  Gravitational waves from core-collapse supernovae are produced by the
excitation of different oscillation modes in the proto-neutron star (PNS) and
its surroundings, including the shock. In this work we study the relationship
between the post-bounce oscillation spectrum of the PNS-shock system and the
characteristic frequencies observed in gravitational-wave signals from
core-collapse simulations. This is a fundamental first step in order to develop
a procedure to infer astrophysical parameters of the PNS formed in
core-collapse supernovae. Our method combines information from the oscillation
spectrum of the PNS, obtained through linear-perturbation analysis in general
relativity of a background physical system, with information from the
gravitational-wave spectrum of the corresponding non-linear, core-collapse
simulation. Using results from the simulation of the collapse of a 35
$M_{\odot}$ presupernova progenitor we show that both types of spectra are
indeed related and we are able to identify the modes of oscillation of the PNS,
namely g-modes, p-modes, hybrid modes, and standing-accretion-shock-instability
(SASI) modes, obtaining a remarkably close correspondence with the
time-frequency distribution of the gravitational-wave modes. The analysis
presented in this paper provides a proof-of-concept that asteroseismology is
indeed possible in the core-collapse scenario, and it may serve as a basis for
future work on PNS parameter inference based on gravitational-wave
observations.
