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

  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.