  Dynamic mode decomposition (DMD) is utilised to identify the intrinsic
signals arising from planetary interiors. Focusing on an axisymmetric
quasi-geostrophic magnetohydrodynamic (MHD) wave -called torsional Alfv\'{e}n
waves (TW) - we examine the utility of DMD in two types of MHD direct numerical
simulations: Boussinesq magnetoconvection and anelastic convection-driven
dynamos in rapidly rotating spherical shells, which model the dynamics in
Earth's core and in Jupiter, respectively. We demonstrate that DMD is capable
of distinguishing internal modes and boundary/interface-related modes from the
timeseries of the internal velocity. Those internal modes may be realised as
free TW, in terms of eigenvalues and eigenfunctions of their normal mode
solutions. Meanwhile it turns out that, in order to account for the details,
the global TW eigenvalue problems in spherical shells need to be further
addressed.
