  Results of forward modelling of acoustic wave propagation in a realistic
solar sub-photosphere with two cases of steady horizontal flows are presented
and analysed by the means of local helioseismology. The simulations are based
on fully compressible ideal hydrodynamical modelling in a Cartesian grid. The
initial model is characterised by solar density and pressure stratifications
taken from the standard Model S and is adjusted in order to suppress convective
instability. Acoustic waves are excited by a non-harmonic source located below
the depth corresponding to the visible surface of the Sun. Numerical
experiments with coherent horizontal flows of linear and Gaussian dependences
of flow speed on depth are carried out. These flow fields may mimic horizontal
motions of plasma surrounding a sunspot, differential rotation or meridional
circulation. An inversion of the velocity profiles from the simulated travel
time differences is carried out. The inversion is based on the ray
approximation. The results of inversion are then compared with the original
velocity profiles. The influence of steady flow on the propagation of sound
waves through the solar interior is analysed. Further, we propose a method of
obtaining the travel-time differences for the waves propagating in
sub-photospheric solar regions with horizontal flows. The method employs
directly the difference between travel-time diagrams of waves propagating with
and against the background flow. The analysis shows that the flow speed
profiles obtained from inversion based on the ray approximation differ from the
original ones. The difference between them is caused by the fact that the wave
packets propagate along the ray bundle, which has a finite extent, and thus
reach deeper regions of the sub-photosphere in comparison with ray theory.
