  We report the first comprehensive investigation of the line profile variation
caused by non-radial pulsation in a magnetic oscillating chemically peculiar
star. Spectrum variation of the well-known roAp star HR 3831 is detected using
very high-resolution high signal-to-noise spectroscopic time-series
observations and are followed through the whole rotation cycle of the star. We
confirm outstanding diversity of pulsational behaviour of different lines in
the HR 3831 spectrum and attribute this phenomenon to an interplay between
extreme vertical chemical inhomogeneity of the HR 3831 atmosphere and a running
pulsation wave, propagating towards the upper photospheric layers with
increasing amplitude. Rapid profile variation of the NdIII 6145 A line is
characterized by measuring changes of its equivalent width and the first three
moments. We demonstrate that rotational modulation of the radial velocity
oscillations cannot be fully explained by an oblique axisymmetric dipole
(ell=1, m=0) mode, implied by the classical oblique pulsator model of roAp
stars. Pulsational variation of the higher moments reveal substantial
contribution of the high-order (ell=3) spherical harmonics which appear due to
distortion of pulsations in HR 3831 by the global magnetic field. We interpret
observations with a novel numerical model of the pulsational variation and
rotational modulation of the line profile moments in roAp stars. The comparison
between observed and computed amplitudes and phases of the radial velocity and
line width variation is used to establish parameters of the oblique pulsator
model of HR 3831. Furthermore, definite detection of pulsational variation in
lines of light and iron-peak elements enables the first 3-D mapping of
pulsations in non-radially oscillating star.
