Ratio of Joint Inversion Using Bias-Corrected Variance Component Estimation Method[J]. Geomatics and Information Science of Wuhan University, 2022, 47(4): 508-516.
 Citation: WANG Leyang, GU Wangwang, ZHAO Xiong, XU Guangyu, GAO Hua. Determination of Relative Weight Ratio of Joint Inversion Using Bias-Corrected Variance Component Estimation Method[J]. Geomatics and Information Science of Wuhan University, 2022, 47(4): 508-516.

## Determination of Relative Weight Ratio of Joint Inversion Using Bias-Corrected Variance Component Estimation Method

• 摘要: 在大地测量联合反演中，方差分量估计法用于确定相对权比时并没有考虑大地测量反演的病态性，利用正则化解代替最小二乘解会引入偏差，会造成方差分量估计不准确问题。针对此提出采用偏差改正方差分量估计方法，以消除正则化解引入偏差的影响，并基于残差的偏差改正方差分量估计与方差分量估计法进行模拟实验。结果表明，进行偏差改正后的方差分量估计法能够较好地反演出滑动分布情况，所提方法针对参数进行偏差改正的方差分量估计考虑了迭代初值引入的偏差，理论更为严密。并将所提方法用于Visso地震和Norcia地震反演中，验证了该方法的可靠性、合理性。

Abstract:
Objectives  When using variance component estimation to determine the relative weight ratio, the least square solution is generally used as the initial value of the iteration. In geodetic joint inversion, the least squares method will cause ill-posed problems, so the regularized solution is used instead of the least square solution. Regularization introduces bias to reduce variance, but when using variance component estimation to determine the relative weight ratio, the influence of bias is not considered, and the introduction of bias will cause inaccurate variance component estimation.
Methods  This paper adopts the bias-corrected variance component estimation method to eliminate the influence of bias introduced by regularization.The residual-based bias-corrected variance component estimation and the variance component estimation method are used for simulation experiments, the Visso earthquake and Norcia earthquake are used for verification.
Results and Conclusions  Simulation experimental result shows that the variance component estimation method after bias correction can better reverse the slip distribution. The bias-corrected variance component estimation method takes into account the bias introduced by the iterative initial value, and the theory is more rigorous. Two real earthquakes results show that the bias correction is reasonable and advantageous.

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