Consistency regions in non-linear inversion

A disadvantage of fully non-linear methods of inversion, through exploitation of the properties of model space, is the absence of a well-developed framework for error assessment. To rectify this problem an auxiliary weighting function for ensemble properties is introduced that can be used with suitable thresholds to define consistency regions of suitable models. This approach requires neither a detailed knowledge of the misfit distribution nor an underlying probabilistic model. The use of a polyhedral representation of such consistency regions is illustrated with an example from non-linear seismic event location, showing the effect of different choices for the misfit measure. The auxiliary weight function can be used directly with the composite misfit measure used to drive the exploration of model space in the non-linear inversion. Such composite measures usually combine a data misfit and regularization term. However, considerable benefit can be obtained by storing the data misfit and associated model characteristics for each investigated model, as well as the composite measure. The properties of the model ensemble can then be used retrospectively to define preferred models by the intersection of a consistency region in data misfit with zones constrained by desirable model properties.