The Prediction Error Filter (PEF) is a widely used tool in various geophysical applications such as signal-noise separation and interpolation of missing data. Over the years, SEP has developed tools to estimate non-stationary Prediction Error Filters. Non-stationary PEFs are successfully used for multiple removal, ground-roll attenuation, and in other geophysical problems. I apply a non-stationary PEF to a velocity stack to remove artifacts caused by a limited offset of the data. My first goal is to create an artifact-free model in which individual reflections are easier to identify. To do this I create a simple model of the artifacts in the space. This ``noise'' model is data-independent and relies only on the geometry of the data acquisition and parameters of the velocity stack. Then I estimate a non-stationary PEF on this ``noise'' model and use it to improve the velocity stack.
In the second part of the paper, I test the possibility of using the described PEF as a preconditioner for a velocity stack least-squares inversion.