  Proposals aimed at measuring the Electric Dipole Moment (EDM) for charged
particles require a good understanding of the systematic errors that can
contribute to a vertical spin buildup mimicking the EDM signal to be detected.
In what follows, a method of averaging emanating from the Bogoliubov-Krylov
Mitropolski method is employed to solve the T-BMT equation and calculate the
Berry phases arising for the storage ring frozen spin concept. The formalism
employed proved to be particularly useful to determine the evolution of the
spin at the observation point, i.e. at the location of the polarimeter. Several
selected cases of lattice imperfections were simulated and benchmarked with the
analytical estimates. This allowed the proof of the convergence of the
numerical simulations and helped gain better understanding of the systematic
errors.
