协方差阵非负约束的赫尔默特方差分量估计

在多源数据联合反演同震滑动分布过程中，各类观测数据之间相对权比的确定是当今大地测量与地球物理联合反演领域的研究热点和难点。近年来，赫尔默特方差分量估计法因其可以同时估计虚拟观测数据及实际观测数据之间的比例因子的优势，在联合反演滑动分布领域中得到了广泛应用。然而，利用HVCE法确定多源数据联合反演相对权比过程中易出现负方差现象。针对以上问题，本文提出在HVCE法确定联合反演相对权比过程中添加线性不等式约束，利用带有线性不等式约束的平差模型进行求解（LC-HVCE），解决计算过程中出现负方差问题。为了验证LC-HVCE法的有效性，开展模拟地震试验，结果表明LC-HVCE法可以有效地解决HVCE法在确定联合反演相对权比过程中存在的不足，保证了同震滑动分布反演精度。蒙特卡洛模拟试验及拉奎拉实际地震反演结果进一步表明了LC-HVCE法在确定正则化参数与相对权比过程中较HVCE法的适用性与稳定性。

Helmert variance component estimation with non-negative constraint of covariance matrix

How to determine the relative weight ratio in geodetic data inversion among various datasets is one of the challenging topics. In recent years, Helmert variance component estimation method (HVCE) has been widely used in the field of relative weights of joint inversion slip distributions due to its advantage of simultaneously estimating the scale factors between virtual and actual observations. However, the HVCE method sometimes suffers from the occurrence of negative variance. To overcome these problems, we propose linear inequality constraints based helmert variance component estimation method (LC-HVCE). We carry out synthetic experiment to verify the effectiveness and robustness of the LC-HVCE method and estimate the uncertainty of LC-HVCE method by Monte carlo method. We apply the proposed method to invert for the source parameters of the 2009 Mw6.3 L'Aquila earthquake (Italy). We find that LC-HVCE method is more applicable and stability than HVCE method in determining relative weight ratio and regularization parameter.