  The magnon dispersion of Ca$_2$RuO$_4$ has been studied by polarized and
unpolarized neutron scattering experiments on crystals containing 0, 1 and 10 %
of Ti. The entire dispersion of transverse magnons can be well described by a
conventional spin-wave model with interaction and anisotropy parameters that
agree with density functional theory calculations. Spin-orbit coupling strongly
influences the magnetic excitations, which is most visible in large energies of
the magnetic zone-center modes arising from magnetic anisotropy. We find
evidence for a low-lying additional mode that exhibits strongest scattering
intensity near the antiferromagnetic zone center. This extra signal can be
explained by a sizable magnetic moment of 0.11 Bohr magnetons on the apical
oxygens parallel to the Ru moment, which is found in the density functional
theory calculations. The energy and the signal strength of the additional
branch are well described by taking into account this oxygen moment with weak
ferromagnetic coupling between Ru and O moments.
