Summary Numerical three-dimensional elastic models are a central piece of information in the geo-modelling workflow as they are often used to predict the spatial distribution of the reservoir properties such as porosity, volume of minerals and fluid saturations. Geostatistical seismic inversion methods have increasing its importance within this context due to their ability to infer high-resolution models while assessing uncertainties related to the spatial distribution of the inverted properties. Iterative geostatistical seismic inversion methods use stochastic sequential simulation and co-simulation as the perturbation technique of the model parameter space and a global optimizer based on cross-over genetic algorithms to ensure the convergence of the method. We propose a new alternative approach for model perturbation based on the concept of self-updating the local distributions of the elastic property. Iteratively, local probability distribution functions of the elastic property of interest are built and updated at seismic samples within the inversion grid based on the local mismatch between observed and synthetic seismic. This method avoids local fast convergence at early steps of the iterative procedure and allows assessment of local uncertainties at the seismic sample scale. The method was implemented in geostatistical acoustic inversion and applied to a non-stationary synthetic and a real case example with a blind well test.