火山形变Mogi模型反演的病态总体最小二乘解算方法

相对最小二乘方法,总体最小二乘顾及了观测方程系数矩阵含有误差的情况,然而,当系统出现病态时,总体最小二乘受病态的影响将更加明显。因此,针对病态总体最小二乘问题解算方法的研究越来越多受到关注。文中基于总体最小二乘进行火山形变Mogi模型反演,针对反演过程中出现的病态性问题,采用虚拟观测解法、谱修正迭代解法、共轭梯度解法,通过模拟算例验证文中方法在抑制病态性方面的有效性。与一般总体最小二乘、正则化总体最小二乘等方法相比存在优势。

The ill-posed total least squares algorithm in volcano inversion of Mogi model

As to the least squares method,the total least squares correlates with the coefficient matrix errors.The result of TLS will be more susceptible in ill-conditioned system.The ill-posed TLS problem leads to more and more research.Due to the ill-posed problem existing in volcano inversion of Mogi model,the methods of ill-posed total least squares are applied.Comparing with general total least squares method and regularized total least squares method,the applicability and effectiveness of the algorithms applied are discussed and analyzed in the simulation example.