  Spin excitations of magnetoelectric LiNiPO$_4$ are studied by infrared
absorption spectroscopy in the THz spectral range as a function of magnetic
field through various commensurate and incommensurate magnetically ordered
phases up to 33\,T. Six spin resonances and a strong two-magnon continuum are
observed in zero magnetic field. Our systematic polarization study reveals that
some of the excitations are usual magnetic-dipole active magnon modes, while
others are either electromagnons, electric-dipole active, or magnetoelectric,
both electric- and magnetic-dipole active spin excitations. Field-induced
shifts of the modes for all three orientations of the field along the
orthorhombic axes allow us to refine the values of the relevant exchange
couplings, single-ion anisotropies, and the Dzyaloshinskii-Moriya interaction
on the level of a four-sublattice mean-field spin model. This model also
reproduces the spectral shape of the two-magnon absorption continuum, found to
be electric-dipole active in the experiment.
