  In this article, we have investigated the possibility to distinguish between
different galactic models through the microlensing parallax studies. We show
that a systematic search for parallax effects can be done using the currently
running alert systems and complementary photometric telescopes, to distinguish
between different lens distance distributions. We have considered two galactic
dark compact objects distributions, with total optical depths corresponding to
the EROS current upper limits. These models correspond to two extreme
hypothesis on a three component galactic structure made of a thin disc, a thick
disc, and a spherically symmetric halo. Our study shows that for sub-solar mass
lenses, an exposure of $8\times 10^7$ star$\times$yr toward LMC should allow to
distinguish between these two extreme models. In addition the self-lensing
hypothesis (lensing by LMC objects) can efficiently be tested through the
method proposed here.
