  Seismology allows for direct observational constraints on the interior
structures of stars and planets. Recent observations of Saturn's ring system
have revealed the presence of density waves within the rings excited by
oscillation modes within Saturn, allowing for precise measurements of a limited
set of the planet's mode frequencies. We construct interior structure models of
Saturn, compute the corresponding mode frequencies, and compare them with the
observed mode frequencies. The fundamental mode frequencies of our models match
the observed frequencies (of the largest amplitude waves) to an accuracy of
$\sim 1 \%$, confirming that these waves are indeed excited by Saturn's
f-modes. The presence of the lower amplitude waves (finely split in frequency
from the f-modes) can only be reproduced in models containing gravity modes
that propagate in a stably stratified region of the planet. The stable
stratification must exist deep within the planet near the large density
gradients between the core and envelope. Our models cannot easily reproduce the
observed fine splitting of the $m=-3$ modes, suggesting that additional effects
(e.g., significant latitudinal differential rotation) may be important.
