The uncertainty estimation for 2D layered models based on seismic travel times inversion

Inversion of travel times is a common way of modelling of the crystalline crust. Quite often it is done manually by trial and error method. In this case it is very difficult to estimate the uncertainty of obtained models. Proposed is an analytical method based on a simple principle of error propagation that will allow the estimation of the uncertainties. Two variants of the method are presented: a simplified one that includes refraction and vertical reflections and the one that includes also wide-angle reflections. Both give a quantitative estimation. For a simple analytical estimation, refracted waves are described using a head-wave approximation in constant velocity layers. This technique can also be applied to models obtained by inversion, especially using layer-stripping modelling strategy. It will evaluate propagation errors commonly excluded in this type of modelling. An example of application of this method is presented for both simple synthetic case and the model based on the field data. For complicated cases the uncertainties for deep layers and interfaces will be larger comparing to commonly used values based on a single parameter sensitivity tests. This method can be also applied to complicated 2D models as a series of local 1D approximations. This simple procedure gives a reliable estimation of the uncertainty for both velocity field and interfaces for tested long transects across complicated tectonic structures. We presents examples of such analysis for the most important profiles from experiments POLONAISE'97, CELEBRATION 2000, and SUDETES 2003. This analysis can verify if an optimal number of layer were used to describe observed data, and if a modeller is not trying to overfit it.