  Jupiter is expected to pulsate in a spectrum of acoustic modes and recent
re-analysis of a spectroscopic time series has identified a regular pattern in
the spacing of the frequencies \citep{gaulme2011}. This exciting result can
provide constraints on gross Jovian properties and warrants a more in-depth
theoretical study of the seismic structure of Jupiter. With current
instrumentation, such as the SYMPA instrument \citep{schmider2007} used for the
\citet{gaulme2011} analysis, we assume that, at minimum, a set of global
frequencies extending up to angular degree $\ell=25$ could be observed. In
order to identify which modes would best constrain models of Jupiter's interior
and thus help motivate the next generation of observations, we explore the
sensitivity of derived parameters to this mode set. Three different models of
the Jovian interior are computed and the theoretical pulsation spectrum from
these models for $\ell\leq 25$ is obtained. We compute sensitivity kernels and
perform linear inversions to infer details of the expected discontinuities in
the profiles in the Jovian interior. We find that the amplitude of the
sound-speed jump of a few percent in the inner/outer envelope boundary seen in
two of the applied models should be reasonably inferred with these particular
modes. Near the core boundary where models predict large density
discontinuities, the location of such features can be accurately measured,
while their amplitudes have more uncertainty. These results suggest that this
mode set would be sufficient to infer the radial location and strength of
expected discontinuities in Jupiter's interior, and place strong constraints on
the core size and mass. We encourage new observations to detect these Jovian
oscillations.
