Theory Development on Uncertainty Estimation for Measures of Data Misfit

摘要

This paper employs Bayesian inference theory to study the uncertainty caused by different measures of data misfit,i.e.sum-of-square measure,Huber measure and robust measure.Probability distributions for various commonly used measures are developed,providing theoretical background for uncertainty estimates caused by a particular choice of misfit measures.Inversion results from a simple 3-layer Magnetotelluric (MT) case show that for Gaussian data,uncertainties caused by sum-of-square measure,Huber measure and robust meausre are generally similar.For the perturbed data with 2 outliers added to the Gaussian data,uncertainty distributions of sum-of-squares are relatively smaller than that of Huber measure and robust measure.The sum-of-square measure artificially generates small uncertainty estimates and gives an illusion that the inversion has been better resolved.