Error-propagation in weakly nonlinear inverse problems

Abstract

In applications of inversion methods to real data, nonlinear inverse problems are often simplied to more easily solvable linearized inverse problems. By doing so one introduces an error made by the linearization. Nonlinear inverse methods are more accurate because the methods that are used are more correct from a physical point of view. However, if data are used that have a statistical error, nonlinear inversion methods lead to a bias in the retrieved model parameters, caused the by nonlinear propagation of errors. If the bias in the estimated model parameters is larger than the linearization error, a linearized inverse problem leads to better estimation of the model parameter. In this paper the error-propagation is investigated for inversion methods that account the nonlinearity quadratically.