  The space-borne missions CoRoT and Kepler have provided a large amount of
precise photometric data. Among the stars observed, red giants show a rich
oscillation pattern that allows their precise characterization. Long-duration
observations allow for investigating the fine structure of this oscillation
pattern. A common pattern of oscillation frequency was observed in red giant
stars, which corresponds to the second-order development of the asymptotic
theory. This pattern, called the universal red giant oscillation pattern,
describes the frequencies of stellar acoustic modes. We aim to investigate the
deviations observed from this universal pattern, thereby characterizing them in
terms of the location of the second ionization zone of helium. We also show how
this seismic signature depends on stellar evolution. We measured the
frequencies of radial modes with a maximum likelihood estimator method, then we
identified a modulation corresponding to the departure from the universal
oscillation pattern. We identify the modulation component of the radial mode
frequency spacings in more than five hundred red giants. The variation in the
modulation that we observe at different evolutionary states brings new
constraints on the interior models for these stars. We also derive an updated
form of the universal pattern that accounts for the modulation and provides
highly precise radial frequencies.
