火山Mogi模型形变反演的虚拟观测法及方差分量估计

针对Mogi模型垂直位移与水平位移联合反演中的病态问题,改进火山形变总体最小二乘(Total Least Squares,TLS)联合反演的虚拟观测法,并使用方差分量估计(Variance Components Estimation,VCE)方法确定病态问题的正则化参数.将附有先验信息的参数作为观测方程,与垂直位移和水平位移的观测方程联合解算,推导了三类观测方程联合反演的求解公式及基于总体最小二乘方差分量估计确定正则化参数的表达式,给出了算法的迭代流程.通过算例实验,研究了总体最小二乘联合反演的虚拟观测法在火山Mogi模型形变反演中的应用;算例结果表明,三类数据的联合平差及方差分量估计方法可以确定权比因子并得到修正后的压力源参数,具有一定的实际参考价值.

Virtual observation method and variance component estimation for deformation inversion on the volcano Mogi model

Considering the ill-posed problem in the joint inversion of the vertical and horizontal observation data of the Mogi model, an improved virtual observation method of Total Least Squares(TLS) joint inversion is proposed, and the variance component estimation method is used to determine the regularization parameters. The parameters with prior information are regarded as observation equations and the actual observation equations are combined. The expressions of parameter estimation and the variance component estimation are derived, and an iterative algorithm is provided. With real examples, the virtual observation method of TLS joint inversion is applied to the inversion of the volcano Mogi model. The results show that the joint adjustment with three kinds of observation data and the variance component estimation can determine the weight ratio factor and obtain revised pressure source parameters, which has certain practical reference value.