  While solar-like oscillations in red giants have been observed at massive
scale by the Kepler mission, few features of these oscillation mode
frequencies, other than their global properties, have been exploited for
stellar characterization. The signatures of acoustic glitches in mode
frequencies have been used for studying main-sequence stars, but the validity
of applying such techniques to evolved red giants, particularly pertaining to
the inclusion of nonradial modes, has been less well-examined. Making use of
new theoretical developments, we characterize glitches using the $\pi$ modes
associated with red giant stellar models, and use our procedure to examine for
the first time how properties of the He II acoustic glitch -- specifically its
amplitude and associated acoustic depth -- vary over the course of evolution up
the red giant branch, and with respect to other fundamental stellar properties.
We find that the acoustic depths of these glitches, in conjunction with other
spectroscopic information, discriminates between red giants in the first-ascent
and core-helium-burning phases. We critically reexamine previous attempts to
constrain acoustic glitches from nonradial (in particular dipole) modes in red
giants. Finally, we apply our fitting procedure to Kepler data, to evaluate its
robustness to noise and other observational systematics.
