A non-parametric resampling method for uncertainty analysis of geophysical inverse problems

Due to non-uniqueness of geophysical inverse problems and measurement errors, the inversion uncertainties within the model parameters are one of the most significant necessities imposed on any modern inverse theory. Uncertainty analysis consists of finding equivalent models which sufficiently fit the observed data within the same error bound and are consistent with the prior information. In this paper, we present a non-parametric block-wise bootstrap resampling method called moving block bootstrapping (MBB) for uncertainty analysis of geophysical inverse solutions. In contrast to conventional bootstrap in which the dependence structure of data is ignored, the block bootstrap considers the dependency and correlation among the observed data by resampling not individual observations, but blocks of observations. The application of the proposed strategy to different synthetic inverse problems as well as to synthetic and real datasets of geo-electrical sounding inversion is presented. The results demonstrated that through the block bootstrap, it is possible to effectively sample the equivalence regions for a given error bound.