  In the same way that seismologists study the interior of the earth from the
waves generated by earthquakes, heliosismology is the science that is
interested in the study of oscillatory waves inside the Sun. Temperature,
chemical composition, rotational velocities at different depths are all factors
that influence the oscillation frequencies of the waves trapped inside the Sun.
The observation and measurement of the frequencies (or velocities) of
oscillations of the principal modes on the surface of the Sun allow us to study
the internal properties of the star. In our study, we use a local helioseismic
method, called "Time-Distance"; the latter, after appropriate treatment
(remapping, tracking, and filtering) of the data, which carried out from the
GONG (Global Oscillation Network Group) observation network, allows us to
deduce, by correlation of the observed signals, the relationship between the
time of the wave path and its crossed distance (hence the name of the method)
between different points on the surface as a function of the different solar
sub-surface parameters, via the dispersion relation. Once the travel times have
been established by approximation of the correlation function by a Gaussian
wave packet and based on the Fermat principle dealing with acoustic waves, we
find the relationship between these times and the internal parameters of the
crossed medium. Two models are considered in this study. The first does not
include the effects of the magnetic field and takes into account the flow
velocity and the sound speed. The second, on the other hand, includes the
magnetic effects, by means of the Alfven velocity (magnetic field perturbation
velocity), in addition to the parameters mentioned above. The last part of this
paper was devoted to the inversion of the obtained times, which allows us to go
back to the solar internal parameters.
